Snake Game -- Binary Operations +-x/^ and square roots

This game is challenging at every level from K-5th grade. The first square must be given and every other square after that is a binary operation (+-x/) (plus, minus, times, and division) and ^ (exponent and square root. Also, the last square is given.

For example, if we start with 2 followed by a +7, the next box is 9. Then we see x2, so the next box is 18 and so on.

The attach pdf has an example for each of K/1, 2/3, 3/4, and 5/6th grade, followed by three game boards for each. Then there are several blank game boards where the students can make their own game.

We developed strategies for each binary operation, addition, subtraction, multiplication, and division. For addition, use the vertical addition algorithm with carries. For subtraction, use the vertical algorithm but always add the difference to the subtracted number and ensure that it equals the number subtracted from. For multiplication use repeated addition, or distributive property (13 x 6 would be 10 x 6 plus 3 x 6 or 60 + 18 = 78). For division, count by the divisor until you reach the dividend (100 / 20 you would count by 20, so 20, 40, 60, 80, 100 and see that you counted 5 multiples of 20 so the quotient is 5). With some of the groups, I including multiplying and dividing positive integers and negative integers. Although your Rabbi or Priest may disagree, this may be one way to remember the algorithm:

Positive x or /. by a Positive = Positive When good things happen to good people, that's good.

Negative x or /. by a Positive = Negative When bad things happen to good people, that's bad.

Positive x or /. by a Negative = Negative When good things happen to bad people, that's bad.

Negative x or /. by a Negative = Positive When bad things happen to bad people, that's good.

I also introduced exponents (^) and square roots. For 2^5 = 2x2x2x2x2 = 32. We focused on what 2^5 is not (it is not 2x10=20). We treated square roots as the opposite of exponents, so the square root of 25 = 5 because 5^2=25. With the 5th graders, I introduced cube roots which is the opposite of a cube, so the cube root of 8 = 2 because 2^3=8. The cube root of 27 = 3, because 3^3=27.

The children could do any of the twelve puzzles I created from level K-5th grade and then create their own snakes where they start with a random whole number and in each shaded square use an operation to be applied to the previous square.