Download Grade 7 Mathematics Unit 6 Equations Estimated Time: 20 Hours

Grade 7 Mathematics
Unit 6
Equations
Estimated Time: 20 Hours
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
181
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
182
Unit 6: Equations
Unit 6 Overview
Introduction
Students will focus on developing skills and knowledge necessary for understanding how to solve
equations using a variety of methods. The big ideas in this unit are:
•
•
•
•
An equation states a relationship between two expressions; specifically, that the two expressions
are equal.
Preservation of equality is at the core of solving equations.
An equation can be solved by systematic trial, using a two-pan balance model, using algebra
tiles, or solved symbolically by using algebraic techniques.
Equations can be used to model and solve problems.
Context
The students will begin to solve equations using systematic trial and inspection. The students will often
know the solution to an equation instantly. However, they will be asked to explain their reasoning before
they move on to solving equations with two-pan balance models and algebra tiles. Students will solve
equations that involve positive and negative integers and they will solve equations that are limited to no
more than two steps. Ultimately students will apply algebraic techniques, requiring the use of
preservation of equality, in order to solve equations.
Why are these concepts important?
Developing a good understanding of solving equations will permit students to:
• Become good problem solvers. Students will be able to decide on an appropriate method for
problem solving and determine if their answer makes sense.
• Be able to manipulate formulas using algebra and know how to verify answers when studying
subjects like chemistry, physics, and calculus to name a few.
“It is hard to convince a high-school student that he will encounter a lot of problems more difficult than
those of algebra and geometry.”
Edgar Watson Howe (1853-1937)
Grade 7 Math Curriculum Guide
183
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
Elaborations: Suggested Learning and Teaching Strategies
It is expected that students will:
It is assumed that students can:
7PR4. Explain the difference
• recognize patterns in a table of values
between an expression and
• write a pattern rule for a number pattern
an equation.
• use a pattern rule to find the value of a given term
[C, CN]
(Cont’d)
This outcome was introduced in Unit 1 (see achievement
indicators 7PR4.2, 7PR4.3, and 7PR4.4). Identifying the
difference between an algebraic expression and an equation
can now be further developed.
Achievement Indicators
7PR4.6 Provide an
example of an expression
and an equation, and
explain how they are
similar and different.
Recall that an algebraic equation is a mathematical statement
that two expressions are equal. In an equation such as 2a + 5 =
11, we are searching for one input value, or value that can be
substituted for a, that would produce the desired output value
of 11.
Students should now be exposed to expressions where the
constant term is negative, e.g.
4x – 7 is equivalent to 4x + -7, thus the constant term is -7.
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
184
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
Resources/Notes
Paper & Pencil
1. Which are expressions? Which are equations? How are they
similar? How are they different?
A. 2 – x
B. 5v = 20
h
C.
=4
3
D. w + 7
2. Does the algebra tile diagram below model an expression or an
equation? Explain.
3. Below are three algebraic expressions and/or equations.
4p + 5 = 55
4p – 5 = 55
4p – 5
A. Which are equations and which are expressions? Explain
why.
B. List ways in which they are similar and ways in which
they differ.
Math Makes Sense 7
Lesson 6.1
Unit 6: Equations
TR: ProGuide, pp. 4–9
Master 6.9, 6.18
CD-ROM Unit 6 Masters
ST: pp. 220–225
Practice and HW Book
pp. 132–134
4. Have students complete concept maps for expressions and
equations such as:
Sample Responses
Essential
Characteristics
Non-Essential
Characteristics
Essential
Characteristics
Non-Essential
Characteristics
= sig
n
Examples
Equation
al
s equ
ssion
xpre
e
o
Tw
Non-Examples
3x
+
4
Two cons
Equation
Examples
6
2x =
ble
Varia
More than one operation
=
7
y=
2
4 +
3 =
7
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
tant term
s
Non-Examples
2x 1
5x
4
4
<
6
185
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in multiple
ways.
Specific Outcome
Elaborations: Suggested Learning and Teaching Strategies
It is expected that students will:
Note: Only whole numbers should be used for a, b, and c.
7PR7. Model and solve,
concretely, pictorially and
symbolically, problems that
can be represented by linear
equations of the form:
• ax + b = c
• ax = b
•
x
a = b, a ≠ 0
where a, b and c are whole
numbers.
[CN, PS, R, V]
Refer to the Achievement indicator 7PR4.4 in Unit 1 for a
discussion of systematic trial (i.e. guess and check) to solve
equations.
Another commonly used concrete model for equations is to use
a two-pan balance approach.
