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## Texas Go Math Grade 4 Lesson 1.1 Answer Key Place Value and Patterns

**Investigate**

**Materials base-ten blocks**

You can use base-ten blocks to understand the relationships among place-value positions. Use a large cube for 1,000, a flat for 100, along with the cube for 10, and a small cube for 1.

Complete the comparisons below to describe the relationship from one place-value position to the next place-value position.

A.

Look at the long and compare it to the small cube.

The long is ________ times as much as the small cube.

Answer:

The given table is:

Now,

From the given table,

We can observe that

The length is 10 times as much as the small cube.

Hence, from the above,

We can conclude that

The length is 10 times as much as the small cube.

Look at the flat and compare it to the long.

The flat is _________ times as much as the long.

Answer:

The given table is:

Now,

From the given table,

We can observe that

The flat is 10 times as much as the long.

Hence, from the above,

We can conclude that

The flat is 10 times as much as the long.

Look at the large cube and compare it to the flat.

The large cube is ___________ times as much as the flat.

Answer:

The given table is:

Now,

From the given table,

We can observe that

The large cube is 10 times as much as the flat.

Hence, from the above,

We can conclude that

The large cube is 10 times as much as the flat.

B.

Look at the flat and compare it to the large cube.

The flat is ___________ of the large cube.

Answer:

The given table is:

Now,

From the given table,

We can observe that

The flat is \(\frac{1}{10}\) of the large cube.

Hence, from the above,

We can conclude that

The flat is \(\frac{1}{10}\) of the large cube.

Look at the long and compare it to the flat.

The long is ___________ of the flat.

Answer:

The given table is:

Now,

From the given table,

We can observe that

The long is \(\frac{1}{10}\) of the flat.

Hence, from the above,

We can conclude that

The long is \(\frac{1}{10}\) of the flat.

Look at the small cube and compare it to the long.

The small cube is ___________ of the long.

Answer:

The given table is:

Now,

From the given table,

We can observe that

The small cube is \(\frac{1}{10}\) of the long.

Hence, from the above,

We can conclude that

The small cube is \(\frac{1}{10}\) of the long.

**Make Connections**

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

3,000 is 10 times as much as 300.

30 is \(\frac{1}{10}\) of 300.

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

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

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

STEP 3. Use the place-value chart to write a number that is of the given number.

Answer:

The given steps are:

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

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

STEP 3. Use the place-value chart to write a number that is of the given number.

Hence, from the above,

We can conclude that

The complete table by using the given steps is:

**Share and Show**

**Complete the sentences.**

Question 1.

500 is 10 times as much as ____________ .

Answer:

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

So,

According to the above definition,

x × 10 = 500

x = \(\frac{500}{10}\)

x = 50

Hence, from the above,

We can conclude that

500 is 10 times as much as 50

Question 2.

20,000 is \(\frac{1}{10}\) of ____________ .

Answer:

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

So,

According to the above definition,

x = 20,000 × \(\frac{1}{10}\)

x = 2,000

Hence, from the above,

We can conclude that

20,000 is \(\frac{1}{10}\) of 2,000

**Use the place-value patterns to complete the table.**

Answer:

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

Hence, from the above,

We can conclude that

The complete table is:

Answer:

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

Hence, from the above,

We can conclude that

The complete table is:

**Complete the sentence with 100 or 1,000**

Question 7.

200 is _______________ times as much as 2.

Answer:

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

So,

According to the above,

2 × a = 200

a = \(\frac{200}{2}\)

a = 100

Hence, from the above,

We can conclude that

200 is 100 times as much as 2.

Question 8.

7,00,000 is ___________ times as much as 700.

Answer:

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

So,

According to the above,

700 × a = 700,000

a = \(\frac{700,000}{700}\)

a = 1,000

Hence, from the above,

We can conclude that

7,00,000 is 1,000 times as much as 700.

Question 9.

4,000 is ___________ times as much as 4.

Answer:

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

So,

According to the above,

4 × a = 4,000

a = \(\frac{4,000}{4}\)

a = 1,000

Hence, from the above,

We can conclude that

4,000 is 1,000 times as much as 4.

