Unit 4 Plan - Grade 4

Lesson 1

Decimal Numbers

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What Does It Represent? (1 problem)

The large square represents 1.
1. What fraction does the shaded portion represent?
2. Write the fraction in decimal notation.
The large square represents 1. Shade the diagram to represent 0.7.

Show Solution

1. $\frac{28}{100}$
2. 0.28
Sample response:

Lesson 2

Equivalent Decimals

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Equal or Not Equal? (1 problem)

Select all the statements that are true.
1. $0.2 = 0.20$
2. $5.40 = 5.04$
3. $1.30 = 1.3$
4. $0.07 = 0.70$
5. $2.05 = 2.5$
Which of these numbers is equivalent to 0.9? Explain how you know.
1. 0.09
2. 0.90
3. 9.0
4. 9.09

Show Solution

1. A and C
2. B. 0.90. Sample response: 0.9 is

\frac{9}{10}

, which is equivalent to

\frac{90}{100}

.

\frac{90}{100}

written as a decimal is 0.90.

Lesson 3

Decimals on Number Lines

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More to Compare (1 problem)

Write $<$ , $>$ , or $=$ to make each comparison statement true. Use a number line if it is helpful.

$1.1 \underline{\hspace{0.5in}} 1.10$
$0.9 \underline{\hspace{0.5in}} 0.19$
$0.03 \underline{\hspace{0.5in}} 0.32$
$5.91 \underline{\hspace{0.5in}} 5.01$
$4.60 \underline{\hspace{0.5in}} 4.6$
$3.73 \underline{\hspace{0.5in}} 3.83$

Number line. 11 evenly spaced tick marks with no labels.

Show Solution

$=$
$>$
$<$
$>$
$=$
$<$

Lesson 4

Compare and Order Decimals

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From Least to Greatest (1 problem)

Order the numbers from least to greatest.

5.01
0.05
0.5
5.1
0.1
0.51

Show Solution

0.05
0.1
0.5
0.51
5.01
5.1

Lesson 5

Compare and Order Decimals in Different Notations

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Order Up (1 problem)

Order the numbers from least to greatest.
- 3.2
- $3\frac{2}{100}$
- 2.92
- $2\frac{2}{10}$
- 3.09
Use two numbers from your ordered set and the symbols $>$ , $<$ , or $=$ to write a true comparison statement.

Show Solution

$2\frac{2}{10}$ , 2.92, $3\frac{2}{100}$ , 3.09, 3.2
Sample response: $3.09 > 2.92$ or $2\frac{2}{10} < 3.2$

Section A Check

Section A Checkpoint

Problem 1

The large square represents 1.

What number is represented by the shaded parts?

Write your answer both as a fraction and as a decimal.

Show Solution

\frac{55}{100}

or 0.55

Problem 2

Estimate the location of the following numbers on the number line:

0.43

0.3

0.09

1.2

1.02

number line. 14 evenly spaced tick marks. First tick mark, 0. Eleventh tick mark, 1.

Show Solution

Problem 3

Choose 4 different decimals to complete the comparison statements. Use the number line if it is helpful.

6.52

6.4

6.39

6.53

6.6

________ is greater than ________.
________ is less than ________.

Show Solution

Sample responses:

6.6 is greater than 6.53. 6.53 is greater than 6.52. 6.52 is greater than 6.4,. 6.4 is greater than 6.39.
6.39 is less than 6.4. 6.4 is less than 6.52. 6.52 is less than 6.53. 6.53 is less than 6.6.

Lesson 6

How Much Is 10,000?

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Represent Numbers (1 problem)

How many thousands are in 12,000?
Draw a diagram to represent 15,400.

Show Solution

Twelve thousands
A diagram showing 1 unit of ten-thousand, 5 units of a thousand, and 4 units of a hundred

Lesson 7

Numbers Within 100,000

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Count Ten-thousands (1 problem)

Consider the number 57,000.

How many thousands are in it?
How many ten-thousands are in it?
Write the number in words.

Show Solution

57
5
Fifty-seven thousand

Lesson 8

Beyond 100,000

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Represent 234,000 (1 problem)

Draw a diagram to represent 234,000.
Write 234,000 three different ways.

Show Solution

Sample responses: 2 units representing hundred-thousands, 3 units representing ten-thousands, 4 units representing thousands
Sample responses:
1. $200,000 + 30,000 + 4,000$
2. 2 large squares, 3 long rectangles, and 4 small cubes, the small cube is worth 1,000
3. 23 long rectangles and 4 small cubes, the small cube is worth 1,000

Lesson 9

Same Digit, Different Value

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The Value of Digits (1 problem)

Here are two numbers: 58,487 and 531,690.

