enVision MATH 2.0 Texas Grade 1 (2024)

Evaluation for 2.1

Evaluation for 2.1
Materials dedicate most attention to the development of the primary focal area for the grade-level.

The materials provide strategic and integrated instruction in conceptual understanding, procedural fluency, and primary focal areas for grade 1, which are place value, solving problems with addition and subtraction, identifying and creating two-dimensional shapes and three-dimensional solids, and principles of length measurement. They showcase the focal concepts throughout the program and provide practice opportunities for students to master the content.

Evidence includes but is not limited to:

The materials devote 11 of the 17 topics to the focal areas as outlined in the grade 1 TEKS. Concepts of place value are the primary focus in Topics 8–10. While concepts of adding and subtraction are interwoven throughout the instructional materials, solving problems with addition and subtraction is the primary focus in Topics 1–6. Identifying and creating two-dimensional shapes and three-dimensional solids is the primary focus area in Topic 12; principles of length measurement are the primary focus in Topic 14.

The design of the materials informs the teaching and learning of math concepts and develops students’ content knowledge. The “Lesson Overview” section in the “User’s Guide” provides the philosophy and review of key concepts for the teacher to incorporate into each lesson. The instructional material provides scaffolding by reviewing basic concepts required prior to beginning each topic in a “Review What You Know” section. The curriculum spirals each focal area by introducing the content and then gradually readdressing the focal area numerous times in a slightly more rigorous manner with each repetition. For example, addition first appears in Topic 1 and is readdressed in Topics 4–6 and 17.

First-grade materials provide various practice opportunities in multiple contexts, including guided practice, independent practice, and homework practice, and a variety of settings, including center activities, online games, “Problem Solving Reading Mats,” and “Math and Science Project” pages. For example, the Math and Science Project for Topic 4 directs students to discuss the weather with family and friends and to keep track of how many sunny days and how many rainy days there are during a week. Students then make a graph on a poster showing and labeling how many days were sunny and how many days were rainy. Students circle the greater number to determine if there were more rainy days or more sunny days in the week.

Evaluation for 2.2

Evaluation for 2.2
Materials strategically develop students’ conceptual understanding by following a progression of learning from concrete to representational to abstract (CRA) as is appropriate for the grade-level and content.

The materials partially meet the criteria for the indicator. While they include a variety of support for the CRA continuum (e.g., concrete models and manipulatives, pictorial representations, and abstract representations) as appropriate for grade-level content, the materials do not give explicit instructions for how to use the models, manipulatives, and representations. The related teacher professional development and resources are inferred rather than directly presented to the teacher.

Evidence includes but is not limited to:

The materials include a variety of types of concrete models and manipulatives, pictorial representations, and abstract representations, as appropriate for the content and grade level, which are used for concept exploration and attainment for the first-grade primary focal areas throughout the curriculum. For example, Topic 1, Lesson 1, introduces counters and connecting cubes used throughout the curriculum. Students are explicitly taught how to work with models, manipulatives, and representations used for concept exploration and attainment. In another instance, in Topic 1, Lesson 7, the instructional material provides many addition stories for the students to solve. Each story is accompanied by pictures so that the students can count the items to help determine the answer. A “Center Games Manipulatives Kit” is available for tangible, hands-on learning in centers. Throughout Topic 2, students use tools such as connecting cubes to model different subtraction stories (e.g., separating stories, comparing stories, stories about missing parts). In Topic 2, Lesson 4, students solve separating stories, including those where the change is unknown. In Topic 6, Lesson 5, the “Solve and Share” section shows a picture of cubes on a pan balance. Students are asked to find out how many more shells the second person needs to have the same number as the first person. Students then draw that number of cubes and write a number sentence to show that the number of shells is now equal (i.e., 13 = 6 + 7). Although number tiles are used throughout the curriculum, students progress to the less concrete connecting cubes during centers later in the curriculum. For example, in Topic 7, Lesson 5, the students use connecting cubes to help them determine patterns in charts.

The “Teacher’s Edition” includes guided activities using the CRA continuum to evaluate for grade 1 readiness. For example, Topic 1 contains a suggestion that students who have trouble visualizing what the numbers in the table represent could use red and yellow counters to show each row of the table. Evidence does not show that the materials consistently and explicitly support teachers to understand the entirety of the CRA continuum or provide strategic instructional suggestions to help students to progress along it.

Progressions from concrete to pictorial to abstract can occur across lessons and within lessons. The main focus of a specific lesson might be concrete, pictorial, abstract, or a combination of those. The “Essential Understanding” and “Math Background” on the first page of each lesson in the Teacher’s Edition highlight the focus of the lesson and make connections to progression across the grade.

Solve and Share begins the lesson, and students can solve this problem in any way they choose. They use concrete materials at times (e.g., counters, snap cubes, place-value blocks, fraction tiles) and pictorial representations at times (e.g., number lines, arrays, grids, area models, bar diagrams). When students share and discuss their solutions, rich conversations deepen conceptual understanding of connections between concrete, pictorial, and abstract. The “Visual Learning Bridge” then provides instruction that connects students’ work in Solve and Share to new ideas taught in the lesson. The Visual Learning Bridge at times shows pictures of concrete materials, drawings of concrete materials, or diagrams that are representations of mathematical concepts. These representations are connected to abstract numbers, symbols, and procedures. The Teacher’s Edition provides sample student work and guiding questions to help facilitate this as part of a classroom conversation.

Evaluation for 2.3

Evaluation for 2.3
Materials support coherence and connections between and within content at the grade-level and across grade levels.

The materials include support for students to build their vertical content knowledge by accessing prior knowledge and understanding of concept progression. They support coherence and connections between and within content at and across grade levels. They also support the horizontal and vertical alignment guiding the development of concepts. The teacher guidance documents explain an increase in depth, breadth, and complexity to prepare students for the next year’s work.

Evidence includes but is not limited to:

Materials include supports for students to build their vertical content knowledge by accessing prior knowledge and understanding of concept progression. The materials connect new learning to previously learned concepts, knowledge, and skills. The “Math Background” for Topic 2, Lesson 3, for example, states, “One way to express subtraction is to use symbols in symbolic equations. Number sentences, such as 9 - 4 = 5, are one way to express subtraction.” This lesson reinforces the importance of making the transition from models to symbols. In another example, Topic 4 starts with a “Review What You Know” section, which reviews the basic subtraction taught in Topic 2. Additionally, as students begin Topic 14, Lesson 1, in the “Activate Prior Knowledge” section, students draw three snakes of different lengths on the board; teachers invite students to comment on their lengths and ask, “Which snake is longer? Which is shorter? Which snake is the longest? Which is the shortest?” Teachers then ask students to suggest tools they might use to measure all of the snakes to compare their lengths better.

Materials include tasks that require students to recognize and make connections among mathematical ideas and demonstrate that mathematics is used in many real-world situations. In Topic 11, Lesson 4, students practice skip counting and counting on skills. In Topic 15, Lesson 6, students use the terms more and less to make comparisons from bar and picture graphs. Another example is found in Topic 15, Lesson 6. In this section, students take information from a graph and then use addition or subtraction to solve the problem (i.e., “How many fewer friends have cats than dogs? How many friends have dogs or cats for pets?”)

The materials provide opportunities for students to explore relationships and patterns within and across concepts, including in tasks that require students to understand how mathematical ideas interconnect and build on one another to produce a coherent whole. An extended example of this begins with the skills practiced in Topic 3, Lesson 1. Students practice writing the correct number of counters on a ten-frame. Then, in Topic 3, Lesson 3, students apply skills learned in Lesson 1 of the topic and practice identifying parts of ten on the ten-frames. These lessons on identifying numbers on ten-frames are applied within Topic 5 when students practice doubles +1, doubles +2, making 10 to add, and making 10 to subtract. This skill carries over into Topic 8 when students begin adding tens and ones and identifying place value. In another example, in Topic 4, Lesson 9, addition and subtraction facts and fact families are used to emphasize the inverse relationship between addition and subtraction and that every subtraction fact has a related addition fact.

The instructional materials include teacher supports that help teachers understand how concepts build over time and the horizontal and vertical alignment guiding the development of concepts. Each topic includes a section titled “Math Background,” which provides the TEKS covered in that specific topic and lists the “Essential Understandings” for the TEKS in each of the lessons for the topic. Materials build students’ vertical content knowledge by referencing or showing how concepts progress in rigor. The three-step lesson format is highly dependent on the teacher modeling or using questions effectively to promote student discourse and connect previous learning to the current objective. Materials reference familiar models and strategies to facilitate rigor and concept development. The materials include tasks and problems that intentionally connect concepts in the “Solve and Share” problems and the “Visual Learning Bridge.” The “Student Edition” and center activities use story problems to help students discuss and apply math to real-world problems.

Evaluation for 2.4

Evaluation for 2.4
Materials are built around quality tasks that address content at the appropriate level of rigor and complexity.

The materials include quality tasks that address content at the appropriate level of rigor and complexity. The materials provide guidance for the teachers on how to appropriately revise content to be relevant to their specific students, their backgrounds, and their interests. The materials provide teachers with possible student responses and or strategies to practice questions and tasks. The materials provide teachers with common misconceptions of student responses and strategies. The materials provide teacher guidance on preparing for and facilitating strong student discourse grounded in the quality tasks and concepts.

Evidence includes but is not limited to:

Tasks are designed to engage students in the appropriate level of rigor (conceptual understanding, procedural fluency, and application) as identified in the TEKS and as appropriate for the development of the content and skill. Math manipulatives such as counting cubes are provided with the instructional materials for students to use across the topics. In Topic 1, Lesson 1, students look at pictorial models to recognize spatial patterns; in Lesson 4, students count two different groups of pictorial items to find the sum of both groups together. In Topic 5, students use counting cubes and spatial patterns to add doubles +1 facts. The “Guided Practice” section shows pictorial models as well as blank lines for the students to write the corresponding addition sentence that matches the pictorial model. The exercises in the “Independent Practice” section have students solve a doubles addition sentence and then the matching doubles +1 addition sentence. In Topic 14, Lesson 6, students begin by using cubes to measure the length of a pencil, which prepares them for the next lesson, where they use tools such as paper clips. Students then find objects that are similar in size and compare the measurements. After finding objects that are similar in size, students begin to estimate the length of an object. The materials display an appropriate progression of rigorous tasks throughout each topic and across the year. For example, Topic 1 introduces addition. Addition is readdressed in Topic 4, Topic 5, Topic 6, and Topic 17, where repeated addition is related to multiplication.

Math concepts addressed in the instructional materials are explained to the teacher before students engage in the tasks. The “Topic Planner” sections of the instructional materials list the TEKS that are covered and explain the “Essential Understandings” for the lesson. In Topic 4, Lesson 3, the standard is TEKS 1.3D: Apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10. The related mathematical process standards are 1.1C, 1.1F, and 1.1G. Topic 4, Lesson 1, addresses adding with 0, 1, 2, as explained by the Topic Planner. The planner lists TEKS 1.3D: Apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10. The mathematical process standards are identified as 1.1C, 1.1D, and 1.1F. The Essential Understanding for this lesson is explained as “The number relationships of 0, 1 more than, and 2 more than are the basis for addition facts with 0, 1, and 2.” Topic 14, Lesson 4 has the following Essential Understanding: “The hour hand tells the hour and the minute hand tells the number of minutes after the hour.” The “Math Background” for the same lesson explains: “Research says that the understanding of numbers is a powerful idea used by students for organizing quantitative information and developing quantitative skills, such as telling time (Case and Griffin, 1990). This lesson connects the skill of telling time to students’ previous work with numbers.”

The materials include tasks that are meaningful to students, set in real-world contexts, and allow them to demonstrate mastery of math concepts. Topic 1, Lesson 9 has a “Math Science Connection” activity that discusses how the mathematical concepts being taught could be used in a veterinary clinic. The math and science topic for Topic 5 asks students to discuss what different animals eat and why the animals may have different types of teeth. Students draw pictures of animals and what they eat and then make up and solve addition and subtraction problems about the animals and their food. In another example, in Topic 16, Lesson 1, students connect making money to real-life activities such as raking leaves or receiving a gift. Students determine how much money is made by adding given amounts and discuss earning money versus getting money as gifts. This activity prepares them for the next part of the lesson, where they learn that making money is income, and income is used to buy things.

