Kindergarten - Gateway 2

The instructional materials for enVision Mathematics Common Core Kindergarten meet the expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The structure of the lessons include several opportunities that address conceptual understanding. For example:

• Math Background: Rigor page contains information about where conceptual understanding is built within the topic.
• The Lesson Overview includes a narrative on how conceptual understanding is included in the lesson.
• The Solve & Share activity’s purpose is “to elicit productive struggle that builds understanding by connecting prior knowledge to new ideas.”
• Lessons are introduced via video, Visual Learning Animation Plus, at PearsonRealize.com building on conceptual understanding.
• Students have the opportunity to independently demonstrate conceptual understanding through Independent Practice and Problem Solving pages within lessons.

Materials include problems and questions developing conceptual understanding throughout the grade-level and provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. For example:

• Lesson 4-1, Lesson Overview, “Students further their understanding of comparison as they compare larger groups to determine which is greater or less in number.” In the Visual Learning Bridge, students compare groups of yellow and black chicks, “draw a line from each chick in the top group to a chick in the bottom group, and then draw a circle around the group that is greater in number than the other group.” (K.CC.6)
• In Lesson 6-3, Solve and Share, students build understanding of Put Together addition situations as they add 2 green tomatoes and 3 red tomatoes by putting counters on pictures of plants. In the Visual Learning Bridge, students investigate the essential question, “How can you solve addition problems?” as they look at a picture of tomatoes and create a word problem for it. (K.OA.1)
• In Lesson 7-1, Lesson Overview, “By utilizing multiple representations, students conceptualize problems in order to solve them.” In the Visual Learning Bridge, students “listen to the story, and then do all of the following to find out how many are left: give an explanation of a mental image, use objects to act it out, and hold up fingers.” (K.OA.1)
• In Lesson 7-3, Solve and Share, students build understanding of subtraction as take from as they solve a take from situation: “Marta is watching bugs. She sees 4 ladybugs in a group. Look at the picture and decide how many are left.” (K.OA.1)
• In Lesson 10-4, Solve and Share, students build conceptual understanding that the number 13 can be decomposed into two parts by solving the task, “13 students wait for the train. There are only 10 seats in each train car. How many students will have to ride in a second car?” (K.NBT.1)
• In Lesson 10-6, Guided Practice, students create 18 with cubes using 10 of one color and 8 of another color. They then color to match the cubes in ten frames and complete the equation __ = __ + __. (K.NBT.1)

​The instructional materials for enVision Mathematics Common Core Kindergarten meet the expectations that they attend to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency throughout the grade-level. 

In the Teacher Edition, each Topic begins with Math Background: Rigor, where procedural skill and fluency for the topic is outlined for teachers. The structure of the lessons include several opportunities to develop procedural skills and fluency, including:

• Math Background: Rigor page contains information about where procedural skill and fluency is built within the topic.
• The Lesson Overview includes a narrative on how procedural skills are addressed in the lesson, when applicable. 
• A Steps to Fluency Success chart details steps to move students to fluency and provides resources to use for practice, intervention, and enrichment. 

Later Topics include Additional Practice and Fluency worksheets, Math Diagnosis and Intervention Systems, and My Fluency Progress Forms. Additional practice is located online at PearsonRealize.com. 

Materials include Items and questions intended to develop procedural skill and fluency throughout the grade-level and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade. For example:

• In Lesson 3-6, Guided Practice, Items 1-3, “Have students count the boats and write the number to tell how many.” Students practice counting and writing the numbers 10 and 8. (K.CC.3, K.CC.5)
• In Lesson 5-2, Guided Practice, Item 2, “Have students draw lines in the chart as they count the animals that have 8 legs and the animals that do NOT have 8 legs, and then write the numbers to tell how many are in each category on another chart.” Item 3, “Have students draw lines in the chart as they count birds that are in the trees and birds that are NOT in the trees, and then write the numbers to tell how many are in each category in another chart.” (K.CC.5)
• In Lesson 6-7, Guided Practice, Items 2-5, “Have students color the boxes to complete the pattern of ways to make 4 started on the previous page, and then write an equation to match the boxes.” Item 3, “__ + 3 = 4”, students color 1 box to represent the missing addend and write the number 1. (K.OA.5, K.OA.1)
• In Lesson 8-2, Guided Practice, guidance for Items 2-3, “Have students use cubes for these facts with 4. Have them decide whether the cubes show addition or subtraction. Encourage students to make up their own stories to match the cubes. Then have them write equations to tell the related facts.” (K.OA.5)
• In Lesson 10-2, Guided Practice, Item 4, “Draw counters to match the equation.  Then have them tell how the picture and equation show 10 ones and some more ones.”  (K.CC.5)