Write each number in expanded form.
Use the numbers to make this statement true:

The 5 in _______________ is ten times the value of the 5 in _______________.

Show Solution

$50,000+8,000+400+80+7$ , $500,000+30,000+1,000+600+90$
The 5 in 531,690 is ten times the value of the 5 in 58,487.

Lesson 10

Ten Times As Much

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Same Digit, Different Place (1 problem)

Here are two numbers: 872,000 and 700,208.

1. What is the value of the 2 in each number?
2. Write a multiplication or division equation to show the relationship between these two values.
1. What is the value of the 7 in each number?
2. Write a multiplication or division equation to show the relationship between these two values.

Show Solution

1. In 872,000, the 2 is 2,000 and in 700,208, the 2 is 200.
2. $2,000 \div 10 = 200$ or $200 \times 10 = 2,000$
1. In 872,000, the 7 is 70,000 and in 700,208, the 7 is 700,000.
2. $70,000 \times 10 = 700,000$ or $700,000 \div 10 = 70,000$

Lesson 11

Large Numbers on a Number Line

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Ten Times on a Number Line (1 problem)

Estimate the location of 28,500 on the number line and label it with a point.
Which point—A, B, or C—could represent a number that is 10 times as much as 28,500? Explain your reasoning.

Show Solution

Response shows a point to the left of A, about a third of the way or halfway between 0 and A.
Point B. Sample response: Ten times 28,500 is 285,000, which would be between the tick marks that show 200,000 and 300,000, closer to 300,000. Point A is in the 80,000s and point B is in the 300,000s.

Section B Check

Section B Checkpoint

Problem 1

Write the number 436,089 in expanded form and in word form.

Show Solution

Expanded form: $400,000 + 30,000 + 6,000 + 80 + 9$

Word form: four hundred thirty-six thousand eighty-nine

Problem 2

Select all numbers in which the value of the 7 is 70,000.

Show Solution

B, F

Problem 3

Write a number where the value of the 5 is 10 times the value of the 5 in 152,318.

Show Solution

Sample response: 517,908

Lesson 12

Compare Multi-Digit Numbers

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Two Numbers to Compare (1 problem)

Here are two numbers, each with the same digit missing in different places.

$\large \boxed{1} \ \boxed{7}\ , \boxed{\phantom{0}} \ \boxed{4} \ \boxed{2}$

$\large \boxed{1} \ \boxed{\phantom{0}}\ , \boxed{7} \ \boxed{2} \ \boxed{4}$

If the missing digit in both numbers is 1, which number will be greater: the first or the second?
Name all the digits from 0 to 9 that will make the second number greater. Explain how you know.

Show Solution

The first number. Sample response: The first number will be 17,142 and the second number 11,724. Seventeen thousand is greater than eleven thousand.
8 and 9. Sample response: Using 8 or 9 in the second number makes 18,724 or 19,724, which is greater than a number in the 17,000s. Using 7 makes 17,724, which is still less than 17,742.

Lesson 13

Order Multi-Digit Numbers

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From Least to Greatest (1 problem)

Order the following numbers from least to greatest.

94,942
9,042
279,104
9,420
59,000
500,492
279,099

Show Solution

9,042
9,420
59,000
94,942
279,099
279,104
500,492

Lesson 14

Multiples of 10,000 and 100,000

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Near 627,800 (1 problem)

number line. Scale, 6 hundred thousand to 7 hundred thousand, by 10 thousands.

1. Which two multiples of 10,000 are closest to 627,800?
2. Of the two multiples of 10,000, which one is closer to 627,800?
1. Which two multiples of 100,000 are closest to 627,800?
2. Of the two multiples of 100,000 which one is closer to 627,800?

Show Solution

1. 620,000 and 630,000.
2. 630,000 is the nearest to 627,800.
1. 600,000 and 700,000.
2. 600,000 is the nearest to 627,800.

Lesson 15

The Nearest Multiples of 1,000, 10,000, and 100,000

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The Nearest Multiples (1 problem)

Find each nearest multiple for the number 248,640. Use the number lines if they are helpful.
1. The nearest multiple of 100,000 is ____________________.
2. The nearest multiple of 10,000 is ____________________.
3. The nearest multiple of 1,000 is ____________________.
What is the nearest multiple of 1,000 and multiple of 10,000 for the number 173,500?

Show Solution

1. 200,000
2. 250,000
3. 249,000
Sample responses:
- There are two nearest multiples of 1,000: 173,000 and 174,000. The nearest multiple of 10,000 is 170,000.
- The nearest multiple of 1,000 is 174,000.

