Love For MathCreative Math Education

DIY Challenge 1: Tiling with trominoes

Which of the following can you tile using tromino tiles?

Do you think it is impossible to tile some of them?

Here’s the link to the online activity:
https://jrmathfestivals.github.io/TilingChallenge/

What students worked out8

  • Student 7

    Only 3 and 6 are possible because 3×3=9 & 6×6=36 and 9 (3+6 and of Corse 3×3) is divisible by three. 4 and 5 are not possible because (4×4 =16,1+6=7)&(5×5=25,2+5=7) 7 is not divisible by 3 .Hence 4 and 5 are not possible

  • Student 7

    In 4 and 5 we would need to use a blocking square then only 4 and 5 would be possible

  • Student 1

    Only the 3×3 and 6×6 grid are possible to fill because 3 is a factor of 9(3×3) and 36(6×6),also 36 and 9 are multiples of 3.

  • Student 13

    Sir, here is my answer:
    3×3…………Yes, (0 squares remaining);
    4×4…………No, (4 squares remaining);
    5×5…………No, (1 square remaining);
    6×6…………Yes, (0 squares remaining).

    • Student 2

      IS 4X4 1 SQUARE CAN BE REMAINING

  • Student 2

    2×2=NOT POSSIBLE
    3X3=POSSIBLE
    4X4=NOT POSSIBLE
    5X5=NOT POSSIBLE
    6X6=POSSIBLE
    7X7=NOT POSSIBLE
    8X8=NOT POSSIBLE
    9X9=POSSIBLE
    5X9=POSSIBLE
    3X4=POSSIBLE
    4X6=POSSIBLE
    2X4=NOT POSSIBLE
    8X7=NOT POSSIBLE
    OBSERVATION:-
    ALL THE NUMBERS WHEN WE MULTIPLY THEM LIKE IF IT IS 2×2 THEN 2×2=4 SO WE CAN DO THIS WAY FOR ALL NUMBERS IF THEY ARE DIVISIBLE BY 3 THEN IS IS POSSIBLE

  • Student 4

    Only the 3×3 and 6×6 are possible

  • Student 3

    only 3×3
    6×6 possible