4 Mathematics Curriculum

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2 NYS COMMON CORE MATHEMATICS CURRICULUM Topic F 4 A Teaching Sequence Towards Mastery of Addition and Subtraction Word Problems Objective 1: Solve additive compare word problems modeled with tape diagrams. (Lesson 17) Objective 2: Solve multi-step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding. (Lesson 18) Objective 3: Create and solve multi-step word problems from given tape diagrams and equations. (Lesson 19) Topic F: Addition and Subtraction Word Problems 1.F.2

3 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 17 4 Lesson 17 Objective: Solve additive compare word problems modeled with tape diagrams. Suggested Lesson Structure Fluency Practice Application Problems Concept Development Student Debrief Total Time (10 minutes) (8 minutes) (35 minutes) (7 minutes) (60 minutes) Fluency Practice (10 minutes) Change Place Value 4.NBT.2 Convert Units 4.MD.1 (5 minutes) (5 minutes) Change Place Value (5 minutes) Materials: (S) Personal white board, place value chart to the millions Note: Reviewing this fluency will help students work towards mastery of using place value skills to add and subtract different units. T: (Project place value chart to the millions place. Write 4 hundred thousands, 6 ten thousands, 3 thousands, 2 hundreds, 6 tens, 5 ones.) On your personal white boards, write the number. S: (Students do so.) T: Show 100 more. S: (Students write 463,365.) Possible further sequence: 10,000 less, 100,000 more, 1 less, 10 more. T: (Write = ). On your place value chart, write the number. Possible further sequence: 7, ; 20, , ; 30, , Convert Units (5 minutes) Note: Reviewing these unit conversions that were learned in third grade will help prepare the students to solve problems with kilometers and meters in Topic A of Module 2. T: (Write 1 km = m.) How many meters are in a kilometer? S: 1 km = 1,000 m. Lesson17: Solve additive compare word problems modeled with tape diagrams. 1.F.3

4 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 17 4 Repeat process for 2 km, 3 km, 8 km, 8 km 500 m, 7 km 500 m, and 4 km 250 m. T: (Write 1,000 m = km.) Say the answer. S: 1,000 m = 1 km. T: (Write 1,500 m = km m.) Say the answer. S: 1,500 m = 1 km 500 m. Repeat process for 2,500 m, 3,500 m, 9,500 m, and 7,250 m. Application Problem (8 minutes) A bakery used 12,674 kg of flour. Of that, 1,802 kg was whole wheat and 888 kg was rice flour. The rest was all-purpose flour. How much all-purpose flour did they use? Solve and check the reasonableness of your answer. Note: This problem leads well into today s lesson and bridges as it goes back into the work from Lesson 16. Concept Development (35 minutes) Materials: (S) Problem Set Suggested Delivery of Instruction for Solving Topic F s Word Problems 1. Model the problem. Have two pairs of students who you think can be successful with modeling the problem work at the board while the others work independently or in pairs at their seats. Review the following questions before solving the first problem. Can you draw something? What can you draw? What conclusions can you make from your drawing? As students work, circulate. Reiterate the questions above. After 2 minutes, have the two pairs of students share only their labeled diagrams. For about 1 minute, have the demonstrating students receive and respond to feedback and questions from their peers. Lesson17: Solve additive compare word problems modeled with tape diagrams. 1.F.4

6 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 17 4 Problem 3 Solve a two-step problem using how much more. A pair of hippos weighed 5,201 kg together. The female weighed 2,038 kg. How much more did the male weigh than the female? MP.2 Many students will want to draw this as a single bar showing the combined weight to start. That works. However, the second step will most likely require a new double bar to compare the weights of the male and female. If no one comes up with the model pictured, you can show it quickly. Students generally do not choose to draw a bracket with the known total to the side until they are very familiar with two-step comparison models. However, be aware that students will have modeled this problem type since Grade 2. Problem 4 Solve a three-step problem using how much longer. A copper wire was 240 m long. After 60 m was cut off, it was double the length of a steel wire. How much longer was the copper wire than the steel wire at first? T: Read the problem, draw a model, write equations both to estimate and calculate precisely and write a statement. I ll give you 5 minutes. NOTES ON MULTIPLE MEANS OF ACTION AND EXPRESSION: For students who may find Problem 4 challenging, remind them of the work done earlier in this module with multiples of 10. For example, 180 is ten times as much as 18. If 18 divided by 2 is 9, then 180 divided by 2 is 90. Circulate, using the bulleted questions to guide students. Encourage the students when they get stuck to focus on what they can learn from their drawing: Show me the copper wire at first. Show me in your model what happened to the copper wire. Show me in your model what you know about the steel wire. Lesson17: Solve additive compare word problems modeled with tape diagrams. 1.F.6

