Solve linear inequalities in one variable Grade 5 Solve linear inequalities in one variable Solve linear inequalities in one variable If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl.org.uk

Lesson Plan Lesson Overview Progression of Learning Objective(s) Solve linear inequalities in one variable Grade 5 Prior Knowledge Solving linear equations Expanding brackets Duration 45 minutes are needed for this objective provided students can solve linear equations. Resources Print slides: 4, 6, 13, 16, 25 Equipment Progression of Learning What are the students learning? How are the students learning? (Activities & Differentiation) The meaning of the 4 inequality signs Give students slide 4 printed. Ask them to state whether each of the inequalities are true or false. Identifying numbers which satisfy an inequality Continuing on slide 4. Students need to list the integer values which satisfy each inequality. Review answers using slide 5. How to solve linear inequalities Give students slide 6 printed. This includes 6 questions increasing in difficulty. Use slides 7 to 12 to explain how to solve each inequality. Ensure that students do not change the inequality sign to equal and that they complete one step at a time. Give students slide 13 printed. Complete one or both sets of practice questions to consolidate understanding. 10 Solving linear inequalities in contextualised problems Give students slide 16. Students to attempt individually. Support may be need in terms of setting up the inequality first in order to solve after. 15 Solving linear inequalities in OCR exam questions (from specimen papers) Give students slide 25. This includes 2 exam questions related to objective. Students need to use notes from lesson to answer the questions. Ensure that all steps are shown. Relate to mark scheme to show how the marks are allocated. Next Steps Using set notation to represent solutions More complex inequalities (double inequalities, quadratics) Inequalities on graphs Assessment PLC/Reformed Specification/Target 5/Algebra/Solve Linear Inequalities in one variable

Key Vocabulary Solve Linear Inequality Unknown Variable

Inequalities State whether each of the inequalities are true or false: List the integers (n) which satisfy: 2 > 7 3 ≥ -3 0 > -5 4 ≤ 4 -5 < 5 3 ≤ -8 ½ ≥ ¼ 2 < n < 7 0 < n < 3 -8 < n < -2 2 ≤ n < 5 -6 < n ≤ -4 -2 ≤ n ≤ 1 ½ < n ≤ 3 Student Sheet 1

Inequalities State whether each of the inequalities are true or false: List the integers (n) which satisfy: 2 > 7 3 ≥ -3 0 > -5 4 ≤ 4 -5 < 5 3 ≤ -8 ½ ≥ ¼ False 2 < n < 7 0 < n < 3 -8 < n < -2 2 ≤ n < 5 -6 < n ≤ -4 -2 ≤ n ≤ 1 ½ < n ≤ 3 3, 4, 5, 6 True 1, 2 True -7, -6, -5, -4, -3 True 2, 3, 4 True -5, -4 False -2, -1, 0, 1 1, 2, 3 True

Solving Linear Inequalities - Demo 11 > 3x + 2 x + 5 > 10 2x + 3 < 17 4 (x + 5) < 6x 5 (x + 2) > 2 (x + 11) 2x + 17 < 7x + 2 Student Sheet 2

How to solve linear inequalities Aim is to leave x on its own x + 5 > 10 Remember to keep x on the same side and bring inequality sign down. - 5 - 5 x > 5

What is the biggest integer that satisfies the inequality? How to solve linear inequalities 2) 2x + 3 < 17 - 3 - 3 Question: What is the biggest integer that satisfies the inequality? 2x < 14 ÷ 2 ÷ 2 x < 7 7

How to solve linear inequalities 3) 11 > 3x + 2 Question: Does it matter which side of the inequality x is? - 2 - 2 9 > 3x ÷ 3 ÷ 3 3 > x

How to solve linear inequalities 4) 2x + 17 < 7x + 2 - 2x - 2x 17 < 5x + 2 - 2 - 2 15 < 5x ÷ 5 ÷ 5 3 < x

How to solve linear inequalities 5) 4 (x + 5) < 6x 4x + 20 < 6x - 4x - 4x 20 < 2x ÷ 2 ÷ 2 10 < x

