Expectations:

B 1.3

represent equivalent fractions from halves to twelfths, including improper fractions and mixed numbers, using appropriate tools, in various contexts

• Key Concepts

• Big Ideas (from Marian Small):

• -There is usually more than one way to show a number or relationship and each of those ways might make something more obvious about that number relationship.

• - A fraction is not meaningful without knowing what the whole is.

• -Fractions can represent parts of regions, parts of sets, parts of measures, parts of division.

Learning Goals Success Criteria

Focus #4 Build Relationships and Communicate Effectively, as students apply the mathematical process of communicating: express and understand mathematical thinking and use appropriate math terminology in a variety of representations so students can work collaboratively on math problems- expressing their thinking, listening to the thinking of others.

https://www.dcp.edu.gov.on.ca/en/curriculum/elementary-mathematics/grades/g4-math/strands#strand-a

Recipe Task

Instructional Sequence

1. Pair students

2. Introduce task using BLM 1: You want to bake some cookies but you only have 1/4 measuring cup.

3. Allow students to work toward a solution using strategies of their choice (eg. concrete models or drawings of area or set models)

4. Consolidate their learning by having a few students share their work using the Key questions (consolidation) as guidance.

5. Get the students to independently place all of the recipe fractions on a number line. Have the students also write the equivalent fractions in fourths (1 1/2=1/4 + 1/4+1/4+1/4+1/4+1/4=6/4)

http://www.edugains.ca/newsite/DigitalPapers/FractionsLearningPathway/ComparingFractions-A-RecipeTask.html

Teacher Notes:

Comparing and ordering fractions allows students to develop a sense of fraction as quantity, as well as a sense of the size of a fraction, both necessary prior knowledge components for understanding fraction operations (Johanning, 2011).

Comparing and ordering fractions with different fractional units (or denominators) leads students to identify the need for equivalent fractions. When students determine an equivalent fraction they are changing the unit of measure by either splitting or merging the partitions of the original fraction. The following illustration demonstrates these concepts using an area model:

Splitting to determine an equivalent fraction for 2/3

Merging to determine an equivalent fraction for 6/8

The exploration of equivalence allows students to develop an understanding of equivalent fractions as simply being a different way of naming the same quantity; it also supports them in viewing the fraction as a numeric value. A solid understanding of equivalence helps students with fractions operations, especially addition and subtraction.