5th Grade - Gateway 2

The materials reviewed for Eureka Math² Grade 5 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Materials provide opportunities for students to develop conceptual understanding throughout the grade level. These opportunities are most often found within the Launch and Learn portions of lessons. Examples include:

• Module 1, Topic A, Lesson 1: Relate adjacent place value units by using place value understanding, Learn, Problem Set, Compare and Relate the Same Digit with Different Values, students develop conceptual understanding of place value by determining that the same digits in different places do not represent the same value, and articulate how the digits in different place values are similar and different. “Use the place value chart to complete the statement and equation. 3 ten thousands is 10 times as much as ___. 30,000 = 10 x ___.” An image place value chart with millions, hundred thousands, ten thousands, thousands, hundreds, tens, and ones are shown. (5.NBT.1)

• Module 5, Topic B, Lesson 12: Multiply mixed numbers. Land, Debrief, students develop conceptual understanding of multiplying mixed numbers using different strategies and a visual model. “Facilitate a class discussion about multiplying mixed numbers by using the following prompts. Encourage students to restate or add on to their classmates’ responses. Display the area model and work showing 2\frac{3}{5}\times3\frac{1}{8}. How are area models helpful when we are multiplying mixed numbers? How can we use the break apart and distribute strategy when multiplying mixed numbers? How is multiplying mixed numbers similar to multiplying decimals? How is it different?” (5.NF.4)

• Module 5, Topic C, Lesson 17: Find the volume of right rectangular prisms by packing with unit cubes and counting, Learn, Pack Prisms, students develop conceptual understanding of volume by completely filling a rectangular prism with cubes.The teacher gives students a 3 cm\times3 cm\times3 cm cube. “Direct students to pack the prism and count the number of cubes they need to pack it completely without gaps or overlaps.” The teacher then directs students to complete Classwork, Problem 2, “Sketch to show the number of centimeter cubes visible on the faces of the right rectangular prism. Then complete the table.” A table with a place for length (centimeters), width (centimeters), height (centimeters), and volume (cubic centimeters) is shown. (5.MD.3)

Materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade level. The Problem Set, within Learn, consistently includes these opportunities. When appropriate, teachers may use other portions of lessons for independent demonstration of conceptual understanding. Examples include:

• Module 3, Topic A, Lesson 3: Multiply a whole number by a fraction less than 𝟏, Learn, Problem Set, Problem 1, students independently demonstrate conceptual understanding of multiplying fractions by using a number line to multiply a whole number by a fraction. “Use the number line to find the product. Then write a repeated addition sentence to check your work. Write your answer as a whole number when possible. \frac{1}{2}\times4=___.”  An image of a number line from 0-4 is shown. (5.NF.4)

• Module 5, Topic D, Lesson 25: Find the volumes of solid figures composed of right rectangular prisms, Practice, Problems 1 - 4, students independently demonstrate conceptual understanding as they “find the volumes of solid figures composed of right rectangular prisms. They decompose the figures into right rectangular prisms, find the volumes of the prisms, and add the volumes together.” For Problems 1-4, “The solid figures shown are composed of right rectangular prisms. Calculate the volume of each figure.” Four right rectangular prisms with different dimensions are provided. (5.MD.5b and 5.MD.5c)

• Module 6, Topic B, Lesson 5: Identify properties of horizontal and vertical lines, Land, Debrief, students independently demonstrate conceptual understanding as they identify properties of horizontal and vertical lines. The teacher facilitates a class discussion about the properties of horizontal and vertical lines. “Display the coordinate plane showing lines c and m. Which line is parallel to the y-axis? How far is linecfrom the y-axis? What is true about the coordinates of every point on line ? What is true about the coordinates of every point on linem? Are lines c and m perpendicular? How do you know? Why do points on a vertical line have the same x-coordinate? Why do points on a horizontal line have the same y-coordinate? How is the coordinate plane useful for reasoning about horizontal and vertical lines?” (5.G.1)

The materials reviewed for Eureka Math² Grade 5 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. 

The materials develop procedural skill and fluency throughout the grade level, within various portions of lessons, including Fluency, Launch, and Learn. Examples include: 

• Module 1, Topic B, Lesson 8: Multiply two- and three-digit number by two-digit numbers by using the distributive property, Fluency, Whiteboard Exchange: Estimate Products, students develop procedural skill and fluency as they round to estimate products. The teacher displays “19,352\times3≈___\times3. What is 19,352 when rounded to the nearest ten thousand? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. Display the rounded factor. When I give the signal, let’s read the statement together. Ready? 19,352\times3 is about 20,000\times3. Display 19,352\times3≈___. Write and complete the statement with the estimated product.” Students repeat this process with more problems. (5.NBT.5)

• Module 1, Topic B, Lesson 11: Multiply two multi-digit numbers by using the standard algorithm, Launch, students develop procedural skill and fluency as they compare partial products with the standard algorithm for multiplication. The teacher displays shaded work examples that show 1,243\times132. Sample A shows the partial product strategy. Sample B shows the standard algorithm strategy. Sample C shows the area model strategy. The teacher asks, “In all three methods of multiplication, we see the same three partial products of 2,486, 37,290 and 124,300. What does the partial product 2,486 represent? Where is 2,486 represented in sample A? Where is 2,486 represented in sample B? Where is 2,486 represented in sample C? Let’s look at sample B. Why is there an 8 in the tens place of 2,486? Why is there a 4 in the hundreds place of 2,486?What does the partial product 37,290 represent?” (5.NBT.5)

Materials provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade level. The Problem Set, within Learn, consistently includes these opportunities. When appropriate, teachers may use other portions of lessons for independent demonstration of procedural skill and fluency. Examples include:

• Module 1, Topic B, Lesson 10: Multiply three- and four-digit numbers by three-digit numbers by using the standard algorithm, Land, Debrief, Exit Ticket, students independently demonstrate procedural skill and fluency as they multiply three- and four-digit numbers by three-digit numbers using the standard algorithm. “Multiply 704\times236.” (5.NBT.5)

• Module 1, Topic B, Lesson 11: Multiply two multi-digit numbers by using the standard algorithm, Problem Set, students independently demonstrate procedural skill and fluency as they estimate products, then multiply using the standard algorithm. “Estimate the product. Then multiply using the standard algorithm. Problem 1. 382\times547≈___\times___=___. Problem 2. 473\times905≈___\times___=___. Problem 3. 638\times5,29≈___\times___=___. Problem 4. 7,418\times594≈___\times___=___.” (5.NBT.5)

• Module 2, Topic B, Lesson 8: Add and subtract fractions with unrelated units by finding equivalent fractions pictorially. Fluency, Whiteboard Exchange: Multiply Multi-Digit Whole Numbers, students independently demonstrate procedural skill and fluency as they multiply a four- or five-digit number by a one-digit number to build fluency with multiplying multi-digit whole numbers by using the standard algorithm. “Display 3,212\times3=.Write and complete the equation by using the standard algorithm.” (5.NBT.5)

The materials reviewed for Eureka Math² Grade 5 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. 

