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Mathematics Alignment Lesson Grade 5 Quarter 3 Day 97 Common Core State Standard(s) Alignment Lesson 5.NF.1 Add and subtract fractions with unlike Adding and Subtracting Mixed Numbers with Models denominators (including mixed numbers) by replacing given fractions with equivalent 1. Today’s lesson builds on activities from Days 94 and 95 fractions in such a way as to produce an by incorporating mixed numbers into the models. equivalent sum or difference of fractions with like denominators. Reference those activities in the beginning of the lesson For example, 2/3 + 5/4 = 8/12 +15/12 = to remind students of their work with pattern blocks and 23/12. (In general, a/b + c/d = (ad + bc)/bd.) grid or area models to represent the addition and subtraction of fractions. Students may need particular Standards for Mathematical Practice support understanding what the grid or area models will Standard 2 - Reason abstractly and look like when they are drawing models involving mixed quantitatively. numbers. Standard 4 - Model with mathematics. Standard 7 - Look for and make use of 2. Display Transparency/Blackline Master, “Adding and structure. Subtracting Mixed Numbers,” and have students work Standard 8 - Look for and express regularity with a partner to solve the first problem. Once pairs have in repeated reasoning. solved the problem, engage students in Math Talk using the following questions: Materials Needed: Which pattern blocks did you use to model the first mixed number? Blackline Masters, “Adding and Subtracting Mixed Numbers with Which pattern blocks did you use to model the Models,” “Adding and second mixed number? Subtracting Mixed Numbers How did you find the sum using the pattern with Models Journal blocks? Prompt” Transparency/Blackline Master, 3. Follow the same instructions and use similar questioning “Adding and Subtracting Mixed to have students work through problems 2, 3, and 4 on Numbers” Transparency/Blackline Master, “Adding and Pattern Blocks (hexagons, trapezoids Subtracting Mixed Numbers.” (red & brown), rhombi, triangles (green & purple)) 4. Use the remaining time for students to practice and discuss using Blackline Master “Adding and Subtracting Assessment Mixed Numbers with Models.” Informal: Independent student work 5. Students should complete Blackline Master, “Adding and Student discussion during Math Talk Subtracting Mixed Numbers with Models Journal Prompt,” for homework. Homework Blackline Master- “Adding and Subtracting Mixed Numbers with Models Journal Prompt” Vocabulary Source: Teacher Created None Referenced Wake County Public School System, 2012 Transparency/Blackline Master Grade 5 Day 97 Standard 5.NF.1 Name: ________________________ Date: ________________________ Adding and Subtracting Mixed Numbers 1 2 1. Find the value of 1 6 + 1 3 using pattern blocks. 1 1 2. Find the value of 3 12 – 1 2 using pattern blocks. 1 3 3. Find the value of 2 3 + 1 5 using a grid or area model. 3 5 4. Find the value of 4 4 – 1 6 using a grid or area model. Wake County Public School System, 2012 Transparency/Blackline Master Grade 5 Day 97 Standard 5.NF.1 Wake County Public School System, 2012 Answer Key Grade 5 Day 97 Standard 5.NF.1 Adding and Subtracting Mixed Numbers Answer Key 1 2 1. Find the value of 1 6 + 1 3 using pattern blocks. Use one hexagon and one green triangle to model the first mixed number. Use one hexagon and two rhombi to model the second mixed number. To find the sum, trade the two rhombi for four green triangles and combine everything to make two hexagons and five green triangles. 1 2 5 1 6 + 1 3 = 2 6 1 1 2. Find the value of 3 12 – 12 using pattern blocks. Use three hexagons and one purple right triangle to model the first mixed number. To find the difference, you need to take away one hexagon and the equivalent of one red trapezoid. One of the three hexagons must first be traded for two red trapezoids. Once the trade has been made, you have two hexagons, two red trapezoids, and one purple right triangle. To model taking away 1½, take away one hexagon and one red trapezoid. You are left with one hexagon, one red trapezoid, and one purple right triangle. In order to state the answer as one mixed number, you need to have a common shape for the fractional part (or a common denominator). To do this, trade the red trapezoid for six purple right triangles. The resulting difference is one hexagon and seven purple right triangles. 1 1 7 3 12 – 1 2 = 1 12 1 3 using a grid or area model. 3. Find the value of 2 3 + 1 5 Each addend is represented with a different color. The grid shows that 1/3 = 5/15 and 3/5 = 9/15. Because the resulting fraction is less than 1, the fractional part of both addends can be represented on one grid. 1 3 14 2 3 + 1 5 = 3 15 Wake County Public School System, 2012 Answer Key Grade 5 Day 97 Standard 5.NF.1 Adding and Subtracting Mixed Numbers Answer Key (page 2) 3 5 4. Find the value of 4 4 – 16 using a grid or area model. The grid model shows 1 and 5/6 subtracted from 4 and 3/4, leaving 2 + 1/6 + 3/4, which can be changed to 2 + 2/12 + 9/12 = 2 11/12. 3 5 11 4 4 – 1 6 = 2 12 Wake County Public School System, 2012 Blackline Master Grade 5 Day 97 Standard 5.NF.1 Name: ________________________ Date: ________________________ Adding and Subtracting Mixed Numbers with Models Complete each of the following problems using pattern blocks or an area (grid) model. If you use pattern blocks, you must draw a picture of the pattern blocks to show your work. Show your drawings for each problem on a separate sheet of paper. 7 1 1. 2 12 + 1 2 = __________ 2 1 2. 2 3 – 1 6 = __________ 1 5 3. 3 4 + 1 6 = __________ 1 5 4. 