8 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 17 4 Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you assess the students understanding of the concepts that were presented in the lesson today and plan more effectively for future lessons. You may read the questions aloud to the students. Lesson17: Solve additive compare word problems modeled with tape diagrams. 1.F.8

9 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 17 Problem Set 4 Name Date Directions: Model each problem using a tape diagram. Solve using numbers and words. 1. Sean s school raised \$32,587. Leslie s school raised \$18,749. How much more money did Sean s school raise? 2. At a parade, 97,853 people sat in bleachers and 388,547 people stood along the street. How many fewer people were in the bleachers than standing on the street? 3. A pair of hippos weighed 5,201 kg together. The female weighed 2,038 kg. How much more did the male weigh than the female? 4. A copper wire was 240 m long. After 60 m was cut off, it was double the length of a steel wire. How much longer was the copper wire than the steel wire at first? Lesson17: Solve additive compare word problems modeled with tape diagrams. 1.F.9

10 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 17 Exit Ticket 4 Name Date Directions: Estimate, then solve the following problem modeling with a tape diagram. 1. A mixture of 2 chemicals measures 1,034 ml. It contains some of Chemical A and 755 ml of Chemical B. How much less of Chemical A than Chemical B was in the mixture? Lesson17: Solve additive compare word problems modeled with tape diagrams. 1.F.10

11 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 17 Homework 4 Name Date 1. Gavin has 1,094 toy building blocks. Avery has only 816 toy building blocks. How many more building blocks does Gavin have? 2. Container A and B hold 11,875 L of water altogether. Container B holds 2,391 L more than container A holds. How much water does Container A hold? 3. A piece of yellow yarn was 230 inches long. After 90 inches had been cut from it, the piece of yellow yarn was twice as long as a piece of blue yarn. How much longer than the blue yarn was the yellow yarn at first? Lesson17: Solve additive compare word problems modeled with tape diagrams. 1.F.11

12 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 4 Lesson 18 Objective: Solve multi-step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding. Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time (10 minutes) (5 minutes) (33 minutes) (12 minutes) (60 minutes) Fluency Practice (10 minutes) Number Patterns 4.OA.5 Convert Units 4.MD.1 (5 minutes) (5 minutes) Number Patterns (5 minutes) Materials: (S) Personal white boards Note: This fluency bolsters students place value understanding and helps them apply these skills to a variety of concepts. T: (Project 40,100 50,100 60,100.) What is the place value of the digit that s changing? S: Ten thousand. T: Count with me saying the value of the digit I m pointing to. S: (Point at the ten thousand digit as students count.) 40,000, 50,000, 60,000. T: On your boards write what number would come after 60,100. S: (Students write 70,100.) Repeat with the following possible sequence: 82,030, 72,030, 62,030, ; 215,003, 216,003, 217,003, ; 943,612, 943,512, 943,412, ; and 372,435, 382,435, 392,435,. Convert Units (5 minutes) Materials: (S) Personal white boards Note: Reviewing these unit conversions that were learned in third grade will help prepare the students solve problems with kilometers and meters in Topic A of Module 2. Lesson 18: Solve multi-step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding. 4.F.12

13 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 4 T: Count by 200 meters, starting at 200 meters. When you get to 1000 meters, say 1 kilometer. S: 200 m, 400 m, 600 m, 800 m, 1 km, 1,200 m, 1,400 m, 1,600 m, 1,800 m, and 2 km. Repeat process, this time pulling out the kilometer (e.g., 1 km 200 m, 1 km 400 m). T: (Write 1,300 m = km m.) On your boards, fill-in the blanks. S: (Students regroup 1,300 m into 1 km 300 m.) Repeat process for 1,003 m, 1,750 m, 3,450 m, and 7,030 m. Application Problem (5 minutes) In all, 30,436 people went skiing in February and January. 16,009 went skiing in February. How many fewer people went skiing in February than in February? Note: This problem reviews content from the prior lesson and is a comparison subtraction problem. Concept Development (33 minutes) Materials: (S) Student Problem Set Suggested Delivery of Instruction for Solving Topic F s Word Problems 1. Model the problem. Have two pairs of students who you think can be successful with modeling the problem work at the board while the others work independently or in pairs at their seats. Review the following questions before beginning the first problem. Can you draw something? What can you draw? What conclusions can you make from your drawing? As students work, circulate. Reiterate the questions above. After 2 minutes, have the two pairs of students share only their labeled diagrams. For about 1 minute, have the demonstrating students receive and respond to feedback and questions from their peers. Lesson 18: Solve multi-step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding. 4.F.13