The instructional materials for enVision Mathematics Common Core Kindergarten meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step Items, routine and non-routine, presented in a context in which the mathematics is applied.

In the Teacher Edition, each Topic begins with Math Background: Rigor, where application for the topic is outlined for teachers. Math Background: Rigor for Topic 6, Applications states, “Addition Situations Real-world addition situations are used throughout this topic to illustrate the “put together” and “add to” meanings of addition.” Each Topic also includes a variety of application tasks, for example:

• A Topic Opener, containing a contextual STEM problem designed to spark interest in the content of the topic,
• Topic Centers with application problems, 
• 3-Act Math activities where students engage in application problems, and
• Performance Tasks, where students apply mathematics of the topic in multi-step, real-world situations. 

The structure of the lessons includes several opportunities for students to engage in routine and non-routine application problems. Practice & Problem Solving sections provide students with a variety of problem types to apply what they have learned. The way in which application is incorporated into specific lessons is stated in the Rigor section of the Lesson Overview of those lessons. 

Examples of opportunities for students to engage in routine application problems include:

• In Lesson 2-2, Solve and Share, students solve “Marta’s class goes to the park.  Mr. Leeman brings 4 soccer balls and 3 basketballs. Which group of balls has more? How do you know? Use counters to show your work.” (K.CC.6)
• In Lesson 10-5, Solve and Share, students solve “14 students go to the zoo. The first bus takes 10 students. The rest of the students go on the second bus. Use counters to describe this situation. Then complete the equation to match the counters and tell how the counters and equation show 10 ones and some more ones.” (K.NBT.1, K.CC.5)
• In the Topic 2 STEM Project, Severe Weather, students identify different types of severe weather. Then they make a poster that includes up to “5 items people might need to be safe in a snowstorm” and “5 items people might need to be safe during a drought”. Students “write the number of objects in each group, compare them, and then draw a circle around the number that is greater than the other number.” (K.CC.6)
• In Lesson 8-3, Solve and Share, students are presented with the problem “4 - 3 = 1.” Students tell a story to match the equation and illustrate it with a drawing. As they solve the problem, students are asked to think about “What do the numbers stand for?” (K.OA.2)
• In Lesson 1-10, Guided Practice, Item 1, students are given a picture of 4 blue birds and a 4 to trace. “Students make a math argument about how many birds are in each row, and then write the number.” They “use objects, words or a method of their choice to explain their arguments and tell why they are correct.” (K.CC.4a)

Examples of where the instructional materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts include:

• In Lesson 6-6, Independent Practice, Item 7, students draw a picture to show what is happening and write an equation to solve, “Kris eats 2 grapes at lunch and 6 grapes for her snack. How many grapes does she eat in all?” (K.OA.2)
• In Topic 7, enVision STEM Project: Animal Needs, students find out about the basic needs of humans and animals such as food, water, nutrients, shelter and then complete a project. Students “make a poster and draw as many as 5 pictures of a human’s needs and then as many as 5 pictures of an animal’s needs. They cross out the needs that are the same for humans and animals, and then write how many are left.” (K.OA.2)
• In Topic 8, Problem Solving Performance Task, Item 4, students are presented with the problem: 4 + _ = 5 and asked, “What story can you tell to help solve the problem?” (K.OA.1)

​The instructional materials for enVision Mathematics Common Core Kindergarten meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. 

Each Topic Overview contains Math Background: Rigor, where the components of Rigor are addressed. Every lesson within a topic contains opportunities for students to build conceptual understanding, procedural skill and fluency, and/or application. During Solve and Share and Guided Practice, students explore alternative solution pathways to master procedural fluency and develop conceptual understanding. During Independent Practice, students apply the content in real-world applications, use procedural skills and/or conceptual understanding to solve problems with multiple solutions, and explain/compare their solutions.

