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## Texas Go Math Grade 4 Lesson 2.1 Answer Key Model Tenths and Hundredths

**Essential Question**

How can you model tenths and hundredths?

Answer:

We know that,

Our system is base ten, a value of 10 in one place is equal to a value of 1 in the place to the left: 10 thousandths are equivalent to 1 hundredth, 10 hundredths are equivalent to 1 tenth, 10 tenths is equivalent to 1 one, and so on.

**Investigate**

**Materials base-ten blocks**

A decimal is a number with one or more digits to the right of the decimal point, such as tenths and hundredths. If 1 is divided into ten equal parts, each part is one-tenth. If 1 is divided into one hundred equal parts, each part is one hundredth.

A. What if the small cube is an I unit? Use what you know about the relationships of whole numbers to describe the value of the other blocks.

B. **What if** the flat is I unit? I low can you represent the flat, the lung, and the small cube by using the least number of blocks? the greatest number of blocks? What is the value of each block?

Answer:

C. Model 0.4 with base-ten blocks. Use the flat to represent 1. Tell which blocks you used.

Answer:

The representation of the model with ten-base blocks is:

Now,

From the above figure,

We can observe that

The blocks you used to represent the ten-base blocks are:

a. Flat

b. Long

c. Cube

Now,

It is given that

The “Flat” is represented as “1”

So,

The “Long” is represented as one-tenth

The “Cube” is represented as one-hundredth

Hence, from the above,

We can conclude that

The value of the representation of the model is: 0.4

**Make Connections**

You can use your understanding of place-value patterns and a place-value chart to write decimals that are 10 times as much as or \(\frac{1}{10}\) of any given decimal.

5 is 10 times as much as 0.5.

0.05 is \(\frac{1}{10}\) of 0.5

**Use the steps below to complete the table.**

STEP 1 Write the given decimal in a place-value chart.

STEP 2 Use the place-value chart to write a decimal that is 10 times as much as the given decimal.

STEP 3 Use the place-value chart to write a decimal that is \(\frac{1}{10}\) of the given decimal.

Answer:

The given steps are:

STEP 1 Write the given decimal in a place-value chart.

STEP 2 Use the place-value chart to write a decimal that is 10 times as much as the given decimal.

STEP 3 Use the place-value chart to write a decimal that is \(\frac{1}{10}\) of the given decimal.

Hence, from the above,

We can conclude that

The completed table is:

**Share and Show**

**Write the decimal shown by the model. The flat represents 1 unit. Then model the decimal in another way. Tell which blocks you used.**

Question 1.

Answer:

The given model is:

From the given model,

We can observe that

The model is “Long”

So,

When we considered the “Flat” as 1,

The “Long” is considered as 0.1

So,

The decimal represented by the given model = 0.1 × 10

= 1.0

Hence, from the above,

We can conclude that

The decimal represented by the given model is: 1.0

Question 2.

Answer:

The given model is:

Now,

From the given model,

We can observe that

The model consists of:

a. Flat

b. Long

c. Cube

Now,

We know that,

When we considered “Flat” as 1,

The “Long” is considered as 0.1 and the “Cube” is considered as 0.1

So,

The decimal represented by the given model = 1 + (0.1 × 4) + (0.01 × 3)

= 1 + 0.4 + 0.03

= 1 + 0.43

= 1.43

Hence, from the above,

We can conclude that

The decimal represented by the given model is: 1.43

**Model the decimal in two ways. Use the flat to represent 1. Record by drawing a quick picture.**

Question 3.

2.1

Answer:

The given decimal is: 2.1

Now,

We know that,

We will consider

The “Flat” as 1

The “Long” as 0.1

The “Cube” as 0.01

So,

2.1 = 1 + 1 + 0.1

Hence, from the above,

We can conclude that

The representation of the given decimal number in the form of a model is:

Question 4.

0.16

Answer:

The given decimal is: 0.16

Now,

We know that,

We will consider

The “Flat” as 1

The “Long” as 0.1

The “Cube” as 0.01

So,

0.16 = 0.1 + 0.06

Hence, from the above,

We can conclude that

The representation of the given decimal number in the form of a model is:

Question 5.

3.9

Answer:

The given decimal is: 3.9

Now,

We know that,

We will consider

The “Flat” as 1

The “Long” as 0.1

The “Cube” as 0.01

So,

3.9 = 1 + 1 + 1 + 0.9

Hence, from the above,

We can conclude that

The representation of the given decimal number in the form of a model is:

Question 6.