Lesson 16

Round Numbers

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Round Three Ways (1 problem)

Round 569,003 to the nearest hundred-thousand, ten-thousand, and thousand. Explain or show your reasoning.

Show Solution

600,000. It’s closer to 600,000 because it’s more than 550,000.
570,000. It’s less than 1,000 away from 570,000.
569,000. It is only 3 away from 569,003.

Lesson 17

Apply Rounding

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Spatial Distancing (1 problem)

Planes are too close when their altitudes are within 1,000 feet of each other when they fly over the same area.

Jada says Planes C and E are too close.
Noah says Planes C and E are a safe-distance apart.

Use rounding to explain how both statements might be correct.

plane	altitude (feet)
A	40,990
B	39,524
C	36,138
D	40,201
E	35,472
F	30,956

Show Solution

Sample response: Jada might have thought about the actual distance between the two planes, which is only about 700 feet apart, or might have rounded to the nearest hundred (C would round to 36,100 and E to 35,500). If Noah rounded to the nearest thousand, Plane C would round to 36,000 and E would round to 35,000, which is 1,000 feet apart.

Section C Check

Section C Checkpoint

Problem 1

Write comparison statements using heights of mountain peaks in Colorado in the table.

mountain	height (feet)
Grays Peak	14,278
Mount Elbert	14,440
Castle Peak	14,265
Pikes Peak	14,115
Mount Ouray	13,971

Choose 2 values to compare.

$\underline{\hspace{1.5in}}<\underline{\hspace{1.5in}}$
Choose 2 different values to compare.

$\underline{\hspace{1.5in}}>\underline{\hspace{1.5in}}$
Which of these mountains is the highest?

Show Solution

Sample response: $14,265<14,278$
Sample response: $14,115>13,971$
Mount Elbert has the greatest height.

Problem 2

Round the number 569,843 to the:

nearest thousand
nearest ten-thousand
nearest hundred-thousand

Show Solution

570,000
570,000
600,000

Lesson 18

Standard Algorithm to Add and Subtract

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Andre's Steps (1 problem)

Andre started tracking his steps. He walked 14,687 steps on Monday and 10,512 steps on Tuesday.

How many steps did he walk in those two days? Explain or show your reasoning.
How many more steps did he walk on Monday than on Tuesday?

Show Solution

25,199 steps. Sample response:
4,175 steps. Sample response:

Lesson 19

Compose and Decompose to Add and Subtract

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Difference and Then Sum (1 problem)

Use the standard algorithm to find the difference.
1. $1,993 - 118$
2. $1,897 - 116$
Find the value of the sum.

Show Solution

1. 1,875
2. 1,781
907,624

Lesson 20

Add and Subtract within 1,000,000

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Subtract (1 problem)

Use the standard algorithm to find the value of the difference.

subtract. one hundred seventy three thousand, two hundred twenty five, minus, one hundred fourteen thousand, three hundred twenty nine.

Show Solution

58,896

Lesson 21

Zeros in the Standard Algorithm

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Finding Differences (1 problem)

Use the standard algorithm to find each difference.

subtract. six thousand, four, minus, eight hundred forty two.

subtract. ninety thousand, nine hundred, minus, five thousand, eight hundred nineteen.

Show Solution

Lesson 22

Solve Problems Involving Large Numbers

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Populations of Three Cities (1 problem)

The populations, in 2017, of the three largest cities in Wisconsin are shown.

city	population
Milwaukee	595,351
Madison	255,214
Green Bay	105,116

Was the total population of the three cities more than one million people? Explain or show your reasoning.
How much over or under one million is the total? Explain or show your reasoning.

Show Solution

No. Sample response: Milwaukee had about 600,000 people. Madison had about 255,000 people. Green Bay had about 105,000 people. The sum of the three estimates is 960,000 people.
44,319 people below one million. Sample response:
- The sum of populations of Milwaukee and Madison is $595,351 + 255,214$ , which is 850,565 people. Adding the population of Green Bay, $850,565 + 105,116$ gives 955,681 people. Subtracting 955,681 people from 1,000,000 people gives 44,319 people.
- The total population of the three cities is 955,681 people. I kept adding numbers to that total until reaching 1,000,000 people. I first added 40,000 people and then 4,000 people, which gives 999,681 people. Adding 319 people more gives 1,000,000 people. Then I added these numbers: $40,000 + 4,000 + 319 = 44,319$ .
- Subtracting the population of Milwaukee from one million, $1,000,000 - 595,351$ gives 404,649 people. Subtracting the population of Madison from 404,649 people gives 149,435 people. Subtracting the population of Green Bay from 149,435 people gives 44,319 people.