Maths worksheet on square numbers and Pythagorean triples
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This document contains a math worksheet with 20 questions about solving equations involving square numbers. The questions progress from simple equations like 2 x = 22 to more complex problems finding sums of squares or identifying Pythagorean triples. The document provides the questions, spaces to write answers, and a final slide with the correct answers. The goal is for students to practice solving problems involving square numbers at a Level 4 challenge and identify Pythagorean triples at Level 5.
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Maths worksheet on square numbers and Pythagorean triples
- 1. Entry Activity We are going to do 20 quick questions, as soon as we are ready the slides will move on... You need to find the
- 2. Question 1 2 x = 22
- 3. Question 2 8 x = 24
- 4. Question 3 15 - =8
- 5. Question 4 15 + = 99
- 6. Question 5 55 + = 182
- 7. Question 6 9 x = 18
- 8. Question 7 9 x x 3 = 27
- 9. Question 8 9 x - 4 = 15
- 10. Question 9 9 x + 30 = 150
- 11. Question 10 9 x ÷ 4=2
- 12. Question 11 90 ÷ = 10
- 13. Question 12 150 ÷ = 30
- 14. Question 13 75 - = 30
- 15. Question 14 30 + = 27
- 16. Question 15 27 - = 12
- 17. Question 16 12 x - = 12
- 18. Question 17 12 ÷ =1
- 19. Question 18 1 ÷ = 0.1
- 20. Question 19 7 + =3
- 21. Question 20 2 7 + = 100
- 22. Answers 1)11 8)19 15)15 2)3 9)120 16)1 3)7 10)8 17)12 4)84 11)9 18)10 5)127 12)50 19)-4 6)2 13)45 20)10 7)27 14)-3
- 23. Today I will learn to solve problems involving square numbers Level 4 Challenge Objective: identify a Pythagorean triple Level 5 Key Words Square, Pythagoras, Pythagorean, Sum, Ad d, Describe, Solve
- 24. • All will find square numbers • Most will solve problems involving square numbers • Some will identify Pythagorean triples
- 25. Square numbers 1² = 1 x 1 = 1 2² = 2 x 2 = 4 • Draw a diagram/picture for the 1st 10 square numbers in your book. • You must say what the number is you are squaring and what the answer is. • You’ll need this to help you solve problems in a bit...
- 26. Square Numbers
- 27. Level 4
- 28. Answers – Level 4 Number Number squared 3 3×3 9 5 5×5 25 2 2×2 4 6 6×6 36 7 7×7 49 12 12 × 12 144 11 11 × 11 121 0 0×0 0 1 1×1 1 9 9×9 81 4 4× 4 16
- 29. Using your planners which is correct What is 7²? 64 49 36
- 30. Using your planners show me how you found this
- 31. Today I will learn to solve problems involving square numbers Level 4 Challenge Objective: identify a Pythagorean triple Level 5 Key Words Square, Pythagoras, Pythagorean, Sum, Ad d, Describe, Solve
- 32. • All will find square numbers • Most will solve problems involving square numbers • Some will identify Pythagorean triples
- 33. Level 4 from the first activity and answers from Q1
- 34. Answers 2 b square numbers c square numbers d odd numbers e The difference between any two consecutive square numbers is an odd number. 3 e 4 + 9 f 1 + 16 g 9 + 16 h 9 + 25 i 16 + 25 j 25 + 25 or 1 + 49 k 9 + 49 l 16 + 49 m 4 + 64 n 9 + 64 o 16 + 64 p 9 + 81 q 16 + 81 r 25 + 81 s 49 + 81 t 81 + 81
- 35. Using your planners which is correct Write 41 as a sum of square numbers 36 + 5 20 + 21 25 + 16
- 36. Using your planners show me how you found this
- 37. Today I will learn to solve problems involving square numbers Level 4 Challenge Objective: identify a Pythagorean triple Level 5 Key Words Square, Pythagoras, Pythagorean, Sum, Ad d, Describe, Solve
- 38. • All will find square numbers • Most will solve problems involving square numbers • Some will identify Pythagorean triples
- 39. Extension Task – Level 5
- 40. Answers – Extension Task – Level 5 • 52 + 122 = 132 • 62 + 82 = 102 • 102 + 242 = 262 • 72 + 242 = 252
- 41. Using your planners show me how you found this
- 42. Today I will learn to solve problems involving square numbers Level 4 Challenge Objective: identify a Pythagorean triple Level 5 Key Words Square, Pythagoras, Pythagorean, Sum, Add, Describe, Solve
- 43. • All will find square numbers • Most will solve problems involving square numbers • Some will identify Pythagorean triples
- 44. Plenary www…ebi what went well … even better if
- 45. If you would like to print out as a worksheet, please print the following two slides. These can be printed as 2 handouts per page or as individual slides.
- 46. Level 4
- 47. Level 4 from the first activity and answers from Q1
Editor's Notes
- This is an ideal activity to use mini whiteboards, or alternatively you can do as a quick quiz in the students books. The following slides are timed and will move on automatically.
- These are the answers if you have done the entry activity using the students book as a quiz. Not needed if you are using the whiteboards.
- Share the objectives with the class
- All, Most, Some
- Students to show the colour of the correct answer. This will help you to check the progress of the class.
- To check progress of the class, mark the task completed and then ask the students to rate how they found the activity, Green = confident, Yellow = OK, Red = Unconfident/don’t get it. Ask the students to draw the corresponding face next to their work so when marking you can see how the students found the task.
- Share the objectives with the class
- All, Most, Some
- Students to show the colour of the correct answer. This will help you to check the progress of the class.
- To check progress of the class, mark the task completed and then ask the students to rate how they found the activity, Green = confident, Yellow = OK, Red = Unconfident/don’t get it. Ask the students to draw the corresponding face next to their work so when marking you can see how the students found the task.
- Share the objectives with the class
- All, Most, Some
- To check progress of the class, mark the task completed and then ask the students to rate how they found the activity, Green = confident, Yellow = OK, Red = Unconfident/don’t get it. Ask the students to draw the corresponding face next to their work so when marking you can see how the students found the task.
- Share the objectives with the class
- All, Most, Some
- This is a really quick plenary. Get students to write in their book www (what went well) something they found that they were good at and are confident with. They then need to write ebi (even better if) so something that they would like to improve in their work. Get students to share what they have written.
- It maybe helpful to print out the following two slides, as this means that you can let students work at their own pace a bit more and it is easier to differentiate.