The materials provide guidance for the teachers on how to appropriately revise content to be relevant to their specific students, their backgrounds, and their interests. The materials provide teachers with possible student responses and or strategies to practice questions and tasks, but they do not describe which ones are the most appropriate for the task based on grade-level expectations. The materials provide teachers with common misconceptions of student responses and strategies. The materials provide teacher guidance on preparing for and facilitating strong student discourse grounded in the quality tasks and concepts.

The materials provide teacher guidance on anticipating student responses and strategies. For example, in Topic 6, Lesson 2, there is a “Prevent Misconceptions” callout for the teacher: “Some students may think there is only one correct way to group the addends. Emphasize that the sum of 5+4+6 is the same whether 5+4 is added first or whether 4+6 is added first.” In another example, in Topic 9, Lesson 2, the teacher builds understanding by asking, “What are you asked to do? (Find the total number of counters) How are the counters arranged? (In ten-frames).” The materials provide teachers with common misconceptions on student responses and strategies. In Topic 11, Lesson 1, students find the value of a group of pennies and nickels. Teachers ask, “What do you notice about a nickel? (It is larger than the penny; It says five cents on it.) How much is the nickel worth? (5 cents) How do you count the value of nickels? (Skip count by 5s).” In Topic 11, Lesson 5, students make guesses and then use what they learn to make a second guess to solve a problem. Teachers remind students that they can pick any two items to start; if they are too high or too low, they can use their answer to help them make a better guess. In Topic 16, Lesson 1, the teacher asks, “What is income?” A provided sample answer is, “Income is money that you make from working.” However, materials do not sequence the anticipated strategies in order of sophistication so that teachers know how to push students from one strategy to the next.

Throughout each topic, materials provide questions for the teacher to ask students. For example, the Topic 11, Lesson 1 “Solve and Share” section contains teacher guidance for building student understanding. It reads, “What are you asked to find? (The number of groups of 10 that can be made with 34 cubes) What do you know about the number of groups of 10? (There will be at least one group of 10 because 34 is greater than 10).” Topic 12, Lesson 3 (on properties of plane shapes), provides open-ended questions such as “What are you asked to do?” and “What do you know about the shapes?” Each lesson also offers a “Share and Discuss Solutions” section that encourages students to talk about the strategies they used to solve the given Solve and Share problem. In Topic 13, Lesson 1, students complete independent practice; if students have difficulty finding the value of the coins, teachers ask, “What is the value of 3 pennies? What is the value of 1 nickel and 1 penny?” If students still do not understand, there is an “Error Intervention” section.

Every lesson follows the same three-step structure. The first step is called “Problem-Based Learning,” which engages students in the content with the authentic Solve and Share problem. The Teacher Edition includes student work samples and questions to help students think deeply about the problem and analyze each other’s work. The second step is the “Visual Learning Bridge” (VLB), which supports the development of conceptual understanding using interactive features of Problem-Based Learning tasks and the step-by-step “Visual Learning” activity. Error analysis is included in many lessons. There are print and digital resources for both the students and teachers to support this step in the lesson. The materials develop problem-based learning and provide the appropriate level of rigor (conceptual understanding, procedural fluency, or application) as identified in the TEKS.

Evaluation for 2.5

Evaluation for 2.5
Materials include cohesive, year-long plan for students to develop fluency in an integrated way.

The materials include a cohesive, year-long plan for students to develop fluency in an integrated way. The materials provide multiple areas of guidance for the teacher for teaching fluency as well as multiple opportunities for students to practice fluency while building rigor throughout the year. Materials also include scaffolds and supports for teachers to differentiate fluency development for all learners.

Evidence includes but is not limited to:

The instructional materials include guidance and support for teachers for conducting fluency practice. The materials include guidance for teachers on the structure and design of the fluency practice within the program, including the connections between concept development and fluency. The Teacher Edition provides embedded questions throughout the lesson material for the teacher to use to help guide a student through the lesson. Teachers share the definition of fluency with students and why it is important. Topic 4, Lesson 1 provides the following information in the “Summarize & Generalize” section: “Fluency with addition facts means that you can perform basic computations easily.” Number relationships provide the foundation of fact strategies such as counting 0, 1, and 2 more. Students discuss their strategies in daily “Share and Discuss” activities. For example, in Topic 5, Lesson 8, students solve the problem “14 - 5 = ?” Teachers ask, “What number will be the sum of your related addition fact?” and “So what number can you add to 5 to get 14?” The students have counters to help them; some are asked to come up and explain their strategy to solve the problem.

The materials provide a “Scope and Sequence” in the “Content Guide” and a daily scaffold instructional routine. The scope and sequence contains fluency routines showing increasing complexity to achieve grade-level fluency expectations. The teacher guide explains each of the fluency routines used across the year, including when they are introduced, when they are practiced, and when they are applied. The scope and sequence shows, for example, that “number sense” is introduced in kindergarten and then practiced through grade 5. It also shows that using concrete/pictorial models, strip diagrams, and number lines is introduced in kindergarten, practiced in kindergarten through grade 4, and applied in grade 4 and beyond. For each grade level, there is a “Skills Trace” section, located under the Teacher Edition “Program Overview,” at the top of the Table of Contents. It shows how fluency increases from single digits to 20s, including doubles.

The materials purposefully integrate fluency activities throughout each topic by providing multiple strategies for students to use to complete their grade-level tasks and by providing students with multiple opportunities to practice and master solving grade-level tasks. For example, in Topic 3, Lessons 1 through 4 build on knowledge about ten-frames first learned in kindergarten. Lesson 1 reviews how to represent numbers on a ten-frame; in Lesson 2, students recognize numbers on a ten-frame; in Lesson 3, students use the ten-frame for addition facts to 10; and in Lesson 4, students use the ten-frame for subtraction. Grade-level strategies students might use in these lessons include subitizing, counting on, and noticing how many more or how many less are required to fill the frame. In another example, in Topic 4, Lesson 5, students use counters, ten-frames, and paper-and-pencil to solve a problem. The materials also include fluency activities, such as drawing coins needed to buy an item in Topic 11, Lesson 1, before working on a conceptual understanding of counting sets of coins in Topic 11, Lesson 4.

The materials provide guidance that recognizes the need for differentiated supports to include extension and scaffolded fluency activities. An online placement test given at the start of the year helps identify what students already know. The materials provide support for teachers to scaffold fluency for students struggling to meet expectations. For example, the materials include a “Visual Learning Bridge” for each topic that reteaches materials for students struggling to meet grade-level fluency expectations. In Topic 3, Lesson 7, a quick check includes exercises for prescribing differentiation. They include supports for teachers to extend fluency activities for students meeting the fluency expectations of the grade. In Topic 8, Lesson 1, an individual worksheet is used to determine if students need differentiated support using groups of 10s. If the students are having a difficult time grasping this concept, intervention activities allow teachers to help those struggling with the content; for example, the teacher places a rubber band around groups of ten pencils, counts the groups, places that number in the tens place, and places any leftover pencils in the ones place. In another activity, they count cubes in tens rods. The materials provide extensions for students who exhibit efficient and accurate recall of facts and algorithms by extending student thinking to flexibly and strategically apply strategies to solve grade-level problems. In the aforementioned lesson, students ready for extension activities have several options. First, they can make groups of 10 flowers to decorate the room. Another option is to complete the Math and Science activity: drawing schools of at least 10 fish each and then counting their partner’s fish. The materials also include a math diagnosis and intervention system for teachers to use with students.

Evaluation for 2.6

Evaluation for 2.6
Materials support students in the development and use of mathematical language.

The materials support students in developing and strengthening their mathematical vocabulary throughout the lessons and activities. They also provide information for teachers to scaffold and support students’ use of this vocabulary in context.

Evidence includes but is not limited to:

Materials demonstrate a strategic approach to developing mathematical vocabulary. The curriculum provides daily opportunities to practice listening, reading, and speaking. Math vocabulary is provided at the beginning of the lessons as well as embedded within the lessons to give students opportunities to develop and strengthen their mathematical vocabulary. In Topic 7, the provided vocabulary terms to practice are hundred charts, ones digit, tens digit, column, row, and skip count. In Topic 7, Lesson 1, in the “Solve and Share” problem, students listen to the vocabulary word hundred charts. Students then read and write the vocabulary word found in the “Guided Practice” and “Independent Practice” sections. In Topic 11, student vocabulary cards include penny, nickel, value, and cent. In Topic 11, Lesson 1, students receive play nickels and pennies and are then shown items with price tags in a store. First, students have to read the directions on the appropriate page in their textbook. Then, they work with a partner to determine how many of each coin they would need to buy specific items. A glossary appears in the back of the Student Edition. Students can access an online, bilingual, animated glossary that uses motion and sound to build an understanding of math vocabulary.

The materials provide scaffolding to ensure students have opportunities to use math vocabulary in context. The lessons are all formatted similarly; they include vocabulary cards for each topic and daily opportunities to discuss solutions to assigned problems with partners and the class. Vocabulary terms are embedded in many sources, including the reteach lessons, online games, and center games. The differentiated instruction lessons continue to concentrate on the vocabulary while working on the concept development. The guiding questions provided to the teachers in the Teacher Edition include vocabulary terms that are used within the topic being covered and those used in previous topics. For example, the vocabulary terms for Topic 1 are pattern, in all, part, whole, plus, and add. They continue to be used throughout the grade-level content. In Topic 5, Lesson 1, the materials provide vocabulary cards to pre-teach words to the students. Students cut out and study vocabulary cards. They then complete the activity on the back, which consists of sentence frames that ask the students to use what they know to complete the sentence. For extended learning, students write their own sentences using each word. Topic 13 has vocabulary cards with words such as equal parts, halves, fourths, and quarters. The first three lessons refer to “two equal parts” or “four equal parts”; Lesson 4 is where the curriculum introduces the vocabulary halves and fourths. Students can extend their learning by writing their own sentences using each vocabulary word.

Evaluation for 2.7

Evaluation for 2.7
Materials contain opportunities for students to apply mathematical knowledge and skills to solve problems in new and varied contexts, including problems arising in everyday life, society, and the workplace.

The materials include multiple opportunities for students to integrate knowledge and skills to analyze the information given and to problem solve successfully. The materials also provide many opportunities for students to correctly analyze and apply data to problems in an efficient and successful manner through real-world contexts.

Evidence includes but is not limited to:

The program contains many opportunities for students to solve real-world problems in a variety of contexts. As students practice the problem-solving process in activities such as “Solve and Share,” “Math and Science Projects,” independent practice, and reteach lessons, they are given real-world information or situations to apply their math knowledge and skills. Students must refer to previous knowledge to develop strategies to solve problems. For example, Topic 3 begins by activating knowledge from previous work using a five-frame and addition and subtraction to solve problems up to 5. Topic 3 goes on to use a ten-frame with addition and subtraction up to 10. In the “Math and Science Activity” at the beginning of the topic, students sort ten different colored marbles. Then, in the “Interactive Math Story,” students draw ten animals in different forms of transportation in seats that look like a ten-frame. Topic 3, Lesson 1 has a Math Science Activity where students sort rocks into a ten-frame; in Topic 3, Lesson 4, students sort ten leaves into two groups. These are all real-world examples in which students apply previously learned skills and knowledge. In Topic 4, Lesson 2, the “Essential Understanding” states that doubles facts can be associated with memorable real-world situations. In this lesson’s Solve and Share, students solve a word problem regarding how many toys a girl and boy have; it is given that both children have the same number of toys. In Topic 5, Lesson 3, Solve and Share, it is given that Josh has six grapes. Tia gives him five more. Students use the top workmat, cubes, and a number sentence to show how many grapes Josh has in all. Then, Josh eats three grapes. On the bottom workmat, students show how many grapes he has now. In Topic 14, Lesson 1, students connect the concept of telling time with its purpose in everyday life. In the Math and Science Project for Topic 14, they collect, record, and compare information using tools, including clocks, and non-standard measuring items, such as paper clips and clothespins.