There are multiple routine and non-routine application problems throughout the grade level, including opportunities for students to work with support of the teacher and independently. While single and multi-step application problems are included across various portions of lessons, independent application opportunities are most often found within Problem Sets or the Lesson Debrief, Learn and Land sections respectively.

Examples of routine applications of the math include:

• Module 3, Topic C, Lesson 17: Solve word problems involving fractions with multiplication and division, Practice Set, Problem 5, students independently solve routine word problems by multiplying or dividing. “A student misses \frac{1}{5} of the 5 dozen baseballs their coach pitches to them. How many baseballs do they miss?” (5.NF.6, 5.NF.7)

• Module 5, Topic D, Lesson 26: Solve word problems involving perimeter, area, and volume, Land, Exit Ticket, Problems a, b, and c, students independently solve routine real-world problems including perimeter, area, and volume. “A pool is shaped like an L as shown. a. A dog walks around the border of the pool. How far does the dog walk? b. The bottom of the pool is covered with tiles. How much space do the tiles cover? c. Julie fills the pool with water. When the pool is full, the height of the water is 3 feet. How much water does it take to fill the pool?” (5.MD.5)

• Module 6, Topic C, Lesson 15: Use the coordinate plane to reason about perimeters and areas of rectangles, Learn, Perimeters of Rectangles in the Coordinate Plane, Classwork, Problem 1, students solve routine determining the perimeters of rectangles graphed in the coordinate plane with teacher assistance. “Determine the perimeter of rectangle ABCD. A drawing of a coordinate plane is shown. Invite students to share their methods for determining the perimeter. As students share their methods, follow along with your finger on the displayed graph.” (5.G.2)

Examples of non-routine applications of the math include:

• Module 2, Topic B, Lesson 5: Add and subtract fractions with related units by using pictorial models, Launch, students solve non-routine problems analyzing models that show like units, related units, and unlike units with teacher and partner support. “Display the Vertical Block Drop digital interactive. Begin by showing \frac{2}{7} in the top model and \frac{3}{7} in the bottom model. Then drop the blocks. Have students turn and talk about what they noticed before the blocks were dropped and what they noticed after the blocks were dropped. Next, show \frac{3}{5} in the top model and \frac{1}{5} in the bottom model. What addition expression can we write to represent what we see in the model? What do you expect to see when I drop the blocks? The model represents a way to add fractions that have like units. In this case, the like units are fifths and our sum is also in fifths. Let’s analyze another model. What addition expression do you see represented in this model? What do you expect to see when I drop the blocks? What do you think is the total? This model represents two fractions with unlike but related units. The units thirds and sixths are related because 6 is a multiple of 3 and 3 is a factor of 6. When we drop the blocks, we can see the sum in sixths. What addition expression do you see represented in this model? What do you expect to see when I drop the blocks? What do you think is the total? This model represents two fractions with unlike units that are not related. When the blocks were dropped, we saw that the \frac{2}{7} did not completely fill one of the thirds on the bottom, so we cannot determine the sum by looking only at the model.” (5.NF.1)

• Module 5, Topic D, Lesson 24: Solve word problems involving volumes of right rectangular prisms, Land, Exit Ticket, Problem 1, students independently solve non-routine word problems involving volumes of right rectangular prisms. “A right rectangular prism has a volume of 450 cubic centimeters. What is one possible length, width and height for the prism.” (5.MD.5) 

• Module 6, Topic D, Lesson 17: Plot data in the coordinate plane and analyze relationships, Learn, Consonant and Vowel Data, Classwork, Problem 3, students solve non-routine problems by collecting and representing data in the coordinate plane, then using the graph to draw conclusions. Problem 3, “a. Write a word of each type, the number of consonants in the word, and the number of vowels in the word. Do not write the same words as the words in problem 1. A table numbered 1-10 with the type of columns labeled Type of Word, Word, Number of Consonants, Number of Vowels is shown. b. Label the x-axis Number of Consonants and the y-axis Number of Vowels. Label the title Word Data. Use the data collected in part (a) to form ordered pairs. Plot points that represent the ordered pairs in the coordinate plane. c. Based on the data, do you think it is true that the more consonants a word has, the more vowels it has? Why?” (5.G.2)

The materials reviewed for Eureka Math² Grade 5 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade. 

All three aspects of rigor are present independently throughout the grade. Examples where instructional materials attend to conceptual understanding, procedural skill and fluency, or application include:

• Module 3, Topic B, Lesson 5: Convert larger customary measurement units to smaller measurement units,Fluency, Whiteboard Exchange: Multiply Multi-Digit Whole Numbers, students attend to procedural skills and fluency as they multiply multi-digit whole numbers. “Display 15\times23= ___.  Write and complete the equation by using the standard algorithm.” (5.NBT.5) 

• Module 5, Topic B, Lesson 11: Find areas of rectangles with fraction side lengths by using multiplication, Learn, Rectangles with Both Side Lengths That Are Fractions Greater Than 1, Classwork, Problem 1, students attend to conceptual understanding as they find the area of rectangles. “Find the area of the rectangle. What do you notice about this rectangle? What size tiles could we use to tile this rectangle? How do you know? Partition the rectangle and direct students to do the same. What are the side lengths of each rectangular tile? What is the area of each rectangular tile? How do you know? How can we use what we know about the area of each tile to find the area of the rectangle? Explain your thinking. What is the area of the rectangle?” An image of a rectangle is provided. (5.NF.4b)  

