Learning Targets:

I can discover how numerous groups over there are once the variety of groups and also the quantity in each team are not whole numbers.

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

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

Use the pattern blocks in the applet come answer the questions. (If girlfriend need aid aligning the pieces, you deserve to turn ~ above the grid.)

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

1 triangle

1 rhombus

1 hexagon

Use pattern blocks 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 many rhombuses are in a trapezoid?”

Diego says, “1frac 13 . If I put 1 rhombus ~ above a trapezoid, the leftover shape is a triangle, i m sorry is frac 13 of the trapezoid.”Jada says, “I think it’s 1frac12 . Due to the fact that we desire to discover out ‘how countless rhombuses,’ we have to compare the leftover triangle come a rhombus. A triangle is frac12 that a rhombus.” 

Select all equations that can be used to prize the question: “How plenty of 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, draw a diagram for the connection of the amounts to aid you answer the question. Then write a multiplication equation or a department equation because that the relationship. Be prepared to share your reasoning.

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

Are you prepared for more?

How many heaping teaspoons are in a heaping tablespoon? just how would the answer depend on the form of the spoons?

Lesson 5 Summary

Suppose one batch that cookies calls for frac23 cup flour. How plenty of batches deserve to be made v 4 cups of flour?

We deserve to think of the inquiry as being: “How plenty of frac23 s are in 4?” and also represent it utilizing multiplication and division equations.

? oldcdot frac23 = 4 4div frac23 = ?

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


Since 3 rhombuses make a hexagon, 1 rhombus represents frac13 and 2 rhombuses represent frac 23 . We can see that 6 pairs of rhombuses make 4 hexagons, for this reason there space 6 teams of frac 23 in 4.

Other kinds of diagrams can also aid us reason about equal-sized groups involving fractions. This instance shows how we might reason about the same question indigenous above: “How numerous frac 23 -cups space in 4 cups?”


We can see each “cup” partitioned into thirds, and also that there room 6 teams of frac23 -cup in 4 cups. In both diagrams, we view that the unknown worth (or the “?” in the equations) is 6. For this reason we can now write:

 6 oldcdot frac23 = 4 4div frac23 = 6

Lesson 5 practice Problems

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

Mark up and also label the diagram as needed.


What is the value of frac12divfrac13 ? usage pattern block to represent and also find this value. The yellow hexagon represents 1 whole. Define or present your reasoning.


Use a traditional inch ruler to answer each question. Then, write a multiplication equation and a department equation that answer the question.

How numerous frac12 s are in 7?

How numerous frac38 s space in 6?

How many frac516 s room in 1frac78 ?


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

Mark up and label the diagram together needed.


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

There room 12 fourths in 3. 

How countless frac 23 s are in 6?

At a farmer’s market, two vendors sell fresh milk. One merchant sells 2 liters for $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 offers 5 cup of flour for every 2 cups of sugar.

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