Cogito
Grade 3 Math · Chapter 7 · Lesson 2
Equal Areas of a Shape
Each part is a unit fraction of the whole.
10 problems · about 12 minutes · 3.G.A.2
What this lesson teaches
The child partitions a shape into parts with equal areas and names each part as a unit fraction.
- A shape can be split into parts of equal area.
- Each part is a unit fraction of the whole.
- The parts need not be the same shape.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — The Quadrilateral Family: How many sides does every quadrilateral have?
Answer 4
Why All quadrilaterals have 4 sides.
Review — Line Plots With Fractions: Stacks of 2, 3, 4 and 1. How many measurements in all?
Answer 10
Why 2 + 3 + 4 + 1 = 10.
Review — Measuring to Halves and Fourths: How many fourths make three quarters?
Answer 3
Why Three fourths is three of the small marks.
Warm Up
Straightforward practice. Get the method working first.
3 problemsA shape split into 7 equal parts. What is the denominator of one part?
Answer 7
Why Each part is 1/7 of the shape.
What has to be equal about the parts?
Answer The area they cover.
Why Equal parts cover equal areas.
A shape split into 4 equal parts. What is one part called?
Answer One fourth.
Why Four equal parts.
Build It Up
The same ideas with more to keep track of.
1 problemA shape split into 5 equal parts, 2 shaded. What is the numerator?
Answer 2
Why How many are shaded.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsMust the equal parts be the same shape?
Answer No. Only the same area.
Why Same rule as Grade 2 halves.
The Window: A window is split into 6 equal panes. What fraction is one pane?
Answer 6 as the denominator
Why One pane is 1/6 of the window.
Shaded Parts: A shape is split into 8 equal parts and 3 are shaded. What fraction is shaded?
Answer 3 eighths
Why 3/8 is shaded.