7th Grade Mathematics
Unit 2 Curriculum Map: October 28th – January 3rd
ORANGE PUBLIC SCHOOLS
OFFICE OF CURRICULUM AND INSTRUCTION
OFFICE OF MATHEMATICS
7th Grade Unit 1
October 28th – January 3rd
Common Core Standards
7.RP.1
7.RP.2
7.RP.3
7.G.1
GRADE 7 NUMBER SENSE
Compute unit rates associated with ratios of fractions, including ratios of lengths,
areas and other quantities measured in like or different units. For example, if a
person walks ½ mile in each ¼ hour, compute the unit rate as the complex
fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
Recognize and represent proportional relationships between quantities.
a. Decide whether two quantities are in a proportional relationship, e.g., by
testing for equivalent ratios in a table or graphing on a coordinate plane
and observing whether the graph is a straight line through the origin.
b. Identify the constant of proportionality (unit rate) in tables, graphs,
equations, diagrams, and verbal descriptions of proportional
relationships.
c. Represent proportional relationship by equations. For example, if total
cost t is proportional to the number n of items purchased at a constant
price p, the relationship between the total cost and the number of items
can be expressed as t = pm.
d. Explain what a point (x,y) on the graph of a proportional relationship
means in terms of the situation, with special attention to the points (0,0),
and (1,r) where r is the unit rate.
Use proportional relationships to solve multistep ratio and percent problems.
Examples: simple interest tax, markups and markdowns, gratuities and
commissions, fees, percent increase and decrease, percent error
Solve problems involving scale drawings of geometric figures, including
computing actual lengths and areas from a scale drawing and reproducing a
scale drawing at a different scale.
1
October 28th – January 3rd
7th Grade Unit 1
Model Curriculum Student Learning Objectives
SLO
Description
Calculator
Allowed
(PARCC)
1
7.RP.1
Calculate and interpret unit rates of various quantities involving ratios of
fractions that contain like and different units using real world examples
such as speed and unit price. For example, if a person walks ½ mile in
each ¼ hour, compute the unit rate as the complex fraction 1/2/1/4 miles
per hour, equivalently 2 miles per hour.
YES
2
7.RP.2
Determine if a proportional relationship exists between two quantities
e.g. by testing for equivalent ratios in a table or graph on the coordinate
plane and observing whether the graph is a straight line through the
origin.
YES
3
7.RP.2
Identify the constant of proportionality (unit rate) from tables, graphs,
equations, diagrams, and verbal descriptions
NO
4
7.RP.2
Write equations to model proportional relationships in real world
problems. For example, if a recipe that serves 6 people calls for 2 ½
cups of sugar, how much sugar is needed if you are serving only 2
people?
NO
5
7.RP.2
Represent real world problems with proportions on a graph and describe
how the graph can be used to explain the values of any point (x,y) on
the graph including the points (0,0) and (1,r), recognizing that r is the
unit rate.
NO
6
7.RP.3
Solve multi-step ratio and percent problems using proportional
relationships (simple interest, tax, markups and markdowns, gratuities
and commissions, fees, percent increase and decrease, percent error).
YES
7
7.RP.3
7.G.1
Solve multi-step ratio and percent problems using proportional
relationships, including scale drawings of geometric figures, simple
interest, tax, markups and markdowns, gratuities and commissions, and
