Transcript INTEGERS
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 Positive Negative Up Down Add Subtract Good Bad Hotter Colder Gain Loss Profit Debt Strengths Weaknesses Black Red 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: http://matti.usu.edu/nlvm/nav/frames_asid _122_g_3_t_1.html?open=instructions Addition with Integers Pos Neg 4+5 = 9 positives Addition with Integers 3 + (-5) = Addition with Integers 3 + (-5) = One positive and one negative make zero There are 2 negatives remaining Addition with Integers -6 + 2 = Addition with Integers -6 + 2 = Addition with Integers -6 + 2 = 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 A total of 6 negative things 4 x 5 = easy!! Much more complicated when the first integer is negative 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). 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?