Word Sort integers, addition, even numbers, odd numbers prime numbers, composite numbers, negative integer, positive numbers, whole numbers, subtraction, multiplication, division, 0, 12/2, –100, comparing, ordering, thermometer, debts/credits, above/below sea level. Suggestions: Venn Diagram, Web, Tree Need words

Integers (add this to small notebook) Definition   Integers are a set of numbers that include the following: (… –3, –2, –1, 0, 1, 2, 3, …)     Facts Include positive and negative whole numbers. Successive integers differ by one. Every negative number is the opposite of the positive number of the same size. Represents the difference between two objects in a set. Can be represented on a number line. Examples –25 8 Non-examples –2.76 4 1/3 0.2 Integers

Opposite Integers – Concept of Zero Earn $1, Spend $1 (need tiles) Have students share other similar examples. Introduce the term opposite integers and relate it to the example provided above. Earning $1 can be represented by +1. Spending $1 can be represented by -1. +1 and -1 are called opposite integers. Symbolically, (+1) + (-1) = 0. Have students draw a number line and place pairs of opposite integers on the number line. Through discussion, have them verbalize that opposite integers are equidistant from zero on the number line and when you add two opposite integers the sum is always zero.

additive inverse Yellow (–) Red (+) students use the tiles to represent zero, draw diagrams and write number sentences. TT

Which of the following would represent zero, using integer tiles? Yes or No

use integer tiles to answer questions (+2) and (–2) = 0 (+3) and (–3) = __ (–5) and ( ) = 0 ( ) and (+4) = 0

What does this equal? Can you arrange the tiles to show the same answer in a different way?

Use integer tiles to show –2, +3 and –5.

Integers Warm Up Place the following numbers on a number line: 3, –4, 0, 1, –5. Explain how these numbers are ordered. Write <, = or > in the boxes to complete the sentences below correctly. a) –15 􀂅–20 b) –46 􀂅 –31 c) –2 􀂅 5 – 5 Name the negative integers that are greater than –20 and divisible by 3. Explain your answer. The temperature is -15o Celsius on Monday and -8o Celsius on Tuesday. Which day shows the higher temperature? How do you know? Explain why one negative integer is less than another negative integer by using a real world context.

Show the same number using a different number of tiles Show the same number using a different number of tiles. What is the pattern? Integer +2 -2 +3 -5 Number of integer tiles 2, 4, 6, 8, … 3, 5, 7, 9… 5, 7, 9, 11…

Can you represent +3 with 121 tiles? why or why not!? If the integer is an even number, then an even number of tiles greater than or equal to the absolute value of the integer must be used to represent it because an even number plus an even number is an even number. If the integer is an odd number, then an odd number of tiles greater than or equal to the absolute value of the integer must be used to represent it because an odd number plus an even number is an odd number.

Subtract numbers and take the sign of the larger number Adding Integers (+) Positive (+) Negative (-) Positive (+) Add the numbers and use the sign of the numbers Subtract numbers and take the sign of the larger number Example 1: Positive + Positive   Example 2: Negative + Negative Example 3: Positive + Negative

Rule: The sum of two positive integers is a positive integer. +2 + +9 = +11 +17 + +5 = +22 +29 + +16 = +45 Do not confuse the sign of the integer with the operation being performed. Remember that: +29 + +16 = +45 is read as Positive 29 plus positive 16 equals positive 45.

Rule: The sum of two negative integers is a negative integer. -2 + -9 = -11 -5 + -8 = -13 -13 + -7 = -20 Do not confuse the sign of the integer with the operation being performed. Remember that: -2 + -9 = -11 is read as Negative 2 plus negative 9 equals negative 11.

To add a positive and a negative integer (or a negative and a positive integer), follow these steps: Find the absolute value of each integer. Subtract the smaller number from the larger number you get in Step 1. The result from Step 2 takes the sign of the integer with the greater absolute value.

Adding Integers You earn $2 and then spend $5. How much is your profit or loss? Show this on a number line. -5 -4 - 3 -2 -1 0 1 2 3 4 5 Show this using integer tiles.

(+2) + (–5) = (–3) Another example?

(+2) + (+3) = __ (–1) + (+4) = __ (–1) + (–3) = __ (+2) + (–4) = __ add using the integer tiles, drawing diagrams and writing the number sentences (+2) + (+3) = __ (–1) + (+4) = __ (–1) + (–3) = __ (+2) + (–4) = __

Class Practice Regular Problems: P. 280 Evens from #2 – 40, 61 Or Challenge Problems: P. 281 #53, 55, 57, 58, 65, 66

Operation Integers! Yellow cards are negative White cards are positive DIRECTIONS Turn over two cards and add them. Larger answer wins! (Record your addition sentence)

Subtracting Integers You are $2 in debt and spend $4 more. What is your debt now? Tiles Number Line Math Equation Spokesperson

-2 – 4 = -2 + -4 = + -

Sunny has $4 but spends $6. How much money does she have now? Tiles Number Line Math Equation Spokesperson

+4 + (-6) = -2

On your own! (+2) – (+3) = __ (+2) – (–2) = __ I am $1 in debt and I spend $3 more. What is my debt/profit now? (–1) – (–3) = __ I am $3 in debt and someone cancels a $2 debt that I owe him. What is my debt/profit now?

For your small notebook: FACT: Any subtraction equation can be written as an equivalent __________ sentence. Subtracting Integers FACT: The difference of two integers may be ___, ____, or ___ to either of the integers that are subtracted. Examples Not an example

Class Practice Textbook p. 287 Regular #2-32 (evens), 42 or Challenge # 10, 26, 34, 47, 49 GAME: + 100 Integers