Pythagoras 3 D Complete Lesson Preview the presentation

Pythagoras – 3 D – Complete Lesson Preview the presentation to check ability-level, AFL questions, and the animations during demonstrations. It is recommended to delete slides/sections not needed for your class.

Starter A task at the beginning of the lesson that reviews a skill required for the learning. Knowledge Check Questions to assess students’ current understanding and to consequently show progress. Real-Life Example A ‘hook’ to raise interest and provide a concrete example. Demonstration Slides for a teacher to lead students – didactically or via questioning – through a mathematical method. AFL Questions Assessment For Learning Questions, used to assess students’ competency for independent tasks/activities. Plenary An opportunity for students to prove/evaluate their learning.

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STARTER 4 cm 5 cm 11 cm 6. 3 cm 5. 5 m 9 cm 8. 9 m 7. 1 m 8 cm 6 cm 5 m 7 m 6 cm 8 cm 3. 9 cm Give answers to 1 dp. (not to scale!) 7 cm 7. 8 cm 11 cm 2. 8 cm

STARTER 9 cm 4 cm Give answers to 1 dp. (not to scale!) 11 cm 3 cm 8 cm 5. 5 m 5 m 7 m 6 cm 8 cm 7 cm 11 cm 6 cm

January 2022 3 D Pythagoras

What is the distance of AF? KNOWLEDGE CHECK E F 12 cm C D G 6 cm A 8 cm B

What is the distance of AF? KNOWLEDGE CHECK E F 12 cm C D G 6 cm A 8 cm B

Example What is the length of c? Give your answer to 2 d. p. a 5 cm ? c 7 cm b Not to scale a 2 + b 2 = c 2 52 + 72 = 74 c 2 = 74 = 8. 60 cm

Example Your Turn What is the length of c? Give your answer to 2 d. p. (sketch in your book) a 5 cm ? a 7 cm c 7 cm b Not to scale ? c 8 cm b a 2 + b 2 = c 2 52 + 72 = 74 72 + 82 = 113 c 2 = 74 c 2 = 113 = 8. 60 cm Not to scale = 10. 63 cm

Example Your Turn What is the length of c? Give your answer to 2 d. p. (sketch in your book) a 5 cm ? ? c c 7 cm b a 6 cm Not to scale b 11 cm Not to scale a 2 + b 2 = c 2 52 + 72 = 74 62 + 112 = 157 c 2 = 74 c 2 = 157 = 8. 60 cm = 12. 53 cm

Your Turn: Find the missing length. Give your answer to 2 d. p. Example What is the length of c? Give your answer to 2 d. p. a 5 cm ? c 3 cm c 5 cm 7 cm b 9 cm Not to scale a 2 + b 2 = c 2 c 52 + 72 = 74 c 2 = 74 = 8. 60 cm 2. 5 cm x 5 m 14 m

Your Turn: Find the missing length. Give your answer to 2 d. p. Example What is the length of c? Give your answer to 2 d. p. a 5 cm ? 3 cm c Answers c = 5. 83 cm c 5 cm 7 cm b 9 cm Not to scale a 2 + b 2 = c 2 c = 9. 34 c cm 52 + 72 = 74 x c 2 = 74 = 8. 60 cm x = 13. 08 m 5 m 14 m 2. 5 cm

The hunting spider I saw a spider my room… jumps in 9. 9 m. 3 m 5 m 8 m How far does the hunting spider need to jump to catch the ant?

Where is the longest straight line inside this box? How can we calculate the length of the diagonal?

7 cm 7 cm

7 cm 9. 9 cm 7 cm

FIND X 7 cm y x x 5 cm 8 cm To find y, we need to find x first. 8 cm FIND Y y x 9. 43 a 2 + b 2 = c 2 5 2 + 8 2 = x 2 2 89 = x 5 cm x = 9. 43 a 2 + b 2 = c 2 9. 432 + 72 = y 2 2 137. 92 = y 7 cm y = 11. 7 cm (1 dp)

FIND X 9 cm y x x 6 cm 12 cm To find y, we need to find x first. 12 cm FIND Y y x 13. 42 a 2 + b 2 = c 2 62 + 122 = x 2 2 180 = x 6 cm x = 13. 42 a 2 + b 2 = c 2 13. 422 + 92 = y 2 2 261. 10 = y 9 cm y = 16. 2 cm (1 dp)

