Comparing A

# Generate and recognize equivalent fractions using models and symbols

# Recipe Task

#### Description

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.

#### Mathematics

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.

#### Curriculum Connections

Students will:

- decompose fractions into unit fractions
- count by unit fractions
- compare fractions with friendly but unlike denominators
- generate equivalent fractions using models

#### Instructional Sequence

- 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. (1
^{2}⁄_{4}=^{1}⁄_{4}+^{1}⁄_{4}+^{1}⁄_{4}+^{1}⁄_{4}+^{1}⁄_{4}+^{1}⁄_{4}=^{6}⁄_{4})

#### Highlights of Student Thinking

Students may:

- 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.

#### Key Questions

- 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)?

**Materials**