The material provides opportunities for students to analyze developmentally-appropriate data through real-world contexts. In the extension in Topic 2, students keep track of the weather for one week. After one week, students count the number of sunny, cloudy, rainy, windy, and snowy days they recorded. They then use the data to write a story problem for a partner to solve. Each topic begins with an Interactive Math Story and Math and Science Activities that are of interest to the students. Topic 7 includes multiple opportunities for students to analyze the data as they count ants in the pictures in the Interactive Math Story, count legs on animals in the Math and Science Project, and write missing numbers in hundreds charts. The “Daily TEKS Review” for Topic 7, Lesson 3 provides diagrams of a part-part-whole frame and of ten-frames for students to use to answer the accompanying math questions. In the Interactive Math Story in Topic 11, students count pictured coins. The Solve and Share for Topic 11, Lesson 1 shows students school supply items with an accompanying value. Students choose one of the school items, tell which coins are needed to buy the item, and then draw the item and the coins. Topic 15 uses bar graphs, pictographs, and tally marks to teach students ways to manage data. In Topic 15, Lesson 1, students use picture graphs to answer questions based on the information shown. The picture graphs show the total number of each object in a column or row. Students collect information and begin to make their own graphs in later lessons.

Evaluation for 2.8

Evaluation for 2.8
Materials are supported by research on how student develop mathematical understandings.

The materials include some research to aid teachers in understanding mathematical concepts and the validity of the publisher’s approach to the lesson. There is little evidence that materials provide research-based guidance for instruction that enriches educator understanding of mathematical concepts. There is also little evidence that cited research is current, academic, relevant to skill development in mathematics, and applicable to Texas-specific context and demographics. Materials do not provide a bibliography.

Evidence includes but is not limited to:

In the program overview, the materials describe the program’s design as “Problem-Based Learning,” where students must think critically about a real-world math problem, evaluate options, collaborate, and present solutions, followed by “Visual Learning” to solidify the underlying math concepts. However, they do not cite research about the design of the instructional materials.

The “Lesson Overview,” “Math Background,” and “Essential Understanding” sections within the Teacher Edition provide general guidance for instruction to help enrich an educator’s understanding of the mathematical concepts and the validity of the publisher’s recommended approach. Some of the lessons provide research-based guidance. In Topic 2, Lesson 8, research states, “Activities that emphasize part-part-whole relations help students see how addition and subtraction are related” (National Research Council 2001). The Math Background of Topic 5, Lesson 8 states, “Research says the part/whole operations of splitting a number into two or more parts is facilitated by the use of drawings or diagrams in which the number is shown with a diagram to be broken into parts. These diagrams add to the collection of ideas that students can bring to numbers and operations to aid in computational fluency” (Saenz-Ludlow 2004). In another quote in Topic 12, Lesson 2, van Hiele (1986) discusses how children need to understand why a square is a square. In Topic 14 Lesson 1, a quote by Case and Griffin, 1990, discusses how understanding numbers helps organize quantitative information such as telling time. In Topic 14, Lesson 4, the National Research Council (2001) and Campbell (1975) are quoted on their work with young children and measurement. In Topic 15, Lesson 5, Friel, Curcio, and Bright (2001) are quoted in a discussion about graphs. Materials mention research four other times but give no direct quotes.

The most current research quoted is Sáenz-Ludlow (2004), with dates going all the way back to Campbell (1975). It is not possible to determine if the research is academically vetted or demographically aligned with the Texas-specific context. Evidence of a bibliography cannot be located.

The author team and well-known mathematicians bring an impressive level of experience as classroom teachers, teacher educators, researchers, and authors. They have written numerous professional articles based on their research and observations, and their contributions to the program is an implementation of successful teaching methods. The program offers an instructional model based on a research foundation and has proven efficacy shown by statistically significant advantages in independent, scientific research done with randomized controlled trials. enVisionmath2.0 meets ESSA’s “Promising” evidence criteria.

Evaluation for 3.A.1

Evaluation for 3.A.1
Materials develop student ability to use and apply a problem-solving model.

The materials guide students in developing and practicing the use of a problem-solving model that is transferable across problem types and is grounded in the TEKS. The teacher text provides numerous questions for each problem to guide the students through solving and provides guidance for teachers to support students’ reflection on their approach to problem solving.

Evidence includes but is not limited to:

The materials support the development and practice of a consistent problem-solving model across the topics. In Topic 1, Lesson 9, the materials introduce a problem-solving model grounded in the mathematical process standards of analyzing the information, making a plan, forming a strategy, solving the problem, justifying the solution, and evaluating the problem-solving process. In Topic 9, Lesson 5, students analyze different ways to make 113 using hundreds, tens, and ones. The lesson instructs students to make a plan to solve the problem by making a list to keep track of the different ways they can make the number 113; to solve the problem by making the actual list; and then to justify and evaluate their problem by counting to check their answers. Topic 10, Lesson 9 has another example, as the “Math Background” states, “In the previous lesson, students compare and order numbers by sequencing three or more numbers from least to greatest or greatest to least. In this lesson, students revisit the problem-solving plan to create a list of possible answers.” Understanding how to organize a list can help students determine whether all possibilities have been found.

The materials include prompts for students to apply the problem-solving model taught within the materials. For example, the materials contain prompts and supports in the teacher and student materials, such as guiding anchor charts that include the stages of “Analyze,” “Plan,” “Solve and Justify,” and “Evaluate.” The Teacher Edition for Topic 1, Lesson 9 provides questions for teachers to use, such as “What is my plan? How can I justify my answer?” Topic 10 includes several question prompts, such as “How does this problem connect to previous ones? What is my plan? How can I use tools? How can I use number sense? How can I communicate and represent my thinking? How can I organize and record the information? How can I explain my work? How can I justify my answers?”

The materials provide areas for students to reflect on their approach to problem solving. Topic 2 instructs students to think about how addition and subtraction are related as they solve a soccer problem. Topic 2, Lesson 9, provides students with prompts such as “What do you know from reading the story? How can you solve the problems? How do the counters help me solve?” There are also callouts that help guide the students. The callout under the Plan sections reads, “I can use counters to act out the story.” The callout under the Solve and Justify sections reads, “I know the whole and one part. To find the missing part, I subtract.” The Evaluate section reads, “My answer makes sense.” In the “Extend Your Thinking” sections of the lessons, students are prompted to reflect on how they solved math problems. In Topic 6, Lesson 5, for example, the Extend Your Thinking problem states, “Rick says that the scale is balanced,” and students explain whether they think Rick is correct or incorrect and why. In Topic 14, Lesson 3, the lesson includes questions to help analyze, such as “How many minutes are there in an hour? Why do you think a half-hour is 30 minutes?” To help formulate a plan, questions include, “What number is the minute hand pointing to? What does this show? Half-past is another way to say the half-hour.” Students solve and justify with the assistance of several questions, including “Where is the hour hand positioned? The hour hand moves from one number to the next in an hour. The hour hand is halfway between 2 and 3.” Finally, students evaluate; materials provide an example: “When the minute hand points to the 6, the other clock shows 30 for the number of minutes.”

The materials provide teacher prompts and questions in each lesson to use when guiding students to reflect on problem-solving. The Topic 4 “Math Background” explains that process standards 1.1B and 1.1C are discussed; Lesson 9 teaches students how the strategies of drawing a picture and writing a number sentence can help them solve word problems involving addition and subtraction. In a Topic 6, Lesson 5 problem, students use numbers and symbols to create representations of what is happening in a word problem or picture. Next, they are provided with questions to build an understanding of the “Solve and Share” problem: “What are you asked to find? What do the cubes show? How should you show the answer to the problem?” Then, teachers give hints as needed: “Do you need to add or subtract? How many shells do Rosi and James have now?” Students have the opportunity to share and discuss solutions, and then finally summarize and generalize. In another example in Topic 8, Lesson 3, teachers ask provided questions, such as “What do you do to add 20 to 4 on a hundred chart? What are you asked to find? What do you know about the sum?”

Evaluation for 3.A.2

Evaluation for 3.A.2
Materials require students to select appropriate tools for the task, concept development and grade.

The materials provide opportunities for students to select and use real objects, manipulatives, representations, and algorithms as appropriate for the stage of concept development, grade, and task. The materials also provide opportunities for students to select and use technology (e.g., calculator, graphing program, virtual tools) as appropriate for the concept development and grade. However, the materials do not provide explanations for the use of each tool throughout the topics.

Evidence includes but is not limited to:

The instructional materials provide many opportunities for students to learn to use grade-appropriate tools for solving tasks and understanding concepts. Throughout the lessons, materials provide pictorial models, and students also have opportunities to use counting cubes, counters, hundreds charts, etc. Topic 1, Lesson 2, for example, teaches students how to use red and yellow counters to represent number patterns. In Topic 1, Lesson 7, students use connecting cubes and an addition sentence to solve a joining problem with an unknown part. Later in the same lesson, students learn about other joining models that they can create to represent by addition sentences. In Topic 3, Lesson 1, students use single ten-frame mats and counters to represent numbers to 10. In Topic 7, Lesson 1, students use a hundreds chart to locate a number and then tell the number that is one more. Topic 9 introduces students to place value blocks.

The instructional materials include online virtual math tools students can select and use as needed when solving tasks and completing math problems. Some virtual online tools include counters, place value blocks, data and graphs, a number line, an input-output machine, number charts, a pan balance, and strip diagrams. The online assessments all have a “listen” option for those students who need help reading. The online games help the students practice the skills they are currently learning. The games are engaging and offer directions to help the students understand how to play. For example, in Topic 6, Lesson 3, at the end of the lesson, students complete a digital math tools activity to reinforce the lesson content or prerequisite content using a suite of digital math tools.

Students have opportunities to use a variety of tools throughout the lessons, particularly for the “Solve and Share” problems where digital tools are always available. Through this and the discussion and sharing of solutions, students are gaining experience in deciding which tools work best for different situations and seeing the different ways tools can be used. They see, for example, how the same tool can be used differently to reach a correct solution or why they find a particular tool more suitable than another. Student sample work is provided in the Teacher’s Edition that can encourage further discussion as needed.

The materials use many tools and recommend specific tools for use in each lesson. There is no guidance provided to the teacher about why the designated tool is being used, which tools are appropriate and efficient for a task, or which tool might be more appropriate than any other tool.

Evaluation for 3.A.3

Evaluation for 3.A.3
Materials require students to select appropriate strategies for the work, concept development, and grade.

Materials support teachers in understanding how to apply appropriate strategies and provide opportunities for students to use multiple strategies to solve problems. The materials also provide teacher guidance to gradually move students to more efficient ways to solve problems, from manipulatives to pictures to number sentences. Additionally, materials provide opportunities for students to solve problems using multiple appropriate strategies.

Evidence includes but is not limited to:

The materials prompt the students to select techniques for solving a task. In Topic 1, Lesson 9, students have the option to explain their solution to a joining problem using pictures, models, or words. In Topic 2, Lesson 1, in the “Essential Understanding” section, the materials suggest that teachers encourage students to use manipulatives or real-world models to help them find the missing part of a whole. In Topic 5, Lesson 5, students circle which way they chose to solve the doubles or doubles + 1 problem: doubles, near doubles, plus 10, or “my own way.” In the “Do You Understand?” section of the same lesson, students choose a strategy to solve 8 + 7 and explain why they chose that strategy. For Topic 16, Lesson 1, the “Share and Discuss Solutions” section reads, “Start with students’ solutions. Have them share their strategies for dividing the circle. If needed, project and analyze Jack’s work to discuss where he drew the line for each circle.”