• Module 6, Topic C, Lesson 15: Use the coordinate plane to reason about perimeters and areas of rectangles, Problem Set, Problem 2, students attend to application as they determine the perimeters and areas of rectangles graphed in the coordinate plane. “Rectangle EFGH and rectangle HIJK are each graphed in one of the coordinate planes shown. a. The interval length of the axes of the coordinate plane with rectangle HIJK is ___ times as much as the interval length of the axes of the coordinate plane with rectangle EFGH. b. Which rectangle has a greater perimeter?” (5.G.2)

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single unit of study throughout the materials. Examples include:

• Module 1, Topic A, Lesson 3: Use exponents to multiply and divide by powers of 10, Learn, Whiteboard Exchange: Exponential Form and Standard Form, students engage with conceptual understanding and procedural skills and fluency as they write powers of 10 as equations, in standard form, and in exponential form. “Display each of the following expressions one at a time. Write an equation that shows each power of 10 equal to a multiplication expression that uses only 10s: 10^2=, 10^3=, 10^5=, 10^6=, 10^4=, 10^1=. Write an equation that shows each number rewritten in exponential form. Invite students to turn and talk about how they determined how each number is represented in exponential form: 1,000 = ; 100,000 = ; 100 = ; 10,000 = ; 10 = ; and 1,000,000 = ).” (5.NBT.2)

• Module 3, Topic B, Lesson 8: Multiply fractions less than 1 pictorially, Learn, Choose a Method, Classwork, Problem 2, students engage with conceptual understanding and  application, as they choose models to solve real-world problems involving multiplication of two fractions less than 1. “Sasha buys a bag of almonds that weighs \frac{2}{3} pound. She uses \frac{3}{4} of the bag to make trail mix. How many pounds of almonds does Sasha use to make the trail mix?” (5.NF.4)

• Module 5, Topic D, Lesson 23: Find the volumes of right rectangular prisms by multiplying the edge lengths, Learn, Use Edge Lengths to Find Volume, Classwork, Problem 1, students engage with conceptual understanding and application as they use unit cubes to write formulas to solve problems involving volume. “Which right rectangular prism has the greater volume?” Both prisms are shown. Prism A has dimensions 14 in, 3 in, 6 in and Prism B states, “The area of the base is 20 square inches and the height is 12 inches.” (5.MD.5a and 5.MD.5b)

The materials reviewed for Eureka Math² Grade 5 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Students have opportunities to engage with MP1 and MP2 across the year and they are identified for teachers within margin notes called, “Promoting the Standards for Mathematical Practice.” According to the Grade 3-5 Implementation Guide, “Promoting the Standards for Mathematical Practice highlights places in the lesson where students are engaging in or building experience with the Standards for Mathematical Practice (MPs). Although most lessons offer opportunities for students to engage with more than one Standard for Mathematical Practice, this guidance identifies a focus MP within each lesson. The notes also provide lesson-specific information, ideas, and questions that you can use to deepen students’ engagement with the focus MP. Often, the suggested questions for a particular MP repeat. This intentional repetition supports students in understanding the MPs in different contexts.”

Materials provide intentional development of MP1 to meet its full intent in connection to grade-level content. Students make sense of problems and persevere in solving them as they work with the support of the teacher and independently throughout the units. Examples include:

• Module 1, Topic C, Lesson 14: Divide three-digit numbers by two-digit numbers in problems that result in one-digit quotients, Learn, Division Word Problems, Classwork, Problems 1 and 2, students make sense of problems and persevere in solving them as they, “make estimates, adjust their estimates, and interpret remainders to solve real-world problems by using division. Use the Read–Draw–Write process to solve each problem. 1. A school activity has 301 students split into 43 equal-size groups. How many students are in each group? 2. Eddie has 34 days to read a 170-page book. If he reads the same number of pages each day, how many pages does he need to read each day to finish the book in 34 days?” Teachers are prompted to ask the following question to support MP1: “(a) How can you simplify the problem? (b) Does your estimate work? Is there something else you could try? (c) Does your answer make sense? Why?”

• Module 4, Topic B, Lesson 10: Add decimal numbers by using place value understanding, Learn, Add Decimal Numbers to Solve Word Problems, Classwork, Problem 1, “When students solve word problems involving decimal-number addends by finding entry points, monitoring their own progress, and questioning whether their answer is reasonable, they make sense of problems and persevere in solving them (MP1). Use the Read-Draw-Write process to solve the problem. Sana orders a sandwich and a salad from a café. The sandwich costs $8.55. The salad costs $2.54 more than the sandwich. How much does the sandwich and the salad cost in all?” Teachers are prompted to ask the following questions to support MP1: “(a) What steps can you take to start solving the problem? (b) What is your plan to find the sum of the decimal-number addends? (c) Does your answer make sense? (d) Why?”

• Module 6, Topic B, Lesson 3: Identify and plot points by using ordered pairs, Exit Ticket, Problem 3, as “students plot points in the coordinate plane where the interval length on the axes is not 1 and when they determine the best scale for axes in order to plot points, they make sense of problems and persevere in solving them (MP1). Use the graph to complete parts (a) - (e). a. Plot and label the following points. Point E (0, 4); Point F (4, 0); Point H (\frac{1}{2}, 2\frac{1}{2}); Point I (2\frac{3}{4}, 5). b. Point H is ___ units above the x-axis. c. Point H is ___ units above the y-axis. d. The interval length of the x-axis is ___ units. e. The interval length of the y-axis is ___ units.”

Materials provide intentional development of MP2 to meet its full intent in connection to grade-level content. Students reason abstractly and quantitatively as they work with the support of the teacher and independently throughout the units. Examples include:

• Module 2, Topic C, Lesson 11: Add mixed numbers with unrelated units, Learn, Mixed Number Addition and Application, as “students use their understanding of addition and mixed numbers to create a word problem based on an addition expression, they are reasoning abstractly and quantitatively (MP2).” Students work with a partner and visit three stations: “Station 1: Rename to Add, Station 2: Write an Equation to Match a Model, Station 3: Create a Word Problem to Match an Expression. Station 1: Add. If you have time, find the sum a different way. 5\frac{7}{9}+3\frac{2}{4}=___. Station 2: Write an equation with unrelated units to match the work shown. If you have time, write another equation with different unrelated units. Station 3: Create a word problem to match the expression. If you have time, write a second word problem to match the expression. 7\frac{1}[3}+6\frac{11}{16}.”

