The instructional materials for Big Ideas Math: Modeling Real Life Grade 1 partially meets expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. 

Cluster 1.NBT.B addresses understanding place value of ones and tens. Some lessons in Chapters 4, 6-9, 11, and 12 explore ways for students to develop and demonstrate conceptual understanding of ones and tens through the use of tens frames, 100 charts, and number lines. Examples from these chapters include:

• Chapter 4, Lesson 6, Explore and Grow, students use counters to fill in a double 10 frame to show how to make a ten to solve 9 + 5. Students are asked, “Do 9 + 4 and 10 + 3 have the same sum? If so, why?” Supporting Learners states, “Ask students if they added or subtracted any counters when you were finding the sum.” Students must also write an addition sentence that shows that thinking (ex. 9 + 1 + 4 = 10 + 4 = 14), 1.OA.6. 
• Chapter 6, Lesson 3, Dig In, Circle Time, “Students will describe teen numbers as a group of ten and some leftover ones. This will lay the foundation for formalizing place value…Create two large ten frames with tape on the floor so that students can stand or sit in each cell to model the numbers…Every teen number has a group of ten, and some extra ones. Remember that a group of ten is really ten ones that have been put together.” Students color in ten frames to represent numbers and use a picture to circle objects into a group of ten and some more ones as a representation of teen numbers, 1.NBT.2. 
• Chapter 6, Lesson 5, Think and Grow, students solve “Your teacher has 2 packages of dice and 3 extra dice. Each package has 10 dice. How many dice are there in all?” Students need to understand that two packages represents 20 then add in the three extra die by understanding that the two digits of a two-digit number represents amounts of tens and ones, 1.NBT.2.
• Chapter 6, Lesson 4, Show and Grow, students circle groups of ten in a picture, write how many “tens” and how many “ones”, then write the number. For example, if a student circles 7 groups of 10 cubes, the students will fill in the sentence “7 tens and 0 ones is 70”. This develops the understanding of numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones), 1.NBT.2c.
• Chapter 7, Lesson 1, Think and Grow, students see “16 is greater than/is less than 13” as a ten and six ones for the 16 and a ten and three ones for 13. Students circle the “is greater than” after comparing the two models based on meanings of the tens and ones digits, 1.NBT.3.

Cluster 1.NBT.C addresses understanding place value of ones and tens and properties of operations to add and subtract. Some lessons in Chapters 8-9 explore ways to develop and demonstrate conceptual understanding of addition and subtraction using properties of operations as well as place value within 100. A variety of representations are used to help develop the conceptual understanding of place value including models, base ten blocks, quick sketches, 120 charts or hundred chart, and open number lines. Examples include:

• Chapter 8, Lesson 2, Explore and Grow, teaching notes, “Have students model each of the subtraction problems with base ten blocks and with the 120 Chart. You can continue to use partners and have them exchange the models as in the Dig In.” Example problems, “How did you find the differences? What do you notice about the differences for exercises?” “33 - 10 = ___; 67 - 10 = ___; 82 - 10 = __”. This supports conceptual understanding for 1.NBT.6, because students subtract multiples of 10 using concrete models. In Laurie’s Notes, “To begin Circle Time, explain to students that today they will subtract 10 from a number. Have students tell the strategies they have developed for subtracting 10 from a number. Have them describe what happens to the digits of a number when they subtract.” 
• Chapter 8, Lesson 3, Explore and Grow (note at bottom of page, bullet 1), “Tell students to use base ten blocks to model the two equations side-by-side in the space above the equations. Have students discuss each question with their partners.” Example problems “Model each problem. How are the problems alike? How are they different? 3 + 2 = ___; 30 + 20 = ___”. This supports conceptual understanding for 1.NBT.4, because students add multiples of 10 using concrete models and strategies based on place value. 
• Chapter 8, Lesson 3, Explore and Grow, “Which choices match the model?” The choices include a model of “50 using ten rods, the numeral 50, 20 + 30, 2 tens + 3 ones, 1 ten + 4 tens.” This supports conceptual understanding for 1.NBT.2, because students show how to represent two-digit numbers in a variety of ways that show understanding of place value. 

Some opportunities for students to demonstrate conceptual understanding independently are evident. The instructional materials do not always provide students opportunities to independently demonstrate conceptual understanding throughout the grade-level. Within the Apply and Grow, and Homework and Practice sections, students have limited opportunities to independently demonstrate conceptual understanding. 

The instructional materials for Big Ideas Math: Modeling Real Life Grade 1 partially meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. 

The instructional materials present opportunities for students to engage in routine applications of grade-level mathematics. For example: 

• Chapter 1, Lesson 9, Show and Grow, includes “put together/take apart with addend unknown” problems. “You have 8 beads. 5 are pink. The rest are orange. How many orange beads do you have?” The students show an addition and subtraction equation they could use to solve the problem.
• Chapter 2, Lesson 4, Show and Grow, “You and your friend have the same number of flowers. There are 8 flowers in all. How many flowers do you each have?” Students draw a picture and write an equation to solve.
• Chapter 3, Lesson 4, Show and Grow, Question 1, “Your friend has 7 trading cards. You have 3 more than your friend. How many trading cards do you have?” Students model the problem using a bar model and write an equation to solve. 
• Chapter 5, Lesson 7, Think and Grow: Modeling Real Life, “You have some stuffed animals. You give 3 away. You have 8 left. How many stuffed animals did you have to start?”  
• Chapter 8, Lesson 7, Show and Grow, “An art room has 70 bottles of glitter. 30 have been used. How many are left? Model: (students are given a number line), Subtraction equation: ____ bottles.”
• Chapter 14, Lesson 1, Think and Grow: Modeling Real Life: “You and your friend each design a kite. Your kite has 2 equal shares. Your friends has 2 unequal shares. Draw each kite.”