The materials support teachers in understanding the appropriate strategies students can apply to solve math problems and how to guide them to more efficient strategies. In Topic 1, Lesson 2, students use counters to show patterns for six and then draw two of their patterns. Next, the students are shown patterns and must identify the numbers without counting them. The teacher instructs the students to “count on” to recognized patterns for any additional dots in the second group. By following this guidance, the teachers guide students to more efficient strategies. The “Focus on Content” and “Focus on Process” sections in the “Math Background” help to support teachers in understanding which strategies are appropriate for specific math problems. In Topic 4, Lesson 3, the Math Background explains to the teacher that when the addends of a problem have a difference of one, that students are taught to treat it as a near double. Topic 5 explains to teachers that finding an answer to the first part of the question is necessary for students to solve the second part of the question; if the first part of the question is not solved, then their answer is not reasonable. It also informs teachers that using a part-part-whole model to explore fact families allows students the opportunity to discover that the parts can be added in any order to find the whole and that either part can be taken away from the whole to find the other part. In Topic 6, Lesson 2, the Math Background reads, “Students can apply the Associative Property of Addition to help them find strategies for adding three numbers to solve word problems. This property states that the sum of three or more addends does not change even if the addends are grouped and added in different ways.” At this level, the focus is on the idea of flexible grouping rather than on symbolic notations using parentheses.

Materials provide opportunities for students to solve problems using multiple appropriate strategies. In Topic 1, Lesson 9, the Math Background states, “It is important for the students to realize that there are many different approaches and strategies that can be used to solve problems.” In this lesson, students solve problems using words, numbers, and pictures as they write to explain. In Topic 2, students learn to subtract by finding the missing parts, comparing, and connecting addition and subtraction. In Topic 4, students practice addition and subtraction facts using the following techniques: doubles; near doubles; facts with five on a ten-frame; making ten on a ten-frame; addition with zero, one, two; and subtraction with zero, one, two. In Topic 5, Lesson 10, students are encouraged to think of addition to subtract or make ten to subtract. They are prompted to use words, counters, pictures, or number sentences to explain their solutions. In Topic 8, Lesson 3, students learn to use a hundreds chart to add tens and ones; in Lesson 4, they use counting cubes to add tens and ones.

Evaluation for 3.A.4

Evaluation for 3.A.4
Materials develop student’s self-efficacy and mathematical identity by providing opportunities to share strategies and approach to tasks.

The materials support students to see themselves as mathematical thinkers who can learn from solving problems, make sense of mathematics, and productively struggle. The materials also help students see that there are numerous ways to solve problems. Finally, the curriculum helps teachers ensure students are given many opportunities to share their thinking in problem-solving.

Evidence includes but is not limited to:

The materials support students to see themselves as mathematical thinkers who can learn from solving problems, make sense of mathematics, and productively struggle. While many of the areas in each topic foster students’ thinking, three specific areas within the lessons that do so are “Solve and Share,” “Build Your Understanding,” and “Extend Your Thinking.” The Solve and Share sections foster a mathematical community that, with the teacher’s guidance, can ensure all students participate and engage as mathematical thinkers. For each Solve and Share problem, there are always two student solution examples, which sometimes include misconceptions and struggles. In Topic 5, Lesson 10, students are told, “Jeff has 12 apples. He gives away 6 apples. How many apples are left? Use words, counters, pictures, or number sentences to explain how many are left.” This question allows students to choose a method that helps them to make sense of the problem best. By working on this with a partner, they can productively struggle through numerous ways of thinking to ultimately reach a solution to the problem. The materials use drawings of children from all races and genders to give guidance in the Student Edition (SE). This art helps students to understand that everyone can be a mathematical thinker. The Solve and Share for Topic 7, Lesson 5, asks students to complete the table to help them solve the question “How can you find the number of shoes they are wearing in all?” A guiding question provided to the teacher helps foster the students’ thinking: “What tools do you have to help you solve the problem?” In this same lesson, the “Do You Understand” section asks, “How can you use skip counting to find the number of socks that 8 children wear?” The Extend Your Thinking section for the lesson provides students with information for how many cans one color of boxes can hold versus how many cans another color of boxes can hold and asks students to determine which color boxes to use if their goal is to use the most boxes to hold 24 cans. In Topic 10, Lesson 4, posed questions assist students in answering the problem, such as “Why does 45 go in the middle of the number line? How do you decide where to place 47 on the number line? What is the closest ten to 42? What is the closest ten to 47? Why does the closest ten to 47 have a 5 in the tens place rather than a 4?” This questioning allows all students to participate.

The materials often provide problems that have multiple pathways to a solution. For example, in Topic 4, Lesson 2, students use doubles to add. In the next lesson, students use near doubles to add, and in Lesson 5 of the same topic, students use a ten-frame to add. In Topic 5, Lesson 10, students review different ways to solve subtraction facts, such as part-part-whole; double ten-frames; thinking of a number that is the same; one less or two less to subtract zero, one, and two. In Topic 8, Lesson 7, students work in partners and use 42 stacking cubes to see how many ways they can make 42 using different numbers of tens and ones. Topic 12 gives teachers the following questions to guide students in solving problems that focus on efficient and generalizable ways to solve problems: “How does this problem connect to previous ones? What is my plan? How can I use tools? How can I use number sense? How can I communicate and represent my thinking? How can I organize and record my information? How can I explain my work? How can I justify my answer?”

The materials provide many problems that encourage divergent solution strategies. Each lesson has a Solve and Share worksheet. The Solve and Shares in the SE introduce a lesson by giving students problems that embed some important math ideas. Students solve the problem in any way they choose. In Topic 1, Lesson 2, pairs of students receive six counters and a two-part mat. They must find different ways to represent the number 6 on the mat. In Topic 3, Lesson 1, in a “Share and Discuss Solutions” section, students share their solutions. The teacher projects a student’s work to discuss how they showed six, so the counters are easy to count. In Topic 6, Lesson 5, teachers guide students to formulate a plan and connect ideas: “What do you need to find? How do you decide whether to add or subtract to solve the problem? How can 5 + 7 help you find the missing addend for 6 +… so that the two addition facts are equal? What is 12 - 6? What other strategies can you use to find the missing addend? How does the picture in Box 2 show what happened in the story? How can you use subtraction to check your answer?” In Topic 13, Lesson 4, Exercises 2–4, teachers explain to students that equal parts are the same size. For Exercise 5, teachers remind students how many parts are in fourths. For Exercise 6, teachers ask how many people there would be if Emily and her three friends were eating pizza. Finally, for Exercise 8, students talk about how many halves are in a whole and then look for shapes with that many pieces. Prompts help the teacher monitor students while they develop solution strategies as well as sequence the discussion of student strategies.

Evaluation for 3.B.1

Evaluation for 3.B.1
Materials prompt students to effectively communicate mathematical ideas, reasoning, and their implications using multiple representations.

The materials provide students the opportunity to communicate mathematical ideas and solve problems using multiple representations, as appropriate for the task. The materials also guide teachers in prompting students to communicate mathematical ideas and reasoning in multiple representations, including writing and the use of mathematical vocabulary. They also prompt teachers to encourage students to use correct mathematical terminology in oral and written communication and to use a variety of representations in solving and explaining problems.

Evidence includes but is not limited to:

The materials provide students the opportunity to communicate mathematical ideas and to solve problems using multiple representations as appropriate for the tasks. The “Solve and Share” section found at the beginning of the lessons provides this opportunity. In Topic 3, Lesson 3, students show multiple ways to represent the number of hats Jackson and a friend could have bought if they bought 10 hats altogether. Students draw counters to show the different ways and also write the number of hats. In Topic 5, Lesson 9, during the first eight problems of the independent practice, the teacher prompts the students to solve the problems by choosing to write a related addition sentence, using mental math by counting on from the given part or using a part-part-whole mat to find the missing part. In Topic 6, Lesson 1, students explore different strategies to add three numbers. In Topic 8, Lesson 6, students work in pairs and create and use representations of the same number with different combinations of tens and ones.

The materials include mathematical vocabulary throughout the lessons. Topics 1–16 each include vocabulary cards; the vocabulary words on these cards are used and referred to often within the topic and in subsequent topics. The materials also guide teachers in prompting students to communicate mathematical ideas and reasoning in multiple representations, both with writing and using mathematical vocabulary. In Topic 1, Lesson 7, students use connecting cubes to model five train cars on a track; three are yellow, and the rest are red. Students explain how they modeled the problem and write an addition sentence. In Topic 4, teachers read a story aloud and ask, “How many students are at the front of the group?” Students then use their fingers to trace a circle around the total number of students. Students receive “Interactive Math Story” books and color the students’ clothing in the front group red. In Topic 6, Lesson 3, students make a fact family for a doubles fact and answer the prompt, “How many facts did you make? Why?” In Topic 13, Lesson 4, the teacher explains to students that although a shape may be divided into two parts, the two parts are not necessarily equal. Then have students fold a piece of paper into two unequal parts. The students then fold a piece of paper in half equally. Students explain how the parts on each piece of paper are alike and how they are different. In Topic 15, Lesson 5, students use a tally chart and a picture graph. In Topic 16, students think about how they can connect problems about money to other things they learned about math this year.

Evaluation for 3.B.2

Evaluation for 3.B.2
Materials provide opportunities to discuss mathematical ideas to develop and strengthen content knowledge and skills.

Materials provide opportunities for students to discuss mathematical topics with partners, small groups, and the whole class; they integrate discussion opportunities for the students as they engage in the different mathematical skills and concepts. Materials also guide teachers in structuring and facilitating discussions as appropriate for the concept and grade level.

Evidence includes but is not limited to:

The materials provide opportunities for students to engage in mathematical discourse in a variety of settings (e.g., whole group, small group, peer-to-peer). Many of the “Solve and Share” problems at the beginning of each lesson have students work in pairs; then, some students share out with the whole class. The center games provide opportunities for students to share mathematical discussions as they play games with one another and are prompted to explain how they solved the math questions. In Topic 5, Lesson 10, the Solve and Share problem at the beginning of the lesson has students work in pairs to solve a subtraction problem using words, counters, pictures, or number sentences. The teacher selects some of the pairs with different strategies to share their solution with the class. The whole class then does guided practice together using part-part-whole and ten-frame strategies. After the teacher assesses their independent practice, students either work with the teacher in a small group for intervention practice with subtraction on a ten-frame or in small groups, working on reading mats. In Topic 6, Lesson 1, students formulate a plan to add three numbers using the commutative and associative properties. Teachers build their understanding through provided prompts, such as “What are you asked to find? What do you know about the stacks of books?” Then, students share and discuss their solutions with one another and the entire class. In Topic 16, Lesson 4, the materials prompt the teacher to put students in small groups so that the students can take turns asking one another questions, such as “How would you spend 80 cents?” Students also define spend, save, and share.

The materials provide opportunities for discussion in all phases of concept and skill development. The lessons begin with Solve and Share problems, which introduce the concept in the lesson and allow for discussion as students try their different strategies to solve the problem. Students solve the problem any way they choose; for each Solve and Share problem, there are “Build Understanding” and “Give Hints as Needed” sections. During the lessons, students may participate in problem-solving reading activities, which allow them to share their learning further as they solve more math problems related to the lesson. The “Center Games” and Concept Reviews” wrap up the lessons and allow additional opportunities for students to share their mathematical ideas in discussion. In Topic 8, Lesson 3, students begin by connecting the ideas of skip counting and a hundreds chart. Teachers ask, “What are you asked to find? What do you know about the sum?” Students then solve the problem and share solutions. In the middle of the lesson, students answer questions and discuss: “What does it mean to add ones? What are some tens that you know? What happens when you skip count by 10s?” Then, they complete guided questions. At the end of the lesson, students work on an intervention activity where they also discuss questions posed to them. Topic 10, Lesson 5 starts with pairs of students comparing the numbers 37 and 73 using place value blocks. Some of the pairs then discuss their solutions with the class. In the middle of this lesson on comparing numbers, during guided practice, the whole class discusses the topic. Then, after independent practice, students either discuss the topic with a small group directed by the teacher or in centers.

The materials offer guidance for teachers on how to structure a discussion that is appropriate for the grade level. The Teacher Edition provides guiding questions with the Solve and Shares as well as within the problem-solving reading activity guides; these include questions to ask the students to discuss with their peers. Questions can be found within the center games, which teachers can use for guided small groups. There are also tips for facilitating problem-based learning. For example, in Topic 7, Lesson 7, before students discuss and share solutions, the materials ask teachers to give hints as needed to make sure each student is able to share and discuss his or her solution with the class. Another example of this is found in Topic 12, Lesson 3. In this lesson, students are sorting plane shapes. The teacher prompts the students, “What do you know about the shapes? How can you sort objects? Which shapes have corners? Do those shapes have the same numbers of sides?”

