PICTURE PROOFS

Picture Proof for . Since x and y are different, they can not be combined. (Note: the overall size of the bar remains the same whether we begin with the x-bar or the y-bar and then add the y-bar or the x-bar.)

Picture proof for

Picture proof for the distributive property, showing that .

Picture proof showing

Picture proof showing the evaluation of , if . If , , will be 23. In order to see this, students would replace the x’s with 2 unit bars, the with 4 unit bars and the with a cube made up of 8 unit pars. By counting all of the unit bars, students can see that the value of he expression , where is 23.