- representing fractions
- finding equivalent fractions
- decomposing fractions into like denominators
- decomposing fractions into unlike denominators
- composing fractions in different ways
- multiplying a fraction by a whole number
- adding fractions
- subtracting fractions
- critical thinking
- finding and proving math theories
Who knew those little geometric shapes could be so useful, right? (We'll also be using them for geometry and angles soon) It's also been nice because, when paired with a really good math task question, the kids differentiate themselves and level out at their own stage of difficulty within the task. So enough talk, here's what we did with them.
On the board I wrote the following task question:
"If this is equal to one whole, what would the other pieces represent?"
Right away they were able to determine the red hexagons equaling 1/2, the blue rhombus equaling 1/3 and the green triangle equaling 1/6. That was where they got stumped. And therefore assumed the other pieces were impossible. I had them trace the pieces on paper and cut them out so they could better manipulate the pieces. Eventually they discovered a triangle fit on the orange square, as well as another triangle cut in half vertically with the pieces turned upside-down. This meant the square totaled 2/6. The cut-and-turn strategy got them thinking they could do the same to figure out the tan rhombus, which they did. One tan rhombus cut in half horizontally can fit together in a green triangle, so we determined they were both equal to 1/6. This led to a great conversation about how things can be different shapes but take up the same amount of space.