Cogito
Grade 5 Math · Chapter 8 · Lesson 5
The Shape Hierarchy
A property of a group belongs to everything in it.
10 problems · about 15 minutes · 5.G.B.3, 5.G.B.4
What this lesson teaches
The child classifies two-dimensional figures in a hierarchy based on properties.
- Shape groups sit inside each other.
- A property of a group belongs to everything inside it.
- One shape can have several correct names.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Patterns as Pairs: A adds 3, B adds 12, from 0. What is B when A is 9?
Answer 36
Why 36.
Review — The Coordinate Plane: In (6, 1), how far across do you go?
Answer 6
Why 6 across, then 1 up.
Warm Up
Straightforward practice. Get the method working first.
4 problemsIs every rectangle a parallelogram?
Answer Yes.
Why A rectangle sits inside the parallelogram group.
If a group has a property, what do the shapes inside it have?
Answer That property too.
Why Every shape in a group has that group’s properties.
How many right angles does a rectangle have?
Answer 4
Why Every corner.
How many pairs of parallel sides does a parallelogram have?
Answer 2
Why Both pairs of opposite sides.
Build It Up
The same ideas with more to keep track of.
2 problemsIs every square a parallelogram?
Answer Yes.
Why Opposite sides are parallel.
Can one shape have several correct names?
Answer Yes.
Why A square is three things at once.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsOne Way Round: Is every rectangle a square?
Answer No. Its sides need not be equal.
Why The relationship only works one way.
The Other Way: Is every square a rectangle?
Answer Yes. It has 4 right angles.
Why A square is inside the rectangle group.