Answer Key - Lesson 2: Divisibility Rules
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3Answer Key • Lesson 2: Divisibility Rules
Student Guide
Questions 1–24 (SG pp. 258–262)
See Figure 1 in Lesson 2.
1.
*
1. On a copy of the 100 Chart in your Student Activity Book, use a blue crayon
or pencil to circle all the multiples of 2. Then, describe any patterns you see.
Save your copy of the 100 Chart to use later in the lesson.
2.
In the column with the 8.
*
2. Shannon’s book is 318 pages long. In which column would 318 be if the
100 Chart kept going beyond 100?
3. A. 216, 784, 1000, 1358, 2462; These numbers
3. A. Which of the following numbers are divisible by 2? Why do you think so?
are even. The ones digit is 0, 2, 4, 6, or 8.
Check your predictions using a calculator.
109
213
216
275
784
B. 108
2
216; 216
2
108; 392
2
1000
1358
2462
6767
8091
B. Write a multiplication sentence and a division sentence for each number
784; 784
2
392; 500
2
1000; 1000
that is divisible by 2. For example, 216 ÷ 2 = 108 and 108
2 = 216. Use
a calculator to help you.
2
500; 679
2
1358; 1358
2
4. How can you tell if a number is divisible by 2?
Is It Divisible by 3?
679; 1231
2
2462; 2462
2
1231
12 is divisible by 3.
21 is divisible by 3.
30 is divisible by 3.
4. A number is divisible by 2 if it is a multiple of
4
3 = 12
7
3 = 21
10
3 = 30
12 ÷ 3 = 4
21 ÷ 3 = 7
30 ÷ 3 = 10
2. Multiples of 2 are even. The ones digit is 0,
3 is a factor of 12, 21, and 30. A factor of a number can be divided evenly or
exactly into the number. That is, when you divide a whole number by one of its
2, 4, 6, or 8.
factors, the answer (or quotient) is a whole number. Since 12, 21, and 30 can be
divided by 3 evenly, we say that 12, 21, and 30 are divisible by 3.
See Figure 2 in lLsson 2.
5.
5. Use your copy of the 100 Chart that you used earlier. The multiples of 2
*
should be circled in blue. Using a red crayon or pencil, mark all the multiples
of 3 with an “X.” Your 100 Chart should look like the one below.
See lesson.
6.
*
1
2
3
4
5
6
7
8
9
10
7. A. Yes; 9
3
27
11
12
13
14
15
16
17
18
19
20
B. Yes; 27
3
9
21
22
23
24
25
26
27
28
29
30
C. Yes; 17
3
51
6. Describe any patterns you see.
258
D. Yes; 51
SG • Grade 4 • Unit 7 • Lesson 2
Divisibility Rules
3
17
8. A. No; Explanations will vary. 3 and no other
Student Guide - Page 258
whole number will multiply to make 14; 14
is not reached when you skip count by 3s; If
you divide 14 by 3, you do not get a whole
number answer.
B. R2; 4
3
2
14 or 14
3
4 R2
7. Use your copy of the 100 Chart and your calculator to help you answer the
C. The calculator does not show a whole
following questions:
A. Is 27 a multiple of 3? Write a multiplication sentence.
number so 14 is not divisible by 3.
B. Is 27 divisible by 3? Write a division sentence.
C. Is 51 a multiple of 3? Write a multiplication sentence.
It shows 4.6666667.
D. Is 51 divisible by 3? Write a division sentence.
8. A. Is 14 a multiple of 3? How do you know?
9. 75; 75
3
25
B. If 14 is divided by 3, what is the remainder? Write a multiplication or
division sentence. Remember to include the remainder.
14
3
10. A. Predictions will vary. No, 101 does not fall
C. Use your calculator. Press:
÷
=
How does your calculator show whether 14 is divisible by 3?
on the diagonals made on the 100 Chart.
Is the answer a whole number?
9. Is 74, 75, or 76 divisible by 3? Use your copy of the 100 Chart or a calculator
On the calculator, 101
3 does not give a
to decide. Write a division sentence showing which number is divisible by 3.
10. Look carefully at your 100 Chart. Write in more numbers below it if you need to.
whole number; therefore, 101 is not
A. Predict: Is 101 divisible by 3? Check your prediction with a calculator.
B. Predict: Is 102 divisible by 3? Check your prediction with a calculator.
divisible by 3.
C. Predict: Which of the following is divisible by 3? 116, 117, or 118? Why
do you think so? Check your prediction with a calculator.
B. Predictions will vary. Yes, 102 falls on the
11. Mrs. Dewey started listing
Number
Sum of Digits
numbers from the 100 Chart
same diagonal as 84 and 93. On the
that were divisible by 3. Then
18
1 + 8 = 9
she made the table on the
calculator 102
3
34, a whole number.
right. Roberto saw a pattern.
42
4 + 2 = 6
Do you? Explain.
102 is divisible by 3.
51
5 + 1 = 6
84
8 + 4 = 12
C. Explanations will vary. If you extend the
99
9 + 9 = 18
100 Chart, you can see that 117 falls on the
diagonal with 90 and 99. On the calculator,
117
3
39, a whole number. 117 is
259
Divisibility Rules
SG • Grade 4 • Unit 7 • Lesson 2
divisible by 3. 116 and 118 are not divisible
by 3.
Student Guide - Page 259
Answers will vary. See lesson.
11.
*
*Answers and/or discussion are included in the lesson.
1
TG • Grade 4 • Unit 7 • Lesson 2 • Answer Key
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