• Module 3, Topic C, Lesson 13: Divide a nonzero whole number by a unit fraction to find the size of the group, Learn, Use a Tape Diagram and a Number Line to Divide, Classwork, Problem 2, “When students read, interpret, and solve real-world problems with the division of a nonzero whole number by a unit fraction, they are reasoning abstractly and quantitatively (MP2). Tyler has 5 lemons. This is \frac{1}{4} of the number of lemons he needs to make a pitcher of lemonade. How many lemons does Tyler need to make a pitcher of lemonade?” The teacher is prompted to ask the following questions to promote MP2: “What does the problem ask you to do? How does 5\div\frac{1}{4} represent the context in problem 2? Does your answer make sense in this context?”

• Module 5, Topic B, Lesson 15: Solve multi-step word problems involving multiplication of mixed numbers, Classwork, students reason abstractly and quantitatively as they, “determine the meaning of each real-world problem, estimate a solution, represent it with an expression, and recontextualize the solution while attending to units.” Students rotate through stations, Station 1 being the least challenging and Station 4 being the most challenging. “Use the Read-Draw-Write process to complete the problem at each station. Estimate before you solve the problem.” The teacher is prompted to circulate among stations and ask the following questions to promote MP2: “What does the problem ask you to do? How do the units involved in the situation help you think about the problem? Does your answer make sense in this context?”

The materials reviewed for Eureka Math² Grade 5 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with MP3 across the year and it is explicitly identified for teachers within materials in margin notes called, “Promoting the Standards for Mathematical Practice.” According to the Grade 3-5 Implementation Guide, “Promoting the Standards for Mathematical Practice highlights places in the lesson where students are engaging in or building experience with the Standards for Mathematical Practice (MPs). Although most lessons offer opportunities for students to engage with more than one Standard for Mathematical Practice, this guidance identifies a focus MP within each lesson. The notes also provide lesson-specific information, ideas, and questions that you can use to deepen students’ engagement with the focus MP. Often, the suggested questions for a particular MP repeat. This intentional repetition supports students in understanding the MPs in different contexts.”

Students construct viable arguments and critique the reasoning of others in connection to grade-level content as they work with support of the teacher and independently throughout the units. Examples include:

• Module 1, Topic B, Lesson 11: Multiply two multi-digit numbers by using the standard algorithm, Learn, Critique a Flawed Response, students estimate, calculate, and check their teammates’ work for the product of multi-digit numbers during the Pass the Whiteboard activity, they are constructing viable arguments and critiquing the reasoning of others (MP3). Students are placed in groups of four. “Each person writes a three-digit by four-digit multiplication problem on their whiteboard. Once you write your problem, pass the whiteboard to the person on your left. When you receive a whiteboard with a multiplication problem, estimate the product and write it on the whiteboard. Then pass the whiteboard to your left. When you receive a whiteboard with a multiplication problem and an estimate, use the standard algorithm to multiply the two numbers. Use the estimate to check the reasonableness of your answer. When you think your answer is correct, pass the whiteboard to your left. When you receive a whiteboard with an answer, check your teammate’s work. How can you check a teammate’s work? If you think they made a mistake, ask the teammate to explain their thinking. Suggest ways they could change their work to make it correct.” 

• Module 2, Topic D, Lesson 16: Solve problems by using data from a line plot, Learn, Solve Problems with Mixed Number Measurements, Classwork, “When students turn and talk about whether the claim that most of the pumpkins sold weighed more than 12\frac{1}{4} pounds is true based on the data on the line plot, they are constructing viable arguments and critiquing the reasoning of others (MP3). 1. Mr. Sharma weighs each pumpkin he sells at his pumpkin farm. He records the data on a line plot. a. How many pumpkins did Mr. Sharma sell? b. What is the weight of the heaviest pumpkin? c. What is the most frequent weight of the pumpkins sold? d. What is the total weight of the two lightest pumpkins? e. How many pumpkins weigh at least 12\frac{1}{4} pounds? f. Julie bought two pumpkins that have a total weight of 25 pounds. Based on the data on the line plot, what could be the weights of Julie’s pumpkins?” The teacher is prompted to, “Encourage students to compare their work and identify any errors. Ask students who found errors to discuss with their partner why they made the error and what they will do differently when they see a similar question in the future.” The teacher is prompted to ask the following questions to promote MP3: “Is the claim that most of the pumpkins sold weighed more than 12\frac{1}{4} pounds true? How do you know? Which parts of Mr. Sharma’s claim do you question?”

• Module 5, Topic A, Lesson 3: Classify parallelograms based on properties, Learn, Hierarchy of Quadrilaterals, Learn, students construct viable arguments and critique the reasoning of others as they “justify their thinking and respond to their peers’ thoughts during the Always Sometimes Never routine.” Teachers, “Present the following statement: A parallelogram is a trapezoid. Use the Always Sometimes Never routine to engage students in constructing meaning and discussing their ideas.Give students a few moments of silent think time to evaluate whether the statement is always, sometimes, or never true. Have students discuss their thinking with a partner. Circulate and listen as they talk. Identify a few students to share their thinking. Then facilitate a class discussion. Invite students to share their thinking with the whole group. Encourage them to provide examples and nonexamples to support their claim. Conclude by coming to the consensus that the statement is always true because a parallelogram is a special type of trapezoid with parallel opposite sides.” The teacher is prompted to ask the following questions to promote MP3: “Is what you said a guess, or do you know for sure? How do you know for sure? Can you find a situation where the statement is not true? What questions can you ask your classmate to make sure you understand their thinking?”

