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Exploring Tak-Tiles: Mastering Algebraic Area Combinations

Dive into the world of algebra with Tak-Tiles as we explore the concept of area through innovative shapes. Learn to express the areas of various configurations using algebraic expressions like area A and area B. By manipulating shapes and their areas, discover how to combine and simplify various expressions, including forms like 2(a + b) and more complex combinations. Challenge yourself to find multiple ways to represent these areas. This engaging approach to algebra not only enhances comprehension but also fosters creativity, problem-solving, and critical thinking skills.

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Exploring Tak-Tiles: Mastering Algebraic Area Combinations

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Presentation Transcript

  1. Introducing Tak-tiles Algebra using areas

  2. 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

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

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

  5. How did you do 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

  6. 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)

  7. 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

  8. What about this shape? 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

  9. 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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