Evaluation for 3.B.3

Evaluation for 3.B.3
Materials require students to justify mathematical ideas using multiple representations and precise mathematical language.

The materials provide opportunities for students to construct and present arguments that justify mathematical ideas using multiple representations. They also assist teachers in facilitating students to construct arguments using grade-level-appropriate mathematical ideas.

Evidence includes but is not limited to:

The materials provide students with opportunities to construct arguments to justify their mathematical ideas using multiple representations. The “Solve and Share” problems provide an opportunity for students to solve the math question using any strategy, share how they solved the math problem with their peers, and share why they chose the way they did to solve the math problem. One example of this is in Topic 1, Lesson 9. Students receive a problem in which Mia needs eight movie tickets. She buys five online, and her mother gives her three. The materials ask, “Does she have enough tickets?” Students can justify their answers using pictures, models, words, number sentences, or equations. They then share and discuss their solution with the class. In Topic 3, Lesson 5, the materials provide tasks for students to discuss different patterns in the tables related to making numbers and justify their answers using tables. In Topic 16, Lesson 3, students sort sentences and construct arguments to explain why they placed each sentence into a group.

The materials aid teachers in helping students construct grade-level-appropriate justifications for mathematical ideas. In the Solve and Share section of each lesson, the materials pose the problem, build understanding, and give hints to help students solve the problem and then justify their answers to their partners and the class. In Topic 3, Lesson 5, the materials provide questions to help elicit different types of responses from students as they present their arguments, including “How do the counters help you make a table? How do you know the table is correct? Why do the rows have to add up to 10? How did the table help you solve the problem?” The Teacher Edition of the Solve and Share for Topic 6, Lesson 2 has a section titled “Give Hints as Needed.” This section provides the following guided questions to help facilitate students’ construction of arguments: “What two parts will you add first? What other two parts could you add first?” In Topic 10, Lesson 6, in the guided practice section, provided teacher prompts help students to justify their answers to a “greater than, less than, equivalent” problem. The teacher asks, “If the two numbers have the same digits, are they always equal? How do you know?” Topic 14, Lesson 6 has an exercise where students estimate and then measure pictures of straws and crayons with cubes. In the “Do You Understand?” section, students can use real straws, cubes, and crayons to justify their answers. In Topic 15, Lesson 5, teacher prompts help to facilitate students’ arguments. In the “Construct Argument” section, the teacher asks, “What does each picture stand for?” (one choice or one vote) “What is the favorite choice?” (soccer) “Would it be easier to see that soccer is the favorite choice in a picture graph or in a tally chart? Why?”

Evaluation for 4.1

Evaluation for 4.1
Materials include developmentally appropriate diagnostic tools (e.g. formative and summative progress monitoring) and guidance for teachers and administrators to monitor progress.

The materials include a variety of diagnostic tools that are developmentally appropriate. They include some guidance in each lesson for how to grade and use the individual practice assignment to place students in appropriate groups (intervention, on level, or advanced) for the remainder of the lesson. They include diagnostic tools to measure all content and process skills for the grade level, as outlined in the TEKS and Mathematical Process Standards. However, the instructional materials do not provide a process for the students to track their own progress and growth.

Evidence includes but is not limited to:

The materials provide a variety of diagnostic tools that are developmentally appropriate. These tools are formal and informal, grade-level appropriate, and designed to allow students to demonstrate understanding in a variety of ways and settings. Materials provide two grade-level diagnostic test forms: Form A and Form B. Materials also include digital assessments that are taken online and auto-scored. Assessments can be customized online and allow teachers to upload a district assessment. There is an online placement test of 20 questions at the beginning of the grade 1 instructional materials. This test has an option to have questions read to the students for struggling readers. The test provides teachers with a list of what students need more work on and what they have mastered. Online quick checks may also be used; they include five questions for students to answer based on specific skills. Data from these quick checks are provided in an online report for the teacher to assess student mastery of the skill. Within the “Teacher Resources” section, there are 12 basic fact timed tests. Six of the timed tests are addition, and six are subtraction. The materials include a “Math Diagnosis and Intervention System” (MDIS). Ongoing assessments are given during a lesson throughout various sections, such as questions used with “Visual Learning Bridge,” “Visual Learning Animation Plus,” “Do You Understand,” and guided practice. Each lesson starts with a short worksheet to review what students know. Independent practice worksheets in each lesson can also be used for diagnostic purposes. The Teacher Edition explains how to grade the sheets and sort students into groups that need intervention, are on level, or are advanced. For example, in Topic 4, Lesson 3, the teacher uses the independent practice as a quick check. Students who score 0–3 points go to interventions, 4 points are on-level, and 5 points are advanced. Follow-up activities challenge each group on the topic of the lesson. Further teacher support for the formal and informal assessments in the program is provided at the publisher training website, which explains how to use assessment data to inform instruction. Support includes tutorials and downloadable resources for placement tests, topic assessments, performance tasks, lesson assessments, practice, cumulative assessments, state test preparation, and MDIS.

The materials provide some guidance, tips, and recommendations to support consistent and accurate administration of diagnostic tools. Materials instruct teachers to make elements explicit when discussing students’ answers; they inform the teachers of what to look for when observing students. In Topic 2, for example, “Subtraction can help you find a missing part. Example: Tina has 7 balloons. Some are red, and some are yellow. 4 balloons are red. How many are yellow? 7 - 4 = 3. Tina has 3 yellow balloons.” The independent practice section is used as a diagnostic check to determine mastery of the concept taught in that lesson. In Topic 5, Lesson 10, the teacher manual explains how to grade the quick check and the category into which students should be placed for the remainder of the lesson based on the number of questions answered correctly (intervention 0–3, on-level 4, or advanced 5). The MDIS includes a “Teacher’s Guide for K–3,” which provides an “Individual Record Form” and a “Class Record Form.” For assessment, it explains that an “Entry Level Assessment Form A” is given for a student entering a grade; “Form B” is used as a diagnostic test to check performance after providing instruction or intervention. For diagnosis, teachers use the “Class Record Form”; the MDIS gives a brief explanation of how to use the form to make placement decisions. “Intervention” lessons can be used for the content taught during the year. For monitoring, there is an “Individual Record Form” to help record student progress. Further in the MDIS, in-depth details explain these four areas and instructions for how to use the system.

The materials do not include tools for students to track their own progress and growth. The materials include informal and formal assessments aligned to the grade-level TEKS and Mathematical Process Standards. The materials also include diagnostic tools to measure all content and process skills for the grade level, as outlined in the grade-level TEKS. For example, at the start of the year, there is a placement test and diagnostic test measuring all content skills for that grade level. The instructional materials provide a “Texas Assessment Resources for Teacher’s Guide.” This guide contains performance tasks pages for students to complete and includes 4-point scoring rubrics that outlines the four levels of achievement for students’ understanding of the concepts and skills in that topic, as well as answer keys. The questions in the performance tasks are matched to specific TEKS; there are several open-ended questions included for each topic. A TEKS correlation chart is located in the Teacher Edition “Program Overview” “Correlations” booklet; it shows required growth from previous grade levels for each topic.

Evaluation for 4.2

Evaluation for 4.2
Materials include guidance for teachers to analyze and respond to data from diagnostic tools.

The materials support teachers with guidance and direction to respond to individual students’ needs in all areas of mathematics based on developmentally-appropriate student data. Evidence also shows that diagnostic tools yield meaningful information for teachers to use when planning instruction and differentiation. The materials provide a variety of resources and teacher guidance on how to leverage different activities to respond to student data. The materials provide administrator-level data and guidance.

Evidence includes but is not limited to:

The instructional materials give guidance and direction to teachers to respond to individual students’ needs in all areas of mathematics based on measures of student progress that are developmentally appropriate. The “Texas Assessment Resources” guide explains that comprehensive test reports are available to use with each of the end-of-course tests provided within the Texas Assessment Resource guide. On the report, each item tested references specific TEKS. The items tested are also referenced to the “Math Diagnosis and Intervention System 2.0” (MDIS). When teachers see an item on the end-of-course assessment that a student has not mastered, the teacher can identify lessons that give students additional reviews and practice through the corresponding MDIS listed on the report. For example, if a student missed question number 33 on the practice test, which is asking for another way to show the number 86, the “Practice Test Report” shows that this question tests TEKS 1.2B and that the teacher can use MDIS lessons A23 and A25 to have the student review and practice this skill. Lesson A23 includes exercises to count how many items there are and then identify how many groups of tens and ones there are in all. Lesson A25 shows base-ten blocks, and students identify the number in standard form, expanded form, and on a tens-and-ones place value chart. At the end of each lesson, there is an “Assess and Differentiate” section. The teachers use the quick check on the previous page to prescribe differentiated instruction. For example, in Topic 3, Lesson 5, students start with a part-part-whole mat and ten counters to determine all the ways they can create the number 10. They then learn how to record their results in a table. Students learn how to look for patterns in the tables. Margin notes explain to the teacher that if students are having difficulty finding parts of 10, they can use a ten-frame or go back to the counters to help them. Students who struggle on the quick check return to using counters in a part-part-whole mat to create ways to make 9. They then advance to using a chart and looking for patterns. Additional worksheets for remediation are available if the student needs additional practice after intervention time. Students who are on level or advanced move on to reading mats or online games that challenge them at their level. In the end-of-course tests, there is a comprehensive test report that provides information for each student once an assessment has been taken. Each item in this assessment is referenced to a TEKS standard and the MDIS for review. It allows the teacher to identify whether a student has reached proficiency on each specific concept assessed within each test. It also provides lesson references to provide students who have not yet reached proficiency with additional reviews and practice.

The materials include guidance to support teachers in understanding the results of diagnostic tools and provide teachers support for planning instruction and differentiation based on data gathered from the diagnostic tools. The materials contain “Item Analysis for Diagnosis and Intervention” charts in the Teacher Edition and auto-generated reports for online assessments. They also provide suggestions for remediation, students on level, and enrichment based on student mastery of the concept being assessed. The Texas Assessment Resources guide and the MDIS list the corresponding TEKS. This list helps the teacher understand which lessons/activities to use for a student who needs additional practice to master a specific skill. For example, the Practice Test Report in the Texas Assessment Resource guide informs the teacher to use the MDIS lessons B7 and B8 for a student who did not answer test questions 9 and 30 correctly, which cover TEKS 1.5D. Online reports based on the online activities that students complete allow teachers to see individual and class views of progress. TEKS reports show mastery of individual TEKS. Assignment reports show the status of resources that have been assigned online. Assessment reports show performance on items in the online assessments. Teachers can use these reports to identify areas that students need to review and practice. The lessons and activities within the instructional materials list the corresponding TEKS, guiding teachers on activities to use. If a student needs more practice on specific TEKS, the teacher can also find additional activities related to the TEKS within the centers’ activities. If a student has mastered a skill, a teacher can look in the “Scope and Sequence” within the “Content Guide” to find the related higher-level skill students work on next so that the student can begin working toward those skills. A “Leveled Assignment Guide” in the Teacher Edition provides intervention, on-level, and advanced assignments.

The materials provide daily small group hands-on interventions, online opportunities, and paper-and-pencil activities to support those in need of additional instruction based on student assessments. A daily quick check lets the teacher know who needs additional instruction. At the end of the quick check, it tells the students any areas they need more practice with and also provides the data to the teacher so that the teacher may assign activities based on the data. There are a variety of resources a teacher can choose when assigning activities, including “Visual Learning Animation Plus,” online math games, digital math tools activities, “Reteach to Build Understanding” activities, center games, and intervention lessons in the MDIS. For example, Topic 11, Lesson 4 suggests providing play coins to those struggling with the content. Students pick five coins and skip count to get the value of all the coins. Once students understand this, there is a reteach worksheet that has them add values of coins based on their pictures. The material includes an “Item Analysis for Diagnosis and Intervention” for each of its tests. Each item or problem is correlated with a grade-level TEKS, and most are given an intervention system with additional support for students who need it. The materials also provide interventions that can be auto-assigned with online resources. Customizable digital intervention is available through the use of online resources, eText pages, printable PDFs, animations, online tools, and math games.

