Learning Targets:

I can discover how countless groups there are as soon as the number of groups and the amount in each team are not totality numbers.

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Write a portion or entirety number as an answer for every question. If you get stuck, use the fraction strips. Be all set to share your strategy.

How many frac 12 s space in 2?How countless frac 15 s space in 3?How countless frac 18 s are in 1frac 14 ?

Use the pattern blocks in the applet come answer the questions. (If you need aid aligning the pieces, you have the right to turn top top the grid.)

If the trapezoid to represent 1 whole, what perform each of the adhering to shapes represent? Be all set to display or define your reasoning.

1 triangle

1 rhombus

1 hexagon

Use pattern block to stand for each multiplication equation. Usage the trapezoid to represent 1 whole.

3 oldcdot frac 13=1

3 oldcdot frac 23=2

Diego and also Jada to be asked “How plenty of rhombuses room in a trapezoid?”

Diego says, “1frac 13 . If I placed 1 rhombus on a trapezoid, the leftover form is a triangle, which is frac 13 the the trapezoid.”Jada says, “I think it’s 1frac12 . Since we want to find out ‘how many rhombuses,’ we should compare the leftover triangle come a rhombus. A triangle is frac12 the a rhombus.” 

Select all equations that have the right to be provided to price the question: “How countless rhombuses are in a trapezoid?”

frac 23 div ? = 1

? oldcdot frac 23 = 1

1 div frac 23 = ?

1 oldcdot frac 23 = ?

? div frac 23 = 1

5.3 illustration Diagrams to show Equal-sized Groups

For each situation, attract a diagram because that the partnership of the quantities to help you answer the question. Then create a multiplication equation or a department equation for the relationship. Be prepared to share her reasoning.

The distance roughly a park is frac32 miles. Noah speak his bicycle approximately the park because that a total of 3 miles. How countless times roughly the park did the ride?You need frac34 garden of ribbon because that one gift box. You have actually 3 yards the ribbon. How countless gift boxes do you have actually ribbon for?The water hose fills a bucket in ~ frac13 gallon per minute. How many minutes walk it require to fill a 2-gallon bucket?

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How numerous heaping teaspoons space in a heaping tablespoon? just how would the answer depend on the shape of the spoons?

Lesson 5 Summary

Suppose one batch the cookies needs frac23 cup flour. How many batches can be made with 4 cup of flour?

We can think that the concern as being: “How countless frac23 s space in 4?” and represent it utilizing multiplication and division equations.

? oldcdot frac23 = 4 4div frac23 = ?

Let’s usage pattern blocks to visualize the situation and say that a hexagon is 1 whole. 


Since 3 rhombuses make a hexagon, 1 rhombus represents frac13 and 2 rhombuses represent frac 23 . We deserve to see that 6 pairs of rhombuses make 4 hexagons, therefore there are 6 teams of frac 23 in 4.

Other type of diagrams can also help us reason about equal-sized teams involving fractions. This instance shows how we could reason about the same question native above: “How countless frac 23 -cups space in 4 cups?”


We have the right to see every “cup” partitioned into thirds, and also that there room 6 groups of frac23 -cup in 4 cups. In both diagrams, we check out that the unknown worth (or the “?” in the equations) is 6. Therefore we deserve to now write:

 6 oldcdot frac23 = 4 4div frac23 = 6

Lesson 5 practice Problems

Use the ice cream diagram to represent and also find the value of frac12divfrac13 .

Mark up and also label the diagram as needed.


What is the worth of frac12divfrac13 ? use pattern blocks to represent and find this value. The yellow hexagon represents 1 whole. Define or display your reasoning.


Use a standard inch leader to answer every question. Then, write a multiplication equation and also a department equation that answer the question.

How countless frac12 s space in 7?

How many frac38 s are in 6?

How numerous frac516 s space in 1frac78 ?


Use the ice cream diagram come represent and answer the question: How numerous frac25 s are in 1frac12 ?

Mark up and label the diagram as needed.


Write a multiplication equation and also a department equation to stand for each question, statement, or diagram. 

There space 12 fourths in 3. 

How countless frac 23 s room in 6?

At a farmer’s market, two vendors sell fresh milk. One vendor sells 2 liters because that $3.80, and another merchant sells 1.5 liters for $2.70. I beg your pardon is the far better deal? define your reasoning.

A recipe uses 5 cups of flour for every 2 cup of sugar.

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How lot sugar is supplied for 1 cup of flour?How much flour is offered for 1 cup of sugar?How lot flour is supplied with 7 cup of sugar?How lot sugar is offered with 6 cup of flour?
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