Big Idea(s):

Relating the size and number of equal parts in a 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

C4. Mathematical Modelling: apply the process of mathematical modelling to:

• represent, analyse, make predictions, and provide insight into real‐life situations

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”.

Discuss everyday situations where students share fairly. Research bannock, a type of Indigenous bread. Read the story about sharing bannock on Master 47. Use 2 circular bannock of the same size (Master 48) to model sharing the bannock with 2 and 4 people. Have students share their answers and justify their thinking (e.g., the table where it is shared with 2 people because the pieces are bigger).

Give each pair scissors and 3 congruent paper squares of different colours (Master 49). You may also use one of the shapes on Master 50.

• Take one square. Cut or fold it into 2 equal parts. Label each part.

• Take another square. Cut or fold it into 4 equal parts. Label each part.

• Take another square. Cut or fold it into 8 equal parts. Label each part.

• Which colour has the most parts? the fewest? the biggest? the smallest?

• Compare one part from two squares. Which is bigger: one fourth or one eighth? one half or one fourth? one half or one eighth? How do you know?

LOOK-FORS:

• What strategies are students using to cut/fold the square into 8 equal parts (e.g., are they further dividing the fourths into 2 equal parts?)?

• Are students able to cut or fold each square into the correct number of parts? Are the parts equal?

• How are students comparing the different-sized parts?

• Are students able to accurately compare the parts? Are they using math language to make the comparisons?

How to Differentiate:

Accommodations: Students use 2 colours of squares and cut or fold them into 2 equal parts and 4 equal parts.

Extension: Students cut or fold the squares into 2, 3, and 6 equal parts.

Combined Grades Extension: Students divide a set of 16 counters into halves, fourths, and eighths; draw a picture to show each unit fraction; and then compare the fractions.

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