The three aspects of Rigor are present independently throughout the instructional materials. For example:

• In Lesson 1-9, Independent Practice, Item 4, students are given pictures of boxes with 0, 1, 2, 3, 4, and 5 toys. Students count the toys in each box, write the corresponding numbers, “and draw a circle around the number that comes just after 4 when counting how many.” Students develop fluency with counting to five.  (K.CC.4c)
• In Topic 2, Topic Centers, “Watch them Grow,” students plant beans and watch them grow in a cup.  Each cup is assigned a number from 1 to 5, and that number of beans is planted in the cup. As the plants grow, “students count the number of sprouts and compare them with the number of seeds in each cup.  Which has more? Which has fewer?” This activity allows students to apply their knowledge of counting and comparing. (K.CC.5; K.CC.6)
• In Lesson 6-4, Solve and Share, students are provided an opportunity to represent an addition situation in any way they want to solve. “Daniel counts 4 drums in a parade. Then he sees 1 more drum. What numbers do you add to find how many drums he sees in all? How can you show the adding?” Allowing students to solve problems in different ways deepens conceptual understanding. (K.OA.2)
• In Lesson 11-4, Solve and Share, procedural skill and fluency are the focus as students count forward beginning at 48, 75, and 95. On a hundred chart, students “count forward from the yellow number. (48, 75, 95) Stop at the red number. (54, 86, 100) Tell how many numbers you counted aloud. Color the boxes of the numbers you counted aloud to show your work.” (K.CC.1, K.CC.2)

Multiple aspects of Rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example:

• Lesson 3-4, Lesson Overview, “Conceptual Understanding: Students see that 8 and 9 can be made in different ways. They learn the unique symbol for each of these numbers. Procedural Skill: Students practice how to write 8 and 9 to tell how many are in a group.” Students demonstrate both aspects of rigor in the Independent Practice, Item 10, as they look at a picture of sea creatures, “count each group of animals, and then write the numbers that tell how many.” (K.CC.3)
• Lesson 4-1, Lesson Overview,  “Conceptual Understanding: Students further their understanding of comparison as they compare larger groups to determine which is greater or less in number.” Procedural Skill: “Students use a 1 to 1 matching strategy to compare groups.” Students demonstrate both aspects of rigor in the Guided Practice, Item 1, as they compare groups of yellow and black chicks and by drawing a line from each chick in the top group to a chick in the bottom group. Then they draw a circle around the group that is greater in number than the other group. (K.CC.6;  K.CC.5)
• Lesson 6-5, Lesson Overview, “Conceptual Understanding: Students build upon their understanding of addition as they work more closely with interpreting, representing, and solving addition word problems. Application: Students apply what they have learned in this topic as they solve Add To Result Unknown problem types in real-world situations.” Students demonstrate both aspects of rigor in the Guided Practice, Item 5, as they solve, “2 turtles swim in the water. 5 more join them. How many turtles are swimming in all?” (K.OA.2)
• In Lesson 8-2, Lesson Overview, “Conceptual Understanding: Students deepen their understanding of addition and subtraction as individual operations as they see how the two related to one another. Fluency: The connection between the two operations aids in the development of students’ ability to fluently solve both addition and subtraction basic facts.” Students demonstrate both aspects of rigor in the Visual Learning Bridge, as they “listen to a story and use connecting cubes to help act out each story to choose an operation.” Then students complete the equations to tell the related facts. (K.OA.5)

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout the grade level, and are not treated separately.

The math practices are identified throughout the materials. For example: 

• Every Topic includes a Math Practices and ETP (Effective Teaching Practices) page with an explanation of how students engage with the MPs throughout the topic.
• Every lesson includes a Lesson Overview where an explanation of how students engage with the math practice during the lesson.  
• Special Item Solving lessons in each topic focus on specific math practices. 
• Specifically flagged comments and Items in all lessons focus on specific math practices. 
• Math Practice Animation videos for each MP provide a student-friendly explanation with demonstration Items. These can be found in the Digital Resources in Pearson Realize. 
• The Math Practices and Item Solving Handbook contains a detailed explanation for each MP, identifies “Thinking Habits” unique to each MP, connections to content and other MPs, and student behavior look-fors to monitor progress toward proficiency.

