Starter: Speed Test You will see 10 questions. Each question will stay on the screen for 30 seconds Calculators not allowed

What is 1) 45 - 50 2) 24 - -98 3) -22 - -100 4) 89 - -37 5) 28 - 53 6) 17 - 45 7) 88 - -57 8) 8 - -55 9) 11 - 55 10) 63 - 68

L.O. Multiply and divide by negative numbers. Grade D Date:3 January, 2019 Integer numbers L.O. Multiply and divide by negative numbers. Grade D

Rules for multiplying When multiplying negative numbers remember: + × = 4 × 7 = 28 – + × = –4 × –7 = 28 – + × = –4 × 7 = -28 – + × = 4 × –7 = -28 These rules have been drawn graphically to make it easier for pupils to spot the pattern. As each rule appear read it as, for example, A positive number multiplied by a positive number always equals a positive number. Remind pupils of the meaning of ‘inverse operation’ – one ‘undoes’ the other. For example, if 4 × –3 = –12, then –12 ÷ –3 must equal 4. Tell pupils that easiest way to remember these rules is that when we multiply together (or divide) two numbers with different signs (a positive number times a negative number or a negative number times a positive number) the answer will always be negative. If we multiply together (or divide) two numbers with a different sign (a positive number times a positive number or a negative number times a negative number) the answer will always be positive. Encourage pupils to first work out whether their answers will be positive or negative and then multiply or divide. Ask pupils to write down rules for multiplying (or dividing) three numbers. For example, negative × positive × negative = positive and negative × negative × negative = negative. L.O. Multiply and divide by negative numbers

Mixed multiplication square Work out the numbers in the empty squares by multiplying and dividing. L.O. Multiply and divide by negative numbers

Rules for dividing 5 x 7 =35, so 35 ÷ 5 = 7 –35 ÷ –5 = 7 –35 ÷ 5 = -7 = -7 35 ÷ –5 When dividing negative numbers remember: + ÷ = – + = ÷ – + = ÷ – + = ÷ L.O. Multiply and divide by negative numbers

Mixed division square L.O. Multiply and divide by negative numbers Work out the numbers in the empty squares by multiplying and dividing. L.O. Multiply and divide by negative numbers

Sums and products What two integers have a sum of 2 and a product of –8? Start by writing down all of the pairs of numbers that multiply together to make –8. Since –8 is negative, one of the numbers must be positive and one of the numbers must be negative. We can have: –1 × 8 = –8 1 × –8 = –8 –2 × 4 = –8 or 2 × –4 = –8 Pupils will need to solve this type of problem when factorizing quadratic expressions. Explain that we start by looking for products because there are less of these. There are infinitely many pairs of integers with a sum of 2. Link: A1.4 Factorization –1 + 8 = 7 1 + –8 = –7 –2 + 4 = 2 2 + –4 = –2 The two integers are –2 and 4. L.O. Multiply and divide by negative numbers

Complete this table L.O. Multiply and divide by negative numbers This exercise may be completed orally as a class. Alternatively, give pupils a time limit to complete the task in writing before going through the answers. L.O. Multiply and divide by negative numbers

Multiplying and dividing integers Complete the following: –3 × 8 = –24 –36 ÷ = –4 9 42 ÷ = –6 –7 ÷ –90 = –6 540 × –8 = 96 –12 –7 × = 175 –25 47 × = 141 3 –4 × –5 × –8 = –160 For each example ask pupils what sign the missing number will have and then what the number is. Links: Mental methods – multiplication and division Equations – solving equations –72 ÷ –6 = 12 3 × –8 ÷ = 1.5 –16 L.O. Multiply and divide by negative numbers