• Module 6, Topic C, Lesson 15: Use the coordinate plane to reason about perimeters and areas of rectangles, Launch, “When students discuss the lengths of line segments in coordinate planes with different scales, they are constructing viable arguments and critiquing the reasoning of others (MP3).” Teachers, “Introduce the Take a Stand routine to the class. Draw students’ attention to the signs hanging in the classroom that list various orders of A, B, and C. Display the graphs of the line segments. Invite students to mentally list the line segments from shortest to longest and to stand beside the sign that best describes their thinking. When all students are standing near a sign, allow 1 minute for groups to discuss the reasons why they chose that sign. Then call on each group to share reasons for their selection. Invite students who change their minds during the discussion to join a different group. If needed, confirm that the list of line segments from shortest to longest is C, A, B. Have students return to their seats. As a class, reflect on determining lengths of line segments in the coordinate plane.” The teacher is prompted to ask the following questions to promote MP3: “Why does your method work? Convince a classmate. What questions can you ask your partner about why they believe their method is correct? Is this segment the longest? How do you know?”

The materials reviewed for Eureka Math² Grade 5 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with MP4 and MP5 across the year and they are explicitly identified for teachers within materials in margin notes called, “Promoting the Standards for Mathematical Practice.” According to the Grade 3-5 Implementation Guide, “Promoting the Standards for Mathematical Practice highlights places in the lesson where students are engaging in or building experience with the Standards for Mathematical Practice (MPs). Although most lessons offer opportunities for students to engage with more than one Standard for Mathematical Practice, this guidance identifies a focus MP within each lesson. The notes also provide lesson-specific information, ideas, and questions that you can use to deepen students’ engagement with the focus MP. Often, the suggested questions for a particular MP repeat. This intentional repetition supports students in understanding the MPs in different contexts.”

MP4 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students model with mathematics as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 1, Topic D, Lesson 19: Solve multi-step word problems involving multiplication and division, Learn, Represent Word Problems with Models and Expressions, Classwork, Problem 1, “When students use the Read–Draw–Write process to create models to represent word problems and demonstrate methods for multiplication and division to solve the word problems, they are modeling with mathematics (MP4). Use the Read–Draw–Write process to solve each problem. 1. A florist uses 2,448 flowers to make bouquets. They put 24 flowers in each bouquet and sell the bouquets for $25 each. If the florist sells all the bouquets of flowers, how much money do they earn?” Teachers are prompted to ask the following questions to promote MP4: “What key ideas in this problem do you need to include in your model? How do you represent the key ideas in this problem in your model? How can you improve your model to better represent the problem?”

• Module 3, Topic A, Lesson 2: Interpret fractions as division to find fractions of a set with tape diagrams and number lines, Learn, Solve a Real-World Problem, Classwork, Problem 4, “When students decide how to model and solve a real-world problem that asks for a fraction of a whole number and how to assess the reasonableness of their answers, they are modeling with mathematics (MP4). Have students read the problem and work with a partner to use the Read–Draw–Write process to solve the problem. Blake has 19 yards of fabric. He uses \frac{1}{3} of the fabric to make a quilt. How many yards of fabric does Blake use for the quilt?” Teachers are prompted to ask the following questions to promote MP4: “What can you draw to help you understand this real-world problem? How are the key ideas in this real-world problem represented in your diagram? How could you make a simpler problem to estimate an answer?” 

• Module 6, Topic D, Lesson 20: Reason about patterns in real-world situations, Learn, The Coin Drive Challenge, Classwork, Problem 2, “When students collect, organize, and analyze data, make predictions, and develop a method for determining the number of nickels put into the jar on the last day of the fundraiser, they are modeling with mathematics (MP4).” Teachers, “Invite students to turn and talk with their group about how many nickels they think were put into the jar on the last day of the coin drive. What is an unreasonable estimate for the number of nickels put into the jar on the last day? What is a number that is too low? What is a number that is too high?” Teachers are prompted to ask the following questions to promote MP4: “What math can you write or draw to represent the coin drive problem? What assumptions can you make to help you determine the number of nickels put into the jar on the last day? What do you wish you knew that would help you find the answer?” 

MP5 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students choose tools strategically as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 2, Topic C, Lesson 10: Add whole numbers and mixed numbers and add mixed numbers with related units, Learn, Make the Next Whole Number to Add, Classwork, Problem 2, “When students choose among visual models such as number lines, number bonds, or the arrow way to help them find the sum of two mixed numbers, they are using appropriate tools strategically (MP5).” Teachers, “Direct students to problem 2. 2\frac{3}{4}+8\frac{7}{8}=___.” Teachers are prompted to ask the following questions to promote MP5: “What visual models could help you find the sum? Why did you choose a number line to help you find the sum? Did it work well?” 

• Module 5, Topic B, Lesson 12: Multiply mixed numbers, Learn, Multiply Two Mixed Numbers, Classwork, Problem 2, “When students choose between using the area model, writing mixed numbers as fractions greater than 1, and using the break apart and distribute strategy to multiply mixed numbers and provide reasoning for their choice, they are using appropriate tools strategically (MP5). Use two different methods to evaluate 2\frac{3}{5}\times3\frac{1}{8}.” Teachers are prompted to ask the following questions to promote MP5: “How can you estimate the product? Does your estimate sound reasonable? What kind of model or strategy would be helpful? Which method or strategy would be the most efficient to use to multiply mixed numbers? Why?”

• Module 6, Topic C, Lesson 14: Solve mathematical problems with rectangles in the coordinate plane, Learn, Determine the Locations of Two Unknown Vertices, “Students use appropriate tools strategically (MP5) when they choose and discuss the methods of using parallel and perpendicular lines, side lengths, and symmetry to determine the locations of the vertices of rectangles when only some of the vertices are given.” Teachers, “Let’s begin part A of Rectangle Vertices. In the coordinate plane for part A, plot any two points on intersecting grid lines that do not lie on the same horizontal or vertical line. Write each point’s ordered pair next to that point. When you finish, trade papers with your partner. Your partner plotted two opposite vertices of a rectangle. Determine the locations of the other two vertices. Plot the points, draw the rectangle, and write each vertex’s ordered pair next to that vertex. Give students a minute or two to complete part A. Then ask them to turn and talk with their partner to check one another’s work and to share methods for how they determined the ordered pairs for the two unknown vertices.” Teachers are prompted to ask the following questions to promote MP5: “What methods can help you find the vertex of the rectangle? Why did you choose to use the side lengths of the rectangle? Did that work well?”

