Big Idea(s):

Comparing the sizes of different unit fractions of the same whole.

Expectations:

B1. Number Sense: demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life

• Fractions: B1.6 use drawings to represent, solve, and compare the results of fair‐share problems that involve sharing up to 10 items among 2, 3, 4, and 6 sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts

teacher background

Students may benefit from prior experience with:

• sharing items fairly

• partitioning shapes into equal parts

• using ordinal number names to tenth

• comparing and ordering quantities

Key concepts

• Fair-sharing or equal-sharing means that quantities are shared equally. For a whole to be shared equally, it must be partitioned so that each sharer receives the same amount.

Note

• Words can have multiple meanings. It is important to be aware that in many situations, fair does not mean equal, and equal is not equitable. Educators should clarify how they are using the term “fair share” and ensure that students understand that in the math context fair means equal and the intent behind such math problems is to find equal amounts.

• Fair-share or equal-share problems provide a natural context for students to encounter fractions and division. Present these problems in the way that students will best connect to.

• Whole numbers and fractions are used to describe fair-share or equal-share amounts. For example, 4 pieces of ribbon shared between 3 people means that each person receives 1 whole ribbon and 1 one third of another ribbon.

• When assigning these types of problems, start with scenarios where there is a remainder of 1. As students become adept at solving these problems, introduce scenarios where there is a remainder of 2 that needs to be shared equally.

• Fractions have specific names. In Grade 2, students should be using the terminology of “halves”, “fourths”, and “thirds”.

Show students a yellow Pattern Block. Have a volunteer find 2 Pattern Blocks (red block) that cover the yellow block. Ask, “What part does each red block represent?” (one half)

Repeat; this time have a volunteer find 3 blocks that cover the yellow block (blue block; one third). Then have a volunteer find 6 blocks that cover the yellow block (green block; one sixth).

Have students compare the sizes of the different parts.

Repeat the activity with Cuisenaire Rods.

Give each pair a set of Cuisenaire Rods and a set of questions (Line Master 53).

• Take the dark green rod. Find 2, then 3, then 6 rods of the same colour that cover the rod exactly. Draw pictures and label each part.

• What do you notice about the number and size of the different parts?

• Which is bigger: two thirds or three sixths? How do you know?

• Take the brown rod. Find 8, then 4, then 2 rods that cover the brown rod exactly. Choose questions. Use the rods to answer the questions.

LOOK-FORS:

• Are students able to use rods to show different parts of a whole?

• Are students able to label each part with a fractional name?

• Are students able to compare fractional parts to determine which is bigger?

• Do students realize that the whole covered with the most rods has the smallest parts?

How to Differentiate:

Accommodations: Have students focus on finding 2 rods of the same colour that cover the dark green and brown rods.

Extension: Have students show thirds using the blue rod, and halves, fifths, and tenths using the orange rod.

Combined Grades Extension: Have students choose any rod and then show and record as many different unit fractions as they can.

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SEL Self-Assessments (English) and Teacher Rubric

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