2Algebra TilesManipulatives used to enhance student understanding of subject traditionally taught at symbolic level.Provide access to symbol manipulation for students with weak number sense.Provide geometric interpretation of symbol manipulation.
3Algebra TilesSupport cooperative learning, improve discourse in classroom by giving students objects to think with and talk about.When I listen, I hear.When I see, I remember.But when I do, I understand.
4Algebra TilesAlgebra tiles can be used to model operations involving integers.Let the small green square represent +1 and the small red square (the flip-side) represent -1.The green and red squares are additive inverses of each other.
5Zero PairsCalled zero pairs because they are additive inverses of each other.When put together, they cancel each other out to model zero.
6Addition of Integers Addition can be viewed as “combining”. Combining involves the forming and removing of all zero pairs.For each of the given examples, use algebra tiles to model the addition.Draw pictorial diagrams which show the modeling.
10So, what are the rules for addition of integers When adding two positive integers, the answer is always positive.When adding two negative integers, the answer is always negative.When adding two integers of opposite sign, you subtract the numbers & the answer is the sign of the bigger number.
11Subtraction of Integers Subtraction can be interpreted as “take-away.”Subtraction can also be thought of as “adding the opposite.”For each of the given examples, use algebra tiles to model the subtraction.Draw pictorial diagrams which show the modeling process.
12Subtraction of Integers (+5) – (+2) =Remove or take away +2 of the tiles:(+1) – (+1) =(-4) – (-3) =(-7) – (-2) =So,….What’s left?
13Subtracting Integers Add zero pairs! (+3) – (-5) =+3 “remove” -5, but you do not have any negatives to remove.Add zero pairs!
14Subtracting Integers Now you can remove -5 (+3) – (-5) = Zero pair(+3) – (-5) =Now you can remove -5And, your left with……Now, try: (-4) – (+1) =
15Subtracting Integers Add a zero pair. Now you can remove +1 (-4) – (+1) =Add a zero pair.Now you can remove +1And, your left with……Now, try these: (+3) – (-3) =(-8) – (+3) = 4 – (-7) = -6 – (+9) =
16So, what are the rules for subtracting integers? Look at the second number to see if you can remove that many from what you have.If not, add zero pairs.Remove the tiles you need to remove.Count tiles left.Your end result will be to simply add the opposite of whatever the sign is.
17Multiplication of Integers Integer multiplication builds on whole number multiplication.Use concept that the multiplier serves as the “counter” of sets needed.For the given examples, use the algebra tiles to model the multiplication. Identify the multiplier or counter.Draw pictorial diagrams which model the multiplication process.
18Multiplication of Integers The counter indicates how many rows to make. It has this meaning if it is positive.(+2)(+3) =or, 2 rows of +3 =(+3)(-4) =or, 3 rows of -4 =
19Multiplication of Integers If the counter is negative it will mean “remove” __ sets of __ (-2)(+3) =“Remove 2 sets of +3.”Nothing to remove,so start with zero pairs.Now remove 2 sets of +3…..And, what are you left with?Now, Try it using the flip method:
20Multiplication of Integers If the counter is negative it will mean “take the opposite of.” (flip-over)(-2)(+3) means to take 2 sets of 3….…but, because the counter isNegative, you must flip them over.Try These:(-3)(-1) (-4)(+3) (-5)(-3) (2)(-6) (-1)(5)(3)(-1) (-4)(-3) (5) (3) (-2)(6) (-1)(-5)
21Rules for Multiplication of Integers If the two signs are both negative or both positive the answer will be positive.If the two signs are both different, the answer will be negative.
22Division of IntegersLike multiplication, division relies on the concept of a counter.Divisor serves as counter since it indicates the number of rows to create.For the given examples, use algebra tiles to model the division. Identify the divisor or counter. Draw pictorial diagrams which model the process.
23Division of Integers (+6)/(+2) = Then split it into 2 groups So, how many in each group?So, how about this one:(-8)/(+2) =Split it into 2 groups:And, how many in each group here?
24Division of IntegersA negative divisor will mean “take the opposite of.” (flip-over)(+10)/(-2) =First, split:Then flip:Third, Answer:
25Division of Integers (-12)/(-3) = First, split: Then flip: Third, Answer:Now, try these:(12)/(-3) (-8)/4 (8)/(-2) -12/(-6) (+6)/(+3)
26Rules for Division of Integers If the two signs are both negative or both positive the answer will be positive.If the two signs are both different, the answer will be negative.