Example: Solve the equation 2x + 1 = 5 using guess and check:
Too
Heavy!
5
2(3) + 1
2(1) + 1
Too
Light!
5
Balance!
2(2) + 1
5
Achievement Indicators
7PR7.2 Solve a given
linear equation by
inspection and by
systematic trial.
Students will need to recall, from Unit 1, how to write an
algebraic equation from a number sentence. Refer to Student
Text pages 221-223.
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
186
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
Resources/Notes
Paper and Pencil
1. A hockey school charges $80 per day to use the facility plus
$20 per play per day for food, use of equipment and lessons. A
team raised $320 for a one-day practice.
A. Write an equation you can solve to find the number of
athletes that can attend the hockey school?
B. Solve the equation by inspection, then by systematic trial.
Which method was easier, and why?
2. The formula for the area of a triangle is A = b × h ÷ 2 .
Find all the possible whole number values for b and h that will
result in an area of 72 cm2.
Journal/Interview
1. Ryan was given the equation 5d + 7 = 22 and asked to solve for
d. He indicated that d = 15, but was told that his answer was
incorrect. Explain what his misconception was and how you
would help him to correctly solve for d.
2. When solving 4d + 24 = 36 , Sarah chose 3 for her first value for
d and Billy chose 6. Which number is the better choice, and
why?
Informal Observation
1. Play ‘I Have, Who Has’. See Teacher Resource Master 6.6a and
6.6b.
2. Play ‘Equation Concentration’. See Teacher Resource Master
6.7a and 6.7b.
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
Math Makes Sense 7
Lesson 6.1
(continued)
187
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
Elaborations: Suggested Learning and Teaching Strategies
It is expected that students will:
Students should use concrete materials to investigate the
process of solving equations. Refer to Outcome 7PR7 in Unit 1
for discussion.
7PR3. Demonstrate an
understanding of
preservation of equality by:
• modelling preservation of
equality, concretely,
pictorially and
symbolically
• applying preservation of
equality to solve equations.
[C, CN, PS, R, V]
When solving linear equations, the idea is to isolate the
variable while preserving equality at each step of the process.
To move from the concrete stage to the symbolic stage,
students should record each step of a concretely modelled
process in symbolic form, e.g.
Concrete Representation
Symbolic Representation
2x + 1 = 5
Remove a unit tile from each
side:
2x + 1 – 1 = 5 – 1
Simplify:
2x = 4
Since we have two x tiles, we
separate both sides into two
equal groups.
Each x-tile is paired with 2
unit tiles. Therefore, the
solution is: x = 2
One other approach for solving equations symbolically might
be to revisit the skills of writing related equations learned in
primary and elementary grades. For example:
• 3 + 2 = 5 A related equation that isolates the 3 is 3 = 5 – 2.
6
• 3 × 2 = 6 A related equation that isolates the 3 is 3 = .
2
• 4(3) + 1 = 13. A related equation that isolates the 3 is
13 − 1
3=
.
4
• Similarly, when writing 2N + 1 = 201, a related equation
201 − 1
that isolates the N is N =
. Therefore, we can
2
calculate that the input value must have been 100.
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
188
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
Resources/Notes
189
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
Elaborations: Suggested Learning and Teaching Strategies
It is expected that students will:
Note: Students should consider in advance what might be a
reasonable solution, and be aware that once they acquire a
7PR3. Demonstrate an
solution, it can be checked for accuracy by substitution into the
understanding of
preservation of equality by: original equation.
• modelling preservation of
equality, concretely,
pictorially and
symbolically
• applying preservation of
equality to solve equations.
[C, CN, PS, R, V]
(Cont’d)
Achievement Indicators
7PR3.1 Model the
preservation of equality
for each of the four
operations, using concrete
materials or pictorial
representations; explain
the process orally; and
record the process
symbolically.
7PR3.2 Write equivalent
forms of a given equation
by applying the
preservation of equality,
and verify, using concrete
materials; e.g., 3b = 12 is
the same as 3b + 5 = 12 +
5 or 2r = 7 is the same as
3(2r) = 3(7).
Build understanding of equality by using number sentences to
explore what must be done to preserve equality when one side
is changed. Balance scales can be used to help illustrate an
equality and then to connect the concrete to the pictorial and
symbolic representations. Consider:
6+4+2
4×3
Since 6 + 4 + 2 = 4 × 3 , the pans are balanced. Ask students to
consider what would happen if a number, such as 5, is added to
the left pan only (the pan tips to the left). Discuss why this
happens (the left side is greater than the right side) and what
must be done in order to rebalance the pans (add 5 to the right
side). Students should come to realize that what is done to one
side must also be done to the other in order to preserve
equality. Demonstrate similar examples using each of the four
operations.
