web viewsource: . grade 4unit 4: block 19. 4.19 solve word problems. common core state standards

Assessments

Automaticity

4.19 Solve Word ProblemsCOMMON CORE STATE STANDARDSBuild fractions from unit fractions by applying and extending previous understanding of operations on whole numbers.4.NF.B.3 – Number and Operations – FractionsUnderstand a fraction a/b with a > 1 as a sum of fractions 1/b.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

BIG IDEAStudents will solve word problems involving addition and subtraction of fractions.

Standards of Mathematical Practice

□ Make sense of problems and persevere in solving them

Reason abstractly and quantitatively Construct viable arguments and critique the

reasoning of others Model with mathematics□ Use appropriate tools strategically□ Attend to precision Look for and make use of structure□ Look for and express regularity in repeated

reasoning

Informal Assessments:

□ Math journal□ Cruising clipboard□ Foldable□ Checklist Exit ticket Response

Boards Problem Set Class Discussion

PREPARING FOR THE ACTIVITY MATERIALS Personal response

boards Problem Set 4.19 Exit Ticket 4.19 Additional Practice 4.19

VOCABULARY

AUTOMATICITY TEACHER NOTESCount by Equivalent Fractions

1. Starting at zero, count by twos to 12. (0, 2, 4, 6, 8, 10, 12.)

2. Count by 2 twelfths from 0 twelfths to 12

twelfths. Write as students count. (012

, 212

,

412

, 612

, 812

, 1012

, 1212

.)

3. Point to1212

. 12 twelfths is the same as 1 of what

Select appropriate activities depending on the time allotted for automaticity.

Count by Equivalent

Source: http://www.engageny.org/resource/grade-4-mathematics-module-5 Grade 4 Unit 4: Block 19

http://www.engageny.org/resource/grade-4-mathematics-module-5

unit? (1 whole.)

4. Beneath 1212

, write 1 whole. Count by 2 twelfths

again from zero to 1 whole. Try not to look at the

board. (0, 212

, 412

, 612

, 812

, 1012

, 1 whole.)

5. Point to 612

. 6 twelfths is the same as what unit

fraction? (12

.)

6. Beneath 612

, write 12

. Count by 2 twelfths again. This

time, convert 612

to 12

and 1212

to 1 whole. Try not to

look at the board. (0 , 212, 4

12, 1

2, 8

12, 10

12, 1 whole.)

7. Point to 212

. What’s 212

simplified? (16

.)

8. Beneath 212

, write 16

. Point to 412

. What’s 412

renamed as sixths? (26

.)

9. Continue, renaming 812

and 1012

as sixths. (0, 16

, 26

, 12

, 46

, 56

, 1 whole.)

10. Continue, renaming 26

and 46

as thirds. (0, 16

, 13

, 12

,

23

, 56

, 1 whole.)

11. Direct students to count back and forth from 0 to 1 whole, occasionally changing directions.

Fractions: This activity builds fluency with equivalent fractions. The progression builds in complexity. Work the students up to the highest level of complexity in which they can confidently participate.

Add and Subtract Fractions: This fluency activity reviews Block 18.



Add and Subtract Fractions

1. Write 36

+ 16

+ 16. Write the complete number

sentence on your board. Students write36

+ 16

+ 16

=

56.

2. Write 78

– 28

= __. Write the complete number

sentence on your board. Students write 78

– 28

= 58

.

3. Continue the process for the following possible sequence: 5

10 + 2

10 + 2

10, 2

5 + 2

5 + 2

5 , 5

6 – 1

6 – 3

6 ,

1 – 15

, 1 – 35

, 1 – 38

, 1 – 710

, 1 910

– 310

– 510

, and

1 712

– 512

– 1112

.

SETTING THE STAGE TEACHER NOTESApplication Problem

1. Display the following problem. Allow students to use RDW to solve. Discuss with students after they have solved the problem.

Fractions are all around us! Make a list of times that you have used fractions, heard fractions, or seen fractions. Be ready to share your ideas.

Connection to Big IdeaToday, we will solve problems involving addition and subtraction of fractions.

Note: The Application Problem encourages students to think of real life examples of fractions. The Application Problem contextualizes previously learned skills in the unit and prepares students for today’s problem-solving lesson involving fractions. Have students spend a few minutes brainstorming together in small groups and then share out ideas whole group.

EXPLORE THE CONCEPT TEACHER NOTES



TeachingNew

Concepts

Problem 1: Use the RDW process to solve a word problem involving the addition of fractions.

1. Display the following problem:

Sue ran 910

mile on Monday and 710

mile on Tuesday. How many miles did Sue run in the 2 days?

2. Students may initially represent the problem by drawing number bonds or number lines as they did in the previous lessons to model addition. Assist students to find the parts and wholes.

3. In Problem 1, the 2 parts, 910

and 710

, make the

whole, 135

. Encourage students to represent this relationship as a tape diagram to model, as done with whole number addition.

4. In contrast to their previous solutions, students are not drawing the fractional units to count. Instead they are seeing the relationship the two fractions have with each other and calculating based on what they know about whole number and fraction addition.

Problem 2: Use the RDW process to solve a word problem involving the addition and subtraction of fractions.

1. Display the following problem:Mr. Salazar cut his son’s birthday cake into 8 equal pieces. Mr. Salazar, Mrs. Salazar, and the birthday boy each ate 1 piece of cake. What fraction of the cake was left?

2. Although each person had 1 piece of cake, the students must consider the 1 piece as a fractional unit of the whole. The whole is represented as 1, and students may choose to take from or add to the whole.

