grade 7 mathematics unit 6 equations - ed.gov.nl.ca · unit 6: equations grade 7 math curriculum...
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Grade 7 Mathematics Curriculum Outcomes 181
Outcomes with Achievement Indicators
Unit 6
Grade 7 Mathematics
Unit 6
Equations
Estimated Time: 20 Hours
[C] Communication [PS] Problem Solving
[CN] Connections [R] Reasoning
[ME] Mental Mathematics [T] Technology
and Estimation [V] Visualization
Unit 6: Equations
Grade 7 Math Curriculum Guide 183
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)
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 184
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
It is expected that students will: 7PR4. Explain the difference
between an expression and
an equation.
[C, CN]
(Cont’d)
Achievement Indicators
Elaborations: Suggested Learning and Teaching Strategies
It is assumed that students can:
• recognize patterns in a table of values
• write a pattern rule for a number pattern
• use a pattern rule to find the value of a given term
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.
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.
7PR4.6 Provide an
example of an expression
and an equation, and
explain how they are
similar and different.
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 185
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
Paper & Pencil
1. Which are expressions? Which are equations? How are they
similar? How are they different?
A. 2 – x
B. 5v = 20
C. 43
=h
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.
4. Have students complete concept maps for expressions and
equations such as:
Sample Responses
Equation
Essential Characteristics
Non-Essential Characteristics
Examples Non-ExamplesEquation
Essential Characteristics
Non-Essential Characteristics
Examples Non-Examples
= sign
Two expr
essions eq
ual
Two constant terms
More than one operation
2x = 6 5x 2x - 1
44 + 3 = 7
Variable
4 < 6
3x +
4 = 7
y = 2
Resources/Notes
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
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 186
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in multiple
ways.
Specific Outcome
It is expected that students will:
7PR7. Model and solve,
concretely, pictorially and
symbolically, problems that
can be represented by linear
equations of the form:
• ax + b = c
• ax = b
• 0x
= ≠b, aa
where a, b and c are whole
numbers.
[CN, PS, R, V]
Achievement Indicators
Elaborations: Suggested Learning and Teaching Strategies
Note: Only whole numbers should be used for a, b, and c.
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:
2(3) + 1
5Too
Heavy!
2(1) + 1
5
Too
Light!
2(2) + 1 5
Balance!
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.
7PR7.2 Solve a given
linear equation by
inspection and by
systematic trial.
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 187
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
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 2÷×= hbA .
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 2275 =+d 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 36244 =+d , 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.
Resources/Notes
Math Makes Sense 7
Lesson 6.1
(continued)
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 188
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
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]
Elaborations: Suggested Learning and Teaching Strategies
Students should use concrete materials to investigate the
process of solving equations. Refer to Outcome 7PR7 in Unit 1
for discussion.
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.
• 3 × 2 = 6 A related equation that isolates the 3 is 6
32
= .
• 4(3) + 1 = 13. A related equation that isolates the 3 is
13 13
4
−= .
• Similarly, when writing 2N + 1 = 201, a related equation
that isolates the N is 201 1
2N
−= . Therefore, we can
calculate that the input value must have been 100.
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 189
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
Resources/Notes
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 190
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
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
Elaborations: Suggested Learning and Teaching Strategies
Note: Students should consider in advance what might be a
reasonable solution, and be aware that once they acquire a
solution, it can be checked for accuracy by substitution into the
original equation.
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:
246 ++ 34 ×
Since 246 ++ = 34 × , 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.
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).
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 191
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
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 3 1 5n + =
B. Use the balance scales below to illustrate your equations
Interview
1. Consider:
6 2× 10 4+
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?
Resources/Notes
This outcome is covered
throughout:
Lesson 6.2
Lesson 6.3
Lesson 6.4
Lesson 6.5
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 192
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
It is expected that students will:
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
b aa
= ≠ 0
where a, b and c are whole
numbers.
[CN, PS, R, V]
(Cont’d)
Achievement Indicators
Elaborations: Suggested Learning and Teaching Strategies
A two-pan balance can be used to model and visually represent
equations of the form ax b+ = c and ax b= .
Consider the following: 14 22x+ =
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).
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 4426 =+x ,
Left side: 2)7(6 + Right side :44
= 242 +
= 44
Since the left side equals the right side, x=7 is correct.
7PR7.3 Draw a visual
representation of the steps
used to solve a given
linear equation.
7PR7.5 Verify the
solution to a given linear
equation, using concrete
materials and diagrams.
14g ? 22g
7PR7.6 Substitute a
possible solution for the
variable in a given linear
equation into the original
linear equation to verify
the equality.
7PR7.4 Solve a given
problem, using a linear
equation, and record the
process.
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 193
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in multiple
ways.
Suggested Assessment Strategies
Paper and Pencil
1. Find the values of the unknown mass on each balance scale.
Sketch the steps you use.
A.
B.