fees.
YES
2
7th Grade Unit 1
October 28th – January 3rd
Connections to the Mathematical Practices
1
2
3
4
5
6
7
8
Make sense of problems and persevere in solving them
- Students make sense of ratio and unit rates in real-world contexts. They
persevere by selecting and using appropriate representations for the given
contexts.
Reason abstractly and quantitatively
- Students will reason about the value of the rational number in relation the
models that are created to represent them.
Construct viable arguments and critique the reasoning of others
- Students use arguments to justify their reasoning when creating and solving
proportions used in real-world contexts.
Model with mathematics
- Students create models using tape diagrams, double number lines,
manipulatives, tables and graphs to represent real-world and mathematical
situations involving ratios and proportions. For example, students will examine
the relationships between slopes of lines and ratio tables in the context of given
situations
Use appropriate tools strategically
- Students use visual representations such as the coordinate plane to show the
constant of proportionality.
Attend to precision
- Students attend to the ratio and rate language studied in grade 6 to represent
and solve problems involving rates and ratios.
Look for and make use of structure
- Students look for patterns that exist in ratio tables in order to make connections
between the constant of proportionality in a table with the slope of a graph.
Look for and express regularity in repeated reasoning
- Students formally begin to make connections between covariance, rates, and
representations showing the relationships between quantities.
3
October 28th – January 3rd
7th Grade Unit 1
Vocabulary
Term
Constant of
Proportionality
Definition
Constant value of the ratio of proportional quantities x and y. Written as y =
kx, k is the constant of proportionality when the graph passes through the
origin. Constant of proportionality can never be zero.
Directly
Proportional
Equivalent
Fractions
If y = kx, then y is said to be directly proportional to x
Fraction
A number expressed in the form a/b where a is a whole number and b is a
positive whole number
Inversely
Proportional
Multiplicative
Inverse
y is inversely proportional to x if y = k/x.
Origin
The point of intersection of the vertical and horizontal axes of a Cartesian
Grid
A rate of change expressed as a percent. Example: if a population grows
from 50 to 55 in a year, it grows by (5/50) = 10% per year
Percent rate of
change
Proportional
Relationship
Proportion
Two fractions that have the same value but have different numerators and
denominators; equivalent fractions simplify to the same fraction.
Two numbers whose product is 1r. Example (3/4) and (4/3) are multiplicative
inverses of one another because (3/4) x (4/3) = (4/3) x (3/4) = 1
Two quantities are said to have a proportional relationship if they vary in
such a way that one of the quantities is a constant multiple of the other, or
equivalently if they have a constant ratio.
An equation stating that two ratios are equivalent
Ratio
A comparison of two numbers using division. The ratio of a to b (where b ≠ 0)
can be written as a to b, as (a/b), or as a:b.
Similar Figures
Figures that have the same shape but the sizes are proportional
Unit Rate
Ratio in which the second team, or denominator, is 1
Scale Factor
A ratio between two sets of measurements
4
7th Grade Unit 1
October 28th – January 3rd
Potential Student Misconceptions