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
190
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
Resources/Notes
Paper and Pencil
1. Have students write the equation based on the balance scale
model (all pieces are positive). Then solve the equation both
pictorially and symbolically to show the connections between
the two.
2.
A. Write two equations equivalent to 3n + 1 = 5
B. Use the balance scales below to illustrate your equations
Interview
1. Consider:
6×2
10 + 4
This outcome is covered
throughout:
Lesson 6.2
Lesson 6.3
Lesson 6.4
Lesson 6.5
A. Are the pans balanced? How do you know?
B. How can you balance the pans?
2. Consider:
4+ 3−9
6−4−4
A. Are the pans balanced? How do you know?
B. What would happen if you add 5 to the right hand side?
C. How can you rebalance the pans to preserve the equality?
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
191
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
Elaborations: Suggested Learning and Teaching Strategies
It is expected that students will:
A two-pan balance can be used to model and visually represent
equations of the form ax + b = c and ax = b .
7PR7. Model and solve,
concretely, pictorially and
symbolically, problems that
can be represented by linear
equations of the form:
• ax + b = c
• ax = b
•
x
a = b, a ≠ 0
where a, b and c are whole
numbers.
[CN, PS, R, V]
(Cont’d)
Achievement Indicators
Consider the following: 14 + x = 22
14g
?
22g
Many students will immediately arrive at the value of the
unknown. However, it is important for students to recognize
what will happen if a mass is removed from one side of the
balance only and what they must do to compensate for this.
This will help develop the method for solving an equation
algebraically (Lesson 6.4).
7PR7.3 Draw a visual
representation of the steps
used to solve a given
linear equation.
7PR7.4 Solve a given
problem, using a linear
equation, and record the
process.
7PR7.5 Verify the
solution to a given linear
equation, using concrete
materials and diagrams.
7PR7.6 Substitute a
possible solution for the
variable in a given linear
equation into the original
linear equation to verify
the equality.
We can verify the solution by replacing the unknown mass
with 8g.
Check:
Left Pan: 14g + 8g = 22g
Right Pan: 22g
So, the solution is correct!
Students are required to substitute their answer for the variable
and check to make sure that it makes the equation true.
To verify that x=7 is a solution to 6 x + 2 = 44 ,
Left side: 6(7) + 2
Right side :44
= 42 + 2
= 44
Since the left side equals the right side, x=7 is correct.
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
192
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in multiple
ways.
Suggested Assessment Strategies
Resources/Notes
Paper and Pencil
1. Find the values of the unknown mass on each balance scale.
Sketch the steps you use.
A.
w
w
4g
16g
12g
8g
x
10g
B.
15g
15g
20g
2.
A. Sketch balance scales to represent each equation
B. Solve each equation. Verify the solution.
i.
2 y = 18
ii.
3n + 2 = 17
3. Solving Equations:
A. Write a problem that can be solved using the equation
x + 3 = 12 .
B. How would your problem change if the equation was
3 x = 12 ?
x
C. What new problem can you write for = 12 ?
3
D. Solve each equation in parts A,B, and C. Show the steps
you followed.
4. Write an equation for each sentence. Solve each equation, and
verify you answer.
A. The cost shared by 5 people amounts to $35 each.
B. There are 38 boys. This is 6 more than double the number
of girls.
C. Sixty centimetres is one half of Bob’s height
Math Makes Sense 7
Lesson 6.2
Unit 6: Equations
TR: ProGuide, pp. 10–14
Master 6.10, 6.19
CD-ROM Unit 6 Masters
ST: pp. 226–230
Practice and HW Book
pp. 135–137
Note: This is continued
throughout Lesson 6.4 and
Lesson 6.5.
5. Show whether or not x = 7 is the solution to each equation.
A. 6 x = 48
B. 3x + 2 = 20
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
193
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
Elaborations: Suggested Learning and Teaching Strategies
It is expected that students will:
When students solve a linear equation symbolically
(algebraically), it is important to visualize the balance scale
model. In order to preserve the equality, whatever is done to
the left pan of the balance must be done to the right pan. The
same is true for an algebraic equation; always perform the
same operation on both sides of the equation.
7PR7. Model and solve,
concretely, pictorially and
symbolically, problems that
can be represented by linear
equations of the form:
• ax + b = c
• ax = b
•
x
a = b, a ≠ 0
n
5g
n
where a, b and c are whole
numbers.