The materials offer guidance for administrators to analyze and respond to data from diagnostic tools, including the following, available on mysavvastraining.com:

• Progress Monitoring and Reporting
• Realize Reports Administrator Guide
• Realize Reports: Getting Started for Administrators
• Realize Administrator Assessments Recorded Webinar
• Realize Reports FAQ
• Realize: Data and Security FAQs

Evaluation for 4.3

Evaluation for 4.3
Materials include frequent, integrated formative assessment opportunities.

The instructional materials include ways to measure student progress in a routine, accurately and systematically. These assessments are performed frequently and provide ways to track student progress through a variety of assessment types (observational, anecdotal, formal, and informal). The frequency of progress monitoring is appropriate for the age and content skill.

Evidence includes but is not limited to:

The instructional materials provide routine and structural progress monitoring opportunities to track and measure student growth. The materials include suggested timelines for checking students’ progress. For example, the materials include an online placement test at the start of the year. At the start of the topic, there is a review of what students know. During the lesson, students are assessed by a “Do You Understand?” section and through guided practice. The “Texas Assessment Resources” provide summative testing at the end of each topic, a benchmark test for every four topics, and two end-of-course practice exams to ensure students are prepared for state testing. These tests are all aligned with grade-level TEKS and specified program goals. The tests include a variety of grade-appropriate question formats. In the first-grade tests, there are word problems, multiple-choice problems, gridabble (open-ended) problems, and short-answer problems. Materials also include digital assessments that are taken online and auto-scored. Teachers can track the data on the online assessments or activities they assign, and the program shows the data on the standards students have mastered and have not mastered. The data can be sorted by class results by assignment or by class mastery by standard. TEKS reports show which TEKS have been mastered. Links to resources for practice in any needed areas are also provided with this data. For example, when a student completes a quick check, they are assigned an activity based on their results. The activity may be an intervention assignment, an on-level assignment, or an advanced-level assignment. The instructional materials also allow assessments to be customized. Teachers can customize assessments or upload district-created or teacher-created assessments for data tracking. Online data tracking of the instructional materials allows teachers to monitor student progress closely and know when extra support is needed. The usage data lets teachers know how much time students are spending in the online course.

The materials include appropriate and frequent assessments that reflect student learning at their current age. Materials guide teachers to administer progress monitoring assessments regularly, allowing students to demonstrate their learning as appropriate for the age and content skill. Formal assessments are available at the end of each topic. The materials suggest assessments for the start of the year, at the start of a topic, during a lesson, at the end of a lesson, at the end of every four topics, and at the end of the year. The end-of-course exams provide a report for each student, which is linked to the “Math Diagnostic and Intervention System 2.0.” This report provides students who have yet to achieve mastery with additional reviews and practice. The materials include suggestions to support more frequent monitoring of students demonstrating difficulty in order to support instructional interventions and response to intervention. The materials provide an ongoing assessment during the lesson through questions in the “Visual Learning Bridge,” in “Visual Learning Animation Plus,” in the Do You Understand? section, and through guided practice. Informal assessments are also conducted during each lesson with quick checks, anecdotal checks, and observational assessments. The material includes learning support for students who need an intervention, students on-level, and for students who are advanced in that content area. For example, based on the students’ data from the quick check, students either do the reteach to build understanding or the on-level and advanced activity centers.

Evaluation for 5.1

Evaluation for 5.1
Materials include guidance, scaffolds, supports, and extensions that maximizes student learning potential.

Throughout each lesson, the materials provide support to meet the diverse learning needs of all students. There are enrichment questions asked throughout each lesson in the “Extend Your Thinking” and “Daily Challenge” sections. There are differentiation tools after each topic, and teachers can base every four topics on the results of the online topic benchmark tests. The materials provide recommended targeted instruction and activities for students who have mastered the content.

Evidence includes but is not limited to:

The materials provide guidance for scaffolding instruction and differentiating activities based on targeted areas in which students are developing. Within each of the 16 topics, the “Begin Topic” folder contains sections titled “Review What You Know” to allow students to activate prior knowledge or practice precursor skills needed for the specific topic. In 14 of the 16 topics, the folder also contains “Vocabulary Cards” for students to practice vocabulary terms before beginning the lessons. “Reteach to Build Understanding” worksheets, found within the lessons under the “Assess and Differentiate” section, provide additional opportunities to practice the given skill for that lesson. Additionally, the Teacher Edition provides intervention activities at the end of each lesson for struggling learners. For example, in Topic 1, Lesson 3, the teacher uses a part-part-whole frame to help the students see that two numbers can be added together to create a third.

Throughout the material, opportunities exist to support students who have mastered the content. Topics 1–16 include a section titled “Today’s Challenge,” which provides extension activities in the form of various math problems for students who have mastered the content of that specific lesson. Additionally, the “Extend Your Thinking” section can be found throughout each topic on the “Independent Practice” worksheet as well as the homework worksheets. One example of Extend Your Thinking, in Topic 12, Lesson 1, states: “Tony drew 2 shapes. The shapes have straight sides. Draw 2 shapes Tony could have drawn.”

Each lesson provides multiple activities in an activity book; also, online games and center game suggestions provide a variety of ways to practice the lesson content. One example of an online game is “Jungle Quest,” in Topic 9, Lesson 5, which helps students with subtraction. Extend Your Thinking and “Extensions for Early Finishers” allow students to apply new learning. In Topic 2, the materials include an enrichment activity in the “Extension section,” which allows students to explore and apply new learning: Students track the weather for one week and count the cloudy and sunny days.

There are lessons and support materials for struggling, on-level, and advanced students during and after each lesson. Intervention activities within the lesson reinforce the same model and problem-solving strategy used in the main lesson. Activities for on-level and advanced students provide extension within the same topic and encourage application to real-world tasks and discussion between peers.

A “Differentiated Instruction” page near the beginning of a topic shows these resources organized by Ongoing Intervention during the core lesson (RTI 1), Strategic Intervention at the end of the lesson (RTI 2) and intensive intervention, or more instruction for struggling students and enrichment for advanced students, as needed (RTI 3). These are also shown as they apply to specific lessons in each Topic Planner.

The online resources can auto-assign differentiation based on the results of online Topic Tests and online Benchmark Tests. These include both students who struggle to master content and those who have mastered the content. Examples include: “Visual Learning Animation Plus,” “Online Math Game,” “Digital Math Tools Activity,” Reteach to Build Understanding Master, “Center Games Master,” and lessons from MDIS 2.0.

Evaluation for 5.2

Evaluation for 5.2
Materials provide a variety of instructional methods that appeal to a variety of learning interests and needs.

The materials incorporate a variety of different instructional approaches using multiple teaching strategies to meet students’ different learning needs. The materials support developmentally appropriate instructional strategies, flexible grouping (e.g., whole, small, individual), multiple types of practices (e.g., guided, independent, collaborative), and provide guidance and structures to achieve effective implementation.

Evidence includes but is not limited to:

The materials include a variety of instructional approaches to engage students in the mastery of the content. They incorporate a wide variety of teaching strategies. There are manipulatives to use for concrete practice, technological options for independent practice, cross-curricular stories and related science topics to demonstrate how math applies to everyday life, visual representations, videos, and symbolic abstractions that can be taught to large or small groups. Intervention lessons in the “Math Diagnosis and Intervention System 2.0” provide an opportunity for teacher time with struggling students. The lessons incorporate multiple teaching strategies to meet students’ different learning needs. For example, in Topic 3, Lesson 1, the problem-based learning instruction involves repetitive interaction of the learner with the content. Students create representations of the number six with counters in a ten-frame. Students build an understanding by determining how many counters to use. They are provided with help as needed and then share and discuss solutions, making the connection of how they showed six, so the counters are easy to count. They then summarize and generalize their solutions.

The materials guide teachers in selecting appropriate teaching strategies depending on the learning objective, specific context, and needs of individual students. The Teacher Edition (TE) gives ideas for center work for those on and above level, small group work or online assistance for those struggling, and differentiated homework for each level. The material guides teachers to select appropriate teaching strategies to support instructional delivery, including supporting the language with visual support, manipulatives and online tools, and “Solve and Share.” For example, in Topic 7, Lesson 1, materials provide guiding questions for the various levels of English Learners (ELs). Beginning ELs point to the first row of the hundreds chart to learn to count forward on a hundred chart. Intermediate ELs look at the hundreds chart and think about how the numbers going across and down are similar. Advanced ELs receive index cards of six numbers from 1 to 100 and must locate a number on the hundreds chart. Advanced High ELs summarize how a hundreds chart helps put numbers in order.

Materials support flexible grouping. The TE does not specify the size of groups for instruction. Although some sizes may be inferred, such as two-person center games, or individual online games, materials do not provide guidance for group size for teacher-led instruction. Any of the lessons could be done with an individual, small group, or large group, and the text also provides examples of activities to do with struggling learners. The Solve and Share sections in each topic provide a routine activity for whole group or small group instruction. The center games offer activities that students can play with a partner.

Evidence from instructional material supports multiple types of practices throughout each topic and lesson. The framework of each lesson in the online teacher text starts with a guided activity followed by independent work that is assessed for content mastery. Those who are on level or have mastered the content have centers or collaborative opportunities to practice the content or expand on their learning. Students who struggle are provided with intervention work with the teacher to reteach the topic. The materials walk the teacher through the process step-by-step. For example, the Topic 1, Lesson 6, Solve and Share section lets students solve and discuss solutions. Teachers say, “You see 2 train cars on the track. Then 1 more train car joins them. How can you use connecting cubes to show this story? What addition sentence can you write?”

Evaluation for 5.3

Evaluation for 5.3
Materials include supports for English Learners (EL) to meet grade-level learning expectations.

The instructional materials include accommodations for linguistics commensurate with various levels of English language proficiency (Beginning, Intermediate, Advanced, and Advanced High). They also include an “ELPS Toolkit,” which offers research-based scaffolds as an intentional and natural part of the lesson. They encourage the strategic use of students’ first language as a means to develop linguistic, affective, cognitive, and academic skills in English (e.g., to enhance vocabulary development).

Evidence includes but is not limited to:

The materials include accommodations for linguistics for various English proficiency levels. The instructional materials provide instruction in one or more ELPS for English Learners (ELs) at Beginning, Intermediate, Advanced, and Advanced High levels of English proficiency, within the lessons and through additional activities in the ELPS Toolkit. Materials include visual learning in math instruction, such as “Visual Learning Animation Plus,” “Visual Learning Bridge,” an animated glossary, and visual learning in exercise. At the beginning of each lesson, guidance tells the teacher which ELPS is addressed in the lesson. ELPS are used with specified parts of the lessons such as “Solve and Share,” the Visual Learning Bridge, and “Do You Understand?” activities for students to complete with the teacher based on their individual English language proficiency level. For example, in Topic 4, Lesson 1, the ELPS focus on listening (3g). For Beginning ELs, the teacher draws five carrots in a pot and says, “He has five. He needs one more.” The teacher draws one more and then asks the students, “Do I have to count them again?” If a student responds yes, the materials advise the teacher to start with five and count one more. Intermediate ELs draw the picture to represent the problem. The teacher says, “The rabbit needs five carrots. He draws one more. How can you find how many are in all?” Then, the teacher provides the following sentence frame: “I can find how many in all by ….” For Advanced ELs, teachers talk about the math problem in the instructional materials and ask, “Can you find how many there will be in all without counting all the carrots?” Students discuss their strategies. Advanced High ELs list several ways they can find how many carrots the rabbit has in all. They then explain how they would solve the problem. In Topic 6, materials include prompts for a variety of proficiency levels. For Beginning ELs, teachers ask students to look at the notes they wrote: “What numbers did you write in your notes? (7 and 3) Draw 7 counters. How many are red? (3).” Intermediate ELs work with a partner. They use their notes to draw the number of counters in all and circle the counters that are red. Teachers ask, “What is the missing part? (4).” Advanced ELs use their notes to talk about what they know about the counters and what part is missing: “Circle the number of counters that are red. How many counters are not red? (4)” Advanced High ELs are provided with an additional problem to use for recording notes: “You may use a guided practice problem or make up one of your own.” Another example of this is in Topic 12, where the ELPS focus on teaching ELs the meaning of the word sort. Beginning ELs receive a variety of plane shapes and put shapes that are alike in a group. The teacher explains to them that this is sorting. Intermediate ELs do the same activity and also define the word sort. Advanced ELs work in partners to sort the plane shapes and then, given a correct and incorrect definition, pick the correct one, and explain to their partners how they know it is correct. Advanced High ELs define the word sort. Then, they draw and cut out eight different shapes and give them to their partner. They sort the shapes and use the sentence “I sorted the shapes like this because…” to explain their work. These exercises are interactive, playful, and allow opportunities for repetition of the desired word.

