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Cogito

Grade 2 Math · Chapter 8 · Lesson 8

Practice Worksheet

Equal Shares, Different Shapes

Two halves of a shape need not look the same.

10 problems · about 13 minutes · 2.G.A.3

NameDate

Figures — use these to answer the problems

A rectangle cut into equal strips.
How many shares2
Figure 1
A circle cut into equal wedges. Different shape, same idea.
How many shares2
Figure 2
These two pieces are not the same size, so they are not halves.
How many pieces2
Figure 3

Warm-Up Review

From earlier lessons. Loosen up before the new work.

3 problems

  1. From “Fourths”

    How many fourths make one whole?

    Answer

  2. From “Thirds”

    How many thirds make one whole?

    Answer

  3. From “Halves”

    How many halves make one whole?

    Answer

Warm Up

Straightforward practice. Get the method working first.

3 problems

  1. Two halves of a square are triangles. Is that allowed?

    • Yes, if they are the same size.
    • No. Halves are always rectangles.

  2. What has to be equal about equal shares?

    • How much they cover.
    • What shape they are.

  3. Must two halves be the same shape?

    • No. Only the same size.
    • Yes. Always.

Build It Up

The same ideas with more to keep track of.

1 problem

  1. Must two halves be the same size?

    • Yes. That is what equal means.
    • No. Roughly is fine.

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

3 problems

  1. How many different ways can a square be halved?

    Answer

  2. Two Cuts

    A square is cut corner to corner into two triangles. Are they halves?

    • Yes. Both pieces are the same size.
    • No. Halves must be rectangles.

  3. Not Fair

    A rectangle is cut into a big piece and a small piece. Are they halves?

    • No. They are not the same size.
    • Yes. There are two pieces.