4.4 From Hundredths to Hundred-thousands
Unit Goals
- Students read, write and compare numbers in decimal notation. They also extend place value understanding for multi-digit whole numbers and add and subtract within 1,000,000.
Section A Goals
- Represent, compare, and order decimals to the hundredths by reasoning about their size.
- Write tenths and hundredths in decimal notation.
Section B Goals
- Read, represent, and describe the relative magnitude of multi-digit whole numbers up to 1 million.
- Recognize that in a multi-digit whole number, the value of a digit in one place represents ten times what it represents in the place to its right.
Section C Goals
- Compare, order, and round multi-digit whole numbers within 1,000,000.
Section D Goals
- Add and subtract multi-digit whole numbers using the standard algorithm.
Section A: Decimals with Tenths and Hundredths
Problem 1
Pre-unit
Practicing Standards: 3.NBT.A.1
Round each number to the nearest 10 and to the nearest 100.
-
63
-
350
-
485
Solution
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Problem 2
Pre-unit
Practicing Standards: 3.NBT.A.1
- Round \(P\) to the nearest multiple of 100. Explain your reasoning.
- Can you tell what \(P\) is if rounded to the nearest multiple of 10? Explain your reasoning.
Solution
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Problem 3
Pre-unit
Practicing Standards: 3.NBT.A.2
Find the value of each expression. Show your reasoning.
- \(523 + 278\)
- \(418 - 235\)
Solution
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Problem 4
Pre-unit
Practicing Standards: 2.NBT.A.1
Here are three numbers: 265, 652, and 526. For each question, explain your reasoning.
- Does the digit 6 have a greater value in 265 or 652?
- Does the digit 5 have a greater value in 265 or 652?
- In which number does the digit 2 have the greatest value? In which one does it have the least value?
Solution
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Problem 5
Each large square represents 1.
-
Write a fraction and a decimal that represent the shaded part of the large square.
Fraction: __________Decimal: __________
-
Shade a part of each square to represent each given number.
Fraction: \(\frac{13}{100}\)Decimal: __________
Fraction: __________Decimal: 0.44
Solution
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Problem 6
Select all the numbers equivalent to \(\frac{2}{10}\).
Solution
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Problem 7
- Locate and label 0.6 and 0.35 on the number line.
- Compare 0.6 and 0.35 using < or >.
Solution
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Problem 8
Order the numbers from least to greatest:
5.90
9.05
5.95
0.59
5.59
Solution
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Problem 9
Order the numbers from least to greatest:
\(\frac{13}{10}\)
1.25
1.46
\(\frac{7}{5}\)
\(\frac{155}{100}\)
Solution
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Problem 10
Exploration
The table shows the distances, in miles, some students walked during the school week.
Order the numbers from least to greatest.
student | distance (miles) |
---|---|
Han | \(5\frac{3}{4}\) |
Tyler | \(5\frac{7}{8}\) |
Mai | 5.95 |
Elena | \(5\frac{8}{10}\) |
Andre | 5.79 |
Solution
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Problem 11
Exploration
In a recent lesson, you learned about the lengths of the jumps made by Carl Lewis and other athletes.
Create and label a number line to show the distances of all ten jumps made by the athletes.
Solution
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Section B: Place-value Relationships through 1,000,000
Problem 1
- Write the name of the number 8,500 in words.
- How many hundreds are there in 8,500? Explain how you know.
Solution
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Problem 2
- Count by 10,000 starting at 6,500 and stopping at 66,500. Record each number:
- Pick two numbers from your list and write their names in words.
Solution
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Problem 3
- If each small square represents 1, what number does the picture represent?
- If each small square represents 10, what number does the picture represent?
Solution
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Problem 4
- Write the names of the numbers 702,150, and 73,026 in words.
- How is the value of the 7 in 702,150 related to the value of the 7 in 73,026?
Solution
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Problem 5
- What is the value of the 6 in 65,247?
- What is the value of the 6 in 16,803?
- Write multiplication and division equations to represent the relationship between the value of the 6 in 65,247 and the value of the 6 in 16,803.
Solution
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Problem 6
-
Locate and label each number on the number line:
- 100,000
- 10,000
-
1,000
- Which numbers were easiest to locate? Which were most difficult? Why?
Solution
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Problem 7
Exploration
For each question, use only the digits 1, 0, 5, 9, and 3. You may not use a digit more than once and you do not need to use all the digits.
- Can you make three numbers greater than 3,000 but less than 3,500?
- Can you make three numbers greater than 9,000 but less than 10,000?
- Which numbers can you make that are greater than 39,500 but less than 40,000?
Solution
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Problem 8
Exploration
Estimate the value of the number labeled A on the number line. Explain your reasoning.
Solution
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Section C: Compare, Order, and Round
Problem 1
Jada writes the same digit in the two blanks to make the statement true. Which digits could she write?
