Math: Integers

In this unit we will be investigating the addition, subtraction, multiplication, division, and ordering of integers. Students will be able to order rational numbers, solve problems involving operations with integers, and evaluate expressions involving integers using the order of operations.

9.5A - Rational Numbers
Friday, January 29 
Homework: Worksheet

Goal for the lesson

All integers are rational, all numbers are fractions with a denominator of 1.

When we are given rational numbers in the form of positive and negative fractions, decimals and integers, we have to use some strategies in order to find out where they can be place on a number line.
We can make all the numbers in to fractions by finding the smallest common denominator.
But it is much easier to divide fractions into decimals, and then order them and sort positive and negative numbers.

An example of how ordering rational numbers would look on a stretched out number line.

Class problem solving on how we can order rational numbers.
It was easy to place all the decimals first where we think they might go.
And then divide fractions to find decimals and fill the rest in.

9.4/9.5 - Multiplying and Dividing Integers
Tuesday, January 26
Homework: Worksheets
Textbook: p 384 #8b + 9 only

Goal for the lesson

Students were given this chart as a blank.
Using their calculators they were asked to calculate positive and negative integers on the table.
What we noticed: That when we multiplied two negative our answer was positive.
When we multiplied a negative and a positive our answer was negative.
These are our rules.

Using the rules we determined through the table activity. We went through a few examples.
In order to understand why negatives and positives give us a negative and why 2 negatives give us a positive we went over the love/hate analogy.

Notes for students: our two rules and some examples.
Also: The Sleeping Man diagram. If you are looking at two signs from your question, the left over sign will be the sign of your answer.

The same rules on multiplying integers apply to dividing integers.
Students need to know that dividend is the number to be divided
The divisor is the number you are dividing by.
And the quotient, which is the answer.

We went over a few more examples before playing Integer Bingo!

9.1/9.2 - Adding and Subtracting Integers

Thursday, January 21
Homework and Practice Book: 9.1 pg 185-186 #1-7
9.2 pg 187-188 #1-5
Textbook: Assessment Focus pg. 379 #3

We first did a recap of what we know about integers already. And where we can find positive and negative numbers in real-world situations.

Our goal for adding and subtracting with integers.

Numbers get larger as we move closer to the positives. Numbers get smaller as we move further into the negatives.
-10 is a smaller number than -1.

We follow two rules when adding and subtracting integers:
1. Adding a negative is the same as subtraction, so we move left down the number line.
2. Subtracting a negative is the same as addition. We move right up the number line.

There is also the zero principle which is when we add two numbers with opposite signs, you will get zero.

An example of moving up and down the number line.
3 questions you should ask yourself:
1. Am I starting with a positive or negative?
2. Am I making that number bigger or smaller?
3. Will my answer be positive, negative, or 0?

An activity we did with playing cards.
Students were given an integer and had to use the number line to find out a number of combinations they could add together to bring them to their integer.