The materials reviewed for Eureka Math² Grade 5 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with MP6 across the year and it is explicitly identified for teachers within materials in margin notes called, “Promoting the Standards for Mathematical Practice.” According to the Grade 3-5 Implementation Guide, “Promoting the Standards for Mathematical Practice highlights places in the lesson where students are engaging in or building experience with the Standards for Mathematical Practice (MPs). Although most lessons offer opportunities for students to engage with more than one Standard for Mathematical Practice, this guidance identifies a focus MP within each lesson. The notes also provide lesson-specific information, ideas, and questions that you can use to deepen students’ engagement with the focus MP. Often, the suggested questions for a particular MP repeat. This intentional repetition supports students in understanding the MPs in different contexts.”

Students attend to precision in mathematics, in connection to grade-level content, as they work with support of the teacher and independently throughout the units. Examples include:

• Module 1, Topic B, Lesson 9: Multiply two- and three-digit numbers by two-digit numbers by using the standard algorithm, Learn, Relate the Area Model to the Standard Algorithm, Classwork, Problem 1, “When students decompose factors and find partial products when they multiply a two-digit number by a two- or three-digit number by using the standard multiplication algorithm, they are attending to precision (MP6). 1. Mr. Perez paints the gymnasium wall. The wall is 24 feet wide and 33 feet long. How many square feet does Mr. Perez paint? Have students turn and talk to discuss what they know and what they do not know from the story. Encourage students to model with a tape diagram as needed. What do we know and what do we need to know? If we need to determine how many square feet he paints, what does the question ask us to find? What should we do to find the total area of the wall? About how many square feet of wall does Mr. Perez paint? How do you know? Direct students to record their estimates. In other problems, we used multiplication facts to find the partial products after decomposing one factor. Can we use multiplication facts to find the product 33\times34? Should we decompose one or both factors? Why? What is the width of the wall? What is 24 in expanded form? Label 20 and 4 along the left side of the area model and direct students to do the same. What is the length of the wall? What is 33 in expanded form? Record 30 and 3 along the top of the area model and direct students to do the same. Let’s multiply each part, one at a time, starting with the ones. Gesture to each corresponding part of the area model and record the partial products in standard form as you ask the following questions and ask for a choral response. In unit form, what is 4 ones \times 3 ones? In unit form, what is 4 ones x 3 tens? In unit form, what is 2 tens x 3 ones? In unit form, what is 2 tens \times 3 tens? What is 4 groups of 33 equal to? What is 20 groups of 33 equal to? What is 24 \times 33? Let’s use the standard algorithm to show what we did. Gesture to each corresponding part of the standard algorithm as you ask the following questions. In unit form, what is 4 ones \times 3 ones? 12 ones can be renamed as 1 ten 2 ones. Watch as I record 12 ones. Record 1 ten 2 ones and direct students to do the same. In unit form, what is 4 ones \times 3 tens? What is 12 tens plus 1 more ten? Record 1 hundred 3 tens and cross out the additional 1 ten to show it was added. Direct students to do the same. In unit form, what is 2 tens \times 3 ones? What is 6 tens in standard form? Record 60 and direct students to do the same. In unit form, what is 2 tens \times 3 tens? Record 6 hundreds and direct students to do the same. What is 132 \times 600? Is 792  a reasonable answer based on our estimates? Have students write the final answer statement: Mr. Perez paints 792 square feet. Where do you see the partial products from the area model in the standard algorithm? Highlight or circle the partial products in both methods and direct students to do the same. How is multiplying by using the area model like multiplying by using the standard algorithm? Now that we know how the area model relates to the standard algorithm for multiplication, let’s multiply by using the standard algorithm.” Teachers are prompted to ask the following questions to promote MP6: “How can you write the partial products when you use the standard algorithm? Where might you make mistakes when you use the standard algorithm?”

• Module 3, Topic D, Lesson 18: Compare and evaluate expressions with parentheses, Learn, Write Equations to Find Unknown Values, Classwork, Problem 1, “When students analyze a tape diagram to write an equation that can be used to find the value of the unknown, they are attending to precision (MP6).” Teachers, “Direct students to problem 1 in their books and invite them to study the tape diagram. 1. Write an equation that can be used to find the unknown value for each tape diagram. Then use the equation to find the value of the unknown.” A tape diagram is shown. “Based on this tape diagram, what do we know? What do we need to find? Because the unknown value x is 2 of the 3 parts of the tape diagram, we can find the value of x by finding \frac{2}{3} of 21. What is the value of the unknown? Guide students to write an equation to represent how they found the unknown value in problem 1. Let’s record our thinking by writing an equation. Record x =. We found the value of x by finding \frac{2}{3} of 21. Where does 21 come from? Record (9+12). To show we found the sum first, let’s put parentheses around 9+12. Record \times\frac{2}{3} and direct students to check that they wrote the equation in problem 1. Write x = 23 x (9 + 12). Invite students to turn and talk about whether the equation x=23\times(9+12) also gives the same value of x. Write x=\frac{2}{3}\times9+12. Point to the equation. Does this equation, x=\frac{2}{3}\times9+12, also give the same value of x? Why? Without a tape diagram or context, you may think we need to multiply \frac{2}{3} and 9 first and then add 12. That would mean x=18. But we found x=14. To ensure we all find the same value of the unknown, we use parentheses to show what we need to do first.” Teachers are prompted to ask the following questions to promote MP6: “How are you using parentheses in your equation? What details are important to think about when you write an equation to represent the unknown value in the tape diagram?”

