Algebra Problem Solving with the
new Common Core Standards
Join Bill as he uses the Common Core Standards and
builds excitement, enthusiasm, and problem-solving
skills with FREE easily customized activities.
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An Online Resource Manual for Math Teachers
Incorporating the Common Core Standards
1
Pride
Power
Passion
2
3
4
Standards for Mathematical Practices
Describe habits of mind of a mathematically expert student
1. Make sense of problems and persevere in solving them.
5
Algebra Problem Solving with the new Common Core Standards
Standards for Mathematical Practices
Describe habits of mind of a mathematically expert student
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
6
Algebra Problem Solving with the new Common Core Standards
Standards for Mathematical Practices
Describe habits of mind of a mathematically expert student
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
7
Algebra Problem Solving with the new Common Core Standards
Standards for Mathematical Practices
Describe habits of mind of a mathematically expert student
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
8
Algebra Problem Solving with the new Common Core Standards
Standards for Mathematical Practices
Describe habits of mind of a mathematically expert student
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
9
Algebra Problem Solving with the new Common Core Standards
Standards for Mathematical Practices
Describe habits of mind of a mathematically expert student
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
10
Algebra Problem Solving with the new Common Core Standards
Standards for Mathematical Practices
Describe habits of mind of a mathematically expert student
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
11
Algebra Problem Solving with the new Common Core Standards
Standards for Mathematical Practices
Describe habits of mind of a mathematically expert student
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
12
Algebra Problem Solving with the new Common Core Standards
Design and Organization
Balance of concepts and skills
13
Algebra Problem Solving with the new Common Core Standards
Design and Organization
Balance of concepts and skills
Focal points at each grade level
14
Algebra Problem Solving with the new Common Core Standards
Design and Organization
Balance of concepts and skills
Focal points at each grade level
Graded ramp up to Algebra in Grade 8
15
Algebra Problem Solving with the new Common Core Standards
Design and Organization
Balance of concepts and skills
Focal points at each grade level
Graded ramp up to Algebra in Grade 8
Apply and extend previous understandings of . . .
16
Algebra Problem Solving with the new Common Core Standards
Design and Organization
Balance of concepts and skills
Focal points at each grade level
Graded ramp up to Algebra in Grade 8
Apply and extend previous understandings of . . .
Focus on linear equations and functions in Grade 8
17
Algebra Problem Solving with the new Common Core Standards
Design and Organization
Balance of concepts and skills
Focal points at each grade level
Graded ramp up to Algebra in Grade 8
Apply and extend previous understandings of . . .
Focus on linear equations and functions in Grade 8
Organized into domains that progress over several grades
18
Algebra Problem Solving with the new Common Core Standards
Standards from Operations, Algebraic Thinking,
Expressions, Functions, and Equations
• Sample standards taken from
• Several grade levels with
• Supporting activities that can be
• Easily modified
19
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Menu Math
Reason about and solve one-variable equations and
inequalities.
Write, read, and evaluate expressions in which letters
stand for numbers.
Menu Math does the trick !
20
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Menu Math
Hamburger
Cheeseburger
Fries
Sodas:
Small
Medium
Large
$1.85
$2.15
$1.05
Extra Large
$2.05
$0.95
$1.25
$1.55
21
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Menu Math
Hamburger
Cheeseburger
Fries
Sodas:
Small
Medium
Large
$1.85
$2.15
$1.05
Extra Large
$2.05
1. h + f =
$0.95
$1.25
$1.55
22
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Menu Math
Hamburger
Cheeseburger
Fries
Sodas:
Small
Medium
Large
$1.85
$2.15
$1.05
Extra Large
$2.05
1. h + f =
2. c + f + s =
$0.95
$1.25
$1.55
23
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Menu Math
Hamburger
Cheeseburger
Fries
Sodas:
Small
Medium
Large
$1.85
$2.15
$1.05
Extra Large
$2.05
1. h + f =
2. c + f + s =
3. 7f =
$0.95
$1.25
$1.55
24
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Menu Math
Hamburger
Cheeseburger
Fries
Sodas:
Small
Medium
Large
$1.85
$2.15
$1.05
1. h + f =
$0.95
$1.25
$1.55
4. 3h + c + f + 3x =
Extra Large
$2.05
2. c + f + s =
3. 7f =
25
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Menu Math
Hamburger
Cheeseburger
Fries
Sodas:
Small
Medium
Large
$1.85
$2.15
$1.05
1. h + f =
$0.95
$1.25
$1.55
4. 3h + c + f + 3x =
Extra Large
$2.05
2. c + f + s =
3. 7f =
5. 4c + 3f + s + m + l =
26
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Menu Math
Hamburger
Cheeseburger
Fries
Sodas:
Small
Medium
Large
$1.85
$2.15
$1.05
1. h + f =
$0.95
$1.25
$1.55
4. 3h + c + f + 3x =
Extra Large
$2.05
2. c + f + s =
3. 7f =
5. 4c + 3f + s + m + l =
6. 3c + 3d = $11.10
What does d = ?