Examples of the MPs identified within individual lessons:

• MP.1: Lesson 12-6, Lesson Overview, “Students make sense of the meaning of position words in different contexts as they follow directions to name and describe shapes and objects.” 
• MP.2: Lesson 9-7 Lesson, Overview, “Students identify possible answers to word Items that have more than one potential answer.” 
• MP.4: Lesson 2-5, Lesson Overview, “Mathematical Practices MP4 Model with Mathematics: Students compare groups of objects, using models to show how they know those which are greater in number, less in number, and equal in number.” 
• MP.5: Topic 4, Math Practices and ETP, “Students use a variety of tools to represent and compare quantities, including counters, color tiles, and connecting cubes (e.g., p.160, Item 7).” 
• MP.6: Lesson 6-4, Lesson Overview, “Students use the symbols for plus and equals consistently as they begin to use equations to represent addition.”
• MP.7: Lesson 6-7, Lesson Overview, “Students use structure as they see patterns in addition equations to help solve Items.”
• MP.8: Lesson 1-5, Lesson Overview, “Students build on their understanding that the arrangement of objects does not change the total number. They see this as a concept relatable to other numbers.”

Examples of where MPs are identified and used to enrich the content:

• In Lesson 2-5, Independent Practice, Item 4, students engage with MP1 as they are asked to identify the information they know from the problem: “Marta has 2 stickers. Emily has a greater number of stickers than Marta. How many stickers could Emily have?” and “So, is it possible for Emily to have 1 sticker?” (K.CC.6)
• In Lesson 4-2, Lesson Overview, students engage in MP2 as they “represent quantities with written numerals and use those numerals to show which is greater or lesser.”  In Independent Practice, Item 4, “Have students count the seed packets in each group, write the number to tell how many, draw a line from each seed packet in the top group to a seed packet in the bottom group, and then mark an X on the number that is less than the other number.” (K.CC.6,  K.CC.7)
• In Lesson 8-5, Lesson Overview, students engage in MP4 as they “use equations, cubes, and pictures to model and help solve word Items with 6 and 7 where both addends are unknown.” In Guided Practice, Items 2-4, students listen to this story: “Carlos has 7 flowers. He wants to put some in a red vase and some in a blue vase. How many flowers can he put in each vase?” Given pictures of 7 cubes, students “use and color cubes to show 3 different ways you can break apart the flowers and put them in the vases, and then complete the equations to match each way.”  (K.OA.2, K.OA.3)
• In Lesson 6-2, Solve and Share, students engage with MP5 as they solve, “Daniel sees 2 boats on the water. Then 2 more boats go out on the water. Use red and blue cubes to show how many boats are in each group.” (K.OA.1)
• In Lesson 9-2, Solve and Share, students engage with MP6 as they use a ten frame and a picture of 14 leaves to solve, “Carlos collected leaves to put in a scrapbook. How can Carlos show the number of leaves he collected? Use counters, and then draw them to show one way.” (K.CC.3)
• In Lesson 7-6, Lesson Overview, students engage with MP7 as they “see patterns in subtraction equations to help solve Items.” Students work with subtraction patterns in Guided Practice, Item 2, as they observe three rows of three butterflies. In the first row, one butterfly is crossed out. In the second row, two butterflies are crossed out, and in the third row, three butterflies are crossed out. Students explain the pattern they see and write an equation for each row of insects.
• In Lesson 8-10, Independent Practice, Item 7, students draw counters in the ten-frame to show the part that they know, and then draw yellow counters in the empty spaces in the ten-frame and count to find the missing part of 10. Then  students write the missing number in the equation. 3+__=10” (K.OA.4)

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

Specific features of the materials engage students in constructing viable arguments and/or analyzing the mathematical reasoning of others. Examples include:

• Convince Me! prompts provide the opportunity for students to share their thinking and to analyze the reasoning of others.
• Three-Act Math - Students critique other’s reasoning as solution methods for the task are shared with the class. 
• Solve and Share - Students share and justify solutions with the class, and they critique the reasoning of others as teachers select which solutions to share.
• In the Visual Learning Bridge, there are opportunities for students to construct viable arguments.
• “I Can” bubbles prompt students, i.e., “I Can...compare groups of numbers by counting.” 
• The Math Practices and Problem Solving Handbook.

