Multiplying by a 1-Digit Number — Part 2
4A · Chapter 4 · Lesson 3 · MATH-4A-C04-L03
Learning goal. Coordinate successive regroupings and verify products by magnitude estimation.
Before you begin
Recall: Grade 3: multidigit × one digit, arrays; 4A Ch3: multiples; Multiplying by a 1-Digit Number — Part 1. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Calculate 36 × 7.
Show answer & reasoning
36 × 7 = (30 × 7) + (6 × 7) = 252. Each partial product uses its correct place value.
Calculate 46 × 3.
Show answer & reasoning
46 × 3 = (40 × 3) + (6 × 3) = 138. Each partial product uses its correct place value.
Calculate 50 × 9.
Show answer & reasoning
50 × 9 = (50 × 9) + (0 × 9) = 450. Each partial product uses its correct place value.
Key vocabulary
- partial product
- product of one part of each decomposed factor
- distributive property
- multiplication distributed across a sum
- area model
- rectangular representation of a product
- regroup
- exchange ten small units for one larger unit
Understand the concept
Successive regrouping requires attention to each exchanged unit. For 286 × 7, seven sixes make 42 ones: write two ones and exchange four tens. Then include those four tens when multiplying the tens column. Estimate first: about 300 × 7 = 2,100, so a three-digit answer would be suspicious.
Model it: hundreds–tens–ones exchange chart. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
Calculate 110 × 2.
110 × 2 = (110 × 2) + (0 × 2) = 220. Each partial product uses its correct place value.
Check your understanding 1
Calculate 38 × 4.
Show answer & reasoning
38 × 4 = (30 × 4) + (8 × 4) = 152. Each partial product uses its correct place value.
Worked example 2
Calculate 66 × 7.
66 × 7 = (60 × 7) + (6 × 7) = 462. Each partial product uses its correct place value.
Check your understanding 2
Calculate 191 × 4.
Show answer & reasoning
191 × 4 = (190 × 4) + (1 × 4) = 764. Each partial product uses its correct place value.
Worked example 3
Calculate 71 × 9.
71 × 9 = (70 × 9) + (1 × 9) = 639. Each partial product uses its correct place value.
Check your understanding 3
Calculate 47 × 2.
Show answer & reasoning
47 × 2 = (40 × 2) + (7 × 2) = 94. Each partial product uses its correct place value.
Guided practice
Calculate 164 × 9.
Show answer & reasoning
164 × 9 = (160 × 9) + (4 × 9) = 1476. Each partial product uses its correct place value.
Calculate 120 × 5.
Show answer & reasoning
120 × 5 = (120 × 5) + (0 × 5) = 600. Each partial product uses its correct place value.
Calculate 186 × 4.
Show answer & reasoning
186 × 4 = (180 × 4) + (6 × 4) = 744. Each partial product uses its correct place value.
Calculate 17 × 4.
Show answer & reasoning
17 × 4 = (10 × 4) + (7 × 4) = 68. Each partial product uses its correct place value.
Calculate 143 × 3.
Show answer & reasoning
143 × 3 = (140 × 3) + (3 × 3) = 429. Each partial product uses its correct place value.
Independent practice
Calculate 85 × 9.
Show answer & reasoning
85 × 9 = (80 × 9) + (5 × 9) = 765. Each partial product uses its correct place value.
Calculate 36 × 6.
Show answer & reasoning
36 × 6 = (30 × 6) + (6 × 6) = 216. Each partial product uses its correct place value.
Calculate 129 × 7.
Show answer & reasoning
129 × 7 = (120 × 7) + (9 × 7) = 903. Each partial product uses its correct place value.
Calculate 140 × 5.
Show answer & reasoning
140 × 5 = (140 × 5) + (0 × 5) = 700. Each partial product uses its correct place value.
Calculate 167 × 8.
Show answer & reasoning
167 × 8 = (160 × 8) + (7 × 8) = 1336. Each partial product uses its correct place value.
Calculate 197 × 5.
Show answer & reasoning
197 × 5 = (190 × 5) + (7 × 5) = 985. Each partial product uses its correct place value.
Calculate 48 × 8.
Show answer & reasoning
48 × 8 = (40 × 8) + (8 × 8) = 384. Each partial product uses its correct place value.
Calculate 186 × 5.
Show answer & reasoning
186 × 5 = (180 × 5) + (6 × 5) = 930. Each partial product uses its correct place value.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student calculates 43 × 4 using only its tens: 40 × 4. What partial product is missing and what is the correct total?
Show answer & reasoning
The ones part 3 × 4 = 12 must also be included. The complete product is 172.
Calculate 88 × 8.
Show answer & reasoning
88 × 8 = (80 × 8) + (8 × 8) = 704. Each partial product uses its correct place value.
Exit check
Calculate 31 × 6.
Show answer & reasoning
31 × 6 = (30 × 6) + (1 × 6) = 186. Each partial product uses its correct place value.
Calculate 77 × 6.
Show answer & reasoning
77 × 6 = (70 × 6) + (7 × 6) = 462. Each partial product uses its correct place value.
Calculate 182 × 8.
Show answer & reasoning
182 × 8 = (180 × 8) + (2 × 8) = 1456. Each partial product uses its correct place value.