Often there is a misunderstanding that a percent is always a natural number less than or
equal to 100. Provide examples of percent amounts that are greater than 100%, and
percent amounts that are less 1%.

Student fails to interpret interval marks appropriately.

Not understanding that percents are a number out of one hundred; percents refer to
hundredths

Confusing tenths with hundredths

Thinking percents cannot be greater than 100

Not realizing that one whole equals 100%

Treating percents as though they are just quantities that may be added like ordinary
discount amounts
5
October 28th – January 3rd
7th Grade Unit 1
Teaching Multiple Representations
CONCRETE REPRESENTATIONS
Partitioning with manipulatives
Bar model
Paper strips
Number line
PICTORIAL REPRESENTATIONS
Fraction Strips
(Tape Diagrams)
Double Line Diagrams
Table representation
Graphical representation
Equivalent ratios
6
October 28th – January 3rd
7th Grade Unit 1

ABSTRACT REPRESENTATIONS
Scale Factor (within and between)
 Setting up a Proportion


Iteration
Algorithm

Part/Whole Relationships

Part/Part Relationships

Finding the Unit Rate/Constant of
Proportionality

Simplifying Rates

Creating an Equation

Finding the constant of proportionality

Algorithm for Scale Factor:
Image/Actual figure
Actual Figure/Image
a/b = c/d
7
October 28th – January 3rd
7th Grade Unit 1
CMP3 Pacing Guide
Activity
Stretching and Shrinking (CMP3) Investigation 1
Stretching and Shrinking (CMP3)
Investigation 2
Stretching and Shrinking (CMP3) Investigation 3
Stretching and Shrinking (CMP3) Investigation 4
Illustrative Math Task: Cooking with the Whole
Cup
Illustrative Math Task: Track Practice
Illustrative Math Task: Coffee Cost
Illustrative Math Task: Art Class
Illustrative Math Task: Floor Plan
Assessment Check 1
Comparing and Scaling (CMP3) Investigation 1
Comparing and Scaling (CMP3) Investigation 2
Comparing and Scaling (CMP3) Investigation 3
Illustrative Math Task: Road Trip
Illustrative Math Task: How Fast is Usain Bolt?
Illustrative Math Task: The Price of Bread
Assessment Check 2
Unit 1 Assessment
Common Core
Standards/SLO
7.RP.2, 7.G.1
SLO 2, 3, 4, 5, 6, 7
7.RP.2, 7.G.1
SLO 2, 3, 4, 5, 6, 7
7.RP.2, 7.RP.3, 7.G.1
SLO 2, 3, 4, 5, 6, 7
7.RP.2, 7.G.1
SLO 2, 3, 4, 5, 6, 7
7.RP.1
SLO 1
7.RP.1
SLO 1
7.RP.2
SLO 3, 5
7.RP.2
SLO 3, 5
7.G.1
SLO 7
7.RP.1, 7.RP.2
All SLOs
7.RP.2, 7.RP.3
SLO 2, 3, 4, 5, 6, 7
7.RP.1, 7.RP.2, 7.RP.3
All SLOs
7.RP.1, 7.RP.2, 7.RP.3
All SLOs
7.RP.3
SLO 6, 7
7.RP.3
SLO 6, 7
7.RP.3
SLO 6, 7
7.RP.3, 7.G.1
SLO 6, 7
7.RP.1, 7.RP.2, 7.RP.3, 7.G.1
All SLOs
Estimated
Time
2 days
2 days
2 days
3 days
1 day
1 day
1 day
1 day
1 day
1 day
3 days
3 days
2 days
1 day
1 day
1 day
1 day
1-2 days
8
October 28th – January 3rd
7th Grade Unit 1
CMP2 Pacing Guide
Activity
Common Core
Standards/SLO
Common Core Investigation 1: Graphing
