Name ________________

Date _______

Class # ______

Math 7

Strands

Fraction Review 3

Essential Understandings Being able to compute fluently means making smart choices about which tools to use and when to use them.

✓Productive Disposition

Numbers can be represented in multiple ways.

✓Conceptual Understanding

✓Strategic Competence

✓Procedural Fluency

The same operations can be applied in problem situations that seem quite different from another. Knowing the reasonableness of an answer comes from using good number sense and estimation strategies. Key Knowledge The operation of division is used to: • find how many of portions of one quantity is in another quantity. • to share equally • repeated subtraction Asking 8 ÷

1 = 8 × 2 since it takes two groups of one-half of a unit to make a whole 2

unit. Examples: 1 8 ÷ = 8 × 2 since it takes 2 one-half's to make a whole 2 3 4 8 ÷ = 8 × since it takes four-thirds of three-fourths of a unit to make one 4 3 whole unit. Key Questions When does a situation call for division? How is dividing related to multiplying? Why is knowing what the “whole” is important?

Key Skills I can recognize when a situation calls for the use of division. I can represent dividing whole numbers and fractions using multiple representations. I can divide whole numbers and fractions with fluency. After Teaching Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 1

Name ________________

Date _______

Class # ______ Goals

Math 7

Fraction Review 3-1 Story

I can represent dividing whole numbers and fractions using multiple representations.

Calculations

How many equal serving sizes of popcorn could be made if you had a total of 8 cups of popcorn and each serving size was 2 cups?

Drawing

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 2

Name ________________

Date _______

Class # ______

Fraction Review 3-1 Follow-Up A complete answer for each of the problems below will include a clearly labeled diagram, calculations connected to the diagram, and finally a complete sentence which answers the question. 1. How many equal size servings of popcorn could be made (or fractions of servings) if: a. the bag contained 5 cups of popcorn and each serving was 2 cups? b. the bag contained 5 cups of popcorn and each serving was 1 cup? c. the bag contained 5 cups of popcorn and each serving was one-half cup? d. the bag contained two and one-half cups of popcorn and each serving was one-half cup?

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 3

Name ________________

Date _______

Class # ______ Goals

Math 7

I can represent dividing whole numbers and fractions using multiple representations.

Mu to st be wit be s abl h d olv e ivis ed ion .

Fraction Review 3-2 Story

Calculations

Drawing

1

2 3

1

2 3

2 3

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 4

Name ________________

Date _______

Class # ______

Fraction Review 3-23 Follow-Up A complete answer for each of the problems will include a story, calculations connected to the diagram, and finally a complete sentence which answers the question. 1.

1

1

2 3

2 3

2.

1

1

2 3

2 3

2 3

1

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 5

Name ________________

Date _______

Goals

Math 7

Fraction Review 3-3 So lve div two mu isio wa ltip n a ys: lica nd tio n

Class # ______

Story

I can represent dividing whole numbers and fractions using multiple representations.

Calculations

Ms. Phillips brought jars of jellybeans to be shared equally by student teams who won the annual math competition. How much candy will each student get if a four-person team gets a total of one-half of a kilogram of candy.

Drawing

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 6

Name ________________

Date _______

Class # ______

Fraction Review 3-3 Follow-Up A complete answer for each of the problems below will include a clearly labeled diagram, calculations connected to the diagram, and finally a complete sentence which answers the question. 1. What fraction of a kilogram of candy would each member of the winning math team get if a. a four person team wins one-half kilogram of candy and shares it equally? b. a three person team wins one-fourth kilogram of candy and shares it equally? c. a three person team wins one-third kilogram of candy and shares it equally?

So lve div two mu isio wa ltip n a ys: lica nd tio n

d. a two person team wins one-fifth of a kilogram of candy and shares it equally?

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 7

Name ________________

Date _______

Class # ______ Goals

Math 7

Fraction Review 3-4 Story

I can represent dividing whole numbers and fractions using multiple representations.

Calculations

So lve div two mu isio wa ltip n a ys: lica nd tio n

A local candy store donated long chocolate bars that were used for prizes in a team competition. What fraction of a whole bar will each team member get if a two person team wins four-fifths of a bar and shares it equally?

Drawing

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 8

Name ________________

Date _______

Class # ______

Fraction Review 3-4 Follow-Up A complete answer for each of the problems below will include a clearly labeled diagram, calculations connected to the diagram, and finally a complete sentence which answers the question. 1. A local candy store donated long chocolate bars that were used for prizes in a team competition. What fraction of a whole bar will each team member get if a. a four person team wins eight-ninths of a bar and shares it equally?

So lve div two mu isio wa ltip n a ys: lica nd tio n

b. a four person team wins one and three-fourths of a bar and shares it equally?

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 9

Name ________________

Date _______

Class # ______ Goals

Math 7

Fraction Review 3-5

Calculations

So lve div two mu isio wa ltip n a ys: lica nd tio n

Story

I can represent multiplying whole numbers and fractions using multiple representations.

3 ÷ 4 = [? ] 4 ⎡       ⎤ ⎡        ⎤ ⎢⎣      ⎥⎦ × ⎢⎣      ⎥⎦ = [? ]

Drawing

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 10

Name ________________

Date _______

Class # ______

Fraction Review 3-5 Follow-Up 1. A complete answer for each of the problems below will include a story, a clearly labeled diagram, calculations connected to the diagram, the value for [? ] which makes the equation true, and a complete sentence which answers the question posed in your story. a.

1 ÷ 5 = [? ] 3

b.

2 ÷ 8 = [? ] 5

2. Solve each of your story problems from above using multiplication. A complete answer will include how the calculations are connected to the drawings from problem 1.