2. A. Sketch balance scales to represent each equation
B. Solve each equation. Verify the solution.
i. 182 =y
ii. 1723 =+n
3. Solving Equations:
A. Write a problem that can be solved using the equation
123 =+x .
B. How would your problem change if the equation was
123 =x ?
C. What new problem can you write for 123
x= ?
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
5. Show whether or not 7=x is the solution to each equation.
A. 486 =x
B. 2023 =+x
Resources/Notes
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.
w 16g w 4g 12g 8g
15g 15g 20g x 10g
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 194
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
It is expected that students will:
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
b aa
= ≠ 0
where a, b and c are whole
numbers.
[CN, PS, R, V]
(Cont’d)
Achievement Indicators
Elaborations: Suggested Learning and Teaching Strategies
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.
1952 =+n
To isolate 2n, subtract 5 from each side.
519552 −=−+n
142 =n
Divide each side by 2, 2
14
2
2=
n
7=n
Students can verify the solution by substituting n = 7
into 1952 =+n . Since the left side equals the right side, n = 7
is the correct solution.
n n 5g
n 19g n 5g
5g 14g
n n 7g 7g
7PR7.3 Draw a visual
representation of the steps
used to solve a given
linear equation. (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)
7PR7.4 Solve a given
problem, using a linear
equation, and record the
process. (cont’d)
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 195
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in multiple
ways.
Suggested Assessment Strategies
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 7=x is the solution to each equation.
A. 486 =x
B. 17
=x
C. 2023 =+x
Resources/Notes
Math Makes Sense 7
Lesson 6.2
(continued)
Note: This is continued
throughout Lesson 6.4 and
Lesson 6.5.
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 196
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
It is expected that students will:
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
b aa
= ≠ 0
where a, b and c are whole
numbers.
[CN, PS, R, V]
(Cont’d)
Achievement Indicators
Elaborations: Suggested Learning and Teaching Strategies
It will be necessary, however, to model equations of the form
xb
a= , 0a ≠ and to supplement the student text exercises with
examples of this type.
Example: Laurie has 1
3 of a chocolate bar. It weighs 5g. She
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.
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:
By combining these pieces to form a whole bar…
…she concludes that one bar is 15g.
Verify: Left Pan: 33
bb= ÷ Right Pan : 5g
= 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.
7PR7.3 Draw a visual
representation of the steps
used to solve a given
linear equation. (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)
7PR7.4 Solve a given
problem, using a linear
equation, and record the
process. (cont’d)
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 197
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
Paper and Pencil
1. Brigitte is solving the equation 68
f= . This is her solution:
108
8 10 88
2
f
f
f
=
− = −
=
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.
Resources/Notes
This outcome is covered
throughout:
Lesson 6.1
Lesson 6.2
Lesson 6.4
Lesson 6.5
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 198
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
It is expected that students will: 7PR6. Model and solve,
concretely, pictorially and
symbolically, problems that
can be represented by one-
step linear equations of the
form x + a = b, where a and
b are integers.
[CN, PS, R, V]
Achievement Indicators
Elaborations: Suggested Learning and Teaching Strategies
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.
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: 93 −=−x
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.
The tiles show that 6−=x
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.
7PR6.1 Represent a
given problem with a
linear equation; and
solve the equation, using
concrete models, e.g.,
counters, integer tiles.
7PR6.3 Solve a given
problem, using a linear
equation.
7PR6.2 Draw a visual
representation of the
steps required to solve a
given linear equation.
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.
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 199
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
Paper and Pencil
1. Solve each of the equations using algebra tiles. Sketch your
steps. Verify your solution.
A. 43 =−n
B. 21 −=+h
C. 62 −= y
D. 14 −=−w
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 C°5 to C°− 2 . 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 2−=x a solution?
A. 53 −=−x
B. 31 =+x
C. 12 =+x
D. 13 =+x
Resources/Notes
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
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 200
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Specific Outcome
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
Elaborations: Suggested Learning and Teaching Strategies
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.
713 =+y
17113 −=−+y
63 =y
3
6
3
3=
y
2=y
7PR3.3 Solve a given
problem by applying
preservation of equality.
Strand: Patterns and Relations (Variables and Equations)
Grade 7 Mathematics Curriculum Outcomes 201
Outcomes with Achievement Indicators
Unit 6
General Outcome: Represent algebraic expressions in
multiple ways.
Suggested Assessment Strategies
Paper and Pencil
1. Solve the following equations:
A. 243 =x
B. 77
=x
C. 3156 =+x
D. 198 =−x
E. 37 −=+x
2. Are the following algebraic equations solved correctly?
Explain.
A. 23 −=−f
3233 −−=−−f
5−=f
B. 1242 =+w
412442 −=−+w
82 =w
28 ×=w
16=w
3. The table shows the relationship between the number of riders
on a tour bus and the cost of providing boxed lunches.
Customers 1 2 3 4 5
Cost ($) 4.25 8.50 12.75 17.00 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.
Resources/Notes
Math Makes Sense 7
Lesson 6.4
Lesson 6.5
(continued)