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Integers

S3 3. Integers. Ordering integers. Add / Sub Mathematically. Letters and Numbers. www.mathsrevision.com. Multiplying Integers. Dividing Integers. S3 3. Starter Questions. Q1. Explain why. Q2. How many Euros do I get for £20 if exchange rate is £1  1.5 €. www.mathsrevision.com.

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Integers

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  1. S33 Integers Ordering integers Add / Sub Mathematically Letters and Numbers www.mathsrevision.com Multiplying Integers Dividing Integers Created by Mr. Lafferty Maths Dept

  2. S33 Starter Questions Q1. Explain why Q2. How many Euros do I get for £20 if exchange rate is £1  1.5 € www.mathsrevision.com Q3. The answer to the question is 90. What is the question. Created by Mr. Lafferty Maths Dept

  3. S33 Integers Learning Intention Success Criteria • To be put integers in order of size. • 1. To understand how to add positive and negative numbers using the thermometer as an aid. www.mathsrevision.com Created by Mr. Lafferty Maths Dept

  4. Sea Level Temperature Integers S33 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 www.mathsrevision.com Write down 3 places where negative numbers are used Profit and Loss Coordinate Grid Created by Mr. Lafferty Maths Dept

  5. 12 11 10 9 8 7 6 5 Positive + Negaive - -5 -6 -7 -8 -9 -10 -11 -12 Integers S33 Integers can be represented on a thermometer or number line. 4 The further to the top a number is the bigger it is. 3 2 Greater than 1 0 -1 12 > 4 -2 -3 -4 www.mathsrevision.com -2 > -3 Less than -4 < -1 -3.5 < -2.8 Created by Mr. Lafferty Maths Dept

  6. Integers S33 Coordinate Grid Plot the point y - axis (3,2) 3 x-coordinate is 3 2 1 y-coordinate is 2 origin 0 -2 -3 -1 2 4 -4 1 3 x - axis www.mathsrevision.com -1 (-2,2) -2 -3 (-4,-2) Plot the point that makes shape a parallelogram. Created by Mr. Lafferty Maths Dept

  7. Integers S33 Now try Exercise 2.1 Ch2 (page 23) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  8. S33 Starter Questions Q1. Is 7 + 6x2 = 26 or 19 Q2. How many euros do I get for £10 if exchange rate is £1  1.4 € Q3. The answer to the question is 30. What is the question. www.mathsrevision.com Created by Mr. Lafferty Maths Dept

  9. Negative Numbers S33 Addition & Subtraction Learning Intention Success Criteria • To be able to write down mathematically the addition and subtraction of both positive and negative integers. • 1. To explain how to write down mathematically addition and subtraction of negative integers. www.mathsrevision.com Created by Mr. Lafferty Maths Dept

  10. 12 11 10 9 8 7 6 5 -5 -6 -7 -8 -9 -10 -11 -12 Negative Numbers “+ -” side by side replace by single “-” S33 (a) 12 + 4 = 16 4 3 2 Go up 4 Start at 12 1 0 -1 (b) 10 + ( - 8) = -2 -3 “- -” side by side replace by single “+” -4 10 - 8 = 2 www.mathsrevision.com (c) -7 – (- 10)= 3 -7 + 10= Created by Mr. Lafferty Maths Dept

  11. Negative Numbers S33 Examples Remember “+ -” = - “- -” = + (1) 3 - 7 = -4 (2) 4 + (-9) = -5 (3) -7 – (- 8) = 1 www.mathsrevision.com (4) -2 + (-12) = -14 (5) -5 – (-25) = 20 (6) 8 + (-9) = -1 Created by Mr. Lafferty Maths Dept

  12. Integers S33 Now try Ex 3.1 to 4.2 Ch2 (page 26) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  13. S33 Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept

  14. Substitution S33 Learning Intention Success Criteria • To explain the process of working out expressions by substitution method. • Understand process of substitution. • 2. Solving expressions showing working. www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  15. Substitution S33 1 If a = 2 and b = 14 evaluate a + b Sub in a=2 = 2 + 14 www.mathsrevision.com Sub in b=14 = 16 Created by Mr.Lafferty Maths Dept

