Lesson 7What Fraction of a Group?
Learning Goal
Let’s think about dividing things into groups when we can’t even make one whole group.
Learning Targets
I can tell when a question is asking for the number of groups and that number is less than 1.
I can use diagrams and multiplication and division equations to represent and answer “what fraction of a group?” questions.
Warm Up: Estimating a Fraction of a Number
Problem 1
Estimate the quantities:
What is
of 7? What is
of ? What is
of ?
Problem 2
Write a multiplication expression for each of the previous questions.
Activity 1: Fractions of Ropes
Problem 1
The segments in the applet represent 4 different lengths of rope. Compare one rope to another, moving the rope by dragging the open circle at one endpoint. You can use the yellow pins to mark off lengths.
Complete each sentence comparing the lengths of the ropes. Then, use the measurements shown on the grid to write a multiplication equation and a division equation for each comparison.
Rope B is times as long as rope A.
Rope C is times as long as rope A.
Rope D is times as long as rope A.
Print Version
Here is a diagram that shows four ropes of different lengths.
Complete each sentence comparing the lengths of the ropes. Then, use the measurements shown on the grid to write a multiplication equation and a division equation for each comparison.
Rope B is times as long as rope A.
Rope C is times as long as rope A.
Rope D is times as long as rope A.
Problem 2
Each equation can be used to answer a question about Ropes C and D. What could each question be?
and and
Activity 2: Fractional Batches of Ice Cream
One batch of an ice cream recipe uses 9 cups of milk. A chef makes different amounts of ice cream on different days. Here are the amounts of milk she used:
Monday: 12 cups
Tuesday:
cups
Thursday: 6 cups
Friday:
cups
Problem 1
How many batches of ice cream did she make on these days? For each day, write a division equation, draw a tape diagram, and find the answer.
Monday
Tuesday
Problem 2
What fraction of a batch of ice cream did she make on these days? For each day, write a division equation, draw a tape diagram, and find the answer.
Thursday
Friday
Problem 3
For each question, write a division equation, draw a tape diagram, and find the answer.
What fraction of 9 is 3?
What fraction of 5 is
?
Lesson Summary
It is natural to think about groups when we have more than one group, but we can also have a fraction of a group.
To find the amount in a fraction of a group, we can multiply the fraction by the amount in the whole group. If a bag of rice weighs 5 kg,
Sometimes we need to find what fraction of a group an amount is. Suppose a full bag of flour weighs 6 kg. A chef used 3 kg of flour. What fraction of a full bag was used? In other words, what fraction of 6 kg is 3 kg?
This question can be represented by a multiplication equation and a division equation, as well as by a diagram.
We can see from the diagram that 3 is
In any situation where we want to know what fraction one number is of another number, we can write a division equation to help us find the answer.
For example, “What fraction of 3 is
The answer to “What is
The diagram shows that 3 wholes contain 12 fourths, and
We can use diagrams to help us solve other division problems that require finding a fraction of a group. For example, here is a diagram to help us answer the question: “What fraction of
We can see that the quotient is