27
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Menu Math
Hamburger
Cheeseburger
Fries
Sodas:
Small
Medium
Large
$1.85
$2.15
$1.05
Mathematical Properties
A.
3(h + f)
$0.95
$1.25
$1.55
B.
3h + f
C.
3h + 3f
Extra Large
$2.05
28
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Menu Math
Hamburger
Cheeseburger
Fries
Sodas:
Small
Medium
Large
$1.85
$2.15
$1.05
Extra Large
$2.05
$0.95
$1.25
$1.55
Variations on a Theme
A. Donut Shop
B. Board Shop
C. Music Store
D. Pizza Parlor
29
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Menu Math
Hamburger
Cheeseburger
Fries
Sodas:
Small
Medium
Large
$1.85
$2.15
$1.05
Extra Large
$2.05
$0.95
$1.25
$1.55
Extensions of a Theme
A. Tax
B. Shipping
C. Customer Contracts
D. Delivery
30
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Hundreds Magic
Generate and analyze patterns.
Analyze patterns and relationships.
Write and interpret numerical expressions.
Hundreds Magic takes the cake !
31
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Hundreds Magic
32
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Hundreds Magic
Arithmetic
Patterning
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Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Hundreds Magic
Algebra
Generalization
n-1
n
n
n+1
n+1
n+10 n+11
34
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Hundreds Magic
Algebra Reasoning
using Geometry
35
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Backwards Math
Use the four operations with whole numbers to solve
problems.
Write and evaluate numerical expressions involving wholenumber exponents.
Backwards Math can do it all !
36
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Backwards Math
Here are the answers to one hundred math problems.
Use four 4’s to create problems that will give these
answers.
Remember to use the correct order of operations to solve
your problems:
Parentheses, Exponents,
Multiply or Divide,
Add or Subtract.
37
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Backwards Math
Here are the answers to one hundred math problems.
Use four 4’s to create problems that will give these
answers.
Remember to use the correct order of operations to solve
your problems:
Parentheses, Exponents,
1=
Multiply or Divide,
Add or Subtract.
38
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Backwards Math
Here are the answers to one hundred math problems.
Use four 4’s to create problems that will give these
answers.
Remember to use the correct order of operations to solve
your problems:
Parentheses, Exponents,
1=
Multiply or Divide,
2=
Add or Subtract.
39
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Backwards Math
Here are the answers to one hundred math problems.
Use four 4’s to create problems that will give these
answers.
Remember to use the correct order of operations to solve
your problems:
Parentheses, Exponents,
1=
Multiply or Divide,
2=
Add or Subtract.
3=
40
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Backwards Math
Here are the answers to one hundred math problems.
Use four 4’s to create problems that will give these
answers.
Remember to use the correct order of operations to solve
your problems:
Parentheses, Exponents,
1=
Multiply or Divide,
2=
Add or Subtract.
4=
3=
41
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Backwards Math
Here are the answers to one hundred math problems.
Use four 4’s to create problems that will give these
answers.
Remember to use the correct order of operations to solve
your problems:
Parentheses, Exponents,
1=
Multiply or Divide,
4=
2=
Add or Subtract.
5=
3=
42
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Backwards Math
Here are the answers to one hundred math problems.
Use four 4’s to create problems that will give these
answers.
Remember to use the correct order of operations to solve
your problems:
Parentheses, Exponents,
1=
Multiply or Divide,
4=
2=
Add or Subtract.
5=
3=
6=
43
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Backwards Math
Extension ideas for the four 4’s.
Instead of using four 4’s to make expressions, use four 5’s.
44
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Backwards Math
Extension ideas for the four 4’s.
Or use four 6’s,
Or use four 2’s,
Or use four 3’s, . . .
45
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Backwards Math
Extension ideas for the four 4’s.
Look carefully at the expressions used to make the numbers
1=
2=
3=
with different “raw materials.”
Do you see patterns there?
46
Algebra Problem Solving with the new Common Core Standards
Standards  Supporting Activity  Backwards Math
Extension ideas for the four 4’s.
Using four 4’s (or other raw materials), make ten different
expressions equaling:
the number 1,
the number 2,
the number 3, . . .
What did you learn about the number system?
47
Algebra Problem Solving with the new Common Core Standards
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Algebra Problem Solving with the new Common Core Standards
Our most popular
product for the
second year! 
49
Algebra Problem Solving with the new Common Core Standards
Teacher to Teacher Press
Books and DVDs
Are for sale
In the Exhibit Hall
Booth 333 – Think It By Hand
50
Algebra Problem Solving with the new Common Core Standards
Pride
Power
Passion
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