We included **HMH Into Math Grade 4 Answer Key PDF** **Module 12 Lesson 1 Represent Tenths as Fractions and Decimals **to make students experts in learning maths.

## HMH Into Math Grade 4 Module 12 Lesson 1 Answer Key Represent Tenths as Fractions and Decimals

I Can use a visual model and decimal notation to represent fractions, mixed numbers, and decimals in tenths.

**Spark Your Learning**

The diagram shows the heights of a plant at the end of each of 3 weeks. After Week 1, the plant is \(\frac{3}{10}\) meter tall. Another way to represent the height is 0.3 meter. Both \(\frac{3}{10}\) and 0.3 can be read as three tenths. They represent 3 parts of 10 equal parts of a whole.

How can you represent the heights of the plant at the end of each week with a visual model? How can you label the heights of the plant on a number line in two different ways?

Answer:

Explanation:

From the given data the plant grows \(\frac{3}{10}\) in the 1st week.

In the 22nd week it grows \(\frac{5}{10}\) meters.

In 3rd week it grows \(\frac{7}{10}\) meters.

**Turn and Talk** How did you represent a meter with your visual model? How is your representation like those of your classmates? How is it different?

Answer:

There are different ways to represent a meter in visual model.

We can represent with line diagram and bar diagram models.

**Build Understanding**

Question 1.

One of the tomatoes from a garden is 1\(\frac{1}{10}\) pounds.

Represent the weight of the tomato on a tenths model and a number line.

Answer:

1\(\frac{1}{10}\)

A. How did you represent 1\(\frac{1}{10}\) on the tenths models?

Answer:

B. How did you locate the weight of the tomato on the number line?

Answer:

Connect to Vocabulary

A tenth is one of ten equal sized parts. A decimal point is a dot that separates the ones place from the tenths place in a number. A decimal is a number that has one or more digits to the right of a decimal point.

C. How can you represent 1\(\frac{1}{10}\) pounds using digits and a decimal point?

Answer:

1\(\frac{1}{10}\)

Explanation:

One of the tomatoes from a garden is 1\(\frac{1}{10}\) pounds.

1\(\frac{1}{10}\) on the tenths models means each set is divided into ten parts to make a whole.

**Turn and Talk** How is a mixed number similar to a decimal greater than 1?

Answer:

Mixed fraction

using mixed fraction representation.

Explanation:

When we convert an improper fraction to a decimal,

the decimal is always greater than 1.

Question 2.

The tenths models show how many cups of water Tina uses to water a tomato plant.

A. Write a sentence to describe the amount of water Tina uses.

Answer:

Tina uses 2\(\frac{8}{10}\) of water

Explanation:

In the above 10th model given,

two complete blocks filled with blue color and 8/10 part is also filled with blue color.

So, the total amount of water is represented as 2\(\frac{8}{10}\)

B. How can you write the amount of water that Tina as a mixed number and as a decimal?

Answer:

2.8

Explanation:

\(\frac{8}{10}\) = 0.8

2.0 + 0.8 = 2.8

**Check Understanding**

Question 1.

Duke plants each tomato plant meter apart. Represent the distance on the tenths model and the number line.

Write the distance as a decimal. _______

Answer:

0.6

Explanation:

A tenth is one of ten equal sized parts.

To represent a decimal on a number line, divide each segment of the number line into ten equal parts.

Question 2.

Write the amount shown as a mixed number and as a decimal.

Answer:

3.5

1 + 1 + 1 + 0.5 = 3.5

Explanation:

Each box represent 1 whole divided into 10 parts.

From the above information 3 complete sets and in the 4th set 5 are shaded.

So, 3 \(\frac{5}{10}\)

**On Your Own**

Question 3.

**STEM** Hydroponics is a way of growing plants in water rather than soil. The nutrients that plants need to grow are put into the water. Tanya designs a hydroponic system and fills the reservoir with \(\frac{8}{10}\) gallon of water. Use the tenths model to show the amount of water in the reservoir.

Write the amount of water as a decimal. __________

Answer:

0.8

Explanation:

\(\frac{8}{10}\)

A tenth is one of ten equal sized parts.

A decimal point is a dot that separates the ones place from the tenths place in a number.

Question 4.

**Use Tools** Liz plants 1\(\frac{6}{10}\) packs of tomato seeds. On the number line, show the amount of packs of seeds that Liz plants.

Write the amount of packs of seeds as a decimal. __________

Answer:

1.6

Explanation:

A tenth is one of ten equal sized parts.

To represent a decimal on a number line, divide each segment of the number line into ten equal parts.

Question 5.

**Use Structure** Write the amount shown as a mixed number and as a decimal.

Answer:

2.9

2\(\frac{9}{10}\)

1 + 1 + 0.9 = 2.9

Explanation:

Each box represent 1 whole divided into 10 parts.

From the above information 2 complete sets and in the 3rd set 9 are shaded.

So, 2 \(\frac{9}{10}\) = 2.9

**I’m in a Learning Mindset!**

What strategies can I use to write a decimal for a visual model and to draw a visual model for a decimal?

Answer:

Area and Grid models or Number line strategies.

Explanation:

In Area and Grid models we use the tenth model concept.

A tenth is one of ten equal sized parts.

To represent a decimal on a number line, divide each segment of the number line into ten equal parts.