\(\large \boxed{6} \ \boxed{\phantom{8}} \ , \ \boxed{4} \ \boxed{3} \ \boxed{2} < \boxed{6} \ \boxed{5} \ ,\!\boxed{\phantom{8}} \ \boxed{9} \ \boxed{8}\)
Solution
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Problem 2
-
Order these numbers from least to greatest:
-
98,107
-
102,356
-
752,031
-
88,207
-
99,653
-
- How did you pick the smallest number? Explain your reasoning.
Solution
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Problem 3
-
Which multiple of 10,000 is closest to 132,256?
-
Which multiple of 100,000 is closest to 132,256?
- Which multiple of 100,000 is closest to the number labeled A?
Solution
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Problem 4
For the number 583,642:
-
What is the nearest multiple of 100,000?
-
What is the nearest multiple of 10,000?
-
What is the nearest multiple of 1,000?
-
What is the nearest multiple of 100?
-
What is the nearest multiple of 10?
Solution
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Problem 5
-
Describe the numbers that are 460,000 when rounded to the nearest 10,000.
- Where are these numbers located on the number line?
Solution
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Problem 6
When rounded to the nearest 1,000, Airplane X is flying at 30,000 feet, Airplane Y at 31,000 feet, and Airplane Z at 32,000 feet.
- Could Airplanes X and Y be within 1,000 feet of each other? If you think so, give some examples. If you don't think so, explain why not.
- Explain why Airplanes X and Z could not be within 1,000 feet of each other. Use a number line if you find it helpful.
Solution
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Problem 7
Exploration
Rounded to the nearest 10 pounds, one bag of sand weighs 50 pounds.
Jada wants at least 1,000 pounds of sand for a sandbox. How many bags of sand does Jada need to buy to be sure that she has enough sand?
Solution
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Problem 8
Exploration
You will need a set of digit cards 0–9 for this exploration.
Shuffle your cards and stack them face down. Turn over 6 digit cards.
Can you put the 6 digits in the blanks so that all three statements are true?
- \(\large \boxed{4} \ , \boxed{\phantom{8}} \ \boxed{2} \ \boxed{3} > \boxed{\phantom{8}} \ , \boxed{9} \ \boxed{7} \ \boxed{8}\)
- \(\large \boxed{\phantom{8}} \ \boxed{2} \ , \boxed{4} \ \boxed{0} \ \boxed{3} > \boxed{4} \ \boxed{2} \ , \boxed{\phantom{8}} \ \boxed{0} \ \boxed{1}\)
- \(\large \boxed{4} \ \boxed 3 \ \boxed{\phantom{8}} \ , \boxed{2} \ \boxed{5} \ \boxed{7} > \boxed{4} \ \boxed{\phantom{8}} \ \boxed{5} \ , \boxed{{9}} \ \boxed{3} \ \boxed{7}\)
Solution
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Problem 9
Exploration
To answer these riddles, think about rounding to the nearest 10, 100, 1,000, or 10,000. Use a number line if it is helpful.
- I can be rounded to 100 or to 140. What number could I be?
- I can be rounded to 7,500 or to 8,000. What number could I be?
- I can be rounded to 60,000 or to 57,000. What number could I be?
Solution
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Section D: Add and Subtract
Problem 1
Clare took 11,243 steps on Saturday and 12,485 steps on Sunday.
- How many steps did Clare take altogether on Saturday and Sunday?
- How many more steps did Clare take on Sunday than on Saturday?
Solution
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Problem 2
-
Find the value of the sum. Explain your calculations.
-
Find the value of the difference. Explain your calculations.
Solution
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Problem 3
Find the value of each sum and difference using the standard algorithm.
Solution
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Problem 4
Here is how Han found \(300,\!526 - 4,\!472\)
- How can you tell by estimating that Han has made an error?
- What error did Han make?
- Find the value of \(300,\!526 - 4,\!472\).
Solution
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Problem 5
In 2018 the population of Boston is estimated as 694,583 and the population of Seattle is estimated as 744,995.
- Is the population difference between Boston and Seattle more or less than 100,000? Explain how you know.
- Is the population difference more or less than 50,000? Explain how you know.
- Find the difference in the populations of the two cities.
Solution
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Problem 6
Exploration
Han says he has a method to find the value of \(1,\!000,\!000 - 267,\!923\) without any carrying: “I just write 1,000,000 as \(999,\!999 + 1\).”
- How might rewriting 1,000,000, as Han suggested, help with finding the difference of \(1,\!000,\!000 - 267,\!923\)?
-
Try Han's method to find \(1,\!000,\!000 - 267,\!923\).
Solution
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Problem 7
Exploration
Use the information to determine when the airplane, telephone, printing press, and automobile were first invented.
- The airplane was invented in 1903.
- The printing press was invented 453 years before the most recent invention.
- The automobile was invented 15 years before 1900.
- It was 426 years after the invention of the printing press that the telephone was invented.
- The automobile and telephone were invented the closest together in time with only 9 years between them.
Solution
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