1st Grade - Gateway 2

​The instructional materials for enVision Mathematics Common Core Grade 1 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.
• Solve & Share activity whose 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:

• In Lesson 1-7, Solve and Share, students solve a change unknown problem using addition or subtraction to find the missing addend. “There are five train cars.  More train cars join. Now there are 9 train cars. How many train cars joined?” (1.OA.1)
• In Lesson 5-4, Solve and Share, students build their understanding of adding three numbers as they use addition to find the total number of books in three stacks and write two different equations to show the addition. “Carlos made stacks of 6 books, 4 books, and 6 books. How can you use addition to find the number of books in all three stacks? Write two different equations to show how many books in all.” (1.OA.3)
• In Lesson 8-1, Lesson Overview, “Students use models to make the numbers from 11 to 19 and then connect those models with both written numerals and number words. Students are formally introduced to the idea that each of these numbers is made up of 1 ten and some ones.” Solve & Share, students “show different numbers using counters and a ten-frame. They tell how the numbers are alike and different. Their work shows prior and emerging understanding.” (1.NBT.2)
• In Lesson 8-4, Lesson Overview, students build understanding by “Using models to compose numbers establishes a foundation for place-value concepts with three- and four-digit numbers as well as for addition with greater numbers.” Convince Me!, students “use connecting cubes to represent their numbers” (46 and 64). They then “talk about the similarities and differences between the numbers.” (1.NBT.2)
• In Lesson 9-1, Lesson Overview, “students use tens rods and one units to model a two-digit number. Then they build upon that model to show a number that is 1 more, 1 less, 10 more, or 10 less than the original number.” During the Visual Learning Bridge, students use place value blocks to model the number 25 and then show 1 more, 1 less, 10 more and 10 less with the blocks and describe the digit that changes. (1.NBT.5)
• In Lesson 10-1, Solve and Share, students build an understanding of adding multiples of ten as they explore how the sum of 3 + 5 can be used to help add 30 + 50. In the Visual Learning Bridge, students investigate the essential question, “How is adding groups of ten like adding numbers less than 10?” (1.NBT.4)
• In Lesson 10-9, Guided Practice, Problem 1, “Ellen has 27 stickers. Her brother gives her 26 stickers. How many stickers does Ellen have in all? Use drawings to show and solve the problem. Then write the equation.” (1.NBT.4)

The instructional materials for enVision Mathematics Common Core Grade 1 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 skill 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 2-1, Guided Practice, “Count on to find the sum.”  Item 1, Shows a picture of a bucket with a 3 on it and tray with 2 carrots the equation reads “3+ __= ___”.   (1.OA.5) 
• Lesson 2-4, Guided Practice, Items 1 and 2, students “Look at the ten-frames. Write an addition fact with 5. Then write an addition fact for 10.” This develops fluency for adding within 10. Item 1, “ 5 + __ = 7. 7 + __ = 10.” (1.OA.6)
• In Lesson 2-7, Independent Practice, “Think addition to help you subtract. Draw the missing part. Then write the missing numbers.”  Item 1, “6 + __ = 8 so 8 - 6 = ____.” (1.OA.6)
• In Lesson 3-5, Convince me!, “How would you make 10 to find the sum of 9+4?” as a strategy to add within 20. (1.OA.6)
• Topic 4, Fluency Practice Activity, students solve addition and subtraction facts within 10, “Color these sums and differences. Leave the rest white.” Students color sums and differences that are equal to 6, 7, or 8, and write the word that they see after the boxes are colored.
• In Lesson 7-4, Guided Practice, Items 1, 2 and 3, students are directed to “Write the numbers to continue each pattern. Use a number chart to help you.”  Item 1, “Count by 1s: 112, 113, 114, ___, ____, ____, ___, ___,____.” Item 2, “Count by 10s: 22, 32, 42, ___, ___, ___, ___, ___, ___.” Item 3, “Count by 1s: 90, 91, 92, ___, ___, ___, ___, ___, ___.” This works on the development of fluency in counting to 120. (1.NBT.1)
• In Lesson 10- 7, Guided Practice,“Add. Draw blocks to help.” Item 1,  “Find 36 + 24.” Item 2, “Find 19 + 25.” Students are developing procedural skills to add within 100. (1.NBT.4)