How to solve linear inequalities 6) 5 (x + 2) > 2 (x + 11) 5x + 10 > 2x + 22 - 2x - 2x 3x + 10 > 22 - 10 - 10 3x > 12 ÷ 3 ÷ 3 x > 4

Practice Set 1 Set 2 Student Sheet 3 2y + 10 > 7y + 5 3x + 9 < 6x 3 (a + 4) < 6a 8x – 6 > 2(x + 9) 3(y + 4) > 5 (y + 2) 3p – 8 > p + 2 2s + 12 < 6s 5 + 3n < 9n – 4 2 (h + 5) > 6 (h – 5) 5 (z – 6) < 2 (6 + z) Student Sheet 3

Practice Set 1 2y + 10 > 7y + 5 3x + 9 < 6x 3 (a + 4) < 6a 1 > y or y < 1 3 < x or x > 3 4 < a or a > 4 x > 4 or 4 < x 1 > y or y < 1

Practice Set 2 3p – 8 > p + 2 p > 5 2s + 12 < 6s 5 + 3n < 9n – 4 2 (h + 5) > 6 (h – 5) 5 (z – 6) < 2 (6 + z) p > 5 3 < s 1.5 < n 10 > h z < 14

Problem Solving and Reasoning ABC is a triangle. Side AB is longer than side BC. Find the longest possible side lengths. Perimeter of an equilateral triangle is bigger than the perimeter of a regular pentagon. Write down the inequality, solve and write down the biggest even integer that satisfies the inequality. Explain why 5(3a + 4) > 3(5a - 2) cannot be solved. Why do we use inequalities? How can we represent these graphically? Spot the mistake: Student Sheet 4

Problem Solving and Reasoning ABC is a triangle. Side AB is longer than side BC. Find the longest possible side lengths. 3b + 7 C B 5b - 3

Problem Solving and Reasoning + 3 + 3 C B 10 > 2b 5b - 3 ÷ 2 ÷ 2 5 > b

Problem Solving and Reasoning Therefore the largest integer possible for ‘b’ is 4 for longest possible side lengths. 3b + 7 AB => 3b + 7 b = 4 AB => 3x4 + 7 C B 5b - 3 AB => 12 + 7 AB => 19 units

Problem Solving and Reasoning Therefore the biggest integer possible for ‘b’ is 4 for longest possible side lengths. 3b + 7 BC => 5b - 3 b = 4 BC => 5x4 - 3 C B 5b - 3 BC => 20 – 3 BC => 17 units

Problem Solving and Reasoning Perimeter of an equilateral triangle is bigger than the perimeter of a regular pentagon. Write down the inequality, solve and write down the biggest even integer that satisfies the inequality. 2x - 1 3x + 1

Problem Solving and Reasoning Perimeter of an equilateral triangle is bigger than the perimeter of a regular pentagon. Write down the inequality, solve and write down the biggest even integer that satisfies the inequality. 2x - 1 3x + 1 3 (3x + 1) > 5 (2x – 1) 9x + 3 > 10x – 5 8 > x or x < 8 Biggest even integer is 6.

Reason and explain Explain why 5(3a + 4) > 3(5a - 2) cannot be solved. Why do we use inequalities? How can we represent these graphically? Spot the mistake: 5 (x - 2) > 3 (x + 4) 5x - 10 = 3x + 12 2x = 10 + 12 2x = 22 x = 11 - 3x

Reason and explain Explain why 5(3a + 4) > 3(5a - 2) cannot be solved. Why do we use inequalities? How can we represent these graphically? Spot the mistake: Unknown variable (a) cancels from both sides To represent the size of a variable Plotting them and shading region – above or below lines 5 (x - 2) > 3 (x + 4) 5x - 10 = 3x + 12 2x = 10 + 12 2x = 22 x = 11 - 3x

Exam Question – Specimen Papers Student Sheet 5

Exam Question – Specimen Papers

Exam Question – Specimen Papers