**H.O.T.**

**Multi-Step** Tyler said he swam 23 tenths miles this week. His coach said Tyler swam 2.3 miles this week.

To find who is correct, model the distances both Tyler and his coach said Tyler swam. Use the flat as 1 unit.

a. What do you need to use?

Answer:

We need to use the values of the “Flat”, “Long”, and “Cube”

b. What do you know about representing whole numbers and decimals that may help you solve the problem?

Answer:

We know that,

The value of “Flat” is: 1

The value of “Long” is: 0.1

The value of “Cube” is: 0.01

c. Make a model and draw a quick picture to record the distances that Tyler and his coach said he swam.

It is given that

Tyler said he swam 23 tenths miles this week. His coach said Tyler swam 2.3 miles this week.

Now,

From the given information,

23 tenths = 23 × 0.1

= 2.3

So,

2.3 = 1 + 1 + 0.3

Hence, from the above,

We can conclude that

The model to record the distances that Tyler and his coach said he swam is:

d. Complete the sentences.

Are the two models alike or different? ______________________________

Tyler swam __________ tenths, or __________, miles. So, ______________________________ are correct.

Answer:

The two models are alike

Tyler swam 23 tenths or 2.3 miles

So,

Both Tyler and his coach are correct

Question 7.

**Multi-Step:**

**Using Diagrams** Mike and Shantel both drew a quick picture to represent the decimal 1.2. Whose quick picture is correct? Explain the error that either Mike or Shantel made when drawing their quick picture.

Answer:

It is given that

Mike and Shantel both drew a quick picture to represent the decimal 1.2

Now,

We know that,

We will consider “Flat” as 1

We will consider “Long” as: 0.1

We will consider “Cube” as: 0.01

Now,

The model of Mike is:

Now,

From the above model,

The representation of the decimal number = 1 + (2 × 0.01)

= 1 + 0.02

= 1.02

Now,

The model of Shantel is:

Now,

From the above model,

The representation of the decimal number = 1 + (2 × 0.1)

= 1 + 0.2

= 1.2

Hence, from the above,

We can conclude that

Shantel’s quick picture is correct

Mike considered the value of “Cube” as 0.1 which is the error

**Daily Assessment Task**

**Fill in the bubble completely to show your answer.**

Question 8.

**Representations** In the models below, the flat represents 1 unit. The width of an apple seed is 0.31 centimeters. Which model shows 0.31?

(A)

(B)

(C)

(D)

Answer:

It is given that

The width of an apple seed is 0.31 centimeters

Now,

We know that,

The value of “Flat” is: 1

The value of “Long” is: 0.1

The value of “Cube” is: 0.01

So,

0.31 = 0.3 + 0.01

= (0.1 × 3) + 0.01

= 3 Long + 1 Cube

Hence, from the above,

We can conclude that

The model that shows 0.31 is:

Question 9.

**Multi-Step** In the model below, the flat represents 1 unit. Which is another way to model this decimal?

(A)

(B)

(C)

(D)

Answer:

The given model is:

Now,

We know that,

The value of “Flat” is: 1

The value of “Long” is: 0.1

The value of “Cube” is: 0.01

Now,

From the given model,

We can observe that

The representation of the decimal number = 1 + (2 × 0.1) + (2 × 0.01)

= 1 + 0.2 + 0.02

= 1.2 + 0.02

= 1.22

= (12 ×0.1) + (2 × 0.01)

= 12 Long + 2 Cubes

Hence, from the above,

We can conclude that

The another way to model the given model is:

**TEXAS Test Prep**

Question 10.

Suppose the flat represents 1 unit. What decimal is represented by the model?

(A) 62

(B) 0.62

(C) 6.2

(D) 0.26

Answer:

The given model is:

Now,

We know that,

The value of “Flat” is: 1

The value of “Long” is: 0.1

The value of “Cube” is: 0.01

Now,

From the given model,

We can observe that

The representation of the decimal number = (6 × 0.1) + (2 × 0.01)

= 0.6 + 0.02

= 0.62

Hence, from the above,

We can conclude that

The decimal number that is represented by the given model is:

### Texas Go Math Grade 4 Lesson 2.1 Homework and Practice Answer Key

**Model Tenths and Hundredths**

Question 1.

Lucia and Stephen each drew a quick picture to model 2.04. Whose model is correct? Explain the error.