The materials consistently provide opportunities for students to construct viable arguments. Examples include:

• Lesson 2-3, Independent Practice, Item 8, students are given a picture with 4 train engines and 3 dump trucks. “Have students draw lines to match the objects from one group to the other group. Have them mark an X on the group that is less in number than the other group, and then explain why they are correct.” (K.CC.6, K.CC.5)
• Lesson 6-5, Convince Me!, “There are 5 birds in the fountain and 3 more came and joined them. How many birds are there in all? Explain how you know you are correct.” (K.OA.2)
• Lesson 10-7, Problem Solving Performance Task, Item 8, after solving word problems in Items 6-8, students are asked to, “Tell a friend why your answers are correct. Then tell the friend about the pattern you see in the  number chart and how the equations show 10 ones and some more ones.” (K.NBT.1)

The materials consistently provide opportunities for students to analyze the reasoning of others. Examples include:

• Lesson 5-4, Solve & Share, students solve, “Carlos says that the number of blue cubes is equal to the number of cubes that are NOT blue. Does his answer make sense? Use numbers, pictures, or words to explain your answer.” (K.MD.3, K.CC.6, K.CC.7)
• Lesson 8-4, Convince Me!, “Daniel says 2 -1 = 3 because he starts with 2 counters, adds 1 more, and has 3 in all. Is he correct? Explain.”  (K.OA.5)
• Lesson 11-3, Convince Me!, “Mike counts the decade numbers to count by 10s to 40. He counts: 10, 20, 30, 35, 40. Which number should he not have counted. Why?” (K.CC.1)

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

There are multiple locations in the materials where teachers are provided with prompts to elicit student thinking. For example:

• The Math Practices and Problem Solving Handbook provides guidance on implementing MP3 and questions that students might ask themselves as they reflect on MP3. The Problem Solving Lessons which focus on MP3 are identified, such as Lessons 1-10 and 5-4.
• In the teacher’s notes for each lesson, MP3 is identified in red print as “Construct Arguments” or “Analyze Reasoning”. Questions to elicit student thinking are included below the prompts. 
• In the teacher notes for Solve & Share activities, questions to prompt students thinking are included in Share Solution Strategies and Key Ideas.
• The Convince Me! activity, when connected to MP3, provides prompts to assist students in constructing arguments and analyzing the reasoning of others.
• Three Act Math Tasks includes Construct Arguments which provides prompts for the teacher to help students construct arguments.

The materials provide guidance to support teachers in engaging students in constructing viable arguments. Examples include:

• Lesson 1-10, Solve & Share, Construct Arguments: “How can you use math to explain why your counting is correct?” (K.CC.4a)
• Lesson 5-1, in the Visual Learning Bridge, animals were classified in Hair and No Hair categories. In Convince Me!, teachers are prompted to “have students classify the animals in a different way: Brown and Not Brown.” “The cat is white and the frog is green, but they are both in the same category. Is this correct? Explain.” (K.MD.3, K.CC.5)
• Lesson 14-2, Convince Me!, “Hold up 2 glasses of different sizes. Which glass holds more than the other? [Answers will vary.] Encourage students to justify their response. How do you know?” (K.MD.2, K.MD.1)

The materials provide guidance to support teachers in engaging students in analyzing the reasoning of others. Examples include:

• Lesson 2-3, Independent Practice, “Provide students with an opportunity to critique the answer of a fictional classmate: Carly draws 3 counters in the bottom five-frame. Is her answer correct? [No] Why not?” (K.CC.6, K.CC.5)
• In Lesson 5-4, Visual Learning Bridge, students view a picture of vehicles. In Convince Me!, the teacher asks, ”What do you see? [Cars and trucks] Tucker and Olivia counted 6 cars and 5 vehicles that are not cars.  How can you check whether their answers make sense?” The teacher is prompted to say, “Emily says the number of cars is equal to the number of vehicles that are not cars. Does this make sense? Explain.” (K.MD.3)
• Lesson 12-6, Convince Me!, to encourage the critiquing of reasoning, the teacher is prompted to “place 5 different objects on a desk. Stack 2 of the objects. Point to an object and have students name the object and describe its position. Other students tell if they agree and explain why. Have students suggest another way to describe the object’s position.” (K.G.1)

