This fractions unit is very narrowly focused on building the kids up to be able to nail the first gloss question. It is certainly not comprehensive or a guide on the range of things that should be taught. Some of the things below should indicate the full range to teaching and learning that might take place.
For students to really understand fractions, they must experience fractions across many constructs, including part of a whole, ratios, and division.
Three categories of models exist for working with fraction:
Three categories of models exist for working with fraction:
- area (e.g., 1/2 of a garden)
- length (e.g., 1/3 of an meter),
- and set or quantity (e.g., 1/4 of the class
Understanding fractions means understanding all the possible concepts that fractions can represent. One of the commonly used meanings of fraction is part‐whole, including examples when part of a whole is shaded. In fact, part‐whole is so ingrained in elementary textbooks as the way to rep resent fractions, it may be difficult for you to think about what else fractions might represent. Although the part‐ whole model is the most used in textbooks, many who research fraction understanding believe students would understand fractions better with more emphasis across other meanings of fractions (Clarke, Roche, & Mitchell, 2008; Siebert & Gaskin, 2006).
Thinking about fractions
Reference:
Teaching Progression
The progression above is only a snapshot of things that can be taught and ways the ideas can be developed. That i developed as part of an intensive 6 week intervention with a group of students.
Do not forget to use: NZ math planner, NZ math Book 7