  16. Substitution S33 2 If a = 3 and b = -9 evaluate a - b = 3 - (-9) Remember “- -” replace by “+” www.mathsrevision.com = 3 + 9 = 12 Created by Mr.Lafferty Maths Dept

  17. Substitution S33 3 If a = 3 and b = 9 evaluate b2 – a2 9x9 – 3x3 Remember b2 means b x b www.mathsrevision.com - 81 = 9 = 72 Created by Mr.Lafferty Maths Dept

  18. Substitution S33 If a = 5 and b = 6 evaluate 1. a + b =11 4. b - a =1 2. ab =30 5. 4b =24 www.mathsrevision.com 3. 3a =15 6. 3ab =90 Created by Mr.Lafferty Maths Dept

  19. Substitution S33 Now try Exercise 5.1 Ch2 (page 28) Q1 – Q4 www.mathsrevision.com Created by Mr. Lafferty Maths Dept

  20. Tidying Up Like Terms S33 Learning Intention Success Criteria • To explain the process of tidying up expressions. • Understand the term like terms. • 2. Be able to tidy up like terms. www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  21. Tidying Terms S33 WE CAN ONLY TIDY UP “LIKE TERMS” 1, 3 , 5, -6, 8 are like terms simple numbers are like terms in x x, 3x , -2x www.mathsrevision.com are like terms in x2 x2, 3x2, -2x2 x is NOT the same as x2 Created by Mr.Lafferty Maths Dept

  22. Tidying Terms S33 Examples 3a2 – 2a2 = a2 2x – 6y 3x – 4y – x – 2y = www.mathsrevision.com 10x2 – x - y 4x2 – x – y + 6x2 = 12p2 – 4q 6p2 – q – 3q + 6p2 = Created by Mr.Lafferty Maths Dept

  23. S33 Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  24. Integers S33 Multiplication Learning Intention Success Criteria 1. Understand how to multiply positive and negative integers. • 1. Explain how to multiply positive and negative integers. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  25. Rules Multiplying Integers +ve x -ve = -ve -ve x +ve = -ve Integers S33 Multiplication Multiplying Integers 2 1 x (-2) = -2 (-2) x (-1) = -20 (-4) x 5 = (- 2) x (-5) = 10 www.mathsrevision.com -9 (-3) x 3 = 25 (-5) x (-5) = -ve x -ve = +ve +ve x +ve = +ve 32 (-4) x (-8) = -40 5 x (-8) = Created by Mr. Lafferty Maths Dept.

  26. Rules Multiplying Integers +ve x -ve = -ve -ve x +ve = -ve Remember BODMAS Integers S33 Multiplication Multiplying Integers 1 + (-2) x (-10) = 21 28 3 + (-5)2 = www.mathsrevision.com -1 8 – (-3)2 = -ve x -ve = +ve +ve x +ve = +ve 6 5 x (-2)2 + 5 - 19= Created by Mr. Lafferty Maths Dept.

  27. Integers S33 Multiplication Now try MIA Ex 6.1 Ch2 (page 31) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  28. S33 Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  29. Integers S33 Division Learning Intention Success Criteria 1. Understand how to divide positive and negative integers. • 1. Explain how to divide positive and negative integers. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  30. Rules Multiplying Integers +ve ÷ -ve = -ve -ve ÷ +ve = -ve Integers S33 Division Dividing Integers 11 8÷ (-4) = -2 (-22) ÷ (-2) = -4 (-24) ÷ 6 = (- 56) ÷ (-7) = 8 www.mathsrevision.com -1 (-3) ÷3 = 3 (-15) ÷(-5) = -ve ÷ -ve = +ve +ve ÷ +ve = +ve 0.5 (-4) ÷(-8) = -8 16 ÷(-2) = Created by Mr. Lafferty Maths Dept.

  31. Rules Multiplying Integers +ve ÷ -ve = -ve -ve ÷ +ve = -ve Remember BODMAS Integers S33 Division Division Integers 1 + (-20) ÷(-10) = 3 4 100 ÷(-5)2 = www.mathsrevision.com 96 100 - 36 ÷(-3)2 = -ve ÷ -ve = +ve +ve ÷ +ve = +ve 2 -48 ÷(6 - 2)2+ 5 = Created by Mr. Lafferty Maths Dept.

  32. Integers S33 Division Now try MIA Ex 8.1 Ch2 (page 31) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

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