1.4 Numbers to 99

Unit Goals

  • Students develop an understanding of place value for numbers up to 99.

Section A Goals

  • Add and subtract multiples of 10.
  • Represent the base-ten structure of multiples of 10 up to 90 using towers of 10, drawings, numbers, or words.

Section B Goals

  • Add and subtract multiples of 10.
  • Represent the base-ten structure of numbers up to 99 using drawings, numbers, and words.
  • Understand that the two digits of a two-digit number represent amounts of tens and ones.

Section C Goals

  • Compare 2 two-digit numbers based on the values of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Section D Goals

  • Represent two-digit numbers in different ways, using different amounts of tens and ones.
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Section A: Units of Ten

Problem 1

Pre-unit

Practicing Standards:  K.CC.A.1

  1. Mai says the numbers 10, 20, 30.
    What is Mai counting by?

  2. What is the next number Mai will say?

Solution

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Problem 2

Pre-unit

Practicing Standards:  K.NBT.A.1

How many are in each picture?

a.Connecting cubes. 1 tower of 10 cubes. 7 single cubes.
b.Ten frame, full. Below, 5 dots.
c.Ten frame, full. Below, 9 dots.

 ____________

 ____________

 ____________

 

Solution

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Problem 3

Pre-unit

Practicing Standards:  K.NBT.A.1

Ten frame, full. Below, 6 dots.

Which expression shows the number of dots?

A:

\(5 + 1\)

B:

\(10 + 5\)

C:

\(10 + 6\)

Solution

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Problem 4

Pre-unit

Practicing Standards:  K.NBT.A.1

Find the number that makes each equation true.

  1. \(10 + 7 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
  2. \(10 + \boxed{\phantom{\frac{aaai}{aaai}}} = 15\)
  3. \(\boxed{\phantom{\frac{aaai}{aaai}}} + 3 = 13\)

Solution

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Problem 5

How many connecting cubes are in each picture?

a.Connecting cubes. 1 tower of 10 cubes.

b.Connecting cubes. 3 towers of 10 cubes.

c.Connecting cubes. 7 towers of 10 cubes.

Solution

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Problem 6

How many connecting cubes are in the picture?

Connecting cubes. 4 towers of 10 cubes.

Circle the picture that shows 10 more connecting cubes.
Cross out the picture that shows 10 fewer connecting cubes.

AConnecting cubes. 3 towers of 10 cubes.
BConnecting cubes. 4 towers of 10 cubes.
CConnecting cubes. 5 towers of 10 cubes.

Solution

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Problem 7

  1. Find the value of each expression.
    Explain or show your reasoning.

    \(50 + 20\)

    \(80 - 50\)

  2. There are 7 towers of ten on the table.
    Han takes 2 towers away.
    How many connecting cubes are on the table now?
    Explain or show your reasoning.

Solution

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Problem 8

Exploration

You can use towers of 10 cubes to help you with these questions.

  1. Noah has 70 cubes in towers of 10.
    He gave some towers of 10 to Clare.
    Then he gave some towers of 10 to Andre.
    Now Noah has no cubes left.
    What is one way Noah could have done this?
    Show your thinking using drawings, numbers, or words.
    Write equations to represent the problem.

  2. What is another way Noah could have done this?
    Show your thinking using drawings, numbers, or words.
    Write equations to represent the problem.

  3. Diego has 10 cubes in a tower.
    Elena gave him some more towers of 10.
    Then Mai gave him some more towers of 10.
    Now Diego has 60 cubes in towers of 10.
    What is one way this could have happened?
    Show your thinking using drawings, numbers, or words.
    Write equations to represent the problem.

  4. What is another way this could have happened?
    Show your thinking using drawings, numbers, or words.
    Write equations to represent the problem.

Solution

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Section B: Tens and Ones

Problem 1

  1. How many connecting cubes are there?

    Connecting cubes.

  2. How many connecting cubes are there?

    Connecting cubes. 2 towers of 10 cubes. 6 single cubes.

  3. Which collection did you prefer to count? Why?

Solution

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Problem 2

  1. How many connecting cubes are there?
    Show your thinking using drawings, numbers, or words.

    Connecting cubes. 4 towers of 10 cubes. 8 single cubes.

  2. How many connecting cubes are there?
    Show your thinking using drawings, numbers, or words.

    Connecting cubes. 5 towers of 10 cubes. 8 single cubes.

  3. How are the numbers the same? How are they different?

Solution

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Problem 3

Circle 3 representations of 63.

A:  
Base ten diagram. 6 tens. 3 ones.
B:  
Base ten diagram. 3 tens. 6 ones.
C: 6 tens and 3 tens
D: 6 tens and 3 ones
E: \(3 + 60\)

Solution

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Problem 4

Show the number of connecting cubes in as many ways as you can.

Connecting cubes. 3 towers of 10 cubes. 7 single cubes.

Solution

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Problem 5

Write the number that matches each representation.
  1.  