[CN, PS, R, V]
(Cont’d)
Achievement Indicators
7PR7.3 Draw a visual
representation of the steps
used to solve a given
linear equation. (cont’d)
19g
2n + 5 = 19
n
n
5g
14g
5g
To isolate 2n, subtract 5 from each side.
7PR7.4 Solve a given
problem, using a linear
equation, and record the
process. (cont’d)
7PR7.5 Verify the
solution to a given linear
equation, using concrete
materials and diagrams.
(cont’d)
7PR7.6 Substitute a
possible solution for the
variable in a given linear
equation into the original
linear equation to verify
the equality. (cont’d)
2n + 5 − 5 = 19 − 5
2n = 14
n
n
7g
Divide each side by 2,
7g
2n 14
=
2
2
n=7
Students can verify the solution by substituting n = 7
into 2n + 5 = 19 . Since the left side equals the right side, n = 7
is the correct solution.
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
194
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in multiple
ways.
Suggested Assessment Strategies
Resources/Notes
Paper and Pencil
1. Write an equation for each situation. Solve each equation, and
verify your answer.
A. The cost shared by 5 people amounts to $35 each.
B. There are 38 boys. This is 6 more than double the number
of girls.
C. Sixty centimetres is one half of Bob’s height.
2. Show whether or not x = 7 is the solution to each equation.
A. 6 x = 48
x
B.
=1
7
C. 3x + 2 = 20
Math Makes Sense 7
Lesson 6.2
(continued)
Note: This is continued
throughout Lesson 6.4 and
Lesson 6.5.
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
195
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
Elaborations: Suggested Learning and Teaching Strategies
It is expected that students will:
It will be necessary, however, to model equations of the form
x
= b , a ≠ 0 and to supplement the student text exercises with
a
examples of this type.
1
Example: Laurie has of a chocolate bar. It weighs 5g. She
3
wants to know how much a whole chocolate bar weighs. Write
an equation to represent this situation and then solve the
equation using a visual representation. Verify your answer.
7PR7. Model and solve,
concretely, pictorially and
symbolically, problems that
can be represented by linear
equations of the form:
• ax + b = c
• ax = b
•
x
a = b, a ≠ 0
where a, b and c are whole
numbers.
[CN, PS, R, V]
(Cont’d)
Achievement Indicators
7PR7.3 Draw a visual
representation of the steps
used to solve a given
linear equation. (cont’d)
Solution:
In order to solve this problem, students will need to think
about how many pieces Laurie will need to make a whole
chocolate bar. She knows:
She needs 3 pieces to make a whole, so she can draw:
7PR7.4 Solve a given
problem, using a linear
equation, and record the
process. (cont’d)
By combining these pieces to form a whole bar…
7PR7.5 Verify the
solution to a given linear
equation, using concrete
materials and diagrams.
(cont’d)
7PR7.6 Substitute a
possible solution for the
variable in a given linear
equation into the original
linear equation to verify
the equality. (cont’d)
…she concludes that one bar is 15g.
b
Verify: Left Pan: = b ÷ 3
Right Pan : 5g
3
= 15 ÷ 3
= 5g
So the solution is correct!
Balance scales reinforce the idea of the equality on two sides.
If this is well understood, teachers may also wish to use
algebra tiles to represent these types of equations.
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
196
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
Resources/Notes
Paper and Pencil
1. Brigitte is solving the equation
f
= 6 . This is her solution:
8
f
= 10
8
f
− 8 = 10 − 8
8
f =2
A. Is her solution correct or incorrect? Draw a visual to
demonstrate how you know.
B. If you think her solution is incorrect, what would you
change to solve the equation?
2. A clothing store is having a sale. Jacob pays $19 for two shirts
and a pair of sunglasses. The sunglasses cost $5.
A. Write an equation that represents the situation.
B. Draw a model to represent the equation.
C. Use the model to determine how much does Jacob pay for
each shirt?
D. Verify your answer.
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
This outcome is covered
throughout:
Lesson 6.1
Lesson 6.2
Lesson 6.4
Lesson 6.5
197
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
Elaborations: Suggested Learning and Teaching Strategies
It is expected that students will:
Note: When solving linear equations that require
multiplication or division, only whole numbers should be used
as these operations with integers will be addressed in grade 8.
7PR6. Model and solve,
concretely, pictorially and
symbolically, problems that
can be represented by onestep linear equations of the
form x + a = b, where a and
b are integers.