3 2 – 1 6 = __________ 5 3 5. 4 12 – 2 4 = __________ Wake County Public School System, 2012 Blackline Master Grade 5 Day 97 Standard 5.NF.1 Wake County Public School System, 2012 Answer Key Grade 5 Day 97 Standard 5.NF.1 Adding and Subtracting Mixed Numbers with Models Answer Key Student grid or area representations may all look slightly different. Circulate and view student work to determine if their models depict a correct representation of the problem. 7 1 1 1. 2 12 + 1 2 = 4 12 Pattern Blocks: Use two hexagons and seven purple right triangles to model the first mixed number. Use one hexagon and one red trapezoid to model the second mixed number. To find the sum, trade the red trapezoid for six purple right triangles and combine everything to make three hexagons and thirteen purple right triangles. Trade twelve purple right triangles for one hexagon to make four hexagons and one purple right triangle. 2 1 1 2. 2 3 – 1 6 = 1 2 Pattern Blocks: Use two hexagons and two rhombi to model the first mixed number. To find the difference, you need to take away one hexagon and the equivalent of one green triangle. To do this, you must first trade the two rhombi for four green triangles. Then, take away one hexagon and one green triangle. The resulting difference is one hexagon and three green triangles, which is equivalent to one hexagon and one red trapezoid. 1 5 1 3. 3 4 + 1 6 = 5 12 Pattern Blocks: Use three hexagons and one brown right trapezoid to model the first mixed number. Use one hexagon and five green triangles to model the second mixed number. To find the sum, trade the brown right trapezoid for three purple right triangles and trade the five green triangles for ten purple right triangles. Combine everything to make four hexagons and thirteen purple right triangles. Trade twelve purple right triangles for one hexagon to make five hexagons and one purple right triangle. 1 5 2 4. 3 2 – 1 6 = 1 3 Pattern Blocks: Use three hexagons and one red trapezoid to model the first mixed number. To find the difference, you need to take away one hexagon and five green triangles. One of the three hexagons must first be traded for six green triangles. Once the trade has been made, you have two hexagons, six green triangles, and one red trapezoid. To model taking away 1 and 5/6, take away one hexagon and five green triangles. You are left with one hexagon, one green triangle, and one red trapezoid. In order to state the answer as one mixed number, you need to have a common shape for the fractional part (or a common denominator). To do this, trade the red trapezoid for three green Wake County Public School System, 2012 Answer Key Grade 5 Day 97 Standard 5.NF.1 triangles. The resulting difference is one hexagon and four green triangles, which is equivalent to one hexagon and two blue rhombi. Adding and Subtracting Mixed Numbers with Models Answer Key (page 2) 5 3 2 5. 4 12 – 2 4 = 1 3 Pattern Blocks: Use four hexagons and five purple right triangles to model the first mixed number. To find the difference, you need to take away two hexagons and three brown right trapezoids. One of the four hexagons must first be traded for four brown right trapezoids. Once the trade has been made, you have three hexagons, four brown right trapezoids, and five purple right triangles. To model taking away 2¾, take away two hexagons and three brown right trapezoids. You are left with one hexagon, one brown right trapezoid, and five purple right triangles. In order to state the answer as one mixed number, you need to have a common shape for the fractional part (or a common denominator). To do this, trade the brown right trapezoid for three purple right triangles. The resulting difference is one hexagon and eight purple right triangles, which is equivalent to one hexagon and two blue rhombi. Wake County Public School System, 2012 Blackline Master Grade 5 Day 97 Standard 5.NF.1 Name: ________________________ Date: ________________________ Adding and Subtracting Mixed Numbers with Models Journal Prompt Today you used pattern blocks to model addition problems with mixed numbers. Explain how your modeled representation of the problem helps you find the common denominators you need to solve the problem. Use appropriate math vocabulary in your explanation. Wake County Public School System, 2012 Answer Key Grade 5 Day 97 Standard 5.NF.1 Adding and Subtracting Mixed Numbers with Models Journal Prompt Answer Key Today you used pattern blocks to model addition problems with mixed numbers. Explain how your modeled representation of the problem helps you find the common denominators you need to solve the problem. Use appropriate math vocabulary in your explanation. When modeling an addition problem with pattern blocks, you have to create a model of each of the addends and then combine them to find the total sum. When the denominators are not the same in each of the addends, the model contains two different shapes for the fractional parts. In order to find the answer as a whole number and a fraction, you have to trade the pattern blocks for other pattern blocks that represent the same thing. This is the same as finding common denominators in a fraction addition problem. For example, if I am adding 2/3 and 1/6, the 2/3 is represented by 2 rhombi and the 1/6 is represented by 1 green triangle. In order to combine them, I have to trade the 2 rhombi for 4 green triangles so that I have all green triangles. This is the same as making 2/3 into 4/6. They are equivalent fractions and then I have the common denominator of 6 in both of my addends. Wake County Public School System, 2012

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