Question 10.

600 is _____________ times as much as 6.

Answer:

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

So,

According to the above,

6 × a = 600

a = \(\frac{600}{6}\)

a = 100

Hence, from the above,

We can conclude that

600 is 100 times as much as 6.

**Problem Solving**

Question 11.

Mark and Robyn used base-ten blocks to show that 300 in 100 times as much as 3. Whose model makes sense? Whose model is nonsense? Explain your reasoning.

Answer:

It is given that

Mark and Robyn used base-ten blocks to show that 300 in 100 times as much as 3

Now,

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

Now,

According to the given information,

Hence, from the above,

We can conclude that

Mark’s model is nonsense

Question 12.

**Explain** How you would help Mark understand why he should have used small cubes instead of longs.

Answer:

We know that,

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

So,

We considered “Cubes” as 1 unit

We considered “Longs” as a combination of “10 cubes” i.e., 10 units

Hence, from the above,

We can conclude that

Since Mark’s model has a single digit, he considered using “Cubes”

**Daily Assessment Task**

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

Question 13.

Melinda has 500 pennies in a jar. Brenda has 10 times as many pennies as Melinda does. How many pennies does Brenda have?

A. 50,000

B. 5

C. 5,000

D. 50

Answer:

It is given that

Melinda has 500 pennies in a jar. Brenda has 10 times as many pennies as Melinda does

Now,

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

Now,

Let the number of pennies Brenda has to be: y

Now,

According to the given information,

y = 500 × 10

= 5,000 pennies

Hence, from the above,

We can conclude that

The number of pennies does Brenda have is:

Question 14.

Which statement is true?

A. 8,000 is 10 times as much as 80.

B. 80 is \(\frac{1}{10}\) of 8.

C. 800 is 10 times as much as 80.

D. 8 is \(\frac{1}{10}\) of 800.

Answer:

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

Hence, from the above,

We can conclude that

The statement that is true is:

Question 15.

**Multi-Step** Harry has a collection of comic books. He currently has 1,000 comic books. His friend George has \(\frac{1}{10}\) the number of comic books that Harry does. Mike has \(\frac{1}{10}\) the number of comic books that George has. How many comic books does Mike have?

A. 1000

B. 100

C. 10,000

D. 10

Answer:

It is given that

Harry has a collection of comic books. He currently has 1,000 comic books. His friend George has \(\frac{1}{10}\) the number of comic books that Harry does. Mike has \(\frac{1}{10}\) the number of comic books that George has

Now,

Let y be the number of comic books George has

Let z be the number of comic books Mike has

Now,

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

So,

According to the given information,

The number of books George has = \(\frac{1,000}{10}\)

= 100 comic books

The number of books Mike has = \(\frac{100}{10}\)

= 10 comic books

Hence, from the above,

We can conclude that

The number of books Mike has:

**Texas Test Prep
**

Question 16.

Sam has 1,300 dimes. Anna has \(\frac{1}{10}\) the number of dimes that Sam does. How many dimes does Anna have?

A. 13,000

B. 130

C. 13

D. 3

Answer:

It is given that

Sam has 1,300 dimes. Anna has \(\frac{1}{10}\) the number of dimes that Sam does

Now,

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

So,

According to the given information,

The number of dimes does Anna have = \(\frac{1,300}{10}\)

= 130 dimes

Hence, from the above,

We can conclude that

The number of dimes does Anna have:

### Texas Go Math Grade 4 Lesson 1.1 Homework and Practice Answer Key

Question 1.

Emma and Jamie used base-ten blocks to show that 40 is one-tenth of 400. Whose model makes sense? Whose model is nonsense? Explain your reasoning.

Describe the relationship between the value of a dollar and the value of a dime.

Answer:

It is given that

Emma and Jamie used base-ten blocks to show that 40 is one-tenth of 400

Now,

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

Now,

According to the given information,

Hence, from the above,

We can conclude that

Emma’s model makes sense

Jamie’s model is nonsense

**Problem Solving**

Question 2.