Answer:

It is given that

Lucia and Stephen each drew a quick picture to model 2.04

Now,

We know that,

We will consider “Face” as: 1

We will consider “Long” as: 0.1

We will consider “Cube” as: 0.01

Now,

The model of Lucia is:

Now,

From the above model,

We can observe that

The decimal number represented by the above model = 1 + 1 + (4 × 0.01)

= 2 + 0.04

= 2.04

Now,

The model of Stephen is:

Now,

From the above model,

We can observe that

The decimal number represented by the above model = 1 + 1 + (4 × 0.1)

= 2 + 0.4

= 2.4

Hence, from the above,

We can conclude that

Lucia’s model is correct

The error is that Stephen considered “Long” instead of “Cube”

**Problem Solving**

Question 2.

Russell planted a flower bed that is 1.6 square meters. Jackie planted a flower bed that is 16 tenths square meters. Draw a quick picture to model the two areas.

Russell Jackie

Answer:

It is given that

Russell planted a flower bed that is 1.6 square meters. Jackie planted a flower bed that is 16 tenths square meters

Now,

We know that,

We will consider “Face” as: 1

We will consider “Long” as: 0.1

We will consider “Cube” as: 0.01

Hence, from the above,

We can conclude that

The representation of the area models of Russel and Jackie is:

Russel:

Jackie:

Question 3.

Compare the areas of the two flower beds. Explain your reasoning.

Answer:

From Question 2,

It is given that

Russell planted a flower bed that is 1.6 square meters. Jackie planted a flower bed that is 16 tenths square meters

So,

16 tenths = 16 × 0.1

= 1.6

So,

1.6 = 1.6

Hence, from the above,

We can conclude that

The area models of Russel and Jackie are the same

**Lesson Check**

**Fill in the bubble completely to show your answer.**

Question 4.

In the model below, the flat shows 1 unit. What decimal does the model show?

(A) 3.5

(B) 0.53

(C) 0.35

(D) 3.05

Answer:

The given model is:

Now,

We know that,

We will consider “Face” as: 1

We will consider “Long” as: 0.1

We will consider “Cube” as: 0.01

Now,

From the above figure,

We can observe that

The decimal number represented by the given model = 1 + 1 + 1 + (5 × 0.01)

= 3 + 0.05

= 3.05

Hence, from the above,

We can conclude that

The decimal number represented by the given model is:

Question 5.

In the models below, the flat shows 1 unit. Which model shows 0.24?

(A)

(B)

(C)

(D)

Answer:

The given decimal number is: 0.24

Now,

We know that,

We will consider “Face” as: 1

We will consider “Long” as: 0.1

We will consider “Cube” as: 0.01

So,

0.24 = 0.2 + 0.04

= ( 2 × 0.1) + (4 × 0.01)

= 2 Long + 4 Cube

Hence, from the above,

We can conclude that

The representation of the model for the given decimal number is:

Question 6.

**Multi-Step** In the model below, the flat represents 1 unit. Which is another way to model this decimal?

(A)

(B)

(C)

(D)

Answer:

The given model is:

Now,

We know that,

We will consider “Face” as: 1

We will consider “Long” as: 0.1

We will consider “Cube” as: 0.01

Now,

From the above model,

We can observe that

The representation of the decimal number for the given model = 1 + (3 × 0.1) + (4 × 0.01)

= 1 + 0.3 + 0.04

= 1 + 0.34

= 1.34

= (10 × 0.1) + (3 × 0.1) + (4 × 0.01)

= (13 × 0.1) + (4 × 0.01)

= 13 Long + 4 Cube

Hence, from the above,

We can conclude that

The another way to model the given model is:

Question 7.

In the model below, the flat shows 1 unit. What are the fraction and decimals shown by the model?

(A) 1.7, 1\(\frac{7}{10}\)

(B) 1.7, 1\(\frac{1}{7}\)

(C) 0.17, \(\frac{17}{100}\)

(D) 1.07, 1\(\frac{7}{100}\)

Answer:

The given model is:

Now,

We know that,

We will consider “Face” as: 1

We will consider “Long” as: 0.1

We will consider “Cube” as: 0.01

Now,

From the above model,

We can observe that

The representation of the decimal number for the given model = 1 + (7 × 0.1)

= 1 + 0.7

= 1.7

= \(\frac{17}{10}\)

= 1\(\frac{7}{10}\)

Hence, from the above,

We can conclude that

The fraction and the decimal number shown by the given model is: