Computation With Integers Vocabulary: mental divide number line problems order of operations written add digit money compare subtract equivalent operations computation integers place value grouping symbols multiply directed number direction rational

Place Value In your book

Signpost p6 Q1-8

Ways of working with number: Adding? Subtracting Multiplying Dividing? In your book

Order of Operations To avoid confusion, mathematicians developed a set of procedures to ensure that everyone obtained the same answer when they completed calculations; for example… What is the answer to 10÷2(3+2)? The accepted order is: Work with grouping symbols and exponents first 2. Work out multiplications and divisions in order from left to right 3. Work out additions and subtractions in order from left to right e.g. 17 – 52 ÷ (2+3) = In your book

A diagram to help you remember the order of operations. Signpost p 56 Q1-8 Signpost p 58 Q1-5 In your book

Puzzle!

Long Division…the ‘Easy’ way Although you may have learned traditional long division in primary school, an easier, more understandable way is by using the preferred multiples method. e.g. 37 ) 10800

Directed Numbers or Integers Integers are whole numbers. They can be either positive or negative, or zero. An example of a negative integer is ‘The temperature is -4 degrees’. Think of a – sign as meaning the opposite to + -3,-2,-1, 0, +1, +2, +3 Which of the following are integers? In your book

Using Directed Numbers Seven degrees below Celsius _____ Going up four floors on the elevator ______ Owing $50 ______ 150 meters above sea level ______ Move back four spaces ______ Five shots under par ______ In your book

In your book Place these numbers on the number line below in their correct position: Rearrange the numbers below into ascending order, i.e. from smallest to largest.

Ordering Directed Numbers In your book

Using a Number Line with Integers e.g. 4 x -1 = -3 + 7 = (-6) ÷ (-2) = In your book

Operations With Integers We can visualise a number line to help evaluate problems using directed numbers…or just use the one on the wall… 3 – 7 = ? – 2 – 5 = ? 1. - 5 - 2 = 6. -3 +5 = 2. 3 - 6 = 7. 1 - 4 + 8 = 3. -3 - 2 = 8. 2 - 8 - 10 = 4. -4 -3 = 9. 10 - 6 + 4 = 5. -4 + 2 = 10. 10 - (6 + 4) = In your book

In your book

In your book

Multiplying and Dividing Directed Numbers Investigation: 3 x 3 = 9 -4 x 3 = -12 3 x 2 = 6 -4 x 2 = -8 3 x 1 = 3 -4 x 1 = -4 3 x 0 = 0 -4 x 0 = 0 3 x (-1)= -4 x (-1) = 3 x (-2)= -4 x (-2) = 3 x (-3)= -4 x (-3) = Simplify the following: 1. -2 x 3 = 4. 4 x (-5) = 2. -6 x -3 = 5. (-3) x 2 x (-4) = 3. (-3) x 2 = 6. -5 x (-2) x -2 = In your book

When multiplying: positive x positive = positive Rule: When multiplying: positive x positive = positive positive x negative = negative negative x positive = negative negative x negative = positive The same rules apply to division. In your book

Show -12 as the product of at least 3 integers A number and its opposite are 24 units apart on a number line. What are the numbers? Two numbers are 10 units apart on a number line. One is positive and one is negative. Give three pairs of numbers which would fit this description. Give an example of: Two numbers which give a product greater than their sum. Two numbers which give a sum greater than their product. Make up the most difficult question you can (and its answer) for the class to solve.