1. INTEGERS Definitions: consists of all positive, negative numbers and zero. Manipulatives: (common) 1. Two-sided coloured disks (or two different coloured disks) - one colour represents positive (yellow), the other colour represents negative (red). [could also use coins, popsicle sticks (one side coloured)…] 2.Number lines- movement to the right represents positive, movement to the left represents negative.

2. Integer Language PositiveNegative UpDown AddSubtract GoodBad HotterColder GainLoss ProfitDebt StrengthsWeaknesses BlackRed

3. Peers! If you had six friends who were in with the wrong crowd and six friends who were in with the good crowd, how would you turn out? Good crowd: + + + + + + Bad crowd: _ _ _ _ _ _

4. ADDITION AND SUBTRACTION  You should provide students the opportunity to recognize that the addition and subtraction of equal amounts of (+) and (-) disks has a result of zero.  Go to: http://matti.usu.edu/nlvm/nav/frames_asid _122_g_3_t_1.html?open=instructions http://matti.usu.edu/nlvm/nav/frames_asid _122_g_3_t_1.html?open=instructions

5. Addition with Integers Pos Neg 4 + 5 = 9 positives

6. Addition with Integers 3 + (-5) =

7. Addition with Integers 3 + (-5) = There are 2 negatives remaining One positive and one negative make zero

8. Addition with Integers -6 + 2 =

9. Addition with Integers -6 + 2 =

10. Addition with Integers -6 + 2 = There are 4 negatives remaining

11. Subtraction with Integers 5 – 2 =

12. Subtraction with Integers -5 – (+2) =

13. Subtraction with Integers -5 – (+2) = Problem arises because we don’t have 2 positives to take away

14. Subtraction with Integers -5 – (+2) = We can add nothing by adding the same number of positives and negatives

15. Subtraction with Integers -5 – (+2) = Now we can take away the two positives and we are left with 7 negatives

16. Subtraction with Integers -4 – (-5) = We do not have 5 negatives to subtract

17. Subtraction with Integers -4 – (-5) = Therefore let’s add one positive and one negative (zero, really)

18. Subtraction with Integers -4 – (-5) = Therefore let’s add one positive and one negative (zero, really)

19. MULTIPLICATION  Should be an extension of multiplication of whole numbers. (This is easy when the first integer is positive) eg.) 2 x -3 = two groups of negative three 4 x 5 = easy!!  Much more complicated when the first integer is negative A total of 6 negative things

20.  Demands that students become familiar with integer language (alternative words for negative and positive) eg.) -2 x -3 means ‘remove’ 2 sets of -3 Start with ‘zero’

21.  Demands that students become familiar with integer language (alternative words for negative and positive) eg.) -2 x -3 means ‘remove’ 2 sets of -3 Now, remove 2 sets of negative 3

22.  Demands that students become familiar with integer language (alternative words for negative and positive) eg.) -2 x -3 means ‘remove’ 2 sets of -3 Left with 6 positive things

23. Try a few A.-4 x -2 B. -3 x -3

24. Try a few A.-4 x -2 B. -3 x -3

25. Try a few A.-4 x -2 B. -3 x -3

26. DIVISION Use the same language as you would for whole numbers but also incorporate the language of integers (synonyms for negative). 1. 6 ÷ 2 = How many sets of 2 can you get from 6? 2. -10 ÷ (-2) = How many sets of -2 can you remove from -10? 3. -8 ÷ 2 = How many sets of +2 can you get from -8?