Cogito
Grade 3 Math · Chapter 3 · Lesson 1
Breaking an Array Apart
A hard fact is two easy facts in disguise.
10 problems · about 14 minutes · 3.OA.B.5
What this lesson teaches
The child uses the distributive property to break a multiplication into two easier ones.
- A hard fact can be cut into two easy ones.
- 7 × 8 is (5 × 8) + (2 × 8).
- Add the two products to get the answer.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Litres and Millilitres: How many millilitres are in one litre?
Answer 1000
Why 1 litre = 1,000 ml.
Review — Grams and Kilograms: How many grams are in one kilogram?
Answer 1000
Why 1 kg = 1,000 g.
Review — Time Intervals: From 7:45 to 8:10. How many minutes?
Answer 25
Why 15 + 10 = 25 minutes.
Warm Up
Straightforward practice. Get the method working first.
3 problems7 × 8 = ?
Answer 56
Why 40 + 16 = 56.
Why cut an array in two?
Answer To make two facts you already know.
Why Cutting swaps one hard fact for two easy ones.
7 × 6 = ? Try (5 × 6) + (2 × 6).
Answer 42
Why 30 + 12.
Build It Up
The same ideas with more to keep track of.
1 problem9 × 4 = ? Try (5 × 4) + (4 × 4).
Answer 36
Why 20 + 16.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problems8 × 7 = ? Try (5 × 7) + (3 × 7).
Answer 56
Why 35 + 21.
Splitting a Six: 6 × 7 split as (5 × 7) + (1 × 7). What is 35 + 7?
Answer 42
Why 6 × 7 = 42.
Splitting an Eight: 8 × 6 split as (4 × 6) + (4 × 6). What is 24 + 24?
Answer 48
Why 8 × 6 = 48.