FIND X x y 12 cm 8 cm x FIND Y 7 cm 8 cm To find y, we need to find x first. y x 10. 63 a 2 + b 2 = c 2 7 2 + 8 2 = x 2 2 11 = x 7 cm x = 10. 63 a 2 + b 2 = c 2 10. 632 + 122 = y 2 2 154. 63 = y 12 cm y = 12. 4 cm (1 dp)

x= y= ① 5 cm y x ② ③ 4 cm y 4 cm 7 cm y= 5 cm Find the distance AB. B 3 cm A 5 cm 7 cm AB =

x = 7. 1 cm y = 8. 7 cm ① 5 cm y x ② Answers y ③ 4 cm 7 cm y = 9 cm 5 cm Find the distance AB. B 3 cm A 5 cm 7 cm AB = 9. 1 cm

Is there an easier way? y x

Example y 5 cm 10 cm

Example 6 cm y 7 cm 4 cm

Example Your Turn y 6 cm 3 cm y 5 cm 7 cm 4 cm 6 cm

Example Your Turn 6 cm y 7 cm 4 cm 2 cm 4 cm

Example Your Turn y 6 cm 5 cm y 6 cm 7 cm 4 cm 3 cm Calculate the distance AB 9. 7 m A 3. 8 m 5 m B

Example Your Turn y 6 cm 5 cm y 6 cm 7 cm 4 cm 3 cm Calculate the distance AB 9. 7 m A 3. 8 m 5 m B

1) a) Find the distance from A to B (2 dp). b) Use that to find the distance from A to C (2 dp). C 2) Find the distance from D to E (2 dp). D 5 cm 6 cm B 6 cm A 3) G 5 cm E 1) 9 cm 6 cm 4) 4 cm Find the distance from F to G (2 dp). Find the distance from H to J (2 dp). H 6. 5 m 8 cm 4. 5 m 1. 5 m ① 5 cm F J

1) a) Find the distance from A to B (2 dp). b) Use that to find the distance from A to C (2 dp). C 2) Find the distance from D to E (2 dp). D 5 cm 6 cm 10. 39 cm B 6 cm A 3) G 6 cm 4 cm E 1) Answers 5 cm 4) Find the distance from F to G (2 dp). 9 cm 11. 45 cm Find the distance from H to J (2 dp). H 6. 5 m 8 cm 4. 5 m 1. 5 m ① 5 cm F 10. 25 cm 8. 05 cm J

1. 2. A box measures 10 cm by 15 cm by 20 cm. H 15 cm G 20 cm C D A 3. F E 10 cm B Calculate the distances: At the edge of a field is a 15 m tall tree. 1) BE 2) AH to 2 dp 25 m Calculate the diagonal AG. X 20 m A spider is at point B and a fly is at point D. 4. This is a square-based pyramid. 1) If the spider used the edges of the wedge, how far would it need to travel to reach the fly? E D 9 cm C ② F 15 m How far is the distance from point X to the top of the tree? B 12 cm A 15 cm 2) If the spider travelled across the face of the wedge, how far would it have to travel? 25 cm 20 cm Calculate the height of the pyramid. (Hint: Calculate the centre of the base first. )

1. 2. A box measures 10 cm by 15 cm by 20 cm. H 15 cm G 20 cm C 1) 25 cm D E 10 cm A 3. F Calculate the distances: 1) BE 2) AH to 2 dp 35. 36 m X diagonal AG. 1) 29. 49 cm 4. This is a square-based pyramid. 1) If the spider used the edges of the wedge, how far would it need to travel to reach the fly? E 25 cm 2) 21. 21 cm D 9 cm C ② F 14. 14 cm B 12 cm A 15 cm 2) If the spider travelled across the face of the wedge, how far would it have to travel? 25 m Answers 20 m A spider is at point B and a fly is at point D. 15 m How far is the distance from point X to the top of the tree? 2) 26. 93 cm. Calculate the B At the edge of a field is a 15 m tall tree. 20 cm 20. 62 cm 20 cm Calculate the height of the pyramid. (Hint: Calculate the centre of the base first. )

What is the distance of AF? KNOWLEDGE CHECK E F 12 cm C D G 6 cm A 8 cm B

What is the distance of AF? KNOWLEDGE CHECK E F 12 cm C D G 6 cm A 8 cm B

AB is 10. 2 cm in length to the nearest decimal place. What is the height of the box? (1 dp) B 8 cm A 5 cm

AB is 10. 2 cm in length to the nearest decimal place. What is the height of the box? (1 dp) B 3. 9 cm 8 cm A 5 cm

Check your success! I can find the diagonal length inside a box. I can use Pythagoras in 3 D to solve real-life problems. I can use Pythagoras to find lengths, heights and widths of 3 D shapes.

Check your success! I can find the diagonal length inside a box. I can use Pythagoras in 3 D to solve real-life problems. I can use Pythagoras to find lengths, heights and widths of 3 D shapes.

Write a text message to a friend describing… How to calculate the diagonal inside a box.

Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths. co. uk