3A · Chapter 5 · Lesson 1
Multiplying Ones, Tens, and Hundreds
Multiply tens and hundreds using place value.
Today's challenge
Find 4 × 20; explain the units of the product. Try your own method, then compare it with a model.
What you'll learn
- Multiply tens and hundreds using place value.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Basic multiplication facts.
Prerequisite competency: 3A-C04-L02
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Calculate 57 × 2 by splitting 57 into tens and ones.
Show answer and reasoning
Answer: 114
(50+7)×2=(50×2)+(7×2)=114.
- E2
Calculate 64 × 3 by splitting 64 into tens and ones.
Show answer and reasoning
Answer: 192
(60+4)×3=(60×3)+(4×3)=192.
Learn the concept
Words to know
- tens
- groups of ten ones
- hundreds
- groups of one hundred ones
Multiply tens and hundreds using place value.
A quantity such as 40 is four tens. Multiply the four groups, then interpret the result as that many tens. This makes zeros meaningful, not decorative.
Why this works
Multiplying tens or hundreds means counting those units, not attaching zeros by a trick. Six groups of 40 are six groups of four tens, or 24 tens. Twenty-four tens equal 240 ones. The answer is 240, and its size should make sense compared with 6 × 4.
Check the meaning
Check against the base fact: 6 × 4 tens is 24 tens, which equals 240.
Concrete → Pictorial → Abstract
- Build: Use counters, grid paper, or labeled bundles to represent the story or quantity.
- Draw: Sketch an array, place-value exchange, or equal-unit bar; label what is known.
- Calculate: Write an equation matching the representation and solve.
- Verify: Use an inverse operation or a second strategy to check.
For advanced students: if you can already explain this concept, start with the independent or challenge set.
Worked examples and immediate checks
Explain each step aloud or in writing. Work the fresh question before revealing its solution.
Worked example 1
Reason and verify
Find 4 × 20; explain the units of the product.
- A quantity such as 40 is four tens. Multiply the four groups, then interpret the result as that many tens. This makes zeros meaningful, not decorative.
- 20 is 2 groups of 10; 4×2=8 groups of 10 equals 80.
- Check against the base fact: 6 × 4 tens is 24 tens, which equals 240.
Result: 80
Understanding check 1 — your turn
Find 5 × 800; explain the units of the product.
Reveal reasoning
Answer: 4000 — 800 is 8 groups of 100; 5×8=40 groups of 100 equals 4,000.
Worked example 2
Reason and verify
Find 5 × 500; explain the units of the product.
- A quantity such as 40 is four tens. Multiply the four groups, then interpret the result as that many tens. This makes zeros meaningful, not decorative.
- 500 is 5 groups of 100; 5×5=25 groups of 100 equals 2,500.
- Check against the base fact: 6 × 4 tens is 24 tens, which equals 240.
Result: 2500
Understanding check 2 — your turn
Find 6 × 20; explain the units of the product.
Reveal reasoning
Answer: 120 — 20 is 2 groups of 10; 6×2=12 groups of 10 equals 120.
Worked example 3
Reason and verify
Find 6 × 80; explain the units of the product.
- A quantity such as 40 is four tens. Multiply the four groups, then interpret the result as that many tens. This makes zeros meaningful, not decorative.
- 80 is 8 groups of 10; 6×8=48 groups of 10 equals 480.
- Check against the base fact: 6 × 4 tens is 24 tens, which equals 240.
Result: 480
Understanding check 3 — your turn
Find 7 × 500; explain the units of the product.
Reveal reasoning
Answer: 3500 — 500 is 5 groups of 100; 7×5=35 groups of 100 equals 3,500.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Find 4 × 800; explain the units of the product.
Show answer and reasoning
Answer: 3200
800 is 8 groups of 100; 4×8=32 groups of 100 equals 3,200.
- G2
Find 5 × 20; explain the units of the product.
Show answer and reasoning
Answer: 100
20 is 2 groups of 10; 5×2=10 groups of 10 equals 100.
- G3
Find 6 × 500; explain the units of the product.
Show answer and reasoning
Answer: 3000
500 is 5 groups of 100; 6×5=30 groups of 100 equals 3,000.
- G4
Find 7 × 80; explain the units of the product.
Show answer and reasoning
Answer: 560
80 is 8 groups of 10; 7×8=56 groups of 10 equals 560.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Find 2 × 500; explain the units of the product.
Show answer and reasoning
Answer: 1000
500 is 5 groups of 100; 2×5=10 groups of 100 equals 1,000.
- I2
Find 3 × 80; explain the units of the product.
Show answer and reasoning
Answer: 240
80 is 8 groups of 10; 3×8=24 groups of 10 equals 240.
- I3
Find 4 × 200; explain the units of the product.
Show answer and reasoning
Answer: 800
200 is 2 groups of 100; 4×2=8 groups of 100 equals 800.
- I4
Find 5 × 50; explain the units of the product.
Show answer and reasoning
Answer: 250
50 is 5 groups of 10; 5×5=25 groups of 10 equals 250.
- I5
Find 6 × 800; explain the units of the product.
Show answer and reasoning
Answer: 4800
800 is 8 groups of 100; 6×8=48 groups of 100 equals 4,800.
- I6
Find 7 × 20; explain the units of the product.
Show answer and reasoning
Answer: 140
20 is 2 groups of 10; 7×2=14 groups of 10 equals 140.
- I7
Find 8 × 500; explain the units of the product.
Show answer and reasoning
Answer: 4000
500 is 5 groups of 100; 8×5=40 groups of 100 equals 4,000.
- I8
Find 2 × 80; explain the units of the product.
Show answer and reasoning
Answer: 160
80 is 8 groups of 10; 2×8=16 groups of 10 equals 160.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Why is 6 × 40 equal to 240 rather than 24?
Show answer and reasoning
Answer: Because 40 is four tens
6×4 tens=24 tens, and 24 tens=240 ones.
- C2
Estimate 8 × 70 and explain whether 56, 560, or 5,600 could be correct.
Show answer and reasoning
Answer: 560
8×7 tens=56 tens=560. The product must be hundreds, not tens or thousands.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Find 5 × 800; explain the units of the product.
Show answer and reasoning
Answer: 4000
800 is 8 groups of 100; 5×8=40 groups of 100 equals 4,000.
- E2
Find 6 × 20; explain the units of the product.
Show answer and reasoning
Answer: 120
20 is 2 groups of 10; 6×2=12 groups of 10 equals 120.
- E3
Find 7 × 500; explain the units of the product.
Show answer and reasoning
Answer: 3500
500 is 5 groups of 100; 7×5=35 groups of 100 equals 3,500.