Proportions
7.RP.1
SLO 1
Illustrative Math Task: Cooking with the Whole
Cup
Illustrative Math Task: Track Practice
7.RP.1
SLO 1
7.RP.1
SLO 1
7.RP.2, 7.RP.3
SLO 2, 3, 4, 5, 6, 7
7.RP.2, 7.RP.3
SLO 2, 3, 4, 5, 6, 7
7.RP.2, 7.RP.3
SLO 2, 3, 4, 5, 6, 7
7.RP.2, 7.RP.3, 7.G.1
SLO 2, 3, 4, 5, 6, 7
7.RP.2
SLO 3, 5
7.RP.2
SLO 3, 5
7.RP.1, 7.RP.2,
SLO 1, 2, 3, 4, 5
7.G.1
SLO 7
7.G.1
SLO 7
7.RP.2, 7.RP.3, 7.G.1
SLO 2, 3, 4, 5, 6, 7
7.RP.2, 7.RP.3, 7.G.1
SLO 2, 3, 4, 5, 6, 7
7.G.1
SLO 7
7.RP.3
SLO 6, 7
7.RP.3
SLO 6, 7
7.RP.3, 7.G.1
SLO 6, 7
7.RP.1, 7.RP.2, 7.RP.3, 7.G.1
All SLOs
Comparing and Scaling (CMP2) Investigation 1
Comparing and Scaling (CMP3) Investigation 2
Comparing and Scaling (CMP3) Investigation 3
Comparing and Scaling (CMP2) Investigation 4
Illustrative Math Task: Coffee Cost
Illustrative Math Task: Art Class
Assessment Check 1
Stretching and Shrinking (CMP2) Investigation 1
Stretching and Shrinking (CMP2) Investigation 2
Stretching and Shrinking (CMP2) Investigation 4
Stretching and Shrinking (CMP2) Investigation 5
Illustrative Math Task: Floor Plan
Illustrative Math Task: How Fast is Usain Bolt?
Illustrative Math Task: The Price of Bread
Assessment Check 2
Unit 1 Assessment
Estimated
Time
2 days
1 day
1 day
3 days
2 days
2 days
3 days
1 day
1 day
1 day
2 days
2 days
3 days
2 days
1 day
1 day
1 day
1 day
1-2 days
9
7th Grade Unit 1
October 28th – January 3rd
Associated Illustrative Math Tasks
Cooking with the Whole Cup (7.RP.1)
Travis was attempting to make muffins to take to a neighbor that had just moved in down the
street. The recipe that he was making called for ¾ cup of sugar and 1/8 cup of butter.
a. Travis accidentally put a whole cup of butter in the mix.
i.
What is the ratio of sugar to butter in the original recipe? What amount of sugar
does Travis need to put into the mix to have the same ratio of sugar to butter that
the original recipe calls for?
ii.
If Travis wants to keep the ratios the same as they are in the original recipe, how
will the amounts of all the other ingredients for this new mixture compare to the
amounts for a single batch of muffins?
iii.
The original recipe called for 3/8 cup of blueberries. What is the ratio of
blueberries to butter in the recipe? How many cups of blueberries are needed in
the new enlarged mixture?
b. This got Travis wondering how he could remedy similar mistakes if he were to dump in a
single cup of some of the other ingredients. Assume he wants to keep the ratios the same.
i.
How many cups of sugar are needed if a single cup of blueberries is used in the mix?
ii.
How many cups of butter are needed if a single cup of sugar is used in the mix?
iii.
How many cups of blueberries are needed for each cup of sugar?
Track Practice (7.RP.1)
Part A. Angel and Jayden were at track practice. The track is 2/5 kilometers around.