17 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 4 Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you assess the students understanding of the concepts that were presented in the lesson today and plan more effectively for future lessons. You may read the questions aloud to the students. Lesson 18: Solve multi-step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding. 4.F.17

18 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 Problem Set 4 Name Date Directions: Model each problem using a tape diagram. Solve using numbers and words. 1. In one year the factory used 11,650 meter of cotton, 4,950 fewer meters of silk than cotton, and 3,500 fewer meters of wool than silk. How many meters in all were used of the three fabrics? 2. The shop sold 12,789 chocolate and 9,324 cookie dough cones. They sold 1,078 more peanut butter cones than cookie dough cones and 999 more vanilla cones than chocolate cones. What was the total number of ice cream cones sold? 3. In the first week of June, a restaurant sold 10,345 omelets. The second week, they sold 1,096 fewer omelets than the first week. The third week, they sold 2 thousand more than the first week. The fourth week, they sold 2 thousand fewer than the first week. How many omelets did they sell in all in June? Lesson 18: Solve multi-step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding. 4.F.18

19 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 Exit Ticket 4 Name Date Directions: Draw a tape diagram to represent the problem. Use numbers and words to explain your thinking. 1. Park A covers an area of 4,926 square kilometers. It is 1,845 square kilometers larger than Park B. Park C is 4,006 square kilometers larger than the Park A. a. What is the area of all three parks? b. Assess the reasonableness of your answer. Lesson 18: Solve multi-step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding. 4.F.19

20 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 Homework 4 Name Date Directions: Model each problem using a tape diagram. Solve using numbers and words. 1. There were 22,869 children, 49,563 men, and 2,872 more women than men at the fair. How many people were at the fair? 2. Number A is 4,676. Number B is 10,043 greater than A. Number C is 2,610 less than B. What is the total value of numbers A, B, and C? 3. A store sold a total of 21,650 balls. It sold 11,795 baseballs. It sold 4,150 fewer basketballs than baseballs. The rest of the balls sold were footballs. How many footballs did the store sell? Lesson 18: Solve multi-step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding. 4.F.20

21 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 Lesson 19 Objective: Create and solve multi-step word problems from given tape diagrams and equations. Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time (12 minutes) (5 minutes) (30 minutes) (13 minutes) (60 minutes) Fluency Practice (12 minutes) Convert Meters to Kilometers and Meters 4.MD.1 Convert Units 4.MD.1 (8 minutes) (4 minutes) Sprint: Convert Meters to Kilometers and Meters (8 minutes) Materials: (S) Convert Meters to Kilometers and Meters Sprint Note: Reviewing unit conversions that were learned in third grade will help prepare the students to solve problems with meters and kilometers in Topic A of Module 2. Convert Units (4 minutes) Note: Reviewing unit conversions that were learned in third grade will help prepare the students solve problems with centimeters and meters in Topic A of Module 2. Materials: (S) Personal white boards T: (Write 1 m = cm.) How many centimeters are in a meter? S: 1 m = 100 cm. Repeat process for 2 m, 3 m, 8 m, 8 m 50 cm, 7 m 50 cm, and 4 m 25 cm. T: (Write 100 cm = m.) Say the answer. S: 100 m = 1 m. T: (Write 150 cm = m cm.) Say the answer. S: 150 cm = 1 m 50 cm. Repeat process for 250 cm, 350 cm, 950 cm, and 725 cm. Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations. 1.F.21

22 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 Application Problem (5 minutes) For Jordan to get to his grandparents house, he has to travel through Albany and Plattsburgh. From Jordan s house to Albany is 189 miles. From Albany to Plattsburgh is 161 miles. If the total distance of the trip is 508 miles, how far from Plattsburgh do Jordan s grandparents live? Note: This problem reviews two-step problems from the previous lessons. Concept Development (30 minutes) Materials: (S) Problem Set Suggested Delivery of Instruction for Lesson 19 s Word Problem. 1. Draw the labeled tape diagram on the board and give the students the context. Have them write a story problem based on the tape diagram. Have two pairs of students who you think can be successful with writing a problem work at the board while the others work independently or in pairs at their seats. Review the following questions before beginning the first problem. What story makes sense with the diagram? What question will I ask in my word problem? As students work, circulate. Reiterate the questions above. After 2 minutes, have the two pairs of students share their stories. For about 1 minute, have the demonstrating students receive and respond to feedback and questions from their peers. 2. Calculate to solve and write a statement. Give everyone 2 minutes to exchange stories, calculate, and make a statement of the answer. 3. Assess the solution for reasonableness. Give students 1 2 minutes to assess and explain the reasonableness of their solution. Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations. 1.F.22