    Connecting cubes. 2 towers of 10 cubes. 5 single cubes.

  2.  

    Connecting cubes. 5 towers of 10 cubes. 2 single cubes.


  3. Base-ten diagram. 6 tens. 1 one.
  4. \(6 + 10\)

Solution

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Problem 6

Find the number that makes each equation true.
Show your thinking using drawings, numbers, or words.
  1. \(30 + 50 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
  2. \(61 + 10 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
  3. \(14 + 30 = \boxed{\phantom{\frac{aaai}{aaai}}}\)

Solution

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Problem 7

Find the value of each expression.

  1. \(63 + 10\)

  2. \(63 - 10\)

  3. \(19 + 10\)

  4. \(19 - 10\)

  5. What patterns do you notice?

Solution

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Problem 8

Exploration

Tyler drew this representation of 57.

Base ten diagram. Rectangles, 7, each labeled with 1. Squares, 5, each labeled with 10.

What do you think of Tyler's representation?

Solution

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Problem 9

Exploration

Connecting cubes. 4 towers of 10 cubes. More cubes behind a piece of paper,  3 cubes visible,  not as tall as a full tower.

How many connecting cubes could there be in the image?

Solution

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Section C: Compare Numbers to 99

Problem 1

  1. Which number is greater, 54 or 36?
    Show your thinking using drawings, numbers, or words.

  2. Which number is less, 25 or 52?
    Show your thinking using drawings, numbers, or words.

Solution

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Problem 2

Decide if each statement is true or false.
Show your thinking using drawings, numbers, or words.
  1. \(35 < 29\)

  2. \(72 = 27\)

  3. \(81 > 77\)

Solution

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Problem 3

Write <, >, or = in each blank to make the statement true.

  1. \(47 \underline{\hspace{0.9cm}} 43\)
  2. \(73 \underline{\hspace{0.9cm}} 63\)
  3. \(85 \underline{\hspace{0.9cm}} 85\)
  4. \(9 \underline{\hspace{0.9cm}} 96\)

Solution

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Problem 4

Order the numbers from least to greatest:

  • 73
  • 16
  • 84
  • 9
  • 87
  • 75
  • 33

Solution

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Problem 5

Exploration

Noah says that there are more connecting cubes in B because it has more tens than A. Do you agree with Noah?
Show your thinking using drawings, numbers, or words.

AConnecting cubes. 6 towers of 10 cubes. 15 single cubes.
BConnecting cubes. 7 towers of 10  cubes. 3 single cubes.

Solution

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Problem 6

Exploration

Andre correctly solved this problem, but his brother spilled water on some numbers.

Circle the numbers that are


greater than

A splash of water on top of the numbers in the problem.


but less than

A splash of water on top of the numbers in the problem.


.


Andre circled

List of numbers. 89, circled. 82, circled. 77, circled. 24. 19. 68, circled.

What numbers might be hidden from view?
Show your thinking using drawings, numbers, or words.

  

Solution

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Section D: Different Ways to Make a Number

Problem 1

  1. Circle 2 pictures that show 46.

    Base ten diagram. 4 tens. 6 ones.
    Base ten diagram. 5 tens. 6 ones.
    Base ten diagram. 3 tens. 16 ones.
    Base ten diagram. 2 tens. 16 ones.

  2. Show a different way to make 46.

Solution

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Problem 2

Show 4 different ways you can make 35 using tens and ones.

Solution

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Problem 3

Fill in each blank with \(<\), \(>\), or \(=\) to make the equation true.

  1. \(70 + 12 \,\underline{\hspace{1cm}}\, 79\)

  2. \(30 + 15 \,\underline{\hspace{1cm}}\, 20 + 25\)

  3. \(40 + 3 \, \underline{\hspace{1cm}}\, 35\)

Solution

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Problem 4

Exploration

Andre said he is thinking of a 2-digit number.
He makes the number from tens and ones in 8 different ways.
In one way, there is 1 more ten than there are ones.
What is Andre's number?
Show your thinking using drawings, numbers, or words.

Solution

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Problem 5

Exploration

Fill in the blanks so that all three descriptions show the same number.

  • 7 tens + \(\underline{\hspace{1cm}}\) ones

  • 2 tens + \(\underline{\hspace{1cm}}\) ones

  • \(\underline{\hspace{1cm}}\) tens + 35 ones

Is there more than one way you can fill in the blanks?
Show your thinking using drawings, numbers, or words.

Solution

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Problem 6

Exploration

Incomplete Number Riddles

Choose digits from the list to put in the blanks in the riddles.

3

6

5

4

2

1

Then solve the riddles.
You can use cubes or other math tools to help you.

  1. I have _____ tens and _____ ones. What number am I?

  2. I have _____ tens and _____ ones. What number am I?

  3. I have _____ tens and 18 ones. What number am I?

  4. I have _____ tens and 25 ones. What number am I?

Solution

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