Angel ran 1 lap in 2 minutes.
Jayden ran 3 laps in 5 minutes.
a. How many minutes does it take Angel to run one kilometer? What about Jayden?
b. How far does Angel run in one minute? What about Jayden?
c. Who is running faster? Explain your reasoning.
Part B. Molly runs 1/3 of a mile in 4 minutes.
a. If Molly continues at the same speed, how long will it take her to run one mile?
b. Draw and label a picture showing why your answer to part (a) makes sense.
10
7th Grade Unit 1
October 28th – January 3rd
Coffee Cost (7.RP.2)
Coffee costs $18.96 for 3 pounds.
a. What is the cost for one pound of coffee?
b. At this store, the price for a pound of coffee is the same no matter how many pounds you
buy. Let x be the number of pounds of coffee and y be the total cost of x pounds. Draw a
graph of the relationship between the number of pounds of coffee and the total cost.
c. Where can you see the cost per pound of coffee in the graph? What is it?
Art Class (7.RP.2)
The students in Ms. Baca’s art class were mixing yellow and blue paint. She told them that
two mixtures will be the same shade of green if the blue and yellow paint are in the same
ratio.
The table below shows the different mixtures of paint that the students made.
a. How many different shades of paint did the students make?
b. Some of the shades of paint were bluer than others. Which mixture(s) were
the bluest? Show your work or explain how you know.
c. Carefully plot a point for each mixture on a coordinate plane like the one that
is shown in the figure. (Graph paper might help.)
d. Draw a line connecting each point to (0,0). What do the mixtures that are the
same shade of green have in common?
11
7th Grade Unit 1
October 28th – January 3rd
Road Trip (7.RP.3)
Part A. Tom wants to buy some protein bars and magazines for a trip. He has decided to buy
three times as many protein bars as magazines. Each protein bar costs $0.70 and each
magazine costs $2.50. The sales tax rate on both types of items is 6½%. How many of each
item can he buy if he has $20.00 to spend?
Part B. After arriving at his destination, Tom goes into a restaurant. The bill before tax is $52.60
and that the sales tax rate is 8%. He decides to leave a 20% tip for the waiter based on the pretax amount. How much should he leave for the waiter? How much will the total bill be, including
tax and tip? Show work to support your answers.
How Fast Is Usain Bolt? (7.RP.3)
Jamaican sprinter Usain Bolt won the 100 meter sprint gold medal in the 2012 Summer
Olympics. He ran the 100 meter race in 9.63 seconds. There are about 3.28 feet in a meter and
5280 feet in a mile. What was Usain Bolt's average speed for the 100 meter race in miles per
hour?
The Price of Bread (7.RP.3)
Inflation is a term used to describe how prices rise over time. The rise in prices is in relation to
the amount of money you have. The table below shows the rise in the price of bread over time:
For the price in each decade, determine what the increase is as a percent of the price in the
previous decade. Is the percent increase steady over time?
Under President Roosevelt, the Fair Labor Standards Act introduced the nation's first minimum
wage of $0.25 an hour in 1938. The table shows the rise in minimum wage over time:
12
7th Grade Unit 1
October 28th – January 3rd
For hourly wage in each decade, determine what the increase is as a percent of the hourly
wage in the previous decade. Is the percent increase steady over time?
Consumers are not affected by inflation when the amount of money they make increases
proportionately with the increase in prices. Complete the last column of the table below to show
what percentage of an hour's pay a pound of bread costs:
In which decade were people who earn minimum wage most affected by inflation? Explain.
Floor Plan (7.G.1)
Mariko has an 80:1 scale-drawing of the floor plan of her house. On the floor plan, the
7
1
dimensions of her rectangular living room are 1 8 inches by 2 2 inches.
What is the area of her real living room in square feet?
13
7th Grade Unit 1
October 28th – January 3rd
Assessment Checks
Assessment Check 1
1. Your school is having a bake sale. You have volunteered to bake apple pies. Your recipe
requires 3 cups of sliced apples for each pie. You have $25.00 to spend on apples.
As you enter the grocery store, you see that they have four different types of apples that each
can be used to make apple pies. Given the information listed below, which type of apple would
be the best to buy considering the recipe and how much money you have to spend?




