Big Idea(s):

Partitioning a whole into equal parts

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 and solve fair‐share problems that involve 2 and 4 sharers, respectively, and have remainders of 1 or 2

• Fractions: B1.7 recognize that one half and two fourths of the same whole are equal, in fair‐sharing contexts

teacher background

Students may benefit from prior experience with:

• the concept of fair sharing

• identifying common 2-D shapes (square, rectangle, circle, triangle)

• composing and decomposing numbers to 20

• directly comparing objects by length

Key concepts

• When something is shared fairly, or equally as two pieces, each piece is 1 one half of the original amount. Two one halves make up a whole.

• When something is shared fairly, or equally as four pieces, each piece is 1 one fourth of the original amount. Four one fourths make up a whole.

• If the original amount is shared as two pieces or four pieces, the fractions one half and two fourths are equivalent.

• A half of a half is a fourth.

• If something is cut in half, it is not possible for one person to get “the big half” while the other person gets “the small half”. If something is cut in half, both pieces are exactly equal. If there is a “big half”, then it isn’t a half.

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.

• Different fractions can describe the same amount as long as they are based on the same whole.

• The size of the whole matters. If 1 one half and 1 one fourth are based on the same whole, then 1 one half is twice as big as 1 one fourth. But if a small sticky note is cut into halves, and a big piece of chart paper is cut into fourths, then the 1 one fourth of the chart paper is bigger than the 1 one half of the sticky note.

• The fair-share problems that students engage in for learning around B1.6 will provide the opportunity to notice that 1 one half and 2 one fourths are the same amount.

• Students in this grade are not expected to write fractions symbolically; they should write “half”, not “½”

Fold a large paper square to make two equal parts. Show and discuss how the two parts are the same or equal. Say, “When the whole is broken into two equal parts, each part is one-half of the whole.” Fold another square into two parts that are not equal. Ask, “Why can’t we call these two parts halves?”

Repeat the activity, folding into 3 and then 4 equal parts.

Discuss the idea of sharing fairly.

Give each pair a collection of paper strips, paper rectangles, string, ribbon, and balls of modelling clay.

• Look at all of these different items for sharing. Each item is one whole.

• Choose an item. Decide how many people you will share each whole with.

• Work with your partner to share the whole fairly. You can use folding, drawing, scissors, or modelling clay tools to help.

• What do we call the name of the part that each person gets?

• Repeat with different items, sharing among three or four people.

LOOK-FORS:

• Are students able to fold or cut the items to make halves, thirds, fourths, ...?

• Do students attend to the equal size of each part, or do they randomly cut or fold?

• Are students able to connect the number of parts to the correct fraction name?

• Do students notice that different-sized wholes result in different-sized halves, thirds, fourths, ...?

Have students show how they shared different items. Include different wholes and a variety of different ways to partition the whole (e.g., show the same rectangular whole partitioned into halves, thirds, and fourths). For each example say, “When the whole is broken into ___ (3) equal parts, each part is ___ (one-third) of the whole.”

Have students share how they ensured the parts were fair (e.g., “When I folded it, I matched corner to corner”).

Highlight for Students

• Fraction parts have special names that tell us how many equal parts make a whole.

• When we share an item fairly, each person gets the same amount.

Accommodations: Partition one or two items to share with two people.

Extension: Partition four or five items to share with more than four people.

Combined Grades Extension: Use copies of the same item to explore the relation between number of equal parts and the size of the parts.

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