Big Idea(s):

Partitioning a set into equal parts and identifying the parts with fraction

Sorting a set using different attributes

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 20 items among 2, 3, 4, 5, 6, 8, and 10 sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts

teacher background

In this lesson, Pattern Blocks may be used to represent a set model of fractions. In a set model, we identify fractions within a collection of items, where the entire collection represents the whole (e.g., 1/2 of the class, 3/8 of the fruit).

When we look at fractions of a set, the parts do not have to be equally sized. For example, when we look at fractions within the class (e.g., What fraction of the class is wearing blue jeans?), the students don’t all have to be the same size. Likewise, when we look at a collection of Pattern Blocks and look at fractions related to colour within the set, we don’t need to worry about area. In this example, a set that contains 3 red trapezoids, 2 green triangles, and 1 yellow hexagon has a total of 6 items, and each block will represent 1/6 . It is helpful to explore set models of fractions with students because they encounter set models often, both inside and outside of school. Explicit learning about this model allows students to build a deeper understanding of fractions in general, including the ability to think flexibly across models. You may or may not choose to use Pattern Blocks, depending on what was observed in previous lessons (e.g., whether some conflation between set and area models surfaced with Pattern Blocks).

Students may benefit from prior experience with:

• sharing items equally

• partitioning shapes into equal parts

• using ordinal number names

• sorting sets of objects

Have 6 students stand. Use a fraction to label the group (e.g., six-sixths). Choose an attribute (e.g., hair colour) and have students rearrange themselves (e.g., 3 with black hair, 2 with brown hair, 1 with blond hair).

Use fractions to describe each part of the group (e.g., 3 of the 6 students, or three-sixths, have black hair).

Repeat with groups of 8 and 10 students.

Point out that when working with sets, the whole is the total number of objects in the set.

Give each pair a collection of 10 objects. Or project this set of 10 objects. Together, brainstorm a list of attributes that can be used to sort the objects (e.g., colour, shape, type).

LOOK-FORS:

• Are students able to use attributes to sort the objects?

• Are students able to name a fractional part of a set?

• Do students realize that the objects in a set can be different and that the parts do not have to be equal (e.g., can have different numbers of objects in each part)?

• Do students understand that when partitioning a set, the set is the whole (e.g., when using 10 objects, the whole is 10)?

There are 4 equal groups of 3. Each group is one-fourth of 12.

Count the groups: 1 one-fourth, 2 one-fourths, 3 one-fourths, 4 one-fourths.

Discuss what a numerator of 0 means for a set. For example, when there is a set of 2 red buttons and 4 blue buttons, we can say that zero-sixths of the set are green buttons.

To allow students to show what they have learned in this lesson, go to the Exit Ticket and/or Practice.

Highlight for Students

• A set of objects can be considered as one whole.

• When partitioning a set, the groups or parts do not have to be equal size.

• We can use fractions to describe parts of a set.

How to Differentiate:

Accommodation: Provide a set of fewer objects all the same colour (e.g., buttons) and give students the attribute to sort by (e.g. number of holes, shape, or size).

Extension: Provide sets of objects that can be sorted in many different ways.

All assessments, in the moment feedback/prompts, and independent tasks can be accessed by logging into your Mathology/Mathologie account.

SEL Self-Assessments (English) and Teacher Rubric

Log in to your Mathology.ca / Mathologie.ca account to access Intervention and Extension activities, Professional Learning Videos and Assessment tools.