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Integers www.mathsrevision.com S4 Integers – Positive and Negative Add /Sub using Thermometer Add / Sub Integers Mathematica Multiplying & dividing Integers Negative Coordinate Grid 12-May-17 Created by Mr. Lafferty Maths Dept Starter Questions www.mathsrevision.com S4 Q1. Calculate Q2. How many euros do I get for £20 if exchange rate is £1 1.5 € Q3. What is the time difference 09:28 and 10:50 Q4. The answer to the question is 90. What is the question. 12-May-17 10% of £270 Created by Mr. Lafferty Maths Dept Integers www.mathsrevision.com S4 Learning Intention 1. 12-May-17 To understand how to add positive and negative numbers using the thermometer as an aid. Success Criteria 1. To be able to do add and subtract both positive and negative integers using a Created by Mr. Lafferty Maths Dept thermometer. Integers www.mathsrevision.com S4 Definition : An INTEGER is a negative or positive whole number, including 0. e.g. -2, -1, 0, 5, 100 Note : -2.5, -1.2, 23.5 Are NOT INTEGERS Write down 3 places where negative numbers are used Interpreting negative numbers Ex1 Page 16 Round Class 12-May-17 Created by Mr. Lafferty Maths Dept 24 Integers S4 20 www.mathsrevision.com 16 (a) (b) (c) (d) o o 4 C up from 12 C 12 + 4 = 16 o o 8 C down from 10 C 10 - 8 = 2 o o 3 C up from -2 C -2 + 3 = 1 o o 6 C down from 2 C 2 - 6 = -4 12 8 4 0 22 18 14 10 6 2 -4 -8 -12 -16 -20 -24 12-May-17 Created by Mr. Lafferty Maths Dept UP + -2 -6 -10 -14 -18 -22 Down - Integers www.mathsrevision.com S4 Now try Ex 2 Ch1 (page 19) 12-May-17 Created by Mr. Lafferty Maths Dept Starter Questions www.mathsrevision.com S4 Q1. Calculate Q2. How many euros do I get for £10 if exchange rate is £1 1.4 € Q3. What is the time difference 09:45 and 20:30 Q4. The answer to the question is 30. What is the question. 12-May-17 50% of £300 Created by Mr. Lafferty Maths Dept Integers www.mathsrevision.com S4 Addition & Subtraction Learning Intention 1. To explain how to write down mathematically addition and subtraction of negative integers. Success Criteria 1. To be able to write down mathematically the addition and subtraction of both positive and negative integers. 12-May-17 Created by Mr. Lafferty Maths Dept Integers S4 24 20 www.mathsrevision.com 16 (a) 12 + 4 = 16 Go up 4 Start at 12 (b) 10 +(-8) = 2 Start at 10 (c) Go down 8 7 - 10 = -3 Start 12-May-17 at 7 12 8 4 0 22 18 14 10 6 2 -4 -8 -12 -16 -20 -24 Go down 10 Created by Mr. Lafferty Maths Dept UP + -2 -6 -10 -14 -18 -22 Down - Integers S4 www.mathsrevision.com Examples (1) 3-7 = -4 (2) 4 + (-9) = -5 (3) -7 - 8 = -15 (4) -2 + (-12) = -14 (5) -5 - 25 = -30 (6) 8 + (-9) 12-May-17 = -1 Created by Mr. Lafferty Maths Dept Remember “+ -” = “- +” = - Integers www.mathsrevision.com S4 Now try Ex 3 Ch1 (page 20) 12-May-17 Created by Mr. Lafferty Maths Dept Starter Questions www.mathsrevision.com 1. Calculate 3% of 400 2. x + 5 = -3 Find the value of x 3. Put in order, smallest first. 20o 0.25, 0.19, 0.01, 0.026 xo 5. Find the missing angle in the triangle. 