[CN, PS, R, V]
Achievement Indicators
7PR6.1 Represent a
given problem with a
linear equation; and
solve the equation, using
concrete models, e.g.,
counters, integer tiles.
7PR6.2 Draw a visual
representation of the
steps required to solve a
given linear equation.
Consider the sentence:
Three less than a number is -9. Students should be able to
write an equation for the number sentence, and then solve
using algebra tiles. (In the diagram below,
represents a
negative,
represents a positive.)
Example: x − 3 = −9
To model this equation, students need to recall that subtracting
3 is equivalent to adding negative 3.
To isolate the variable tile, add 3 positive tiles to the left side
to make zero pairs. Add 3 positive tiles to the right side to
preserve equality. Remove the zero pairs from both sides.
7PR6.3 Solve a given
problem, using a linear
equation.
The tiles show that x = −6
7PR6.4 Verify the
solution to a given linear
equation, using concrete
materials and diagrams.
7PR6.5 Substitute a
possible solution for the
variable in a given linear
equation into the
original linear equation
to verify the equality.
Students can verify the solution by replacing x, the variable
tile, with 6 negative tiles. They can also verify by replacing x
with -6 in the equation.
Refer to student text page 231-234 for relevant examples.
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
198
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
Resources/Notes
Paper and Pencil
1. Solve each of the equations using algebra tiles. Sketch your
steps. Verify your solution.
A. n − 3 = 4
B. h + 1 = −2
C. 2 = y − 6
D. w − 4 = −1
2. Algebra Tiles:
A. Write an equation you can use to solve each problem.
B. Use algebra tiles to solve each equation. Sketch your
steps.
C. Verify your solution.
i. The temperature dropped 5°C to − 2°C . What was the
original temperature?
ii. Frank is 9 years old. He is 4 years older than Joe. How
old is Joe?
iii. Susan checked out books from the library. She
returned 4 books, and she still has 3 books at home.
How many books did she borrow?
3. Which of the following equations is x = −2 a solution?
A. x − 3 = −5
B. x + 1 = 3
C. x + 2 = 1
D. x + 3 = 1
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
Math Makes Sense 7
Lesson 6.3
Lesson 6.4
Lesson 6.5
Unit 6: Equations
TR: ProGuide,
pp. 15–19
pp. 21–23
pp. 24–28
Master 6.11, 6.20
Master 6.12, 6.21
Master 6.13, 6.22
PM 30
CD-ROM Unit 6 Masters
ST: pp. 231–235
ST: pp. 237–239
ST: pp. 240–244
Practice and Homework
Book
pp. 138–140
pp. 141–144
pp. 145–147
199
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
Elaborations: Suggested Learning and Teaching Strategies
It is expected that students will:
7PR3. Demonstrate an
understanding of
preservation of equality by:
• modelling preservation of
equality, concretely,
pictorially and
symbolically
• applying preservation of
equality to solve equations.
[C, CN, PS, R, V]
(Cont’d)
Achievement Indicators
7PR3.3 Solve a given
problem by applying
preservation of equality.
Students should now be able to move away from the use of
diagrams and concrete materials when solving an equation for
a variable. Students should be able to apply preservation of
equality to solve equations algebraically.
3y + 1 = 7
3y + 1 − 1 = 7 − 1
3y = 6
3y 6
=
3 3
y=2
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
200
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
Resources/Notes
Paper and Pencil
1. Solve the following equations:
A. 3 x = 24
x
B.
=7
7
C. 6 x + 5 = 31
D. x − 8 = 19
E. x + 7 = −3
2. Are the following algebraic equations solved correctly?
Explain.
f − 3 = −2
A.
f − 3 − 3 = −2 − 3
f = −5
B.
2w + 4 = 12
2w + 4 − 4 = 12 − 4
2w = 8
w =8× 2
w = 16
Math Makes Sense 7
Lesson 6.4
Lesson 6.5
(continued)
3. The table shows the relationship between the number of riders
on a tour bus and the cost of providing boxed lunches.
Customers
Cost ($)
1
4.25
2
8.50
3
12.75
4
17.00
5
21.25…
A. Ask students to explain how the lunch cost is related to the
number of riders.
B. Have them write an equation for finding the lunch cost (l)
for the number of customers (n).
C. Ask them to use the equation to find the cost of lunch if
there were 25 people on the tour.
D. Ask how many people were on the bus if the tour-bus
leader spent $89.25 on lunch.
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
201
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes
Outcomes with Achievement Indicators
Unit 6
202