• Module 4, Topic A, Lesson 7: Round decimal numbers to the nearest one, tenth, or hundredth, Learn, Use the Halfway Point to Round, Classwork, Problem 1, “Students attend to precision (MP6) as they carefully specify the units in the given number, the unit they are rounding to, and the halfway point when rounding decimal numbers. 1. Round 12.72 to the nearest tenth. Show your thinking on the number line. 12.72\approx___. Display the vertical number line with three tick marks but no labels from problem 1. How do you say 12.72 in unit form by using only tenths and hundredths? How many tenths are in 12.72? What is 1 more tenth than 127 tenths? Between which two tenths is 12.72? Label the beginning and ending tick marks in standard and unit forms. Have students do the same on their number lines. What number is halfway between 12.7 and 12.8? How do you know? Label the halfway tick mark in standard and unit forms. Have students do the same. Then invite students to plot and label a point for 12.72 on the number line. Which tenth is 12.72 closer to? How do you know? What is 12.72 rounded to the nearest tenth? Have students record the answer. 12.72 is between 12 and 13. So why do you think we used 12.7 and 12.8 as the benchmark numbers rather than 12 and 13? We need to think about the unit we want to round a number to when we decide which benchmark numbers to use on the number line.” Teachers are prompted to ask the following questions to promote MP6: “What details are important to think about when you round decimal numbers? Where might you make mistakes when you round decimal numbers such as 27.96?”

Students attend to the specialized language of mathematics, in connection to grade-level content, as they work with support of the teacher and independently throughout the units. Examples include:

• Module 2, Topic C, Lesson 12: Subtract whole numbers from mixed numbers and mixed numbers from whole numbers, Learn, Decompose the Minuend to Take from 1, Classwork, Problem 1, “As students access their mathematical vocabulary and use terms such as minuend, subtrahend, part, total, difference, decompose, whole number, ones, and fourths to explain the subtraction method used to find 5−2\frac{3}{4}, they are attending to precision (MP6). The expression 5−2\frac{3}{4} is a little different than the previous one, so let’s try a different method to subtract. Let’s decompose the minuend, or the starting value, 5. Display the following number bond: What do you notice? The subtrahend, or the number being subtracted from the starting value, can be decomposed any way and into as many parts as we need. Here, the subtrahend 2\frac{3}{4} is decomposed into a whole number and a fractional part. We can subtract those parts in any order. Which would you subtract first? Why? What is 5-2? What is left to subtract? Build Unifix Cubes to show 3 ones, each one composed of fourths. Use 2 ones of the same color and 1 one of another color. What do you notice? Draw a number bond below 3, showing 3 decomposed into 2 and \frac{4}{4}. We can express 1 by using \frac{4}{4} or any other fraction equivalent to 1. Should we use \frac{4}{4} or some other fraction? Why? Instead of taking \frac{3}{4} from 3, we can take \frac{3}{4} from 1, or \frac{4}{4}.  Remove three cubes from 1 whole, or \frac{4}{4}, to represent taking \frac{3}{4}from 1. Record \frac{4}{4}-\frac{3}{4}=\frac{1}{4}. What is the answer? How do you know? Is the answer \frac{1}{4}? Why? Record 2+\frac{1}{4}=2\frac{1}{4}. Invite students to think–pair–share about how taking from 1 is connected to whole-number subtraction. Display the following equation: 5-2\frac{3}{4}=3-\frac{3}{4}. When we subtracted whole numbers first, we were able to rewrite the original expression as 3-\frac{3}{4}. Does that make the problem simpler? Why? So we can first subtract the whole-number part from the minuend. Doing this gives us a simpler problem. Once we have the simpler problem, we can take from 1 to find the difference. Direct students to problems 1–3 in their books. Have students complete the problems independently but compare their answers with a partner. Circulate and encourage students to subtract by using different methods.” Teachers are prompted to ask the following questions to promote MP6: “How can we describe the subtraction expression 5-2\frac{3}{4} by using the words minuend and subtrahend? What does the word part mean in the number bond? Total? Subtrahend? Minuend? Difference?” 

• Module 4, Topic A, Lesson 4: Relate the values of digits in a decimal number by using place value understanding, Learn, Compare Repeated Digits in Decimal Numbers, “Students attend to precision (MP6) as they carefully recognize 10 times as much as and 1/10 as much as relationships between place value units and values of digits in multi-digit numbers. Students then communicate the relationships precisely by writing statements and equations.” Teachers,  "Direct students to remove Place Value Chart to Thousandths from their books and place it in their whiteboards. Write 63.177. Prompt students to represent 63.177 on their place value chart by using dots and digits. What digit is repeated in this number? What places is the repeated digit in? Draw a box around the 7 in the hundredths place and underline the 7 in the thousandths place. Ask the following questions and record student answers. What is the value of the boxed digit? What is the value of the underlined digit? How are the values of the 7s in 63.177 related? Use statements and equations to describe the relationship. Model any of the statements and equations listed that are not shared. When writing equations and statements, some students may use the unit form of the numbers rather than the decimal form.” There are blue and red cubes shown. Teachers are prompted to ask the following questions to promote MP6: “When describing the relationship between the 7s in 63.177, what steps do you need to be extra careful with? Why? What details are important to think about when you write each equation."

• Module 5, Topic A, Lesson 5: Classify kites and squares based on their properties, Learn, Hierarchy of Quadrilaterals, “Students attend to precision (MP6) when they use the definitions and properties of types of quadrilaterals to determine where to place kites and squares in the hierarchy.” Teachers, “Display the hierarchy of quadrilaterals that students created in the previous lesson. Invite students to turn and talk about where to put kites in the hierarchy. Are all kites trapezoids? Why? All kites have at least 2 pairs of adjacent sides that are the same length. That makes them a special type of quadrilateral. Add kites and their properties to the hierarchy branching off from quadrilaterals. Are there any other quadrilaterals that can be classified as kites? Which ones and why? Connect kites to rhombuses in the hierarchy. Invite students to think–pair–share about where to put squares in the hierarchy. Are all squares parallelograms? How do you know? Are all squares trapezoids? Why? Are all squares kites? Why? What other properties of squares should we list that are not already listed in the hierarchy? Add squares and their property to the hierarchy under rectangles and rhombuses.Then display the four quadrilaterals.Have students turn and talk about how they could use the hierarchy of quadrilaterals to help them identify the names of the quadrilaterals. Say the following statements. Have students give a thumbs-up if they agree with the statement or a thumbs-down if they disagree. Invite volunteers to share their reasoning for why they agree or disagree with each statement. Quadrilaterals B and C are parallelograms.Quadrilateral A is a kite because it has 2 angles that have the same measure. Quadrilateral B is not a kite.Quadrilateral D is not a trapezoid.” Teachers are prompted to ask the following questions to promote MP6: “What details are important to think about when placing kites in the hierarchy? How are you using the definition of a square to determine where to place squares in the hierarchy?”

