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Exploring Algebraic Expressions in Compound Shape Areas

This lesson focuses on developing algebraic expressions to represent the areas of compound shapes. Students will explore different ways of simplifying and writing these expressions.

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Exploring Algebraic Expressions in Compound Shape Areas

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  1. Objective To begin to think about number and algebra in relation to areas of compound shapes.

  2. I will be successful if: -I am able to express areas using algebra -I am able to simplify algebraic expressions

  3. area a area b Adding Areas area b area a This has an area of a and this has an area of b So this shape has area a + b

  4. Think about this shape; It could be made like this Or like this a + b a + b 2a + 2b = 2(a + b) 2a + 2b

  5. How many different ways can you find of writing the areas of these shapes? b) a) c) d) f) e) g)

  6. How did you find g? and I take away area b I’m left with area a - b If this has area a This has area + (a – b) a 4(2a - b) 3 2 4 2a - b 1 times time OR Which is

  7. So now can you do these? Remember to write them in as many different ways as you can find!! b) d) a) c) e) f) g) h)

  8. area b The 5 ‘easy’ Tak-tiles If the area of the square is a area a and the area of the quadrant is b Then the area of this shape is OR a + 2b b + a + b So what about these? area a + 2b area 4a - 2b area 3a - b area 2a

  9. MISSION IMPOSSIBLE Mrs Sipula’s safe

  10. YES! MY KEY WORKS OR a + 2b + 4a - 2b + 3a - b ________________ 8a + 3b - 4b a +4a – 3a +2b - 2b - b This has area ________________ 8a - b 8a - b Which is Which is

  11. Can you do this shape in the same way? 3a - b + a + 2b + 2a 2b 11a + 3b - area + a + 2b 11a + b + 4a - 2b ________________ 11a + b ________________

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