Integers with Manipulatives

Numberlines – Integers (+, -) Adding –Forward direction (direction you are facing) -2 + 3 = 1 + 2 = -3 + 1 = 1 2 3 4 -1 -2 -3 -4 1 3 -2

Numberlines – Integers (+, -) Subtracting – change direction 2 - 3 = -1 - 2 = -1 - - 2 = 2 - + 1 = 1 2 3 4 -1 -2 -3 -4 -1 + -3 +1 - + 1

Integer Chips / Tiles Negative - Positive +

The collections shown here are “zero pairs”. Zero pairs have a value of zero.

What is the value? Has a value of +5. Has a value of +5. Has a value of +5. Has a value of +5. Build a different collection that has a value of +5.

ADDING INTEGERS with Tiles

Build your initial collection, add your other collection, then find the value of the collection. 5 + (+3) = +8

Build your initial collection, add your other collection, then find the value of the collection. zero pairs 5 + (-3) = 2

SUBTRACTING INTEGERS with Tiles

Subtracting - take away Example 1: 9 – 3 = 6 Build your initial collection, then take away the other collection (if you need to add a collection of zero pairs in order to take away then add them), then find the value of the collection take away

Subtracting - take away Example 2: –8 – (–2) = –6 take away Build your initial collection, then take away the other collection (if you need to add a collection of zero pairs in order to take away then add them), then find the value of the collection

Subtracting - take away method Example 3: –8 – (+2) = –10 Build your initial collection, then take away the other collection (if you need to add a collection of zero pairs in order to take away then add them), then find the value of the collection take away

Adding, Subtracting Integers 0 - +3 = 0 - 3 = 1 + -2 = 1 - 2 = -3 - - 5 = -3 + 5 = -3 -1 2

Model MULTIPLYING INTEGERS

3 × 4 3 groups of 4 + 3 × 4 = 12

3 × (–2) 3 groups of –2 + 3 × (–2) = –6

take away 2 groups of positive 3 If multiplying by a positive  add groups, what does it mean to multiply by a negative? Subtract groups! Example: –2 × 3 take away 2 groups of positive 3 So you need a collection to subtract from, so build a collection of zero pairs

= –6 –2 × 3 Take away 2 groups of 3 Example: Have to build a collection of zero pairs = –6

Example 2 (–4) × (–2) = 8

Write as a Multiplication Statement (+3) + (+3) + (+3) + (+3) 4 x +3 4 x (-3) (-3) + (-3) + (-3) + (-3) 3 x (+3) - - - - Two groups of -2 remove

Classwork Page 68-69 #5, 6, 10 12, 13, 16, 18, 20