Students decompose fractional amounts in a recipe using the unit fraction 1⁄4 in order to accurately mix ingredients using only a 1⁄4 measuring cup.They compose equivalent fractions using unit fractions and represent them in a variety of ways. As an option, the recipe can be prepared and baked by the class.
Decomposing fractions aids students in gaining a concrete understanding of the relationship between a pair of equivalent fractions. Using concrete and visual representations like drawings or measuring cups are beneficial when proving equivalency.
- decompose fractions into unit fractions
- count by unit fractions
- compare fractions with friendly but unlike denominators
- generate equivalent fractions using models
- Pair students.
- Introduce task using BLM 1: You want to bake some cookies but you only have a 1⁄4 measuring cup.
- Allow student to work toward a solution using strategies of their choice (e.g., concrete models or drawings of area or set models).
- Consolidate their learning by having a few students share their work using Key Question as guidance.
- Have the students independently place all of the recipe fractions on a number line. Also ask them to name the equivalent fractions using fourths. (12⁄4 = 1⁄4 + 1⁄4 + 1⁄4 + 1⁄4 + 1⁄4 + 1⁄4 = 6⁄4)
Highlights of Student Thinking
- use a variety of concrete models: area, set, volume
- write the fractions on the number line in many ways 1 1⁄2, 1 2⁄4, 6⁄4
- use mixed and improper fractions interchangeably
- make connections to money (0.25 = 1⁄4)
- have difficulties partitioning their number line into unit fractions
- have difficulties transferring knowledge to number line.
- What model did you use to decompose or break down the given fractions?
- How did your unit fraction ( 1⁄4 ) compare to the fractional amounts in the recipe?
- How did you recognize the equivalent fractions on the number line?
- Can you write your mixed fraction as an improper fraction (or vice versa)?