CHAPTER 6
B
The Distributive Property
in Reverse
(Guided Activity)
Assessment for Feedback
What You Will See Students Doing . . .
Students will
When Students Understand
If Students Misunderstand
• factor and simplify expressions
using the distributive property in
reverse
• Students will be able to identify when an expression can be
factored and simplified using the distributive property in
reverse and will be able to accurately factor and simplify
those expressions.
• Some students may forget the pattern used in the distributive
property. Have them refer back to the earlier lesson on the
distributive property to remind them of how the distributive
property can be applied.
• Some students may not understand that sometimes you must
use the commutative property of multiplication to rearrange
the expression before factoring it. Have them go back to
question 4 to see how this step can be applied.
1.
Introduction (Whole Class) ➧ 5–10 min
Review the use of the distributive property to simplify
expressions. Write the following examples on the board:
a) 3(2 1 6)
b) 8(9 2 4)
c) 22(11 2 4)
d) 23(26 1 8)
Have students explain orally how each expression can be
rewritten using the distributive property and then simplified.
3.
Consolidation ➧ 20–30 min
Checking (Independent/Whole Class)
4.–5. Ask students to complete these questions independently,
following the steps given. When all students have had an
opportunity to complete both questions, check their
answers together as a class.
Practising and Extending (Independent)
6.–12. Students should complete these questions
independently.
Closing (Whole Class): Ask, “What property can be used
2.
Teaching and Learning (Whole
Class/Independent) ➧ 15–20 min
Read Tom and Maggie’s situation aloud to the class, along
with the central question. Direct the students’ attention to
prompt A and ask them to complete the equation on their
own. Once everyone has had an opportunity to answer
prompt A, discuss the answer as a group. Now ask students to
complete prompts B and C independently. Finally, give the
class a moment to determine the total spent, in prompt D.
Reflecting: Use these questions to ensure that students
to factor expressions in the form, a 3 b 1 a 3 c, or
a 3 b 2 a 3 c?” Ask students to complete this statement,
“The distributive property in reverse states that for all
numbers a, b, and c, a 3 b 1 a 3 c 5 ?”
Answers
A. a(b 1 c)
C. 4($6.50 1 $5.50)
B. 4 3 $6.50 1 4 3 $5.50
D. $48.00
1.–3. See sample answers under Reflecting.
understand how to factor expressions of the form
a 3 b 1 a 3 c or a 3 b 2 a 3 c, using the distributive
property in reverse.
4. 26(4 1 3)
Sample Discourse:
1. • a(b 1 c)
2. • a 3 b 2 a 3 c 5 a(b 2 c)
3. • You might choose to factor an expression using the
distributive property in reverse in cases where there is a
common factor and performing the addition or subtraction
first is easier than multiplying first.
6. a) yes
5. 8(7 2 5)
b) no
c) no
d) yes
e) yes
7. a) 4(6 1 3)
g) 6(4 1 2)
l) 42(3 1 2)
b) 2(8 2 4)
h) 7(8 2 2)
m) 36(3 2 1)
c) –2(7 1 6)
i) 5(6 2 3)
n) 30(8 1 9)
d) 8(5 2 2)
j) 10(3 2 2)
o) 65(40 1 10)
e) –7(4 2 3)
k) 22(11 1 9)
p) 21(2 1 8)
f ) 9(– 4 1 3)
Copyright © 2009 by Nelson Education Ltd.
6B The Distributive Property in Reverse
1
8. a) 7(2 1 9) 5 77
2
i) 9(7 1 2) 5 81
9. 10 3 $1 1 10 3 $2 1 10 3 $5 1 10 3 $10 1 10 3 $50;
b) 2(6 1 7) 5 26
j) 81(11 2 4) 5 567
c) 4(3 2 7) 5 –16
k) 44(8 2 6) 5 88
d) 6(5 2 2) 5 18
l) 5(4 1 3) 5 35
e) 9(6 1 3) 5 81
m) 14(2 1 6) 5 112
f ) 10(9 2 4) 5 50
n) 61(2 1 4) 5 366
11. yes, 36
g) 15(2 1 3) 5 75
o) 8(12 2 3) 5 72
12. a(a 2 1 b 1 c 2 1 ad )
h) 32(10 2 9) 5 32
p) 25(6 1 7) 5 325
Nelson Mathematics Secondary Year Two, Cycle One
10($1 1 $2 1 $5 1 $10 1 $50); $680
10. a) 9(6 1 4 1 2) 5 108 d) 80(10 1 8 2 9) 5 720
b) 11(8 2 5 2 1) 5 22 e) 100(35 2 19 2 2) 5 1400
c) 16(4 1 9 2 2) 5 176
Copyright © 2009 by Nelson Education Ltd.