CHAPTER 8
B
Addition and Subtraction
of Algebraic Expressions
(Guided Activity)
Assessment for Feedback
What You Will See Students Doing . . .
Students will
When Students Understand
If Students Misunderstand
• add and subtract algebraic
expressions
• Students will accurately add and subtract algebraic
expressions.
• Some students may have difficulty grouping like terms. Have
these students review the previous lesson defining like terms.
• Some students may have difficulty finding the opposite
when subtracting. Give students extra practice similar to
question 7.
• Students may also have trouble with subtraction of expressions.
Explain that just as subtraction has the same result as addition of
the opposite for numbers, the same is true for variable terms
because variables represent real numbers.
1.
Introduction (Whole Class) ➧ 5–10 min
Review the previous lesson on parts of an algebraic expression
with the class. Write the following expression on the board:
16m 2 2 2m 1 3m 1 9. Ask students to list the terms,
coefficients, degree of each term, and like terms found in this
expression.
3.
Consolidation ➧ 20–30 min
Checking (Whole Class)
5.–6. Ask students to complete these questions independently.
After all students have had an opportunity to compete
both questions, check their answers together as a class.
Practising and Extending (Independent)
7.–13. Students should complete these questions
independently.
2.
Teaching and Learning (Whole
Class/Pairs) ➧ 15–20 min
Read aloud to the class the example at the beginning of the
lesson regarding Jordan’s new carpet, as well as the central
question. Direct students’ attention to prompt A. Get them
started drawing the rectangles for prompt A and then ask
them to complete prompts A through C in pairs. Next, have
students complete prompts D through F as you guide them
through the steps for adding algebraic expressions. Then ask
students to complete prompts G and H with their partners.
When all pairs have had an opportunity to complete all eight
prompts, discuss the answers together as a class.
Reflecting: Use these questions to ensure that students are
able to arrange terms in descending order, group like terms,
and add or subtract expressions.
Sample Discourse:
1. • You record the term that has greatest degree, then the term
with the next greatest degree, and so on.
2. • Like terms are terms in which the same variable is
raised to the same exponent.
3. • Yes; if the two expressions contain terms with three
different degrees.
4. • Yes; variables represent real numbers, so any rule that
applies to real numbers applies to variable terms.
Copyright © 2009 by Nelson Education Ltd.
Closing (Whole Class): Ask, “What are the steps for adding
two algebraic expressions? What are the steps for subtracting
two algebraic expressions?”
Answers
A.–C.
x 2 1 7 1 6x
x2 2 3
D. (x 2 1 7 1 6x) 1 (x 2 2 3)
G. 2(3)2 1 6(3) 1 4
E. (1 1 1)x 2 1 6x 1 (7 2 3)
H. 18 1 18 1 4 5 40
F. 2x 2 1 6x 1 4
1.–4. See sample answers under Reflecting.
5. 12x 2 1 5x 1 12
6. 3x 3 1 13x 2 1 x 2 2
7. a) 228x 2 1 4
b) 235x 3 2 4x 1 17
c) 220x 2 1 11x 2 5
d) 246x 4 1 38x 3 2 10x 2 2 x 1 1
e) 2145x 2 1 77x 2 28
8B Addition and Subtraction of Algebraic Expressions
1
8. a) (14 1 7)x 2 1 (26 1 (25))
10. a) 9x 2 1 x 1 14
b) (20 1 2)x 3 1 (7 1 (27))x 1 (1 1 10)
b) 13x 2 1 11x 2 3
c) (18 1 12)x 2 1 (9 1 21)x 1 (24 1 3)
c) 34x 2 1 20x 2 42
d) (1 1 2)x 4 1 (8 1 (25))x 3 1 (11 1 9)x 2 1
d) 10x 4 2 50x 3 2 30x 2 1 6x 1 13
(14 1 22)x 1 (23 1 11)
e) (128 1 91)x 2 1 (99 1 101)x 1 (82 1 66)
9. a) 3x 2 1 4x 2 11
b) 19x 3 1 3x 2 2 6x 1 15
c) 34x 4 2 10x 3 1 14x 2 1 3x 2 14
d) 18x 3 1 2x 2 2 21x 1 22
e) 6x 4 2 x 3 1 24x 2 1 9x 1 10
f ) 4x 2 2 8x 2 5
e) 51x 2 1 x 1 29
f ) 38x 2 2 51x 1 57
g) 6x 2 1 6x 1 3
11. a) 11x 2 1 23
b) 12x 3 1 37x 2 2 3x 1 54
c) 131x 4 1 68x 3 1 25x 2 1 66x 1 60
d) 262x 3 1 241x 2 2 64x 1 138
e) 26x 2 2 37x 1 20
12. 2x 2 1 11x 1 8 square metres
13. (a 1 d)x 2 1 (b 1 e)x 1 (c 1 f )
2
Nelson Mathematics Secondary Year Two, Cycle One
Copyright © 2009 by Nelson Education Ltd.