Description

In this hands-on task, each student independently represents 1⁷⁄₈ by creating either a physical model (e.g., using tiles, folded paper, relational rods, or other items with which students are comfortable working) or a two-dimensional model (e.g., a drawing or a number line) of their choice. Students are then challenged to create as many addition and subtraction number sentences as possible to represent 1⁷⁄₈

Mathematics

This task encourages students to compose and decompose physical, as well as symbolic, representations of fractions (through addition and subtraction number sentences). The task highlights how representation activities requiring composition and decomposition support number sense while serving to introduce and reinforce the foundations of operations (adding and subtracting fractions). The use of concrete models and/or pictures helps students visualize and reason about fraction operations and to develop flexibility in iterating or repeating unit fractions. These processes form a solid basis on which algorithms can be developed and learned.

Curriculum Connections

Students will:

• count forward by halves, fourths and eighths to beyond one whole
• use a variety of mental strategies to solve problems involving the addition and subtraction of fractions
• regroup fractional parts into wholes, using concrete materials

Instructional Sequence

1. Have students work independently at first; each student creates a model of their choice to represent 1⁷⁄₈.
2. Partner students and distribute BLM 1. Have students work through the prompts together using both student models.
3. Consolidate using the key questions.

Materials

• BLM 1 (one copy/pair of students)
• blank and grid paper (one piece/pair of students)
• various manipulatives (such as relational rods, cubes, colour tiles) and everyday items (such as paper clips, construction or graph paper, rulers, markers)