1. How can you use numbers and symbols to represent mathematical ideas?
Rational Numbers and Exponents
How can you use numbers and symbols to represent mathematical ideas?
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2. Identify and use properties of addition and multiplication
Rational Numbers and Exponents
Identify and use properties of addition and multiplication
Use properties to simplify algebraic expressions
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3. Counterexample – an example that shows the conjecture is not true.
Rational Numbers and Exponents
Counterexample – an example that shows the conjecture is not true.
Deductive reasoning – the process of using facts, properties, or rules to justify reasoning.
Simplify – to write an expression in simpler form.
Properties – statements that are true for any number.
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4. Commutative Properties
Rational Numbers and Exponents
Commutative Properties
Words The order in which numbers are added or multiplied
does not change the sum or product.
Symbols For any numbers a and b, a + b = b + a.
For any numbers a and b, a · b = b · a.
Examples = · 7 = 7 · 4
15 = = 28
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5. Associative Properties
Rational Numbers and Exponents
Associative Properties
Words The order in which numbers are grouped when added or
multiplied does not change the sum or product.
Symbols For any numbers a, b, and c, (a + b) + c = a + (b + c).
For any numbers a, b, and c, (a · b) · c = a · (b · c).
Examples (3 + 6) + 1 = 3 + (6 + 1) (5 · 9) · 2 = 5 · (9 · 2)
9 + 1 = · 2 = 5 · 18
10 = = 90
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6. Number Properties Property Words Symbols Examples Additive Identity
Rational Numbers and Exponents
Number Properties
Property
Words
Symbols
Examples
Additive Identity
When 0 is added to any number, the sum is the number
For any number a, a + 0 = 0 + a = a
5 + 0 = 5
0 + 5 = 5
Multiplicative Identity
When any number is multiplied by 1, the product is the number.
For any number a, a · 1 = 1 · a = a.
8 · 1 = 8
1 · 8 = 8
Multiplicative Property of Zero
When any number is multiplied by 0, the product is 0.
For any number a, a · 0 = 0 · a = 0
3 · 0 = 0
0 · 3 = 0
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7. How did what you learned today help you answer the
Rational Numbers and Exponents
How did what you learned
today help you answer the
How can you use numbers and symbols to represent mathematical ideas?
Lesson 1-4

8. Rational Numbers and Exponents
Ratios and Proportional Relationships
Name two properties and explain how the properties help you in mathematics. Your explanations should include examples of the properties.
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9. Mathematical Practices
Rational Numbers and Exponents
7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
7 Look for and make use of structure.
Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
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