USING: INTEGER- TILES and Number Lines

- 3 + 2 - 4 +3 +5 - 7 Show me ? NOTE: COLOURED WHITE NEGATIVE: tiles are POSITIVE : and WHITE NEGATIVE: - 4 +3 +5 - 7 This slide is to establish Rule #1: “Colored tiles are positive and white tiles are negative.”

Identify which produce the Sum of Zero: no yes no Development of Rule #2: “Zero Model/Additive Inverse” It is very important that students truly understand this rule the before other tiles are also presented here in to establish the meaning. Does the example represent a Zero model? In the last quadrant guide the students to group the same size, same shape tiles together then count the remaining tiles and identify the answer of -2. The rule is defined on next slide. yes no

Same SIZE and same SHAPE Opposite COLOUR Zero Value + = Be sure that this conclusion is clear for all students. 1 move animates this slide. + =

ADDITION of INTEGERS:

Addition with Integer-tiles: + 2 + +3 + +5

- 2 + - 1 ______ + - 3 S Adding the tiles of the same colour, white tiles. Addition of alike colour tiles yields same colour.

- 3 + - 2 ______ + - 5 S Adding the tiles of the same colour, white tiles. Addition of alike colour tiles yields same colour.

+ - 3 + 2 -1 ______ Zero Value + S Addition of different colour tiles and the use of the “Zero Model Rule” / additive inverse.

- 6 + + 4 _____ + -2 S Addition of different colour tiles and the use of the “Zero Model Rule” / additive inverse.

+ - 2 + 4 + 2 ________ + Continue with same type of question. Note: “Zero Model Rule” / additive inverse

+ - 3 + 4 + 1 ________ + Continue with same type of question. Note: “Zero Model Rule” / additive inverse

a) (+5) + (+6) = +11 b) (-4) + (-3) = c) (-7) + (+5) = -7 Practice on your own... a) (+5) + (+6) = b) (-4) + (-3) = c) (-7) + (+5) = d) (-5) + (+6) = e) (-5) + (-6) = +11 -7 -2 +1 -11

Let’s build combinations of - 2 Can you show one more example of -2 ? Another Example -2 Transition question to a subtraction operation. Students must practice using the “Zero Model” concept / additive inverse. Create combinations, using different tiles and “Zero Model” concept as illustrated in this slide . -2 Can you show one more example of -2 ?

Let’s build combinations of + 3 Can you show one more example of +3 ? Transition question to a subtraction operation. Students must practice using the “Zero Model” concept / additive inverse. Create combinations, using different tiles and “Zero Model” concept as illustrated in this slide . +3 +3 Can you show one more example of +3 ?

Display a COMBINATION of these numbers using the ZERO GROUPINGS: a) - 1 b) + 5 Transition question to a subtraction operation. Students must practice using the “Zero Model” concept / additive inverse. Create combinations, using different tiles and “Zero Model” concept as illustrated in this slide . c) - 4

SUBTRACTION of INTEGERS:

Can you take away +2 from this amount?? SUBTRACTION with Integer-tiles: Can you take away +2 from this amount?? How about now?? And now?!!? METHOD : 1 - 3 - + 2 ______ - 5 Work through this example very carefully! After the 3 negative tiles appear, ask students the following questions: “What is the meaning of subtraction?” --Take away “Can I take away 2 positive tiles out of a group of 3 negative tiles?” --No! “Then what must we do in order to subtract/take away 2 positive tiles from 3 negative tiles?” --Add 2 groups of Zero Models. “Now, can I take out 2 positive tiles from the group?” --Yes, Take away 2 red tiles and I will be left with 5 white tiles.

Can you take away + 1 from this amount? And now?!!? - 2 - + 1 - 3 Here, the question (symbolic) is represented in a horizontal format. Same strategy previous example for development of understanding.

- 2 - - 4 ______ + 2 Use the same strategy and line of questioning as with the previous example.

+2 - - 4 ______ + 6 Use the same strategy and line of questioning as with the previous example.

