Getting students to understand fractions begins with an understanding of the ‘whole’.

Take a look at the three designs in the photo. Begin with the question, “What do you notice?” Students will say obvious things like, “There is one hexagon and two trapezoids in the first design”, or “The center design is the largest.” Accept and encourage all these responses as they will help students build confidence.

If no-one offers the idea that each design is half red, prompt them by asking, “What do you notice about the color red in each of the designs?” Students will often jump into equating ‘the color red’ with the number of red blocks in each design. Try and get them to move beyond the obvious to see how the color red relates to the design as a whole. “How much of each design is red?” is a good place to start.

From there, ask the question in the photo, “We know that each of these designs is half red. How can that be if there are a different number of red blocks in each design?”

Relate the idea of the whole to: 1/2 of one dollar and 1/2 of one million dollars. Which would they prefer? Why? A fraction only has meaning when it relates to its whole.

Try this: Pass out triangle isometric paper (type into search engine for free templates) and have students create designs that are 1/2 red, 1/4 red, 1/6 green, etc. Share student work. Students should see that even though each student drew a design that was 1/2 red, etc., the areas colored red may be all different.