Granny Smith; 3 apples make 2 cups of slices; Cost = $4.25 a dozen
Gala; 3½ apples make 2 cups of slices; Cost = $4.00 a dozen
Macintosh; 3¾ apples make 2 cups of slices; Cost = $3.25 a dozen
Red Delicious; 3¼ apples make 2 cups of slices; Cost = $3.95 a dozen
2. Helen made a graph that represents the amount of money she earns, y, for the numbers of
hours she works, x. The graph is a straight line that passes through the origin and the point (1,
12.5).
Which statement must be true?
a. The slope of the graph is 1.
b. Helen earns $12.50 per hour.
c. Helen works 12.5 hours per day.
d. The -intercept of the graph is 12.5.
3. Roxanne plans to enlarge her photograph, which is 4 inches by 6 inches. Which of the
following enlargements maintains the same proportions as the original photograph?
a. 5 inches by 7 inches
b. 5 inches by 7½ inches
c. 6 inches by 8 inches
d. 8 inches by 6 inches
4. Roberto is making cakes. The number of cups of flour he uses is proportional to the number
of cakes he makes. Roberto uses 22½ cups of flour to make 10 cakes.
Which equation represents the relationship between f, the number of cups of flour Roberto uses
and c, the number of cakes he makes?
a. 𝑓 =
b. 𝑓 =
c. 𝑓 =
4
𝑐
9
1
24𝑐
1
22𝑐
d. 𝑓 = 10𝑐
14
7th Grade Unit 1
October 28th – January 3rd
Assessment Check 2
1. The town of Mayville taxes property at a rate of $42 for each $1,000 of estimated value.
What is the estimated value of a property on which the owner owes $5,250 in property tax?
2. The tires Mary wants to buy for her car cost $200 per tire. A store is offering the following
deal.
Buy 3 tires and get the 4th tire for 75% off!
Mary will buy 4 tires using the deal. The sales tax is 8%. How much money will Mary save by
using the deal versus paying the full price for all 4 tires?
a. $150
b. $162
c. $185
d. $216
3. Kate bought a book for $14.95, a record for $5.85, and a tape for $9.70. If the sales tax on
these items is 6 percent and all 3 items are taxable, what is the total amount she must pay for
the 3 items including tax?
A. $32.33
B. $32.06
C. $30.56
D. $30.50
4. There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4. There
are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4:5. The two
schools hold a dance and all students from both schools attend. What fraction of the students at
the dance are girls?
5. The sales team at an electronics store sold 48 computers last month. The manager at the
store wants to encourage the sales team to sell more computers and is going to give all the
sales team members a bonus if the number of computers sold increases by 30% in the next
month. How many computers must the sales team sell to receive the bonus? Explain your
reasoning.
15
7th Grade Unit 1
October 28th – January 3rd
6. A scale drawing for a construction project uses a scale of 1 inch = 4 feet. The dimensions of
the rectangular family room on the scale drawing are 7.5 inches by 12 inches.
What will be the actual area of the floor of the family room after the construction project is
completed?
7. A company designed two rectangular maps of the same region. These maps are described
below.
- Map 1: The dimensions are 8 inches by 10 inches. The scale is ¾ mile to 1 inch.
- Map 2: The dimensions are 4 inches by 5 inches.
Which ratio represents the scale on Map 2?
a. ½ mile to ¾ inch
b. ¾ mile to ½ inch
c. ¼ mile to 1 inch
d. 3/8 mile to 1 inch
16
7th Grade Unit 1
October 28th – January 3rd
Extensions
Online Resources
http://www.illustrativemathematics.org/standards/k8
- Performance tasks, scoring guides
http://www.ixl.com/math/grade-7
- Interactive, visually appealing fluency practice site that is objective descriptive
https://www.khanacademy.org/math/
- Interactive, tracks student points, objective descriptive videos, allows for hints
http://www.doe.k12.de.us/assessment/files/Math_Grade_7.pdf
- Common Core aligned assessment questions, including Next Generation Assessment
Prototypes
http://www.learnzillion.com
- Videos organized by Common Core Standard presented with visual representations and
student friendly language
17
7th Grade Unit 1
October 28th – January 3rd
Assessment Resources
7.RP Summative Task
Alyssa sees a lightning bolt in the sky and counts four seconds until she hears the thunder.
a.
There are 5280 feet in a mile and about 3.28 feet in a meter. Given that sound
travels about 343 meters per second, is the lightning strike within one mile of Alyssa?
b.
What is the speed of sound in miles per hour?
7.RP.2 Summative Task
Carlos bought 6½ pounds of bananas for $5.20.
a.
What is the price per pound of the bananas that Carlos bought?
b.
What quantity of bananas would one dollar buy?
c.
Which of the points in the coordinate plane shown below correspond to a quantity of
bananas that cost the same price per pound as the bananas Carlos bought? (Select all that
apply.)
i.
ii.
iii.
iv.
v.
vi.
vii.
A
B
C
D
(10.4, 13)
(13, 10.4)
There is not enough information to determine this.
18
7th Grade Unit 1
October 28th – January 3rd
7.G.1 Summative Task
On the map below, ¼ inch represents one mile. Candler, Canton, and Oteen are three cities on
the map. (No ruler is necessary!)
a.
If the distance between the real towns of Candler and Canton is 9 miles, how far
apart are Candler and Canton on the map?
b. If Candler and Oteen are 3½ inches apart on the map, what is the actual distance
between Candler and Oteen in miles?
19