Teaching Integers in the Elementary Grades
- 1. INTEGERS INTEGERS By: Andrea Bonde & Slideshare.net
- 3. • An integer is a positive or negative whole number, including 0. …-3, -2, -1, 0, 1, 2, 3… Whole Number: Any number over 1.
- 4. There are “4” Integer Operations JUST LIKE IN ALL MATH!
- 6. 4 Integer Operations • Addition + • Subtraction - • Multiplication x • Division ÷
- 7. Rules For Integers • When Signs are the same, add the numbers! -5 - 1 = 5 + 1 • Answer gets the sign of the larger number. 5 is the largest number it’s sign is a (-). Answer is -6.
- 8. Rules For Integers • When Signs are the different subtract the numbers. -5 + 1 = 5 - 1 • Answer gets the sign of the larger number. 5 is the largest number it’s sign is a (-). Answer is -4.
- 9. Let’s Practice 1) 5 - 6 = 2) -3 + 2 = 3) 6 + 5 = 4) -8 + 7 = 5) 9 - 9 = Remember: If signs are the same add the numbers, if signs are different subtract the numbers. Then give the answer the sign of the largest number! -1 -1 +11 -1 0
- 10. Rules for Integers • When Parenthesis ( ) are involved we get to doodle! • This is where you need to draw some faces. (Bet you didn’t know you’d be doing Art in Math!)
- 11. Rules for Adding & Subtracting Integers Continued • When you multiply a (+ x -) you get a (-). • When you multiply a (- x -) you get a (+). • When you multiply a (+ x +) you get a (+). 5 + (-1) = 4 5 – (-1) = 6 5 + (+5) = 10 - + +
- 12. Let’s Practice 1) 4 – (-5) = 2) 9 + (-7) = 3) 6 – (+2) = 4) 8 – (-7) = 5) 9 + (+3) = Remember: DRAW the faces first! If signs are the same add the numbers, if signs are different subtract the numbers. Then give the answer the sign of the largest number! 9 2 6 15 12 + - + - +
- 13. Let’s Practice Cont. 1) 5 + (-2) = 2) 3 – (-4) = 3) 1 – (+2) = 4) 5 – (-3) = 5) 7 – (-6) = Remember: DRAW the faces first! If signs are the same add the numbers, if signs are different subtract the numbers. Then give the answer the sign of the largest number! - + + - + 3 7 -1 8 13
- 14. Rules for Multiplying Integers (x) • The product of two integers with the same signs is POSITIVE. • The product of two integers with different signs is NEGATIVE.
- 15. Rules Summary for Multiplication • Positive x Positive = Positive • Negative x Negative = Positive • Positive x Negative= Negative • Negative x Positive = Negative
- 16. Let’s Practice “Multiplication” 1) 6 x (-3) = 2) 3 x 3 = 3) -4 x 5 = 4) -6 x (-2) = 5) -7 x (-8) = -18 9 -20 12 56 Remember: Positive x Positive = Positive Negative x Negative = Positive Positive x Negative= Negative Negative x Positive = Negative
- 17. Did you know that the rules for multiplication and division are the same?
- 19. The rules for division are exactly the same as those for multiplication. If we were to take the rules for multiplication and change the multiplication signs to division signs, we would have an accurate set of rules for division.
- 20. Rules for Dividing Integers (÷) • The quotient of two integers with the same signs is POSITIVE. • The quotient of two integers with different signs is NEGATIVE.
- 21. Rules Summary for Division • Positive ÷ Positive = Positive • Negative ÷ Negative = Positive • Positive ÷ Negative= Negative • Negative ÷ Positive = Negative
- 22. Let’s Practice “Division” 1) 18 ÷ (-2) = 2) -48 ÷ (-6) = 3) -27 ÷ 9 = 4) 64 ÷ 8 = 5) 30 ÷ (-5) = -9 8 -3 8 -6 Remember: Positive ÷ Positive = Positive Negative ÷ Negative = Positive Positive ÷ Negative= Negative Negative ÷ Positive = Negative
- 23. Let’s Review…
- 24. What is an integer?
- 25. ANSWER • An integer is a positive or negative whole number, including 0.
- 26. Can you give an example of an integer?
- 27. ANSWER • …-3, -2, -1, 0, 1, 2, 3…
- 28. What are the four operations?
- 29. ANSWER • The four operations are: addition, subtraction, multiplication, and division.
- 30. When signs are the same you?
- 31. ANSWER • Add the numbers • Answer gets sign of the larger number.
- 33. ANSWER • You subtract the numbers • Answer gets sign of the larger number.
- 34. How do you multiply integers?
- 35. ANSWER • If the signs are the same, your answer is always positive. • If the signs are different, your answer is always negative.
- 36. How do you divide integers?
- 37. ANSWER • If the signs are the same, your answer is always positive. • If the signs are different, your answer is always negative. *Multiplication and Division Rules are the same!