The instructional materials present few opportunities for students to engage in non-routine applications of the mathematics. Most problems are routine application representing the common addition and subtraction situations in Grade 1.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 1 partially meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. Additionally, MP3 is not identified in Chapters 6, 7, 8, 9, or 14.

Throughout the materials students are presented with “You be the Teacher” problems, where they analyze errors or different representations. For example:

• Chapter 4, Lesson 8, Apply and Grow: Practice, You be the Teacher, Problem 8, “Newton has 9 magnets. Descartes has 8 more than Newton. Your friend uses a bar model to show how many magnets Descartes has. Is your friend correct? Show how you know.” The diagram shows a bar with 9, and another with 8. The number sentence reads: “8 + 1 = 9”.
• Chapter 8, Lesson 8, Apply and Grow: Practice, You Be The Teacher, Problem 9, “Is Newton correct? Explain.” Newton has a thought bubble with the number sentence “36 + 50 = 86.” A diagram is located below the number sentences showing 3 tens, 6 ones, and 5 tens.
• Chapter 9, Lesson 5, Apply and Grow: Practice, You Be The Teacher, Problem 7, “Is the sum correct? Explain.” Students are given the number sentence "17 + 26 = 79". A number line is located below that shows counting by 1’s from 17 to 19, and then counting by 10’s from 19 to 79. 

The instructional materials present few opportunities for students to construct arguments, however, in some instances, students are asked to explain how they know, rather than construct a mathematical argument. Examples include:

• Chapter 7, Lesson 5, Explore and Grow, students are given a number line labeled from 40 to 50 with 45 circled. “Circle a number that is less than 45. Underline a number that is greater than 45. How do you know you are correct?” Students do not need to construct an argument to answer the question. 
• Chapter 10, Lesson 2, Explore and Grow, students are presented with two keys. “Use string to compare the keys. Which key is longer? How do you know?" Students can explain, and do not need to construct an argument.
• Chapter 11, Lesson 2, Explore and Grow, students are presented with two graphs. One graph presents data by tally marks, and the second graph uses circles to represent each data set. Students determine, “How are the graphs similar? How are they different?” Students need to construct an argument on how data is represented, and how those representations are similar and different. 

The instructional materials have missed opportunities to engage students in constructing arguments or analyzing the arguments of others. For example, Chapter 3, Lesson 6, True or False Equations, students determine which equations in a given set are true or false. The materials miss the opportunity for students to engage in MP3 as students do not need to state why an equation is true or false. Nor are they presented with equations that are stated to be true or false and asked to analyze why.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 1 partially meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

The materials identify MP3 in the Teacher Edition. Laurie’s Notes sometimes include guidance to support teachers to engage students in constructing viable arguments and analyze the arguments of others. For example:

• Chapter 1, Lesson 4, Laurie’s Notes, Think and Grow, MP3 is identified and the materials state, “Have students explain their strategies for finding partner numbers and have others respond if they agree with the strategy.”
• Chapter 2, Lesson 2, Laurie’s Notes, Think and Grow, MP3 is identified and the materials state, “Discuss Newton’s thought about subtracting 0 and ask students if they agree with him or not. ‘Will that always be the case? Why?’” MP3 is identified again, and states, “Discuss Descartes’ thought about subtracting all and ask students if they agree with him or not. (You might need to explain what subtracting a number from itself means.) ‘Will that always be the case? Why?’”
• Chapter 2, Lesson 4, Laurie’s Notes, Think and Grow, MP3 example states, “Discuss Newton’s and Descartes’ thoughts. ‘Are they thinking about the same thing? Why or why not?’”
• Chapter 5, Lesson 2, Laurie’s Notes, Think and Grow, MP3 example states, “Ask students to discuss if they think it is easier to model the problem on the number line first and then write the equation, or vise versa. Have them explain why they feel that way.” 
• Chapter 10, Lesson 1, Laurie’s Notes, Think and Grow, MP3 example states, “Have students order Newton’s and Descartes’s yarn from longest to shortest and shortest to longest. Defend how they know. Repeat with pencils.” 
• Chapter 11, Lesson 1, Laurie’s Notes, Think and Grow, “Ask different students to share if the number of roses is greater than or less than the number of daisies. Have them explain how they know. Ask other students to agree or disagree, and how they know.”
• Chapter 11, Lesson 2, Laurie’s Notes, Think and Grow, “Ask different students to share which way they prefer to organize data and answer questions: tally chart or picture graph, and why.” 

There are occasions where the materials do not provide guidance for teachers to engage students in MP3. Not all explanations require students to construct an argument or analyze the arguments of others. For example:

• Chapter 4, Lesson 4, Laurie’s Notes, Think and Grow, MP3 is identified and states, “‘How did you pick the second number so there would be no regrouping?’ Listen for the sum of the ones must be less than 10. Have students look at all of the sample answers to decide if all of them are correct.” This prompt does not give the teacher any assistance in engaging the students in analyzing the arguments of others. 
• Chapter 10, Lesson 3, Laurie’s Notes, Think and Grow, MP3 example states, “Have several students share their explanations for Exercise 6.” 
• Chapter 10, Lesson 5, Laurie’s Notes, Think and Grow, MP3 example states, “Explain why solving a length comparison story is not really different from what we have been doing all year.” 
• Chapter 12, Lesson 5, Laurie’s Notes, Think and Grow, MP3 example states, “Explain why an hour later would add 1 hour and an hour earlier would subtract 1 hour.” 

MP3 is not identified in the materials in Chapters 6, 7, 8, 9, or 14.