INTEGERS Definitions: consists of all positive, negative numbers and zero. Manipulatives: (common) 1. Two-sided coloured disks (or two different coloured.

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Presentation transcript:

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.

Integer Language PositiveNegative UpDown AddSubtract GoodBad HotterColder GainLoss ProfitDebt StrengthsWeaknesses BlackRed

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: _ _ _ _ _ _

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: _122_g_3_t_1.html?open=instructions _122_g_3_t_1.html?open=instructions

Addition with Integers Pos Neg = 9 positives

Addition with Integers 3 + (-5) =

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

Addition with Integers =

Addition with Integers =

Addition with Integers = There are 4 negatives remaining

Subtraction with Integers 5 – 2 =

Subtraction with Integers -5 – (+2) =

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

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

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

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

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

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

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

 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’

 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

 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

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

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

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

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