Cogito
Grade 2 Math · Chapter 8 · Lesson 8
Equal Shares, Different Shapes
Two halves of a shape need not look the same.
10 problems · about 13 minutes · 2.G.A.3
What this lesson teaches
The child recognizes that equal shares of an identical whole can have different shapes.
- A shape can be cut into equal shares in more than one way.
- Equal shares must be the same size.
- They do not have to be the same shape.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Fourths: How many fourths make one whole?
Answer 4
Why Four fourths make a whole.
Review — Thirds: How many thirds make one whole?
Answer 3
Why Three thirds make one whole.
Review — Halves: How many halves make one whole?
Answer 2
Why Two halves make a whole.
Warm Up
Straightforward practice. Get the method working first.
3 problemsTwo halves of a square are triangles. Is that allowed?
Answer Yes, if they are the same size.
Why Equal shares can look different from one another.
What has to be equal about equal shares?
Answer How much they cover.
Why Only the amount has to match.
Must two halves be the same shape?
Answer No. Only the same size.
Why Think about the two triangles.
Build It Up
The same ideas with more to keep track of.
1 problemMust two halves be the same size?
Answer Yes. That is what equal means.
Why Equal shares means equal amounts.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsHow many different ways can a square be halved?
Answer 3
Why Down, across, and corner to corner.
Two Cuts: A square is cut corner to corner into two triangles. Are they halves?
Answer Yes. Both pieces are the same size.
Why Equal size is what matters, not the shape of the pieces.
Not Fair: A rectangle is cut into a big piece and a small piece. Are they halves?
Answer No. They are not the same size.
Why Halves must be equal in size.