The instructional materials for enVision Mathematics Common Core Grade 1 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 problems, 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 applications for the topic are outlined for teachers. Math Background: Rigor for Topic 4, Applications states, “Addition and Subtraction Situations Lesson 4-8 specifically introduces “take from” and “compare” subtraction situations. These situations allow students to apply their understanding of subtraction in context. Students solve problems with unknowns in all positions. In Lesson 4-9, students apply what they know about addition and subtraction to write word problems for addition or subtraction situations.” Each Topic also includes a variety of application tasks, for example:

• 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 and non-routine application problems include:

• In Lesson 3-8, Guided Practice, Item 1, students solve, “Tim writes 9 stories. He writes 3 fewer stories than Daisy. How many stories did Daisy write?” (1.OA.6)
• In the Topic 4 Performance Task, Item 1, students use information from a graph to solve, “How many more moon stickers than sun stickers does Maria have?” (1.MD.4)
• In Lesson 6-3, Convince Me!, students are presented with a picture graph displaying data on what students like to drink for lunch. In addition to typical routine statements about the data, students answer, “What other information do you know about what students like to drink at lunch?” with a sample answer of “The students like juice and milk more than water.” (1.MD.4)
• In Lesson 1-9, Solve and Share, students solve, “7 rabbits, 3 turtles. How many more rabbits than turtles? Do you add or subtract to solve the problem? Tell why. Show how to solve.” (1.OA.1, 1.OA.4)
• In Topic 1, 3-Act Math Task, students determine how many apples were taken from the fruit bowl. In Act Two, they are given the number of red and green apples before and after some were taken out of the bowl. Students draw models to determine the solution. (1.OA.1)
• In Topic 10, Pick a Project - Octopuses, students write and draw an octopus story. “Write an octopus story about octopuses that are seen on a reef and those that are hidden. Draw a picture that relates to your number story. You can draw counters to show the octopuses that are seen. Then write an equation with an unknown for the number story. Have a classmate solve it. They should use the equation and counters to help them solve.” (1.NBT.4, 1.NBT.5)
• In Topic 5, Performance Task, Item 5, students see a picture that includes 5 daisies and 8 lilies. They solve, “Terry says that if there were 2 fewer lilies, then the number of lilies would be equal to the number of daisies. He writes the equation below. Is this equation true or false? Explain how you know. 8 - 2 = 5” (1.OA.7, 1.OA.1)

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 1-6, Independent Practice, Item 4, students solve  “Beth writes on 3 cards. Joe writes on 9 cards. How many fewer cards does Beth write on than Joe?”  (1.OA.1)
• In Lesson 5-6, Independent Practice, Item 4, students solve, “Harry has 5 fewer buttons than Tina. Harry has 7 buttons. How many buttons does Tina have?” (1.OA.1, 1.OA.4)
• In Lesson 10-9, Independent Practice, Item 4, students solve, “There are 16 apples in the bowl. George buys 15 more apples. How many apples are there in all?”  (1.NBT.4)

​The instructional materials for enVision Mathematics  Common Core Grade 1 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 3-4, Solve and Share, students develop conceptual understanding as they solve, “Carlos and I each pick 5 strawberries. What doubles fact shows how many strawberries we have in all? If I pick 1 more strawberry, how could you find how many strawberries in all?” (1.OA.6)
• In Lesson 2-6, Lesson Overview, “As students use the strategy of counting back to solve subtraction problems, they begin to develop fluency for subtraction facts within 10.” In the Visual Learning Bridge, students “count back” 2 on a number line in order to model subtracting 2 from 7. (1.OA.5)
• In Lesson 10-8, Independent Practice, Items 3-4, students find each sum, solve any way they choose, and draw or explain what they did: “27 + 9 = ___, and 50 + 23 = ___.” (1.NBT.4, 1.NBT.5)
• In Lesson 5-5, Solve and Share, students engage with application as they solve, “I have 6 oranges, Alex has 2 pears, and Jada has 4 apples. How many pieces of fruit do we have in all? Write 2 different addition equations to solve the problem.” (1.OA.2, 1.OA.3)