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 11

Name ________________

Date _______

Class # ______ Goals

Math 7

Fraction Review 3-6 Story

I can represent dividing whole numbers and fractions using multiple representations.

Calculations

Sam has a job of decorating conferences badges using ribbon. Each conference badge uses one-sixth of a meter of ribbon. How many badges can be made from one-half of a meter of ribbon? (If there is any left over ribbon, tell what fractional part of another badge Sam could make.)

Drawing

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 12

Name ________________

Date _______

Class # ______

Fraction Review 3-6 Follow-Up A complete answer for each of the problems below will include a clearly labeled diagram, calculations connected to the diagram, and finally a complete sentence which answers the question. 1. How many conference badges can Sam make from the following amounts of ribbon assuming that each badge requires one-sixth of a meter of ribbon? a. Three-fourths meter

b. Five-eights meter

c. Two and two-thirds meters

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 13

Name ________________

Date _______

Class # ______ Goals

Math 7

Fraction Review 3-7 Story

I can represent dividing whole numbers and fractions using multiple representations.

Calculations

Jade is working on a different order of bows for the conference. She uses two-thirds of a meter of ribbon to make one bow. How many bows can Jade make from four-fifths meters of ribbon?

Drawing

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 14

Name ________________

Date _______

Class # ______

Fraction Review 3-7 Follow-Up A complete answer for each of the problems below will include a clearly labeled diagram, calculations connected to the diagram, and finally a complete sentence which answers the question. 1. Jade is working on a different order of bows for the conference. She uses twothirds of a meter of ribbon to make one bow. How many bows can Jade make from each of the following amounts of ribbon. a. Eight-ninths meters

b. One and three-fourths meters

c. Two and one-third meters

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 15

Name ________________

Date _______

Class # ______

Math 7

Fraction Review 3 Practice 1

Goals I can represent dividing whole numbers and fractions using multiple representations.

A complete answer for each of the problems below will include a clearly labeled diagram, calculations connected to the diagram, and finally a complete sentence which answers the question. 1. Max has 2 cups of popcorn. If the size of each serving is two-thirds of a cup, how many servings, and fractions of servings, can he make?

32 yards of material to make a suit. How many suits can she 3 make from 22 yards of material?

2. A tailor needs

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 16

Name ________________

Date _______

Class # ______ Goals

Math 7

Fraction Review 3-8 Story

I can represent dividing whole numbers and fractions using multiple representations.

Calculations

2 cups of popcorn. If the 3 size of each serving is three-fourths of a cup, how many servings, and fractions of servings, can he make? Max has 3

Drawing

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 17

Name ________________

Date _______

Class # ______

Fraction Review 3-8 Follow-Up A complete answer for each of the problems below will include a clearly labeled diagram, calculations connected to the diagram, and finally a complete sentence which answers the question.

3 3 cups of popcorn. If each serving is cups, how many servings, or 4 4 fractions of servings, can Max make?

1. Max has 2

2. Max has 2 cups of popcorn. If each serving is 2

2 cups, how many servings, or 3

fractions of servings, can Max make?

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 18

Name ________________

Date _______

Class # ______ Goals

Math 7

Fraction Review 3-9 Story

I can represent dividing whole numbers and fractions using multiple representations.

Calculations

Kayla is baking bagels. She has 1 kilogram of flour but the recipe calls 4 for of a kilogram. What fraction of 3 a recipe can she make with the flour she has?

Drawing

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 19

Name ________________

Date _______

Class # ______

Fraction Review 3-9 Follow-Up A complete answer for each of the problems below will include a clearly labeled diagram, calculations connected to the diagram, and finally a complete sentence which answers the question.

5 of a kilogram of flour and you have 1 kilogram of flour on 4 hand. What fraction of a recipe can you make?

1. A recipe calls for

2 of a kilogram of flour and you have 1 kilogram of flour on 3 hand. What fraction of a recipe can you make?

2. A recipe calls for

7 of a kilogram of flour and you have 1 kilogram of flour on 8 hand. What fraction of a recipe can you make?

3. A recipe calls for

4. Whatʼs the connection between all of these problems? Why do you think this happens?

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 20

Name ________________

Date _______

Class # ______

A kilograms of flour and you B have 1 kilogram of flour on hand. What fraction of a recipe can you make if:

5. (No drawings need to be made.) A recipe calls for

a.

1 3

b.

4 3

c.

7 5

d.

5 7

A kilograms of flour and you B have C kilogram of flour on hand. What fraction of a recipe can you make if:

6. (No drawings need to be made.) A recipe calls for

a. A = 2, B = 3, C = 2

b. A = 2, B = 3, C = 2

c. A = 2, B = 3, C = 2

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 21

Name ________________

Date _______

Class # ______

Problem Bank Show how to use the diagram below to solve the problems.

1 2 d  of paint you can paint m2 of a wall. How many m2 4 5 can you paint with 1d  of paint? With

0

1

0

1

0

1

2 2 d  of paint you can paint m2 of a wall. How many m2 4 5 can you paint with 1d  of paint? With

3 2 d  of paint you can paint m2 of a wall. How many m2 4 5 can you paint with 1d  of paint? With

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 22

Name ________________

Date _______

Class # ______

A student used the diagram at right to show 3 her answer to the problem, “With d  of paint 4 2 you can paint m2 of a wall. How many m2 5 can you paint with 1d  of paint?” Can you explain her work?

!2 \$ #" ÷ 3&% ' 4 5

0

1

!2 \$ ! 2 1\$ #" ÷ 3&% ' 4 = #" ' &% ' 4 5 5 3 ! 2 ' 1\$ =# '4 " 5 ' 3 &% ! 2\$ =# & '4 " 15 % =

8 15

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding

page 23

Dividing with Fractions

Problems with the intent of helping students developing an understanding of dividing with fractions.