Strand A: Algebra
Big Idea 1: Understand patterns, relations and functions
Concept B: Create and analyze patterns
Problem:
Use words or an expression to describe the following pattern:
1, 9, 25, 49, 81, …
Problem:
Given the following pattern:
3
4
6
5
8
10
1. Complete the table expressing width and length.
Term #
1
2
3
Width
3
4
5
Length
6
8
10
4
5
6
7
8
2. Write an expression in simplest form to determine the width of any
rectangle that fits this pattern.
3. Write an expression in simplest form to determine the length of any
rectangle that fits this pattern.
Problem:
1. Explain the following pattern:
1, 1, 2, 3, 5, 8, …
2. Use your explanation to find the next three numbers in the sequence.
Problem:
Write an equation for each of the patterns below.
1.
x
1
2
3
4
5
y
5
11
17
23
29
x
1
2
3
4
5
y
1
-1
-3
-5
-7
x
1
2
3
4
5
y
4.5
5
5.5
6
6.5
2.
3.
Problem:
The following table shows the cost for a one-day pass to Paradise Park over the last six
years.
If the trend in the cost of passes continues, what do you predict would be the cost of a
one-day pass in the year 2010?
Explain your answer.
One-Day Pass Prices to Paradise Park
Year
2000
2001
2002
2003
2004
2005
Price
($)
18.00 19.25 20.50 21.75 23.00
24.25
Problem:
Use an equation to describe the pattern in the following graph.
Strand: Algebra
Big Idea 1: Understand patterns, relations and functions
Concept C: Classify objects and representations
Problem:
The concession stand profit per day at the County Fair can be represented by the
following:
Equation: Profit = $2.50v - $500, where v represents the number of visitors.
Table:
Number of Visitors
Profit $
0
200
400
600
-500
0
500
1000
800
Graph:
Profit
Profit
1000
500
Profit
0
-500 0
200
400
600
No. of Visitors
1. How much profit would be expected for 450 visitors?
Which is most helpful: the equation, table or graph?
2. How much profit would be expected for 800 visitors?
Which is most helpful: the equation, table or graph?
Problem:
Janet has $140 and she adds $50 to her savings at the end of each month. She asks three
of her friends when she will have $1000. Their work is shown below.
Explain how each method is alike and how each will give a correct solution.
y = 140 + 50x
Ann:
1000 = 140 + 50x
1000 - 140 = 140 – 140 + 50x
860/50 = 50x/50
17.2 = x
Mark:
Months
0
1
2
4
8
12
16
18
Profit $
140
190
240
340
540
740
940
1040
y = 140 + 50x
Emily:
Amount of Money
Amount
1200
1100
1000
900
800
700
600
500
400
300
200
100
0
0
2
4
6
8
10
12
No of Months
14
16
18
20
Strand A: Algebra
Big Idea 1: Understand patterns, relations and functions
Concept D: Identify and compare functions
Problem:
Given the equation y = 3x + 2, answer the following questions.
1. Would the line be straight or curved? How do you know?
2. Would the slope be positive or negative? How do you know?
3. What is the slope of the line? How do you know?
4. What is the y intercept? How do you know?
Problem:
Given the following three representations of the same linear function, describe how each
representation shows the slope of this line.
Representation 1:
y = 2x + 2
Representation 2:
12
10
8
6
4
2
0
0
0.5
1
Representation 3:
x 1 2 3 4
y 4 6 8 10
1.5
2
2.5
3
3.5
4
Strand A: Algebra
Big Idea 2: Represent and analyze mathematical situations and structures using
algebraic symbols
Concept A: Represent mathematical situations
Problem:
The following table represents the cost of renting videos from Video Palace where a
membership fee is charged.
# Videos rented
0
1
2
3
4
5
Cost $
10
12
14
16
18
20
Use the table to answer the following questions:
1. What does the $10 represent for zero videos rented?
2. Use an equation to describe the cost for renting n videos.
3. Find the cost of renting 50 videos.
Problem:
Sam earns the same amount each week babysitting.