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

• In Lesson 2-7, Lesson Overview, “Conceptual Understanding: Bar models help deepen student understanding of the relationship between wholes and parts and addition and subtraction. Fluency: By recognizing the addition-subtraction relationship, students further develop fluency as they use previously learned addition facts to solve subtraction facts.” Students demonstrate both aspects of rigor in the Additional Practice, Item 1, as students view a picture of a row of 4 counters and beneath it a row of 3 counters. Students write an addition fact that will help them write and solve the subtraction problem. (1.OA.4)
• In Lesson 6-3, Lesson Overview, “Conceptual Understanding: Students go deeper to analyze how problems can be solved using data presented in graphs. Procedural Skill: Students continue to develop skills of building graphs. Application: Students apply their knowledge of addition and subtraction to solve problems.” Students demonstrate all three aspects of rigor in the Guided Practice, Item 5, as they interpret data shown in a tally chart applying what they know about addition and subtraction to 10 to solve, “How many more students like purple than red?”  (1.MD.4)
• In Topic 6, Topic Assessment, Item 3, students are given a tally chart titled Favorite Winter Activity: Skating 5, Skiing 3, Sledding 7. Students “use the tally chart to solve” the following problems, “Which is the favorite winter activity of most students?” and “How many more tally marks does skating need to have the most tally marks?” They use an equation to explain their answer. (1.MD.4)
• In Lesson 9-3, Lesson Overview, “Conceptual Understanding: Students use their understanding of using place value to compare 2 two-digit numbers.  Procedural Skill: Students compare 2 two - digit numbers by comparing the tens and then, if necessary, by comparing the ones.” Students demonstrate both aspects of rigor in the Solve & Share when they are presented with the numbers 37 and 73, and answer, “How can place-value blocks help you decide which number is larger?”  (1.NBT.3)

The instructional  materials reviewed for enVision Mathematics Common Core Grade 1 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: Topic 1, Math Practices and ETP,  “Students make sense of Items by using addition or subtraction to help find the missing addend.. (e.g., p. 34, Visual Learning Bridge).”
• MP.2: Lesson 4-1, Lesson Overview, “Mathematical Practices MP2 Reason Abstractly and Quantitatively Students discuss how number lines can be used in different ways to subtract.”
• MP.4: Lesson 10-9, Lesson Overview, “Students use blocks, drawings, or number lines to model Items.”
• MP.5: Lesson 4-2, Lesson Overview, “Students use ten-frames to facilitate their thinking and modeling of making 10 to help subtract.”
• MP.6: Lesson 12-1, Lesson Overview, “Students use appropriate mathematical language in making accurate comparisons of the lengths of objects.”
• MP.7: Topic 5, Math Practices and ETP,  “Students look for structure when they look for compatible numbers or make 10 to add three addends in a strategic way.  (e.g., p. 226, Visual Learning Bridge.)”
• MP.8: Lesson 8-2, Lesson Overview, “Students use repeated reasoning when they see that 10 ones is the same as 1 ten and connect that they can count objects by grouping into tens.”

