Mathematics
Grade 9
15 min
Even or odd numbers on number lines
Even or odd numbers on number lines
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Introduction & Learning Objectives
Learning Objectives
Visualize the parity (evenness or oddness) of integers on a number line.
Model addition and subtraction of even and odd numbers using directed jumps on a number line.
Predict the parity of the result of arithmetic operations (addition, subtraction, multiplication) between integers.
Generalize the rules of parity for operations using algebraic representations (2n and 2n+1).
Apply number line visualization to verify the parity of simple polynomial expressions for integer inputs.
Connect the concept of parity on a number line to the behavior of linear functions like f(x) = x + c.
Ever noticed how adding two odd numbers always results in an even one? 🤔 Let's use a number line to see exactly why this pattern holds true!
This tutorial explores the fundam...
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Key Concepts & Vocabulary
TermDefinitionExample
ParityThe property of an integer indicating whether it is even or odd.The number 17 has a parity of 'odd'. The number -8 has a parity of 'even'.
Even NumberAn integer that is exactly divisible by 2. On a number line, even numbers are located at positions ..., -4, -2, 0, 2, 4, ...The number 0 is even because 0 ÷ 2 = 0, which is an integer.
Odd NumberAn integer that is not exactly divisible by 2, leaving a remainder of 1. On a number line, odd numbers are located at positions ..., -3, -1, 1, 3, ...The number -5 is odd because -5 ÷ 2 = -2.5, which is not an integer.
Number LineA visual representation of numbers as points on an infinitely long line. Positive numbers are to the right of zero, and negative numbers are to the left.A horizontal line with...
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Core Formulas
Parity Rules for Addition and Subtraction
Let E be an even number and O be an odd number. Then: \\ E \pm E = E \\ O \pm O = E \\ E \pm O = O
These rules predict the parity of a sum or difference. On a number line, adding/subtracting an even number results in a jump that lands on a number of the same parity. Adding/subtracting an odd number results in a jump that lands on a number of the opposite parity.
Parity Rules for Multiplication
Let E be an even number and O be an odd number. Then: \\ E \times E = E \\ O \times O = O \\ E \times O = E
These rules predict the parity of a product. The presence of at least one even factor (a factor of 2) in a multiplication guarantees the result will be even.
Algebraic Proof for Odd + Odd
(2n + 1) + (2m + 1) = 2n + 2m + 2 = 2(n + m...
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Challenging
For any integer x, what is the parity of the expression (x+1)(x+2)?
A.Always Even
B.Always Odd
C.Odd if x is even, Even if x is odd
D.The parity cannot be determined
Challenging
If 'a' is an odd integer and 'b' is a non-zero even integer, which expression's parity CANNOT be determined without knowing the specific values of 'a' and 'b'?
A.a + b
B.ab - 1
C.a² + b²
D.(a + 1) / b
Challenging
For any integer n, what is the relationship between the parity of n and the parity of the polynomial P(n) = n³ + n² + n?
A.The parity of P(n) is always the same as the parity of n.
B.The parity of P(n) is always the opposite of the parity of n.
C.P(n) is always even.
D.P(n) is always odd.
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