Cogito
Grade 4 Math · Chapter 2 · Lesson 3
The Area Model and Partial Products
One rectangle, split by place value.
10 problems · about 15 minutes · 4.NBT.B.5
What this lesson teaches
The child multiplies a two-digit number by a one-digit number using an area model and partial products.
- Split one factor by place value.
- Multiply each piece separately.
- Add the partial products.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Multiplying by 10, 100, and 1,000: 8 × 700 = ?
Answer 5600
Why 8 × 7 = 56, so 8 × 700 = 5,600.
Review — Multiplication as Comparison: 4 times as many as 12 is?
Answer 48
Why 4 × 12 = 48.
Warm Up
Straightforward practice. Get the method working first.
4 problems42 × 8 = ?
Answer 336
Why 40 × 8 = 320, and 2 × 8 = 16.
Why do the partial products add to the whole answer?
Answer The pieces cover the whole rectangle.
Why The pieces fill the rectangle exactly.
36 × 4 = ?
Answer 144
Why 120 and 24.
53 × 7 = ?
Answer 371
Why 350 and 21.
Build It Up
The same ideas with more to keep track of.
2 problems48 × 6 = ?
Answer 288
Why 240 and 48.
27 × 9 = ?
Answer 243
Why 180 and 63.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Theatre: 7 rows of 32 seats. How many seats?
Answer 224 seats
Why 30 × 7 = 210, and 2 × 7 = 14. Together 224.
The Packets: 8 packets each hold 45 seeds. How many seeds?
Answer 360 seeds
Why 40 × 8 = 320, and 5 × 8 = 40. Together 360.