Each week she saves all but $10 of her earnings.
If she has saved $160 after 8 weeks, how much does she earn per week?
Set up an equation to model the situation where x = the amount earned in a week.
Then use your equation to solve for x.
Problem:
1. Given the following pattern, find an equation that shows the pattern.
Term 1
Term 2
Term 3
Term 4
2. Use your equation to find the total number of dots in the 25th term.
Problem:
You plan to order a satellite system for your new home.
Super Satellite charges a $50 installation fee and $65 a month for the satellite.
1. Write an equation to calculate the cost of having a satellite system.
2. Determine the cost of satellite for one year.
Problem:
As Roger drove by the Missouri Bank today, the temperature on the sign read 35 degrees
Celsius.
1. Is this an accurate temperature for July?
2. Provide work that shows how you arrived at your answer.
Formula: F = 9/5C + 32, where F = Degree Fahrenheit and C = Degree Celsius
Problem:
In preparing for their spring dance, the Student Council purchased
five tropical trees to create a backdrop for the DJ.
The total bill for the trees was $251.24, including $16.99 sales tax.
The Student Council Sponsor wants to know the cost of one tropical tree.
To find the cost of one tree, solve the equation 5t + 16.99 = 251.24, where t represents
the number of tropical trees.
Provide the work that shows how you arrived at your answer.
Strand A: Algebra
Big Idea 2: Represent and analyze mathematical situations and structures
using algebraic symbols
Concept B: Describe and use mathematical manipulation
Problem:
A rectangle has a length that is three less than twice the width.
1. Using the variable w to denote the width, write an equation for the length in terms of
w.
2. Write two different expressions that represent how to find the perimeter of this
rectangle and simplify the expressions to show they are equivalent.
Problem:
Write an equivalent expression for 3n4.
Problem:
Write the following expression in simplest form, showing your work to support your
answer.
4x + 3y – 6(x + 5) + (-2)y
Strand A: Algebra
Big Idea 3: Use mathematical models to represent and understand quantitative
relationships
Concept A: Use mathematical models
Problem:
The school choir is selling boxes of greeting cards to raise money for a trip.
The table represents the amount of profit they receive for selling various numbers of
boxes.
Use either an equation or a graph to determine how many boxes they need to sell in order
to make $300 profit.
Boxes of Cards
10
20
30
40
50
Profit $
-10
10
30
50
70
Problem:
It cost $8 to park at Buoy Beach without a sticker.
It costs $3 to park at the same beach if you buy a special sticker.
The sticker costs $50 and can be used all summer.
1. Write an equation to model the cost for parking with a sticker at the beach “n” times.
Let (y1) represent parking with a sticker.
2. Write an equation to model the cost for parking with a sticker at the beach “n” times.
Let (y2) represent parking without a sticker.
3. Using graphs, tables, or the equations, determine whether or not you should buy a
sticker.
Strand A: Algebra
Big Idea 4: Analyze change in various contexts
Concept A: Analyze change
Problem:
Lynda borrowed $175 from her parents and is paying them back $10 per week.
Her sister, Maria, borrowed $200 and pays back $15 per week.
1. Write equations to model each girl’s payback plan.
2. Use the equations to determine who would pay back their parents first.
Problem:
Carla, Drey, and Robert decide to get jobs delivering pizza after school at different
restaurants to earn extra spending money.
Pay
The following graph shows the pay plan for each.
Nightly Earnings
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Drey
Carla
Carla
Drey
Robert
Robert
0
1
2
3
4
5
6
Pizzas Delivered
7
8
9
10
1. Who gets paid the least for each additional pizza delivered? How can you tell?
2. How much does each boy get paid for each added pizza delivered?
3. For what number of pizzas will Drey and Carla be paid equal amounts for the
evening?
4. What do the y-intercepts or values where the lines touch the y-axis mean?
5. When is Carla’s pay plan the best?
6. Whose pay plan is best when 12 or more pizzas are delivered on any given night?
How can you tell on the graph?