The material includes suggestions for scaffolds to support students learning English. The material includes routine scaffolds through teaching academic vocabulary, Visual Learning Bridges, and connecting new information to prior experiences and learning using the review of what students know. The materials include resources and support materials that make scaffolding intentional and natural in the lessons. The ELPS Toolkit emphasizes seven specific instructional strategies, including modeling thinking aloud, partner talk, providing a word list, providing sentence stems, rephrasing, suggesting a sequence, and using repetition. Each lesson has a Visual Learning Bridge and an animated glossary. Lessons allow students to collaborate with others often as they discuss the learning. The materials frontload the lesson by activating prior knowledge. An example is in Topic 1, Lesson 2, which is a review of a previous lesson on patterns. To ensure the students understand the word pattern, they are broken into their capability groups. Beginning ELs receive six counters. One set of three is arranged in a triangle. The other set is dropped randomly on the work mat, and the students must determine which set represents a pattern. Intermediate ELs receive six counters and must put them in a pattern. Advanced ELs receive red and yellow counters. They must make their own pattern for the number five with three red and two yellow counters. Advanced High ELs receive a combination of red and yellow counters and must make a pattern for the number eight with the counters. In Topic 6, Lesson 5, the teacher models how to use a scale as a tool to help students show how numbers can be equal or not equal. Some demonstration sentence frames are “I put ... on one side. I put ... on the other side. This makes the ….” In Topic 16, Lesson 4, the ELPS suggests the Intermediate ELs, in small groups, take turns asking one another the following question: “How would you spend 80 cents?” Then, students define spend, save, and share.

The materials encourage the strategic use of the students’ first language to develop linguistic, affective, cognitive, and academic skills in English and include examples of how to use students’ first language as the foundation for developing skills in English. The materials include accessible resources, such as an ELPS Toolkit, that share strategies that teachers can use and that are effective with English learners. The Toolkit provides a chart with mathematical “thinking words” in English, Spanish, Chinese, Vietnamese, and Hmong. Students are encouraged to discuss mathematical concepts with a partner who speaks their language. If this is not available, the materials encourage the use of an online translator, dictionary, or pictures that students can point to in order to communicate their thoughts. The use of cognates is also discussed, as many words are similar enough to determine meaning. The Toolkit gives an example of the Spanish words división, hexágano, ángulo, triángulo, álgebra, circunferencia, and cubo, which are all very similar to the English words for the same things.

Evaluation for 6.1

Evaluation for 6.1
Materials include year-long plans with practice and review opportunities that support instruction.

The materials build students’ concept development by including a cohesive year-long plan and vertically align instruction that builds year to year, within and between the lessons and the grade levels. The material provides review and practice of mathematical knowledge and skills throughout the curriculum.

Evidence includes but is not limited to:

The materials include a cohesive, year-long plan to build students’ concept development and consider how to vertically align instruction that builds year to year. The content plan is cohesively designed to build upon students’ current level of understanding with clear connections within and between lessons and grade levels. A pacing guide is included in the “enVisionMATH Texas 2.0 and Texas” guide in the teacher overview. This guide assumes one lesson per day, which adds up to 110 days, with an additional 10 days for the “Step Up to Grade 2” lessons. This flexibility allows additional time for differentiation, review, local and state testing, and other requirements. A correlation chart can be found in the teacher overview “enVisionMath Texas 2.0 Correlations” guide. This reference shows where each TEKS is taught in the curriculum. Within the “Content Guide,” a “Big Ideas in Mathematics” section lists which mathematical concepts are detailed for grades K–5. The instructional materials state: “Big Ideas are the conceptual underpinnings of the program and the glue that provides conceptual cohesion across lessons, topics, and grades, as well as across TEKS and reporting categories. Big Ideas connect Essential Understandings that occur within and across lessons.” The “Math Background” at the start of each topic shows the “Big Ideas” and “Essential Understandings” for the topic. For example, the fifth Big Idea is “Comparison and Relationships.” The Big Ideas chart shows that this Big Idea can be found in kindergarten Topics 2, 4, 5, 6, 14, and 15. It can be found in grade 1 Topics 4, 10, 13, and 15. For grade 2, this Big Idea can be found in Topics 4, 10, 12, and 15. Vocabulary terms used for the fifth Big Idea, such as order, more (than), fewer (than), and number sentence, are consistent across the grade levels. The Content Guide also includes a “Scope and Sequence” section that charts the mathematical concepts across grade levels K–5 and the grade levels in which they are introduced, practiced, and applied. For instance, “Number and Operations, using concrete/pictorial models, strip diagrams, number lines” is shown to be introduced in grade K, practiced in grades K, 1, 2, 3, and 4, and applied in grades 4 and 5. The materials include a vertical alignment chart, “Skills Trace,” that shows how topics align, both directly and indirectly, to topics outlined for students in preceding and subsequent topics. For example, in kindergarten Topic 9, under “Looking Back TEKS 1.4A,” the materials state that students identify the value of a dime. In grade 2, Topic 10, the materials state that with TEKS 2.5A, students put a set of coins in order from the one with the greatest value to the one with the least value and then count on to find the total value.

The material provides review and practice through the curriculum. Every topic starts with a “Review What You Know” section, and each lesson starts with a review practice sheet to ensure students have the foundation necessary on which to build new skills. Each lesson then has a “Quick Check” to review the lesson and ensure that students learned the required concepts in the lesson. The material includes various components, such as ongoing “Daily TEKS Review,” “Solve and Share,” “Independent Practice,” “Guided Practice,” and “Homework” practice, for each lesson. “Math Tool Activities” can cover more than one lesson concept. For Topic 5, Lesson 4, the Math Tools Activity can be used with both that lesson and the preceding one. “Center Games” provide opportunities for students to use and practice newly taught skills as well as previously taught skills. In the Center Games for Topic 5, Lesson 4, students draw number tiles from a bag labeled red and another bag labeled blue. Students pick a number tile from the red bag and cover the appropriate number of spaces on a ten-frame with red tiles. They draw a number tile from the blue bag and cover the appropriate spaces with blue tiles on another ten-frame. Students then add the appropriate number of blue tiles to the ten-frame with the red tiles to make ten and say the addition sentence. The Skills Trace section details how the materials build upon previously taught content; it shows how TEKS covered in a topic build upon TEKS covered in a previous topic and how they are addressed or built upon in a future topic. For Topic 2, it shows how TEKS 1.3B (use objects or pictures to solve problems about joining) was addressed in Topics 1 and 2, and in Topic 4, students work on TEKS 1.3E (explain how to use addition to solve subtraction problems for sums to 12). “Today’s Challenge Online” has problems that apply to any content taught before the topic.

Evaluation for 6.2

Evaluation for 6.2
Materials include implementation support for teachers and administrators.

The materials provide a TEKS-aligned scope and sequencing, which builds and connects across grade levels. Resources and guidance are included to help administrators support teachers in implementing the materials as intended. The materials include a school year’s worth of math instruction, including realistic pacing guidance and routines.

Evidence includes but is not limited to:

The material includes a “Content Guide” with the “Big Ideas in Mathematics,” “Texas Focal Points,” and “Skills Trace” for each grade 1 topic and a “Scope and Sequence” that supports the teacher in understanding the vertical alignment. This Scope and Sequence shows clear alignment through the “TEKS Correlation” document. The Scope and Sequence outlines which essential knowledge and skills are taught. The chart lists the concepts and skills and the grade level in which they are introduced, practiced, and applied. The “Numbers and Operations” section of the Scope and Sequence details comparing and ordering whole numbers. It charts how “one and two more” and “one and two less” are introduced in kindergarten and practiced in kindergarten and first grade. “Ten more and ten less” are introduced in first grade and practiced in grades 1 and 2. “One hundred more and one hundred less” are introduced and practiced in grade 2. Comparing whole numbers is introduced in kindergarten, practiced in kindergarten through grade 3, and applied in grades 4 and 5. Using comparison symbols <, >, = is introduced in grade 1, practiced in grades 1 through 3, and applied in grades 4 and 5. Ordering whole numbers is introduced in kindergarten, practiced in kindergarten through grade 4, and applied in grade 4. Comparing and ordering on number lines is introduced in grade 1, practiced in grades 1–4, and applied in grade 4. Skills Trace details the order in which the essential knowledge and skills are presented and revisited. It describes how the essential knowledge and skills build and connect across grade levels. Each lesson includes a “Lesson Overview,” which includes TEKS, “Essential Understanding,” vocabulary, materials, and “Math Background” to use with a specific part of the lesson provided prior to learning a topic. A Big Idea chart shows the topics where each conceptual underpinning is taught from kindergarten to fifth grade.

The materials support the teacher by providing teacher prompts, topic planners, Math Backgrounds (“Focus on Process” and “Focus on Content”) differentiation for all three “RtI” levels, and a “Language of Math” section for each topic. These areas provide the teacher with required supplies, TEKS, ELPS, and an understanding of the cognitive requirements for students to master the content in the topic. They provide suggestions for how to assess student progress, how to address struggling students, and how to challenge those who are at grade level or who have achieved mastery. The materials provide resources that include class sets of individually packaged manipulatives for each student and a pocket chart to store them. At the beginning of each lesson, a “Materials List” shows which manipulatives are used. In addition, materials include many online resources, such as assessments, online tools, online games, and review materials. Most of the materials are organized in a repetitive and logical manner that is consistent throughout the topics. The “User Guide” gives guidance for teachers on how to use each page in the student’s workbook. There is the option on “Realize” for users to quickly add resources to create their own Table of Contents (playlist). This resource is then accessed from the “My Library” tab.

The materials include resources and guidance to help administrators support teachers in implementing the materials as intended. For example, the materials contain a TEKS-aligned scope and sequence outlining the essential knowledge and skills that are taught in the program and the order in which they are presented, as well as a Skills Trace to show how knowledge and skills build and connect across grade levels. The “TEKS Correlation” and “Texas Focal Points” indicate mathematics content to emphasize at each grade level. For each focal point, there is a group of related TEKS. The materials provide tools to support teachers in recognizing best instructional practices and arrangements in an elementary math classroom. The materials include guidance to support teachers in understanding developmentally appropriate mathematical practices in elementary classrooms, including the use of small groups and guidance for implementation of the lessons. The teacher’s guide gives much direction and details on how to implement the instructional materials. For each topic, there is a “Topic Planner” section, a Math Background section, a section for “Differentiated Instruction,” and a section for the Language of Math, which all help to give the teacher guidance and support in implementing the instructional materials. The Math Background lists and details the TEKS covered during that topic, along with an explanation of the “Essential Understandings” that are addressed. Detailed information for Focus on Process and Focus on Content is also provided. In Topic 1, Math Background lists and details TEKS 1.3B; the Big Idea that matches this TEKS is also detailed; Essential Understandings are provided for Lessons 3–7 in which this TEKS is taught; Focus on Process provides detailed information for the two process standards featured in Topic 1, “Connect and Formulate a Plan”; Focus on Content provides information on meanings of addition, joining, part-part-whole, compare, representing addition, and the order property. Professional development videos and research-based information is provided within the topics and in the “Content Guide” in the teacher overview section. Administrators could use this information to understand developmentally appropriate practices. The data section of the curriculum provides class and individual charts and tracking sheets to show content mastery or intervention material for those still struggling.