3. Again, encourage students to think about the parts and the whole when drawing a picture to represent the problem. A tape diagram is a good way to connect the part–whole relationship with which they are familiar in whole number addition and subtraction to fraction computation. The parts can be taken or added one at a time, or students may

UDL – NOTES ONF MULTIPLE MEANS OF ENGAGEMENT: Differentiate the difficulty of Problem 1 by adjusting the numbers. Students working above grade level may enjoy the challenge of adding three addends, for example 37100

+ 18100

+ 65100

. Grade 4 expectations in this domain are limited to fractions with like denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.



group them as 38

before computing. See possible solutions below.

Problem 3: Use the RDW process to solve a word problem subtracting a fraction from a whole.

1. Display the following problem:

Maria spent 47

of her money on a book and saved the

rest. What fraction of her money did Maria save?

2. In this problem, students subtract a fraction from a whole. Some may write 1 whole as 7

7 and then

subtract 47

. Alternatively, students may choose to

add up to 77

.

Problem 4: Use the RDW process to solve a word problem involving the subtraction of fractions.

1. Display the following problem:Mrs. Jones had 1 4

8 pizzas left after a party. After

giving some to Gary, she had 78

pizza left. What

fraction of a pizza did she give Gary?2. Students can use an adding up method, but will



Ongoing Learning & Practice

Share Summarize

likely choose one of the subtracting methods. One way is to rewrite the mixed number as 12

8 and

subtract. The other method subtracts from the whole and adds back the fractional part as practiced in Block 17.

Problem SetDistribute Problem Set 4.19. Students should do their personal best to complete the problem set in groups, with partners, or individually. 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 Problem.

REFLECTION TEACHER NOTES1. Invite students to review their solutions for

the Problem Set. They should check their work by comparing answers with a partner before going over answers as a class.

2. Guide students in a conversation to debrief the Problem Set and process the block. You may choose to use any combination of the questions below to lead the discussion.

What strategies did you use to solve the problems in the Problem Set? Did you use the same strategy each time?

Which problem(s) were the most difficult? How were they difficult? What strategies did you use to persevere?

Which problem(s) were the least difficult? Why?

Was it easier to solve Problems 5 and 6 on your own after having completed Problems 1–4 together as a group? Why or why not? Did you use the same strategies that you used in solving Problems 1–4?

UDL - NOTES ON MULTIPLE MEANS OF ACTION AND EXPRESSION: To prepare students working below grade level and others to meaningfully participate in today’s work and closing debrief, quickly review strategies from which students may choose: Take apart and

redistribute (using a number bond).

Counting up to subtract. Thinking part–part–

whole (using a tape diagram).



How was Problem 4 different from the other problems?

What was challenging about Problem 5? About Problem 6?

How did the Application Problem connect to today’s lesson?

3. Allow students to complete Exit Ticket 4.19 independently.



Name: ______________________________ Date: ____________Problem Set 4.19 – page 1Use the RDW process to solve.

1. Sue ran 910 mile on Monday and 710 mile on Tuesday. How many miles did Sue run in the 2 days?

2. Mr. Salazar cut his son’s birthday cake into 8 equal pieces. Mr. Salazar, Mrs. Salazar, and the birthday boy each ate 1 piece of cake. What fraction of the cake was left?

3. Maria spent 47 of her money on a book and saved the rest. What fraction of her money did Maria save?

Problem Set 4.19 – page 2

4. Mrs. Jones had 1 48 pizzas left after a party. After giving some to Gary, she had

78 pizza left. What fraction of a pizza did she give Gary?

5. A baker had 2 pans of corn bread. He served 114 pans. What fraction of a pan

was left?

6. Marius combined 48 gallon of lemonade, 38 gallon of cranberry juice, and 68 gallon of soda water to make a punch for a party. How many gallons of punch did he make in all?

Name: ______________________________ Date: ____________Exit Ticket 4.19Use the RDW process to solve.

1. Mrs. Smith took her bird to the vet. Tweety weighed 1310 pounds. The vet

said that Tweety weighed 410 pound more last year. How much did Tweety weigh last year?

2. Hudson picked 114 baskets of apples. Suzy picked 2 baskets of apples. How

many more baskets of apples did Suzy pick than Hudson?

Name: ______________________________ Date: ____________Additional Practice 4.19 – page 1Use the RDW process to solve.

1. Isla walked 34 mile each way to and from school on Wednesday. How many miles did Isla walk that day?

2. Zach spent 23 hour reading on Friday and 1 13 hours reading on Saturday. How

much more time did he read on Saturday than on Friday?

3. Mrs. Cashmore bought a large melon. She cut a piece that weighed 118

pounds and gave it to her neighbor. The remaining piece of melon weighed 68 pound. How much did the whole melon weigh?

Additional Practice 4.18 – page 24. Ally’s little sister wanted to help her make some oatmeal cookies. First, she

put 58 cup of oatmeal in the bowl. Next, she added another 58 cup of oatmeal.

Finally, she added another 58 cup of oatmeal. How much oatmeal did she put in the bowl?

5. Marcia baked 2 pans of brownies. Her family ate 1 56 pans. What fraction of a

pan of brownies was left?

6. Joanie wrote a letter that was 1 14 pages long. Katie wrote a letter that was 34

page shorter than Joanie’s letter. How long was Katie’s letter?

web viewsource: . grade 4unit 4: block 19. 4.19 solve word problems. common core state standards

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