The materials reviewed for Eureka Math² Grade 5 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with MP7 and MP8 across the year and they are explicitly identified for teachers within materials in margin notes called, “Promoting the Standards for Mathematical Practice.” According to the Grade 3-5 Implementation Guide, “Promoting the Standards for Mathematical Practice highlights places in the lesson where students are engaging in or building experience with the Standards for Mathematical Practice (MPs). Although most lessons offer opportunities for students to engage with more than one Standard for Mathematical Practice, this guidance identifies a focus MP within each lesson. The notes also provide lesson-specific information, ideas, and questions that you can use to deepen students’ engagement with the focus MP. Often, the suggested questions for a particular MP repeat. This intentional repetition supports students in understanding the MPs in different contexts.”

MP7 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and make use of structure as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 1, Topic C, Lesson 15: Divide three-digit numbers by two-digit numbers in problems that result in two-digit quotients, Land, Exit Ticket, “As students estimate and use area models throughout the lesson to divide three-digit numbers by two-digit numbers, they are looking for and making use of structure (MP7). A parking lot has 567 parking spots in 27 rows. If each row has the same number of parking spots, how many parking spots are in each row?” 

• Module 4, Topic B, Lesson 11: Subtract decimal numbers by using different methods, Learn, Subtract Decimal Numbers by Relating Addition and Subtraction, Classwork, “When students apply their understanding of the relationship between addition and subtraction to solve decimal-number subtraction problems, they are making use of structure (MP7).” Teachers state, “We can use the relationship between addition and subtraction to help us subtract whole numbers and decimal numbers. Write 12.3−4.8=⁢⁢⁢⁢___. What related addition equation can we write to help us find 12.3−4.8? Let a represent the unknown value.” Teachers are prompted to ask the following questions to promote MP7: “How are addition and subtraction related? How can that help you subtract two decimal numbers? What is another way you can write the subtraction problem to help you find the difference?”

• Module 6, Topic B, Lesson 7: Generate number patterns to form ordered pairs, Learn, Graph Number Patterns, Classwork, Problem 3, “Students look for and make use of structure (MP7) when they recognize addition patterns in tables and graphs of two number patterns.” Teachers, “Invite students to turn and talk about how they could use two number patterns to generate ordered pairs. 3. Use the table to complete parts (a) - (c). a.Use the rules to complete the patterns. b. Write the ordered pair for each pair of corresponding terms by writing the number from pattern A as the x-coordinate and the number from pattern B as the y-coordinate. c. Plot the points in the coordinate plane.” Teachers are prompted to ask the following questions to promote MP7: “How are the table and graph of two number patterns related? How can what you know about two number patterns help you locate points on the graph that represent the patterns?”

MP8 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and express regularity in repeated reasoning as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 2, Topic B, Lesson 8: Add and subtract fractions with unrelated units by finding equivalent fractions pictorially, Learn, Classwork, Problem 2, “When students add and subtract fractions with unrelated units by using a pictorial model to find like units and notice that both fractions need to be renamed to have like units, they are looking for and expressing regularity in repeated reasoning (MP8). 2. \frac{2}{4}-\frac{2}{6}=___-___= ___.” Teachers are prompted to ask the following questions to promote MP8: “What is the same about how you add and subtract fractions with unrelated units? Is this pattern always true?”

• Module 4, Topic A, Lesson 5: Multiply and divide decimal numbers by powers of 10, Learn, Dividing Decimal Numbers by Powers of 10, Classwork, Problems 7 - 10, “When students repeatedly divide by powers of 10 to notice the relationship between the power of 10 in the divisor, the decimal number dividend, and the quotient; multiply by powers of 10 to notice the relationship between the exponent and the product; and apply this understanding to divide and multiply decimal numbers by powers of 10 more efficiently, they are looking for and expressing regularity in repeated reasoning (MP8). Find the quotient and write it in standard form. Then write a related multiplication equation with the power of 10 expressed as a fraction. 7. 4\div10=___; 8. 0.3\div10^2=___; 9. 72.6\div10^3=___; 10. Determine the power of 10 that makes a true statement. 43.2\div___=0.432.” Teachers are prompted to ask the following questions to promote MP8: “What patterns do you notice when you divide a decimal number by a power of 10? How can that help you more efficiently determine the quotient? What patterns do you notice when you multiply a decimal number by a power of 10? How can that help you more efficiently determine the product? Does the exponent of the power of 10 always represent the number of places that each digit shifts from the decimal number dividend to the quotient? Explain.”

• Module 5, Topic A, Lesson 1: Analyze hierarchies and identify properties of quadrilaterals, Learn, Properties of Quadrilaterals, “When students repeatedly manipulate quadrilaterals to determine that the sum of the angle measures of a quadrilateral is 360\degree, they are looking for and expressing regularity in repeated reasoning (MP8).” Teachers, “Display quadrilateral ABCD. Figure ABCD is a quadrilateral. How do we know it is a quadrilateral? Is having 4 sides a property of quadrilaterals? How do you know? Let’s look for more properties of quadrilaterals. Open and display the Geometry World: Angle Explorer digital interactive. Display a quadrilateral. Invite students to turn and talk about what they notice about the angles in the quadrilateral. Adjust the vertices of the quadrilateral to show that the 4 angle measures in a quadrilateral always sum to 360\degree. Invite students to think–pair–share about the relationship between the angles of the quadrilateral and the degrees of a circle. The measures of the 4 angles inside a quadrilateral sum to 360\degree. Is this a property of quadrilaterals? How do you know? If the angle measures from a figure sum to 540\degree, can the figure be a quadrilateral? How do you know? Three angle measures in a quadrilateral sum to 300\degree. Invite students to turn and talk about what the measure of the fourth angle must be and why.” Teachers are prompted to ask the following questions to promote MP8: “What patterns do you notice when you make different quadrilaterals?  How can that help you determine an unknown angle more efficiently? What is the same about the angles in each quadrilateral?”