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

• In Lesson 3-8, Lesson Overview, students engage with MP1 as they “make sense as they compare quantities to determine the larger, unknown amount in Item situations.”  In Guided Practice, Item 1, students solve: “Tim writes 9 stories. He writes 3 fewer stories than Daisy. How many stories did Daisy write?” (1.OA.1, 1.OA.6)
• In Lesson 8-2, Problem Solving, Item 9, students engage with MP2 as they solve “George has 3 boxes of pens. 10 pens are in each box. How many pens does George have?” (1.NBT.2c)
• In Lesson 10-9, Independent Practice, Item 2, students use drawings to show and solve the Item. Then write the equation. “Barry has 12 red cars. He has 14 blue cars. How many cars does Barry have in all?” (1.NBT.4)
• In Lesson 7-3, Problem Solving, Item 16, students use a 120 number chart to solve, “Sasha counts forward to 115. What are the next 5 numbers she counts? Write the numbers. 115, ___, ___, ___, ___, ___” (1.NBT.1)
• In Lesson 15-1, Problem Solving, Item 17,students engage with MP6 when they are given pictures of two flags, both sectioned into two pieces, one in two equal pieces and the other in two unequal pieces, students solve, “Ruth picks a flag with equal shares. Which flag did she pick? Circle the correct flag.” (1.G.3)
• In Lesson 2-5, Lesson Overview, students engage with MP7 as they “look for patterns and make use of structure when they discover and discuss how changing the order of any two addends does not change the sum.” In Solve and Share, page 73, students are shown one cube tower of 5 green and 2 yellow cubes and another with 2 yellow and 5 green cubes. They “Write an addition equation for the green and yellow cubes in each cube tower.” 5 + 2 = 7 and 2 + 5 = 7 “How are the addition equations  the same? How are they different?” (1.OA.3)
• In Lesson 1-6, Lesson Overview, students engage with MP8 as they “generalize that like with finding ‘how many more’ from the past lesson finding ‘how many fewer’ involves a comparison to find the difference in amount.”  In Independent Practice, Item 3, students use cubes or draw a picture and write an equation to solve, “Emma buys 10 red apples. She buys 5 green apples. How many fewer green apples than red apples does Emma buy?” (1.OA.1)

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 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.  Lesson 3-9, “I Can...critique the thinking of others by using pictures, words, or equations.”  
• Thinking Habits thought bubbles prompt students to critique reasoning and/or construct arguments. Lesson 3-9, Solve & Share, Thinking Habits, “Can I improve on Lidia’s thinking? Are there mistakes in Lidia’s thinking?” 
• The Math Practices and Problem Solving Handbook.  

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

• Lesson 1-9, Solve & Share, students solve, “7 rabbits. 3 turtles. How many more rabbits than turtles?” They are asked, “Do you add or subtract to solve the problem? Tell why? Show how to solve. Use pictures, numbers, or words.”  In the Thinking Habits thought bubble on the page: “How can I use math to explain my work? Is my explanation clear?” (1.OA.1)
• Lesson 5-7, Convince Me!, “Is the equation below true or false? How do you know?  10 + 8 = 9 + 3 + 3” (1.OA.7)
• Lesson 9-4, Convince Me!, “How do you know that 48 is greater than 40?” (1.NBT.3)

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

• Lesson 3-3, Convince Me!, “Becca shows 6 + 7 with cubes and says it is not a doubles fact. Is she correct? How do you know?” (1.OA.6)
• Lesson 3-9, Solve & Share, “ A pet store has 9 frogs. 5 of the frogs are green and the rest are brown. Lidia adds 5 + 9 and says that the store has 14 brown frogs. Circle if you agree or do not agree with Lidia. Use pictures, words, or equation to explain.” (1.OA.1)
• Lesson 8-6, Problem Solving, Item 6, “Nate says 5 tens and 3 ones shows the same number as 3 tens and 13 ones. Do you agree? Explain.” (1.NBT.2)
• Lesson 13-3, Solve & Share, “Look at the clock. Ria says the clock says 12 o’clock. Pat says the clock shows 3 o’clock. Do you agree with Ria or Pat? Tell why.” (1.MD.3)

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 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 for example, Lessons 1-9 and 3-9.
• 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 and 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 1-9, Visual Learning Bridge, during the Classroom Conversation narrative, teachers are prompted to ask, “How did Jada use cubes and counting to show the number of red crayons? How does the model help show Jada’s addition equation 6 + 3 = 9 is correct?” and  “How did Marta use cubes and counting to show the number of red crayons? How does the model help show Marta’s subtraction equation 9 - 6 = 3 is correct?” (1.OA.1)
• Lesson 2-5, Visual Learning Bridge, page 74, students observe two equations, 4 + 2 = 6 and 2 + 4 = 6. The teacher is prompted to say, “Look at the sentences and the addition facts. Do they show the same addends and sum?” The teacher helps “students see how the cubes and equations create a strong argument that when you change the order of the addends, the sum remains the same.” (1.OA.3)
• Lesson 8-6, Convince Me!, students answer the question, “How could you break apart 24 using only 1 ten? Explain.” In order to support students in constructing an argument, teachers are prompted to “Have students use connecting cubes, as needed, to model their method. Ask them to back their claim by counting to prove their method shows 24.” (1.NBT.2)

