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Mathematics Involving Shape and Space a Algebra

Enhance your understanding of geometry and algebra by solving geometrical problems, identifying the properties of 2D shapes, and constructing and solving equations. Have a go at creating different triangles and quadrilaterals with the nine-dot problem, and explore perimeter calculations in relation to algebraic expressions. This interactive activity will strengthen your mathematical skills!

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Mathematics Involving Shape and Space a Algebra

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  1. Mathematics Involving Shape and Space a Algebra

  2. The 9-Dot Problem

  3. Objectives Solve geometrical problems Identify the properties of 2-d shapes

  4. Have a go at Triangles Draw as many different triangles by joining three of the nine dots

  5. Have a go at Quadrilaterals Draw as many different quadrilaterals by joining four of the nine dots

  6. Algebra Walls Constructing and solving equations using Algebra Walls

  7. Algebra walls = 27 n + 19 ? 12 ? n + 7 ? 5 7 n n + 19 = 27 n = 27 - 19 n = 8

  8. Algebra walls = 27 ? 27  12 ? ? 15 5 7 n 8 n = 8 Back substitute to check

  9. Algebra walls = 35 ? 3n + 17 2n + 7 ? n + 10 ? 2n 7 n + 3 3n + 17 = 35 3n = 35 - 17 3n = 18 n = 6

  10. Algebra walls = 35 ? 35  19 ? ? 16 2n 7 n + 3 12 9 n = 6 Back substitute to check

  11. Algebra walls = 42 n = 5 = 27 n = 2 n n + 5 n 5 26 12 = 73 n = 6 = 32 n = 5 Solve for n and back substitute to check n + 14 n -16 2n 16 n + 26 n + 26 n = 2.5 n = 6 = 88 = 33 3n + 4 24 - n 2n + 8 4 - 2n 4n + 6 6n + 7

  12. Constructing and solving equations using the perimeter of shapes

  13. Perimeter and algebra ? The perimeter of this shape is 22cm. Find the length of each side 3n ? 6 n + 2 4 12 6n ? Total perimeter = 3n + n + 2 + 6n = 10n + 2 10n + 2 = 22 10n = 20 n = 2 Substitute n = 2 into the expressions for each length Check: 6 + 4 + 12 = 22 so n = 2 is correct The length of each side is 6, 4 and 12

  14. Perimeter and algebra ? ? 12 - n The perimeter of this shape is 38cm. Find the length of each side 3n - 4 8 8 16 6 n + 2 ? 4n ? Total perimeter = 3n - 4 + 12 - n + n + 2 + 4n = 7n + 10 7n + 10 = 38 7n = 28 n = 4 Substitute n = 4 into the expressions for each length Check: 8 + 8 + 6 + 16 = 38 so n = 2 is correct The length of each side is 8, 8, 6 and 16

  15. Perimeter and algebra The perimeter of each shape is inside the shape. Find the length of each side b) n = 3 a) 3n - 5 n +5 n + 6 50cm n + 30 41cm n + 2 n = 6 n + 6 2n - 4 d) Solve for n and back substitute to check n + 6 c) 2n + 6 15 - n 15 - n n = 4 n = 8 n + 6 63cm 115cm n + 2 24 – 2n 2n + 8 n + 8 2n + 8 8n - 8

  16. THE END!

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