Multiples
4A · Chapter 3 · Lesson 1 · MATH-4A-C03-L01
Learning goal. Recognize and generate integer multiples, including why zero is a multiple.
Before you begin
Recall: Grade 3: arrays and multiplication tables; 4A Ch2: addition strategies. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Alex and Bea have 177,906 points together. Bea has 1,384 more than Alex. How many does Alex have?
Show answer & reasoning
Remove the extra 1,384 from the whole and split the rest into two equal parts: (177,906 − 1,384) ÷ 2 = 88,261.
A library had 21,897 books, received 18,218 more, then lent 9,109. How many books are there now?
Show answer & reasoning
First add 40,115. Then subtract 9,109 to obtain 31,006.
A library had 13,972 books, received 68,131 more, then lent 34,065. How many books are there now?
Show answer & reasoning
First add 82,103. Then subtract 34,065 to obtain 48,038.
Key vocabulary
- multiple
- whole-number product of a given number
- factor
- whole number dividing exactly
- prime
- positive number with exactly two positive factors
- composite
- positive number with more than two positive factors
Understand the concept
Multiples are made by multiplying a whole number by 0, 1, 2, 3, and so on. The positive multiples of six begin 6, 12, 18. Zero is also a multiple because six times zero is zero, though lists of positive multiples omit it. Multiples help us reason about repeated equal groups.
Model it: skip-count line and grouped arrays. 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
Find the 9th positive multiple of 10.
10 × 9 = 90.
Check your understanding 1
Find the 4th positive multiple of 5.
Show answer & reasoning
5 × 4 = 20.
Worked example 2
Find the 9th positive multiple of 15.
15 × 9 = 135.
Check your understanding 2
Find the 11th positive multiple of 14.
Show answer & reasoning
14 × 11 = 154.
Worked example 3
Find the 11th positive multiple of 7.
7 × 11 = 77.
Check your understanding 3
Find the 5th positive multiple of 13.
Show answer & reasoning
13 × 5 = 65.
Guided practice
Find the 2nd positive multiple of 6.
Show answer & reasoning
6 × 2 = 12.
Find the 11th positive multiple of 11.
Show answer & reasoning
11 × 11 = 121.
Find the 7th positive multiple of 6.
Show answer & reasoning
6 × 7 = 42.
Find the 6th positive multiple of 15.
Show answer & reasoning
15 × 6 = 90.
Find the 3rd positive multiple of 7.
Show answer & reasoning
7 × 3 = 21.
Independent practice
Find the 7th positive multiple of 13.
Show answer & reasoning
13 × 7 = 91.
Find the 11th positive multiple of 13.
Show answer & reasoning
13 × 11 = 143.
Find the 2nd positive multiple of 9.
Show answer & reasoning
9 × 2 = 18.
Find the 3rd positive multiple of 11.
Show answer & reasoning
11 × 3 = 33.
Is zero a multiple of 14? Explain.
Show answer & reasoning
0 = 14 × 0, so zero is a multiple of 14.
Find the 10th positive multiple of 14.
Show answer & reasoning
14 × 10 = 140.
Find the 5th positive multiple of 15.
Show answer & reasoning
15 × 5 = 75.
Find the 10th positive multiple of 5.
Show answer & reasoning
5 × 10 = 50.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
Is zero a multiple of 6? Explain using multiplication.
Show answer & reasoning
6 × 0 = 0. A multiple includes zero when the multiplier is a whole number.
Is zero a multiple of 6? Explain.
Show answer & reasoning
0 = 6 × 0, so zero is a multiple of 6.
Exit check
Find the 5th positive multiple of 6.
Show answer & reasoning
6 × 5 = 30.
Find the 7th positive multiple of 12.
Show answer & reasoning
12 × 7 = 84.
Is zero a multiple of 12? Explain.
Show answer & reasoning
0 = 12 × 0, so zero is a multiple of 12.