The material includes lessons and activities for a full year of instruction and realistic pacing guidance for each topic and lesson. The topics allow for reasonable implementation throughout a school year, and the activities and routines in each topic can be completed within the length of the year. For example, the material includes pacing for 16 topics that assumes one lesson per day, which is a total of 110 days. Additional time may be spent on review, remediation, differentiation, and assessment as needed. “Step Up to Grade 2” includes an additional 10 days. In the “enVisionMATH 2.0 and Texas” guide, a year-long “Pacing Guide” is located on page 17. This guide proposes nine days for Topic 1, 11 days for Topic 5, five days for Topic 11, and seven days for Topic 14. The guide proposes 110 days in all for Topics 1–16 and 10 days for Topic 17. The lessons are all formatted similarly and provide spiraling work that keeps content fresh in students’ minds. Additional time is scheduled at the end of each lesson, so the teacher has an opportunity to work with those needing intervention while providing lesson-specific activities, at an appropriate level of challenge, for those on level and those who have achieved mastery.

Evaluation for 6.3

Evaluation for 6.3
Materials provide implementation guidance to meet variability in programmatic design and scheduling considerations.

The instructional materials are sequenced and spiraled in an order that ensures students develop prerequisite skills prior to scaffolding on higher-order concepts. The materials provide guidance for strategic implementation without disrupting the sequence of content that must be taught in a specific order following a developmental progression. Evidence shows that materials are designed in a way that allows LEAs the ability to incorporate the curriculum into district, campus, and teacher programmatic design and scheduling considerations.

Evidence includes but is not limited to:

The materials include strategic guidance for implementation to ensure that content is taught in an order consistent with the developmental progression of mathematics. The materials provide a suggested sequence of units that considers the interconnections between the development of conceptual understanding and procedural fluency; information can be found in the “envisionMATH Texas 2.0 Content Guide.” The curriculum is designed so that teachers can import additional items for use in lessons in accordance with individual, grade-level, school, or even district requirements. The lessons can be customized, and the plans can be organized by day, week, or month. District-created content or teacher content can be uploaded. Topics can be resequenced to match district-level curriculum guides or district scope and sequence preference. The materials provide a “Skills Trace” for each grade 1 topic and a “Scope and Sequence” guide to help ensure the correct sequence of the mathematical concepts is taught. The Skills Trace lists the TEKS that prepared the students for the current topic, the TEKS that the current topic covers, and the TEKS covered in future topics that build upon the current topic’s TEKS. For example, Topic 5 addresses TEKS 1.5D, 1.5E, and 1.5F; the “Looking Back” column shows they are covered in Topic 4. These same TEKS are also shown to be addressed in Topic 6 in the “Looking Ahead” column. The topics are organized in sequential order. In grade 1, Topic 4 addresses addition and subtraction facts to 12, Topic 5 addresses addition and subtraction facts to 2, and Topic 6 addresses more addition and subtraction.

The materials are designed in a way that they can be easily implemented in a variety of ways. Within the materials, it is easy to navigate, assign resources, search, customize, organize plans by day, week, or month, assess, and analyze data. Each topic is flexible enough that it can be expanded with “Math Science Activities,” “Interactive Math Stories,” “Today’s Challenges,” “Daily TEKS Reviews,” “Interventions,” “Centers,” and online math games. It is also possible to shorten in-class instruction and assign quick checks, homework, and assessments in the online program. The curriculum provides support for English Learners, struggling students, students who are on level, and students who have achieved mastery. The lessons can easily be presented to a full class or a small group both in person or online. The instructional materials are designed to allow the ability to incorporate the curriculum into the district, campus, and teacher programmatic design and scheduling considerations. The materials allow the topics to be rearranged online so that LEAs can organize the topics as needed to match their curriculum or district scope and sequence preference. Online, to the right of the topics, the “Rearrange” button allows teachers to click and drag the topics into any order they choose. The ability to create content is also available. A teacher can upload a file, add a link, or build a test.

Evaluation for 6.4

Evaluation for 6.4
Materials provide guidance on fostering connections between home and school.

The materials support the development of relationships between teachers and families. They specify activities for use at home to support students’ learning of appropriate mathematical skills.

Evidence includes but is not limited to:

The instructional materials support the relationships between teachers and families. The materials include level homework for each lesson in which there is a “Home Connection” section. The materials provide suggestions and examples of exemplary family engagement practices. For example, in Topic 1, Lesson 4, the Home Connection states: “Your child identified different ways to make eight and nine. Give your child eight pennies and draw a large circle. Have your child place some pennies inside the circle and the rest outside. Then have your child tell how many are inside, how many are outside, and how many there are in all. Give your child one more penny and repeat the activity.” The materials also include “Home-School Connections” pages that encourage the development of strong relationships between teachers and families by giving families an overview of the content in the topic. The Topic 10 Home-School Connection shares how students are learning to compare and order numbers to 120. It goes on to explain how they learn to use the <, >, and = signs to compare the numbers and shows how a hundreds chart can be used to help to compare numbers. It also explains one more than/less than and ten more than/less than. The Topic 12 Home-School Connection explains plane shapes and solid figures that the students are learning about. It encourages families to look for and identify these shapes and figures around their homes. Student progress reports are located in “Teaching Tools” under the “Teacher Resources” tab on the right side of the “Table of Contents.” This form is intended to be sent home at the end of each topic. It reviews the student’s progress on the topic and has a portion at the bottom that parents/guardians are to sign and return to the teacher. This form ensures that parents are aware of how their students are progressing in math.

The materials include online access to resources that parents can use at home to work with their children on specific skills. Some “Math and Science Projects” included in each topic also provide some activities for students to specifically complete at home. One example is the Math and Science Project for Topic 2, where students discuss with their family and friends how weather can affect their plans for the day. Students keep a journal to keep track of the weather for a week and then make up addition and subtraction problems regarding the data they collected in their journal. Online materials include resources that are easy to use and are related to current skills. There are printable versions of worksheets, an online animated glossary, and online manipulatives and content-specific games for students to practice math skills. On each homework sheet, there is a “Math Tools and Math Games” callout that has a link to a specific math tools activity or math game to use with the lesson. For example, the Topic 15, Lesson 2 Home Connection informs the parents that their child used a bar graph to answer questions and drew conclusions. The “Home Activity” suggests parents have their child explain a provided bar graph in his or her own words and asks them to be sure their child understands that each shaded square stands for one vote. The materials include Home-School Connections pages that give families an overview of the content in each topic. The Home-School Connection at the beginning of Topic 16 explains income, wants, needs, and charity to families, and then suggests they discuss earning money with their child by creating examples for them to solve. The sheet gives the example, “You earn $8.00 for raking the leaves and $5.00 for watering the garden. How much income do you have?” The curriculum is available online, and teachers can assign specific activities for students to complete at home, such as assessments, online games, or practice activities. There are also online manipulatives that students can use to help them solve problems when they are at home and do not have school manipulatives to use. Home support materials are readily available in English and Spanish, and there are suggestions at the beginning of each topic for real-world ways to practice skills being learned in class.

Evaluation for 6.5

Evaluation for 6.5
The visual design of student and teacher materials (whether in print or digital) is neither distracting nor chaotic.

The materials are structured in a way to facilitate ease of instructional support to teachers for planning and implementing lessons that contribute to student learning. The pictures and graphics are supportive of student learning and include appropriate use of white space and design that supports and does not distract from student learning.

Evidence includes but is not limited to:

The materials are designed to support students’ learning. The teacher’s guide is clear and is designed in a way that teachers can locate important information. The materials consistently include a place for instructional support to aid teachers in planning and implementing lessons. For example, the “Topic Planner” at the beginning of each topic provides an overview of the lessons. It gives the lessons, pages, TEKS covered, ELPS, “Essential Understanding,” and the materials needed and where to find them. The teacher’s guide includes instructional support with information that is easily identified throughout the lessons. For example, there are callouts and notes on the side of each page that have guidance questions for teachers to check for students’ understanding. The visuals and graphics that are included are concise and user friendly. The materials adhere to the “User Interface Design” guidelines. For example, the font is clear and easy to read. Items with photographs and colorful pictures do not distract from the text on the page or interfere with learning. Also, under “Visibility” in system status guidelines, the materials allow for the user to immediately enlarge images when clicked upon. Materials meet the “Aesthetic and Minimalist Design” guidelines; icons make for easy access to the “Table of Contents,” “Resources,” “Standards,” “eTexts,” and “Tools.” The design of the student instructional materials is consistent from topic to topic; lessons begin with the “Visual Learning Bridge,” then move into the “Guided Practice,” and end with “Independent Practice.” The student book pages are easy to follow; the print is appropriate, and the pages are not crowded. Any tables, charts, and visuals included are clear and concise. The characters and illustrations are age-appropriate and adequately display the mathematical concepts being taught without being overly distracting.

The same theme of the grade-level robot is used throughout and shows consistency. The graphics used in online games are aesthetically pleasing and engaging for the students without being overwhelming. The interactive “Math Tools,” such as the base-ten blocks and the pan balance, are straightforward to use and allow for easy user control and freedom. New vocabulary and concepts are introduced with pictures and words to help students visualize what they are learning. Page designs are simple, with clear and easy-to-read information and plenty of white space for student work. Online games, assessments, and resources are intuitive, with opportunities to go back and review work before submitting it. The graphics and pictures on the pages are colored and go along with the learning. The publisher provides some text resources like pictures, books, and charts. Items with photographs and colorful pictures do not distract from the text on the page or interfere with learning.

Evaluation for 6.6

Evaluation for 6.6
If present, technology or online components included are appropriate for grade level students and provide support for learning.

The technological components align to the curriculum’s scope and approach to mathematics skill progression; they support the materials’ progression of math content and skills. The materials provide a full suite of online curricular components to reach all students, including math games, science activities, and problem-solving reading activities that promote reasoning and application. Every part of every lesson can be assigned to students to perform at home. This assignment includes videos, stories, assessments, reviews, and games. Students can even participate online in “Solve and Share” using the “DrawPad,” where students can write their solutions during whole-class discussions. At the beginning of each topic, there is a “Today’s Challenge” and an “Animated Math Story.” The “Begin Topic” folder contains vocabulary cards that may be downloaded or printed. It also contains a “Review What You Know” activity. For each topic’s lesson, there is an available “ACTIVe-book” activity. “Visual Learning Animation Plus” includes interactives to build understanding through classroom conversations. An online “Quick Check” assesses student progress. Many lessons include online interactive games to give students additional practice in the lesson’s concepts. These items can be found within each lesson of each of the topics. For every four topics, the instructional materials include an online “Benchmark Test”; there is also an online “End of Year Test” available.

The materials include technology to enhance student participation, colorful interactive math manipulatives, and “Math Games” to help motivate and enhance learning. For example, there is an opportunity for a differentiated assignment after every four topics. Students are assigned remediation or enrichment tasks, which can include Visual Learning Animation Plus, an online Math Game, or a “Digital Math Tools Activity.” The Visual Learning activity provides animated math problems for students to answer via discussion, the drag and drop tool, and text box tools. In Topic 11, Lesson 4, Visual Learning Activity 2 has students drag and drop coins onto the mat to count on and find their value. As a student drags a quarter onto the mat, there is a box that totals the value of the coins on the mat in all. Activity 3 reviews how to count the values of coins by starting with the coin that has the highest value. Activity 4 includes a “Do You Understand?” activity in which students answer a word problem. The word problem states, “You have a pocket full of coins.” It lists the coins and then asks, “What coin should you start counting with? Why?” The material provides teachers with appropriate and sufficient guidance on how to use technology. For example, the teacher guide has sidebars within each lesson that reference what technology can be accessed and where to find it. Online manipulatives and games are engaging and allow students to review new skills. The materials provide intuitive ways for teachers to assign online activities to students and make online learning feasible. The teacher’s “User’s Guide” provides information for the different online activities available for student use. MyPearsonTraining.com features many online tutorials and quick-start guides to help teachers jumpstart their “enVisionMath Texas 2.0 training.”

Evaluation for 7.1

Evaluation for 7.1
Technology Specifications

Information available.

Evaluation for 7.2

Evaluation for 7.2
Price Information

Information available.

Evaluation for 7.3

Evaluation for 7.3
Professional Learning Opportunities

Information available.

Evaluation for 7.4

Evaluation for 7.4
Additional Language Supports

Information available.