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

• Lesson 1-5, Solve & Share, Analyze Student Work, the teacher is prompted to share Mariyah’s Work and asks: “How did Mariyah show the red and blue cars? How was her way of finding how many more alike and different from Charles’s way?” (1.OA.1)
• Lesson 3-9, in the Visual Learning Bridge students listen to the story, “5 dogs are playing. Some more dogs join. Now 8 dogs are playing.” In Convince Me!, the teacher is prompted to say, “Sharon wrote the equation 8 - 5 = 3 to solve the problem and said that 3 more dogs came to play. Do you agree or not agree with her thinking?” (1.OA.1) 
• Lesson 14-2, Solve & Share, Analyze Student Work, the teacher is prompted to share Juan’s Work and ask students, “Choose one of the ways Juan describes the shapes. Do you agree? Explain.”  Also, the teacher shares Erin’s work and asks, “Erin says the shapes are different and cannot be alike. Do you agree? Explain.” (1.G.1, 1.MD.2)

]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 1-9, Solve and Share, students are presented with a problem “Do you add or subtract to solve the problem? Tell why? Show how to solve. Use pictures, numbers, or words.”  While observing students’ work, teachers are prompted to support if needed and ask “How can you use objects or drawings to help explain why you added or subtracted?” Teachers are provided two pieces of work to share: Rita’s Work and Bill’s Work with the following questioning prompts:  “Does Rita argue that you add or subtract for the problem? How does her work support her argument you can subtract?” and “Does Bill argue that you add or subtract for the problem? How does Bill support his argument you can add?” (1.OA.1)
• In Topic 5, 3-ACT MATH: Weighted Down, students are presented with the main question, “ How can you balance the two sides?” In Act 1, Prediction, teachers engage students in their predictions by asking “What is a number of erasers too small to be the number of erasers to balance the scale? What number is too many erasers? Why do you think your prediction is the answer to the Main Question? Who has a similar prediction? Who has a different prediction?” Then in Act 2, students share their work and teachers are provided with Luis’s and Lin’s Work for students to analyze. “Luis says he added the number of erasers on each side. How is his answer unclear?”  Lin says there are 4 too many erasers on the right. How did drawing a picture help her find her answer?” (1.OA.8)
• Lesson 5-1, Solve & Share, students are presented with a problem “Find the missing number in this equation. 7 + __ = 13. Explain how you found the missing number.” After students share their work, teachers are provided two pieces of work to share: Darnell’s Work and Lucy’s Work with the following prompts:  “How did Darnell find the missing number? How do the counters and his writing show his thinking?” How did Lucy find the missing number? Is Lucy correct? Are the two equations related? Do they have the same parts and whole?” (1.OA.8, 1.OA.6, 1.OA.5)

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 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, page 1J, Build Mathematical Literacy, 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, in Topic 2:

• Lesson 2-1, identifies number line 
• Lesson 2-2: identifies doubles fact
• Lesson 2-3: identifies near doubles fact

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 1, Vocabulary Review,  Oral Language, using the vocabulary words in the word bank, students “define the terms in their own words, say math sentences or questions that use the words,” and play a matching game with the class where one partner is the word and the other partner is the definition or example of the word. (equation, difference, part, plus)
• Topic 5, Vocabulary Review, Item 6, Use Vocabulary in Writing,  “Write a story problem with a true equation. Use at least two words from the Word List.” (add, equation, more, subtract)
• Topic 9, Vocabulary Review, Item 4, “Write a problem using the terms from the Word List. Use place-value blocks to help solve your problem.”  (compare, greater than >, less, less than <, more)