23 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 Note: In Lessons 17 19, the Problem Set will be comprised of the word problems from the lesson and is therefore to be used during the lesson itself. Problem 1 Create and solve a simple two-step word problem from the tape diagram below. Suggested context: People at a football game. Problem 2 Create and solve a two-step addition word problem from the tape diagram below. NOTES ON MULTIPLE MEANS OF REPRESENTATION: Students who are ELLs may find it difficult to create their own problem. Work together with a small group of students to explain what the tape diagram is showing. Work with the students to write information into the tape diagram. Discuss what is known and unknown. Together, build a question based on the discussion. Suggested context: Cost of two houses. MP.2 Problem 3 Create and solve a three-step word problem involving addition and subtraction from the tape diagram below. Suggested context: Weight in kilograms of three different whales. NOTES ON MULTIPLE MEANS OF ACTION AND REPRESENTATION: Students below grade level may struggle with the task of creating their own problems. These students may benefit from working together in a partnership with another student. First, encourage them to design a tape diagram showing the known parts, the unknown part, and the whole. Second, encourage them to create a word problem based on the diagram. Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations. 1.F.23

24 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 Problem 4 Students use equations to model and solve multi-step word problems. Display the equation 5, ,094 + k = 12,946. T: Draw a tape diagram that models this equation. T: Compare with your partner. Then create a word problem that uses the numbers from the equation. Remember to first create a context, write a statement about the total and a question about the unknown. Then you can tell the rest of the information. Students work independently. Students can share problems in partners to solve or select word problems to solve as a class. Problem Set Please note that the Problem Set in Topic F is comprised of the lesson s problems as stated at the introduction of the lesson. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students solve these problems using the RDW approach used for Application Problems. Student Debrief (13 minutes) Lesson Objective: Create and solve multi-step word problems from given tape diagrams and equations. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations. 1.F.24

25 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 Guide students in a conversation to debrief the Problem Set and process the lesson. You may choose to use any combination of the questions below to lead the discussion. How does a tape diagram help to solve a problem? What is the hardest part about creating a context for a word problem? To write a word problem, what must you know? There are many different contexts for Problem 2, but everyone found the same answer. How is that possible? What have you learned about yourself as a mathematician over the past module? How can you use this new understanding of addition, subtraction, and solving word problems in the future? Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you assess the students understanding of the concepts that were presented in the lesson today and plan more effectively for future lessons. You may read the questions aloud to the students. Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations. 1.F.25

26 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 Sprint Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations. 1.F.26

27 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 Sprint Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations. 1.F.27

28 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 Problem Set Name Date Directions: Using the diagrams below, create your own word problem and solve for the missing variable. 1. 7,104 4, A ,554 m 90,457 Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations. 1.F.28

29 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 Problem Set 8,200 3.? 3,500 2,010 Draw a tape diagram to model the following equation. Write a word problem and solve for the unknown. 4.,,, A Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations. 1.F.29

30 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 Exit Ticket Name Date Directions: Using the diagram below, create your own word problem and solve for the missing variable. 1. A 15,387 29,435 Directions: Using the equation below, draw a tape diagram and create your own word problem. Solve for the missing variable. 2.,, A, Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations. 1.F.30

31 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 Homework Name Date Directions: Using the diagrams below, create your own word problem to solve for the missing variable. 1. At the local botanical gardens, there are Redwood Cypress Dogwood Redwoods and Cypress trees. There are a total of Redwood, Cypress, and Dogwood trees. How many? 6,294 3,849 12,115 A 2. There are 65,302. There are 37,436 fewer 65,302. T How many 37,436? Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations. 1.F.31

32 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 Homework 3. Use the following tape diagram to create a word problem to solve for the missing variable. A 215,561 42,086 36, Use the equation 27,894 + A + 6,892 = 40,392 to model a tape diagram, create a word problem, and solve. Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations. 1.F.32

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