Lisa had 3 dollars. She went to the bank and exchanged the 3 dollars for 30 dimes.

Describe the relationship between the value of a dollar and the value of a dime.

Answer:

It is given that

Lisa had 3 dollars. She went to the bank and exchanged the 3 dollars for 30 dimes.

Now,

We know that,

1 dollar = 10 dimes

So,

3 dollars = 30 dimes

Now,

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

So,

According to the above information,

(The number of dimes) × 10 = (The number of dollars)

So,

The dollar is 10 times as many as 1 dimes

Hence, from the above,

We can conclude that

The relationship between the value of a dollar and the value of a dime is:

1 dollar = 10 dimes

**Lesson Check**

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

Question 3.

Which statement is true?

A. 500 is 10 times as much as 50.

B. 500 is \(\frac{1}{10}\) much as 50.

C. 50,000 is 1,000 times as much as 5.

D. 5 is \(\frac{1}{10}\) as much as 500.

Answer:

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

Hence, from the above,

We can conclude that

The statement that is true is:

Question 4.

7,000 is ten times as much as what number?

A. 70

B. 7

C. 70,000

D. 700

Answer:

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

So,

According to the above statements,

x × 10 = 7,000

x = \(\frac{7,000}{10}\)

x = 700

Hence, from the above,

We can conclude that

7,000 is ten times as much as:

Question 5.

Which statement is true?

A. 90 is \(\frac{1}{10}\) of 100.

B. 900 is 100 times as much as 9.

C. 9,000 is 1,000 times as much as 90.

D. 9 is \(\frac{1}{10}\) of 900.

Answer:

We know that,

If a number x is as many times as much as the same number and the result is represented as y, then the representation of that operation is:

x × a = y

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

Hence, from the above,

We can conclude that

The statement that is true is:

Question 6.

720 is \(\frac{1}{10}\) of what number?

A. 7,200

B. 72

C. 7

D. 72,000

Answer:

We know that,

If a number y is \(\frac{1}{a}\) the same number and the result is represented as x, then the representation of that operation is:

y × \(\frac{1}{a}\) = x

So,

According to the given information,

y ×\(\frac{1}{10}\) = 720

y = 720 × 10

y = 7,200

Hence, from the above,

We can conclude that

720 is \(\frac{1}{10}\) of:

Question 7.

**Multi-Step** The owner of Pattie’s Party Shop ordered 4 cartons of balloons. How many balloons did she order?

1 carton = 10 boxes

1 box = 10 packages

1 packages = 10 balloons

A. 40

B. 400

C. 40,000

D. 4,000

Answer:

It is given that

The owner of Pattie’s Party Shop ordered 4 cartons of balloons

Now,

We know that,

1 carton = 10 boxes

1 box = 10 packages

1 packages = 10 balloons

So,

The number of balloons did Pattie ordered = 4 × 10 boxes

= 4 × 10 × 10 packages

= 4 × 10 × 10 × 10 balloons

= 4 × 1,000

= 4,000 balloons

Hence, from the above,

We can conclude that

The number of balloons did Pattie ordered is:

Question 8.

**Multi-Step** Greg bought 2 boxes of balloons. He used half of them to decorate his yard. He used 40 to decorate his porch. He used the rest inside his house. How many balloons did he use inside?

A. 6

B. 6,000

C. 60

D. 600

Answer:

It is given that

Greg bought 2 boxes of balloons. He used half of them to decorate his yard. He used 40 to decorate his porch. He used the rest inside his house

Now,

We know that,

1 carton = 10 boxes

1 box = 10 packages

1 packages = 10 balloons

So,

The total number of balloons did Greg bought = 2 × 10 packages

= 2 × 10 × 10 balloons

= 200 balloons

So,

The number of balloons Greg used inside = 200 – (\(\frac{200}{2}\) + 40)

= 200 – 140

= 60 balloons

Hence, from the above,

We can conclude that

The number of balloons did Greg used inside is: