Lesson
1
Name
Operations and Algebraic Thinking
Use Three Bear Family Counters and a Bucket Balance to model each
equation. Find the value of the counter shown in the equation.
1.
= _____________
Papa
2.
= _______________
Mama
Using Three Bear Family Counters and a Bucket Balance, model the
equation. Sketch the model. Find the missing value of the counter in
the equation.
3.
=
___________________ =
4.
=
= ________________
Find the missing value of the counter in each equation.
5.
1
+1
=5
10
Hands-On Standards, Common Core Edition
2
=2
+2
= ______________
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= ______________
6.
Name
Challenge! If you use a balance to solve Problem 6, how
would you substitute for the Mama and Papa Bears and solve the
problem.
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Hands-On Standards, Common Core Edition
11
Lesson
2
Operations and Algebraic Thinking
Name
Use Cuisenaire Rods to build each number and factor pairs shown.
Complete the trains. Write each multiplication sentence.
1.
12
2 × _______ = 12
3 × _______ = 12
4 × _______ = 12
6 × _______ = 12
2.
18
9 × ____ = 18
____ × ____ = 18
____ × ____ = 18
____ × ____ = 18
Build each number and its factor pairs using Cuisenaire Rods.
Sketch your models. Write each multiplication sentence.
3. 20
4. 16
Find factor pairs for each number. Write each multiplication sentence.
5. 14
6. 25
7. 21
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Hands-On Standards, Common Core Edition
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Name
Challenge! Why does Problem 4 have an odd number of factor
pairs? Are there other problems on the previous page that have
an odd number of factor pairs? Explain.
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Hands-On Standards, Common Core Edition
15
Lesson
3
Name
Operations and Algebraic Thinking
Use Color Tiles to model each number. Write the number.
Is the number prime or composite?
2.
1.
_______________
3.
_______________
_______________
Using Color Tiles, model each number to determine if the
number is prime or composite. Sketch the model.
4. 14
_______________
5.
6. 25
5
_______________
_______________
List all the factors of each number.
7. 16
_________________________
9.
45
11. 27
_________________________
18
Hands-On Standards, Common Core Edition
_________________________
10. 28
_________________________
12. 39
_________________________
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_________________________
8. 30
Name
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Hands-On Standards, Common Core Edition
19
Lesson
4
Operations and Algebraic Thinking
Name
Use Color Tiles. Build the array. Answer the questions.
1.
Is 18 a multiple of 6? ________________________
Why or why not? ____________________________
______________________________________________
2.
Is 21 a multiple of 5? ____________________________
Why or why not? ________________________________
___________________________________________________
Use Color Tiles. Make as many arrays as possible for the number.
Draw your arrays.
3.
25
4.
16
5.
10
6.
7
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Hands-On Standards, Common Core Edition
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Name
Challenge! A class of 72 students is going on a field trip. There
are vans for boys and vans for girls. The boys’ vans can each take
7 students, and the girls’ vans can each take 5 students. One
group has 30 students, and the other has 42. Each van will be full.
Using what you know about multiples, find which group is the
boys and which is the girls. Then tell how many vans each group
will need. Explain how you know.
How many boys:
How many boys’ vans:
How many girls:
How many girls’ vans:
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Hands-On Standards, Common Core Edition
23
Lesson
5
Operations and Algebraic Thinking
Name
Use Attribute Blocks to model each pattern. Describe the
repeating part. How many times does it repeat?
1.
________________________________________________________
2.
________________________________________________________
Using Attribute Blocks, sketch a pattern. The repeating part is
given. Repeat it 3 times. How many of each block is used in all?
3.
________________________________________________________
Make a pattern with Attribute Blocks that has the repeating
part given. How many of each block is used?
_________________
_________________
_________________
_________________
_________________
_________________
Hands-On Standards, Common Core Edition
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6.
5.
4.
Name
Challenge! If you repeat the pattern in Question 1 four times,
how many times do you need to repeat the pattern in Question
2 so that both extended patterns will have the same number of
shapes? Explain. Include a picture with your explanation.
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Hands-On Standards, Common Core Edition
27
Lesson
6
Name
Operations and Algebraic Thinking
Use Pattern Blocks to model the pattern. Write the rule for
the pattern. What are the next three steps in the pattern?
1.
Rule ________________________________
Step 5 ______________________________
Step 6 ______________________________
Step 7 ______________________________
1
2
4
3
5
Using Pattern Blocks, model the pattern. Write the rule for
the pattern. Sketch the extended pattern. How many shapes
are in Steps 7–9?
2.
Rule _________________
Step 7 _______________
1
2
3
4
5
6
7
Step 8 _______________
Step 9 _______________
Write the rule for each pattern. Describe the next three steps.
3. 10, 12, 14, 16,
5. 8, 7, 6, 5,
Rule ____________
Rule ____________
Rule ____________
Steps 5–7 ________
Steps 5–7 ________
Steps 5–7 ________
7. 20, 17, 14, 11,
8. 4, 8, 12, 16,
Rule ____________
Rule ____________
Rule ____________
Steps 5–7 ________
Steps 5–7 ________
Steps 5–7 ________
Hands-On Standards, Common Core Edition
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6. 3, 8, 13, 18,
30
4. 2, 10, 18, 26,
Name
Challenge! Write the first 10 steps of a pattern that begins with
4 and each step increases by 4. Describe the pattern in terms of
multiples. Draw a picture to help.
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Hands-On Standards, Common Core Edition
31
Lesson
7
Operations and Algebraic Thinking
Name
Use Centimeter Cubes to model each table. Find the pattern
in the table. Use the pattern to find the missing numbers.
1.
Input
2.
Output
Input
Output
Missing Output ______________
Missing Input
Missing Input
Missing Output ______________
______________
______________
Using Centimeter Cubes, make a table that models each rule.
Sketch the models. Then write the output numbers in each row.
3. Input + 5 = Output
4. Input × 3 = Output
Input
Input
Output
Output
2
4
Find the output values for each set of input values.
5. Input + 4 = Output
Input
2
3
4
3
5
7
9
Output
6. Input × 10 = Output
Input
Output
34
Hands-On Standards, Common Core Edition
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1
Name
Challenge!
Write the output rules for Problems 1 and 2.
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Hands-On Standards, Common Core Edition
35