12-May-17 Created by Mr. Lafferty Maths Dept. xo Integers www.mathsrevision.com Multiplication & Division Learning Intention 1. Explain how to multiply and divide positive and negative integers. 12-May-17 Success Criteria 1. Understand how to multiply and divide positive and negative integers. Created by Mr. Lafferty Maths Dept. With your partner can try and come up (+ve) x (+ve) = (+ve) with the rules for (-ve) x (–ve) = (+ve) Multiplication & Division multiplying integers (-ve) x (+ve) = (-ve) Multiplying Integers (+ve) x (–ve) = (-ve) www.mathsrevision.com Integers 1 x (-2) = -2 (-2) x (-1) = 2 (-4) x 5 = -20 (- 2) x (-5) = 10 (-3) x 3 = -9 (-5) x (-5) = 25 Same signs positive answer 5 x (-8) = -40 (-4) x (-8) = =32 12-May-17 Different signs = negative answer Created by Mr. Lafferty Maths Dept. With your partner can try and come up with the rules for Multiplication multiplying integers (+ve) ÷ (+ve) = (+ve) (-ve) ÷ (–ve) = (+ve) & Division (-ve) ÷ (+ve) = (-ve) (+ve) ÷ (–ve) = (-ve) www.mathsrevision.com Integers (-2) ÷ 1 = -2 20 ÷ (-5) =-4 (-9) ÷ 3 = -3 (-25) ÷ 5 = -5 12-May-17 (-2) ÷ (-1) = 2 (- 20) ÷ (-5) = 4 (-9) ÷ (-3) = 3Same signs = positive answer (-40) ÷ (-8) = 5 Different signs = negative answer Created by Mr. Lafferty Maths Dept. Remember BODMAS www.mathsrevision.com S33 Same signs = positive answer Integers MultiplicationDifferent signs = negative answer Multiplying Integers 1 + (-2) x (-10) = 21 3 + (-5)2 = 28 8 – (-3)2 = -1 5 x (-2)2 + 5 – 19 = 6 12-May-17 Created by Mr. Lafferty Maths Dept. Remember BODMAS www.mathsrevision.com S33 IntegersSame signs Division = positive answer Division Integers Different signs = negative answer 1 + (-20) ÷ (-10) = 3 100 ÷ (-5)2 = 4 100 - 36 ÷ (-3)2 = 96 -48 ÷ (6 - 2)2 + 5 = 2 12-May-17 Created by Mr. Lafferty Maths Dept. Integers www.mathsrevision.com Multiplication & Division Now try MIA Ex 4 Ch1 (page 21) 12-May-17 Created by Mr. Lafferty Maths Dept. Starter Questions S4 www.mathsrevision.com 1. If 25% of £300 2. Calculate the following : (a) 3.45 x 10 (b) 7.5 100 (c) 5789 1000 3. How long between half past eight in the moring to 14 : 20 hrs 12-May-17 Created by Mr. Lafferty Maths Dept www.mathsrevision.com S4 Coordinates Extending the Grid – Negative Numbers Learning Intention 1. To show how we can extend the coordinate grid to include negative numbers. 12-May-17 Success Criteria 1. Identify main parts of coordinate grid. 2. Understand the negative grid both in y-axis direction and x-axis direction. Created by Mr. Lafferty Maths Dept S4 Coordinates Extending the Grid – Negative Numbers www.mathsrevision.com We can further extend the negative grid Plot the point (-2,2) y - axis origin 3 2 1 -4 -3 -2 -1 0 1 2 3 4 -1 -2 -3 1 12-May-17 2 3 4 Created by Mr. Lafferty Maths Dept x-coordinate is -2 y-coordinate is 2 x - axis (-4,-2) x-coordinate is -4 5 y-coordinate is -2 Write down coordinates of the other points Coordinates www.mathsrevision.com S4 Extending the Grid Now try Ex 5 Ch1 (page 23) 12-May-17 Created by Mr. Lafferty Maths Dept