We included **HMH Into Math Grade 3 Answer Key PDF** **Module 14 Lesson 1 Relate Fractions and Area **to make students experts in learning maths.

## HMH Into Math Grade 3 Module 14 Lesson 1 Answer Key Relate Fractions and Area

I Can use a fraction to show that equal parts of a whole shape have the same area.

**Spark Your Learning**

Liddy’s hamsters are Alvin, Betty, Coco, and Doug. Liddy puts up a wall to divide her hamsters’ playground into left and right halves. Then she puts up screens to divide each half of the playground into two halves. Now each hamster has a separate play space.

Which hamster will get the largest play space? Explain your thinking.

Answer:

Explanation:

Each of the hamster gets equal play space as Liddy divided her Hamsters ‘s play area into 2 equal halves first and divided the each halves into 2 equal halves again. So, each hamster has equal play space.

**Turn and Talk** What fraction of the whole playground does each hamster’s play space represent? How do you know?

Answer:

\(\frac{1}{4}\)

Explanation:

Liddy divided her Hamsters ‘s play area into 2 equal halves first and divided the each halves into 2 equal halves again

There are 4 parts and 4 hamsters

So, \(\frac{1}{4}\) is the fraction of the whole play ground with each hamster’ s play space.

**Build Understanding**

Question 1.

Davita draws lines to divide shapes A, B, and C. Which shapes are divided into equal areas?

How can you show which shapes are divided into equal areas?

Answer:

Explanation:

I marked those shapes that are divided into equal areas.

Shape A and C are divided into equal areas.

In the shapes A and C if we take 1 part of the whole and then add some parts of it and try to complete the whole it is possible but in Shape B it is not possible.

Question 2.

Edgar draws lines to divide circles A and B. Each circle is the same size.

Answer:

A. Are the parts of Circle A equal or unequal? How do you know?

Answer:

The parts of the Circle A are equal, we can take 1 part of the whole of circle A and add the same part 3 times more to complete it.

B. Are the parts of Circle B equal or unequal? Explain.

Answer:

The parts of the Circle B are unequal, if we take 1 part of the whole of circle B and add the same part 3 times more to complete it we cannot complete the whole as the parts are of different size.

**Turn and Talk** When two areas appear to be the same size, how can you show that they are actually equal?

Answer:

If two areas appear to be same size we can measure the areas of the shape using their lengths to show that they are actually equal.

Question 3.

Reyna divides a rectangle into parts.

A. Are the parts of the rectangle the same shape? Explain how you know.

Answer:

No, the parts of the rectangle are not same shape, all the shapes are different.

B. Do the parts of the rectangle have the same area? How do you know?

Answer:

Yes, the parts of the rectangles have same area. We can know this by finding the number of boxes each part cover.

Each part has 6 boxes So, all the parts have same area.

C. What fraction of the total area of the rectangle is shaded yellow? How do you know?

Answer:

\(\frac{1}{4}\)

Explanation:

There are 4 parts in the whole. 1 part of the rectangle is shaded yellow. So, the fraction of the total area of the rectangle is shaded yellow is \(\frac{1}{4}\).

**Turn and Talk** A sign painter paints two signs with different shapes. Sign A is a triangle and sign B is a rectangle. How is it possible that both signs require the same amount of paint? Explain.

Answer:

A sign painter paints two signs with different shapes. Sign A is a triangle and sign B is a rectangle. Both triangle and rectangle signs require the same amount of paint if they have same area.

**Check Understanding**

Question 1.

Circle the shape that is divided into parts with equal areas.

Answer:

Explanation:

I drew a circle around the shape that is divided into equal areas.

Question 2.

For the rectangle shown:

Do both parts of this rectangle have the same shape? Explain how you know.

Answer:

No, the both parts of the rectangle are not the same shape as they look different from each other.

Which part of the rectangle covers a greater area? How do you know?

Answer:

Both the rectangles cover the same area as they cover the same number of boxes on the area grid.

**On Your Own**

Question 3.

**Critique Reasoning** Garrick says that the shaded area is \(\frac{1}{3}\) of the whole because it is 1 of 3 parts that all have the same shape. Aidan says that the shaded area is not \(\frac{1}{3}\) of the whole because the three parts do not all have the same area. Which student’s reasoning is correct? Explain.

Answer:

The reasoning of Aidan is correct.

Explanation:

Garrick says that the shaded area is \(\frac{1}{3}\) of the whole because it is 1 of 3 parts that all have the same shape

Aidan says that the shaded area is not \(\frac{1}{3}\) of the whole because the three parts do not all have the same area

Aidan is correct when the whole is not divided into equal parts we cannot write a fraction

A fraction can only be written with equal parts.

Question 4.

Cross out any shapes that have parts with unequal areas.

Answer:

Explanation:

I crossed out the triangle shape that have unequal parts.

The other there shapes have equal parts.

**Use the rectangle for 5-6.**

Question 5.

Are the parts of the rectangle equal in area? How do you know?

Answer:

Yes, all the parts of the rectangle are equal in area as they cover the same number of boxes on the area grid.

Question 6.

What fraction of the rectangle is shaded blue?

Answer:

\(\frac{1}{3}\)

Explanation:

The are 3 parts in the rectangle in whole, 1 part of 3 is shaded blue. So, \(\frac{1}{3}\) is fraction of the rectangle shaded in blue.

**I’m in a Learning Mindset!**

What do I already know about dividing shapes that will help me find whether a shape is divided into equal areas?

Answer: