Mathematics
Grade 3
15 min
Even or odd: arithmetic rules
Even or odd: arithmetic rules
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Introduction & Learning Objectives
Learning Objectives
Predict if the sum of two numbers is even or odd without calculating the exact answer.
Predict if the difference between two numbers is even or odd without calculating the exact answer.
Predict if the product of two numbers is even or odd without calculating the exact answer.
Explain the rule for adding two odd numbers (Odd + Odd = Even).
Explain the rule for adding an even and an odd number (Even + Odd = Odd).
Apply the even and odd arithmetic rules to check their answers in addition, subtraction, and multiplication problems.
If you have an even number of socks and your friend gives you an odd number of socks, will you be able to make perfect pairs with all of them? 🧦
Today, we are going to learn some amazing math shortcuts! These are special rules tha...
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Key Concepts & Vocabulary
TermDefinitionExample
Even NumberA whole number that can be divided into two equal groups with nothing left over. Even numbers always end in 0, 2, 4, 6, or 8.The number 12 is even because you can make two equal groups of 6. (6 + 6 = 12)
Odd NumberA whole number that has one left over when you try to divide it into two equal groups. Odd numbers always end in 1, 3, 5, 7, or 9.The number 7 is odd because if you make two groups of 3, there is 1 left over. (3 + 3 + 1 = 7)
SumThe answer you get when you add two or more numbers together.In 5 + 4 = 9, the sum is 9.
DifferenceThe answer you get when you subtract one number from another.In 10 - 3 = 7, the difference is 7.
ProductThe answer you get when you multiply two or more numbers together.In 2 x 6 = 12, the product is 12.
Arithmetic RuleA patt...
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Core Formulas
Addition & Subtraction Rules
Even ± Even = Even
Odd ± Odd = Even
Even ± Odd = Odd
Use these rules to predict if the sum or difference of two numbers will be even or odd. Notice that if the numbers are the same type (both even or both odd), the answer is Even. If they are different types, the answer is Odd.
Multiplication Rules
Even × Any Number = Even
Odd × Odd = Odd
Use these rules to predict if a product will be even or odd. The most important rule here is that if you multiply ANY number by an even number, the answer will ALWAYS be even.
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Challenging
I am thinking of two different whole numbers. When I multiply them, the answer is even. When I add them, the answer is odd. What must be true about my two numbers?
A.Both numbers are odd
B.Both numbers are even
C.One number is even and one number is odd
D.One number is zero
Challenging
Which of the following will ALWAYS result in an even number, no matter what whole numbers you choose (as long as they fit the description)?
A.An odd number plus an even number
B.An odd number times an odd number
C.The sum of any three odd numbers
D.An odd number subtracted from an odd number
Challenging
Sam's age is an even number. His sister's age is an odd number. Which of the following is IMPOSSIBLE?
A.The sum of their ages is odd
B.The product of their ages is even
C.The sum of their ages is even
D.The difference in their ages is odd
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