+5 - - 3 ______ + 8 Use the same strategy and line of questioning as with the previous example.

a) (+5)- (+6) = -1 b) (-4) - (-4) = c) (-7) - (+5) = d) (-5) - (+6)= A few more for practice !.. a) (+5)- (+6) = b) (-4) - (-4) = c) (-7) - (+5) = d) (-5) - (+6)= e) (-5) - (-6) = -1 -12 -11 +1

(-3) - (+2) = +(-2) = -5 + METHOD : 2 - FLIP Hint FLIP means Change SIGNS! And COLOUR. Hint Method 2 is an algorithm to the process of subtraction. If this method is used, be sure that to indicate that every “FLIP” means multiplying by a negative value.” The strategy is to “FLIP AND ADD”

(-5) – (-2) = + (+ 2) = - 3 + - FLIP

+ . . + 3 + 2 +5 METHOD : 3 ________ Addition on the number line: 2 Right 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 +5 Look at the first number and go to that spot on the number line. If signs are the SAME…..Move Right. If signs are DIFFERENT…..Move Left.

+ . . - 3 - 4 -7 ________ If signs are the SAME…..Move Right. 4 Left 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 -7 Look at the first number and go to that spot on the number line. If signs are the SAME…..Move Right. If signs are DIFFERENT…..Move Left.

+ . . + 3 - 4 -1 ________ If signs are the SAME…..Move Right. 4 Left . . 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 -1 Look at the first number and go to that spot on the number line. If signs are the SAME…..Move Right. If signs are DIFFERENT…..Move Left.

+ . . - 3 + 7 +4 ________ If signs are the SAME…..Move Right. 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 +4 Look at the first number and go to that spot on the number line. If signs are the SAME…..Move Right. If signs are DIFFERENT…..Move Left.

+ . . + 3 + 2 +5 ________ Addition on the VERTICAL number line: Up 2 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 +5 Look at the first number and go to that spot on the number line. If signs are the SAME…..Move UP If signs are DIFFERENT…..Move DOWN.

+ . . - 3 - 4 - 7 ________ Addition on the VERTICAL number line: 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 - 7 . Down 4 Look at the first number and go to that spot on the number line. . If signs are the SAME…..Move UP If signs are DIFFERENT…..Move DOWN.

- . . -3 +2 -5 SUBTRACTION on the number line: ________ 2 Left . 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 -5 Look at the first number and go to that spot on the number line. If signs are the SAME…..Move Right. If signs are DIFFERENT…..Move Left.

- . . -3 -4 +1 ________ If signs are the SAME…..Move Right. 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 +1 Look at the first number and go to that spot on the number line. If signs are the SAME…..Move Right. If signs are DIFFERENT…..Move Left.

- . . +2 -5 +7 If signs are the SAME…..Move Right. 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 +7 Look at the first number and go to that spot on the number line. If signs are the SAME…..Move Right. If signs are DIFFERENT…..Move Left.

- . . -2 +7 -9 If signs are the SAME…..Move Right. 7 Left . 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 -9 Look at the first number and go to that spot on the number line. If signs are the SAME…..Move Right. If signs are DIFFERENT…..Move Left.

- . . - 3 + 4 - 7 ________ Subtraction on the VERTICAL number line: 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 - 7 . Down 4 . Look at the first number and go to that spot on the number line. If signs are the SAME…..Move UP If signs are DIFFERENT…..Move DOWN.

- . . - 3 - 4 + 1 ________ Subtraction on the VERTICAL number line: 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 Up 4 . Look at the first number and go to that spot on the number line. If signs are the SAME…..Move UP If signs are DIFFERENT…..Move DOWN.

(-2) – (-3) +1 METHOD : 4 HINT: Set up 5 zero’s or more. Method 3 is a UNIQUE way to subtract. Create a string of zero models (Hint ; they must equal to or more that the sum of the two numbers) Then, ask yourself to create the sum of -2. Take away 3 negative tiles. Simplify the results, and this becomes the answer. HINT: Set up 5 zero’s or more. Take away (-3 ) value. Make a (-2 ) value.

(+2) – (-4) +6 HINT: Set up 6 zero’s or more. Make a (+2 ) value. Take away (-4 ) value.

(-3) – (+5) -8

(+5) – (+2) +3

BLACKLINE MASTERS

B L A C K L I N E M A S T E R S

Add and Subtract number lines: 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12

Add and Subtract number lines: 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -11 -12