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 baseten 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 baseten structure of numbers up to 99 using drawings, numbers, and words.
 Understand that the two digits of a twodigit number represent amounts of tens and ones.
Section C Goals
 Compare 2 twodigit numbers based on the values of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.>
Section D Goals
 Represent twodigit numbers in different ways, using different amounts of tens and ones.
Section A: Units of Ten
Problem 1
Preunit
Practicing Standards: K.CC.A.1
 Mai says the numbers 10, 20, 30.
What is Mai counting by?  What is the next number Mai will say?
Solution
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Problem 2
Preunit
Practicing Standards: K.NBT.A.1
How many are in each picture?
____________
____________
____________
Solution
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Problem 3
Preunit
Practicing Standards: K.NBT.A.1
Which expression shows the number of dots?
\(5 + 1\)
\(10 + 5\)
\(10 + 6\)
Solution
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Problem 4
Preunit
Practicing Standards: K.NBT.A.1
Find the number that makes each equation true.
 \(10 + 7 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
 \(10 + \boxed{\phantom{\frac{aaai}{aaai}}} = 15\)
 \(\boxed{\phantom{\frac{aaai}{aaai}}} + 3 = 13\)
Solution
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Problem 5
How many connecting cubes are in each picture?
Solution
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Problem 6
How many connecting cubes are in the picture?
Circle the picture that shows 10 more connecting cubes.
Cross out the picture that shows 10 fewer connecting cubes.
Solution
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Problem 7

Find the value of each expression.
Explain or show your reasoning.\(50 + 20\)
\(80  50\)

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

How many connecting cubes are there?

How many connecting cubes are there?
 Which collection did you prefer to count? Why?
Solution
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Problem 2

How many connecting cubes are there?
Show your thinking using drawings, numbers, or words. 
How many connecting cubes are there?
Show your thinking using drawings, numbers, or words.  How are the numbers the same? How are they different?
Solution
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Problem 3
Circle 3 representations of 63.
Solution
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Problem 4
Show the number of connecting cubes in as many ways as you can.
Solution
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Problem 5



 \(6 + 10\)
Solution
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Problem 6
Show your thinking using drawings, numbers, or words.
 \(30 + 50 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
 \(61 + 10 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
 \(14 + 30 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
Solution
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Problem 7
Find the value of each expression.
 \(63 + 10\)
 \(63  10\)
 \(19 + 10\)
 \(19  10\)
 What patterns do you notice?
Solution
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Problem 8
Exploration
Tyler drew this representation of 57.
What do you think of Tyler's representation?
Solution
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Problem 9
Exploration
How many connecting cubes could there be in the image?
Solution
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Section C: Compare Numbers to 99
Problem 1
 Which number is greater, 54 or 36?
Show your thinking using drawings, numbers, or words.  Which number is less, 25 or 52?
Show your thinking using drawings, numbers, or words.
Solution
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Problem 2
Show your thinking using drawings, numbers, or words.
 \(35 < 29\)
 \(72 = 27\)
 \(81 > 77\)
Solution
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Problem 3
 \(47 \underline{\hspace{0.9cm}} 43\)
 \(73 \underline{\hspace{0.9cm}} 63\)
 \(85 \underline{\hspace{0.9cm}} 85\)
 \(9 \underline{\hspace{0.9cm}} 96\)
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.
Solution
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Problem 6
Exploration
Andre correctly solved this problem, but his brother spilled water on some numbers.
greater than
but less than
.
Andre 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

Circle 2 pictures that show 46.

Show a different way to make 46.
Solution
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Problem 2
Solution
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Problem 3
Fill in each blank with \(<\), \(>\), or \(=\) to make the equation true.
 \(70 + 12 \,\underline{\hspace{1cm}}\, 79\)
 \(30 + 15 \,\underline{\hspace{1cm}}\, 20 + 25\)
 \(40 + 3 \, \underline{\hspace{1cm}}\, 35\)
Solution
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Problem 4
Exploration
Andre said he is thinking of a 2digit 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
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.
 I have _____ tens and _____ ones. What number am I?
 I have _____ tens and _____ ones. What number am I?
 I have _____ tens and 18 ones. What number am I?
 I have _____ tens and 25 ones. What number am I?
Solution
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