Download - Dividing with Fractions
Math 7Fraction Review 3Essential UnderstandingsBeing able to compute fluently means making smart choices about which tools to use and when to use them.
Numbers can be represented in multiple ways.
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 KnowledgeThe 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 ÷ 12= 8 × 2 since it takes two groups of one-half of a unit to make a whole
unit.
Examples:
8 ÷ 12= 8 × 2 since it takes 2 one-half's to make a whole
8 ÷ 34= 8 × 4
3 since it takes four-thirds of three-fourths of a unit to make one
whole unit.
Key QuestionsWhen does a situation call for division?
How is dividing related to multiplying?
Why is knowing what the “whole” is important?
Key SkillsI 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
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 1
Strands✓Adaptive Reasoning
✓Strategic Competence
✓Productive Disposition
✓Procedural Fluency
✓Conceptual Understanding
Math 7Fraction Review 3-1
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 2
GoalsI can represent dividing whole numbers and fractions using multiple representations.
Story Calculations
Drawing
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?
Fraction Review 3-1 Follow-UpA 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 serv-ings) 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?
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 3
Math 7Fraction Review 3-2
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 4
GoalsI can represent dividing whole numbers and fractions using multiple representations.
Story Calculations
Drawing
1 1
2
3
2
3
2
3
Must b
e able
to
be so
lved
with
divisi
on.
Fraction Review 3-23 Follow-UpA complete answer for each of the problems will include a story, calcu-lations connected to the diagram, and finally a complete sentence which answers the question.
1.1 1
2
3
2
3
2
3
1
2
3
2
3
2.1 1
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 5
Math 7Fraction Review 3-3
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 6
GoalsI can represent dividing whole numbers and fractions using multiple representations.
Story Calculations
Drawing
Ms. Phillips brought jars of jelly-beans to be shared equally by stu-dent 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.
Solve
two w
ays:
divisi
on an
d mult
iplica
tion
Fraction Review 3-3 Follow-UpA 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?
d. a two person team wins one-fifth of a kilogram of candy and shares it equally?
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 7
Solve
two w
ays:
divisi
on an
d mult
iplica
tion
Math 7Fraction Review 3-4
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 8
GoalsI can represent dividing whole numbers and fractions using multiple representations.
Story Calculations
Drawing
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?
Solve
two w
ays:
divisi
on an
d mult
iplica
tion
Fraction Review 3-4 Follow-UpA 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?
b. a four person team wins one and three-fourths of a bar and shares it equally?
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 9
Solve
two w
ays:
divisi
on an
d mult
iplica
tion
Math 7Fraction Review 3-5
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 10
GoalsI can represent multi-plying whole numbers and fractions using multiple representa-tions.
Story Calculations
Drawing
34÷ 4 = ?[ ]
⎡⎣⎢
⎤⎦⎥×
⎡⎣⎢
⎤⎦⎥= ?[ ]
Solve
two w
ays:
divisi
on an
d mult
iplica
tion
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. 13÷ 5 = ?[ ]
b. 25÷ 8 = ?[ ]
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.
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 11
Math 7Fraction Review 3-6
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 12
GoalsI can represent dividing whole numbers and fractions using multiple representations.
Story Calculations
Drawing
Sam has a job of decorating confer-ences 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 me-ter of ribbon? (If there is any left over ribbon, tell what fractional part of an-other badge Sam could make.)
Fraction Review 3-6 Follow-UpA 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 rib-bon 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
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 13
Math 7Fraction Review 3-7
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 14
GoalsI can represent dividing whole numbers and fractions using multiple representations.
Story Calculations
Drawing
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 me-ters of ribbon?
Fraction Review 3-7 Follow-UpA 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 two-thirds 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
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 15
Math 7Fraction Review 3Practice 1
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?
2. A tailor needs 323
yards of material to make a suit. How many suits can she
make from 22 yards of material?
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 16
GoalsI can represent dividing whole numbers and fractions using multiple representations.
Math 7Fraction Review 3-8
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 17
GoalsI can represent dividing whole numbers and fractions using multiple representations.
Story Calculations
Drawing
Max has 3 23
cups of popcorn. If the
size of each serving is three-fourths of a cup, how many servings, and fractions of servings, can he make?
Fraction Review 3-8 Follow-UpA 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 34
cups of popcorn. If each serving is 34
cups, how many servings, or
fractions of servings, can Max make?
2. Max has 2 cups of popcorn. If each serving is 2 23
cups, how many servings, or
fractions of servings, can Max make?
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 18
Math 7Fraction Review 3-9
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 19
GoalsI can represent dividing whole numbers and fractions using multiple representations.
Story Calculations
Drawing
Kayla is baking bagels. She has 1 kilogram of flour but the recipe calls
for 43
of a kilogram. What fraction of
a recipe can she make with the flour she has?
Fraction Review 3-9 Follow-UpA 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 recipe calls for 54
of a kilogram of flour and you have 1 kilogram of flour on
hand. What fraction of a recipe can you make?
2. A recipe calls for 23
of a kilogram of flour and you have 1 kilogram of flour on
hand. What fraction of a recipe can you make?
3. A recipe calls for 78
of a kilogram of flour and you have 1 kilogram of flour on
hand. What fraction of a recipe can you make?
4. Whatʼs the connection between all of these problems? Why do you think this happens?
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 20
5. (No drawings need to be made.) A recipe calls for AB
kilograms of flour and you
have 1 kilogram of flour on hand. What fraction of a recipe can you make if:
a. 13 b. 4
3 c. 7
5 d. 5
7
6. (No drawings need to be made.) A recipe calls for AB
kilograms of flour and you
have C kilogram of flour on hand. What fraction of a recipe can you make if:
a. A = 2, B = 3, C = 2 b. A = 2, B = 3, C = 2 c. A = 2, B = 3, C = 2
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 21
Problem Bank
Show how to use the diagram below to solve the problems.
With
14d of paint you can paint 2
5m2 of a wall. How many m2
can you paint with 1d of paint?
With
24d of paint you can paint 2
5m2 of a wall. How many m2
can you paint with 1d of paint?
With
34d of paint you can paint 2
5m2 of a wall. How many m2
can you paint with 1d of paint?
0 1
0 1
0 1
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 22
A student used the diagram at right to show
her answer to the problem, “With
34d of paint
you can paint 25m2 of a wall. How many m2
can you paint with 1d of paint?” Can you ex-plain her work?
0 1
2
5÷ 3
!"#
$%&' 4
2
5÷ 3
!"#
$%&' 4 =
2
5'1
3
!"#
$%&' 4
=2 '15 ' 3
!"#
$%&' 4
=2
15
!"#
$%&' 4
=8
15
Name ________________ Date _______ Class # ______
Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 23