The materials provide guidance to support teachers in both the construction of viable arguments and analyzing/critiquing the arguments/reasoning of others. Examples include:

• Lesson 1-10, Solve & Share, while observing students at work, the teacher is directed to ask the guiding question, “Can you explain how you counted or checked your work to explain why your number is right?” Guidance is also provided during whole class discussion: “Based on your observations, choose which solutions to have students share and in what order. Focus on the explanation of ways to tell there are 5. If needed, show and discuss the student work at the right.” (K.CC.4a)
• Lesson 5-4, Solve & Share, teachers are prompted to note how students explain their answers and if needed, ask “What does it mean if the number of cubes in each category is equal? How can you tell or show what you found?” Then, after the sharing of strategies, teacher presents Tim’s Work and asks, “What mistake did Tim make? Why might this mistake make him think Carlos was correct?” (K.MD.3, K.CC.6, K.CC.7)

Topic 9, 3-Act Math, students make predictions for the question, “What is missing  from the box?” (comparing the contents of a box of vegetables with what was ordered). In Act 1, Construct Arguments, guiding questions are provided for the teacher: “What cannot be missing from the box? Why do you think your prediction is the answer to the Main Question? Who has a similar prediction? Who has a different prediction?” In Act 2, Share Solution Strategies Critique Reasoning, teachers are prompted to “have students share their solution methods. If needed, teachers are told to use the Analyze Student Work screen. For Carlos’s Work, teachers are provided this prompt: “Carlos says he drew a picture and then counted the missing items.  What mistakes did he make?” (K.CC.5)

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet the expectations of attending to the specialized language of mathematics.

The materials provide explicit instruction on the use of mathematical language including words, diagrams, symbols, and conventions. Each topic includes:

• My Word Cards are available online. In the Teacher Edition, Build Mathematical Literacy, page 1J, explains how My Word Cards are used: “Students use the example on the front of the card to write the definition on the back” 
• Vocabulary Activities at the beginning of Topics
• Vocabulary Review at the end of each Topic
• Glossary in the Student Edition
• Animated glossary is available online.
• Online vocabulary game in the Games Center

For each topic, the Topic Planner includes a list of the new vocabulary words for each lesson. The vocabulary words are also included in the Teacher Edition, Lesson Overview page for each lesson. For example, (Teacher Edition, page 57A)

• In Lesson 2-1: compare, equal, group, and same number are identified.
• In Lesson 2-2: greater than is identified.
• In Lesson 2-3: less than is identified.

In the Vocabulary Review at the end of each Topic, teachers are provided several activities to help students review the vocabulary. For example, In Topic 8, teachers are provided with suggestions including: 

• “Have students define the terms in their own words.” 
• “Have students say math sentences or math questions that use the words.”
• Play a “What’s My Word?” guessing game in which you or a student thinks about one of the words and says a clue that others listen to before they guess the word.
• Play a “Right or Wrong?” game in which you or a student says a sentence that uses one of the words correctly or incorrectly. Then others say “right” or “wrong.”

The materials use precise and accurate terminology and definitions when describing mathematics, and they provide support for students to use them correctly. Examples include:

• Topic 2, Vocabulary Review, Items 1-4, students review the terms less than, equal, and compare as they “draw 5 counters in group; write the number that is less than” 1; draw a group of counters that is equal in number to the group of counters shown;” and “compare red and yellow counters using matching to find which group is less in number than the other, and then mark an X on that group.” Vocabulary words being reviewed  are equal and less in number.
• Topic 7, Vocabulary Review, Items 1-4, students review the terms minus sign, left, subtraction sentence, and separate as they “write the minus sign to show subtraction; draw a circle around the number that tells how many are left; complete the subtraction sentence; and separate the tower into 2 parts, draw each part, and then write the numbers to tell the parts.”  The vocabulary words being reviewed are minus sign, left, subtraction sentence, and separate.
• Lesson 12-4, Visual Learning Bridge, “Emily is tracing a shape called a hexagon. How many sides does a hexagon have? [6 sides] How many vertices does a hexagon have? [6 vertices]”