

Unit 4 Percents
and Proportional Relationships Grade 7 Math 

Unit
Length and Description: 20 days Unit 4 extends the concepts of
ratio and proportion covered in Unit 1 to include percents. Students use their understanding of ratios
and proportionality to solve a wide variety of percent problems, including
those involving discounts, interest, taxes, tips, and percent increase and
decrease. Additionally, students solve problems involving scale drawings and
percents. 

Standards: 7.RP.A.1 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 1/2 mile in each 1/4 hour, compute the unit rate
as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles per hour.
7.RP.A.2 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 relationships 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 at t = pn. 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.
7.RP.A.3 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.
7.EE.A.2 Understand that rewriting an
expression in different forms in a problem context can shed light on the
problem and how the quantities in it are related. For
example, a + 0.05a = 1.05a means that “increase by 5%” is the same as
“multiply by 1.05.” o
Standards
Clarification: In this unit, this
standard is applied to expressions with rational numbers in them. 7.EE.B.3 Solve multistep reallife
and mathematical problems posed with positive and negative rational numbers
in any form (whole numbers, fractions, and decimals), using tools
strategically. Apply properties of
operations to calculate with numbers in any form; convert between forms as
appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies.
For example: If a woman making $25 an hour gets a 10%
raise, she will make an additional 1/10 of her salary an hour, or $2.50, for
a new salary of $27.50. If you want to
place a towel bar 9 3/4 inches long in the center of a door that is 27 ½
inches wide, you will need to place the bar about 9 inches from each edge;
this estimate can be used as a check on the exact computation. o
Standards
Clarification: The equations and
inequalities in this unit should provide the students an opportunity to work
with all types of rational numbers, not just integers, and especially
including those involving percents and conversions to decimals. 7.G.A.1 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.
Focus Standards of
Mathematical Practice: MP.1 Make
sense of problems and persevere in solving them. MP.2 Reason
abstractly and quantitatively. MP.3
Construct viable arguments and critique the reasoning of others. MP.4 Model
with mathematics. MP.5 Use
appropriate tools strategically. MP.6 Attend
to precision. MP.7 Look for
and make use of structure. MP.8 Look for
and express regularity in repeated reasoning. Instructional
Outcomes: Full Development of the Major Clusters,
Supporting Clusters, Additional Clusters and Mathematical Practices for this
unit could include the following instructional outcomes: 7.RP.A.1 ·
I can compute unit rates associated with ratios of
fractions in like or different units. ·
I can compute fractional by fractional quotients. ·
I can apply fractional ratios to describe rates. 7.RP.A.2a ·
I can determine that a proportion is a statement of
equality between two ratios. ·
I can analyze two ratios to determine if they are
proportional to one another with a variety of strategies (e.g. using tables,
graphs, pictures, etc.) 7.RP.A.2b ·
I can define constant of proportionality as a unit rate. ·
I can analyze tables, graphs, equations, diagrams, and
verbal descriptions of proportional relationships to identify the constant of
proportionality. 7.RP.A.2c ·
I can represent proportional relationships by writing
equations. 7.RP.A.2d ·
I can recognize what (0,0) represents on the graph of a
proportional relationship. ·
I can recognize what (1,r) on a graph represents,
where r is the unit rate. ·
I can explain what the points on a graph of a
proportional relationship means in terms of a specific situation. 7.RP.A.3 ·
I can recognize situations in which percentage
proportional relationships apply. ·
I can apply proportional reasoning to solve multistep
ratio and percent problems, e.g., simple interest, tax, markups,
markdowns, gratuities, commissions, fees, percent increase and decrease,
percent error, etc. 7.EE.A.2 ·
I can write equivalent expressions with fractions,
decimals, percents, and integers. ·
I can rewrite an expression in an equivalent form in
order to provide insight about how quantities are related in a problem
context. 7.EE.B.3 ·
I can convert between numerical forms as appropriate. ·
I can solve multistep reallife and mathematical problems
posed with positive and negative rational numbers in any form (whole numbers,
fractions, and decimals), using tools strategically. ·
I can apply properties of operations to calculate with
numbers in any form. ·
I can assess the reasonableness of answers using mental
computation and estimation strategies. 7.G.A.1 ·
I can use ratios and proportions to create scale
drawing. ·
I can identify corresponding sides of scaled geometric
figures. ·
I can compute lengths and areas from scale drawings
using strategies such as proportions. ·
I can solve problems involving scale drawings of
geometric figures using scale factors. ·
I can reproduce a scale drawing that is proportional to
a given geometric figure using a different scale. 

Enduring
Understandings: ·
Rates, ratios, percentages and proportional relationships can be
applied to solve multistep ratio and percent problems. ·
Proportional reasoning using rates, ratios, percentages and
proportional relationships can be applied to problem solving situations
such as interest, tax, discount, etc. ·
Several
ways of reasoning, all grounded in sense making, can be generalized into
algorithms for solving proportion problems. ·
Scale drawings can be applied to problem
solving situations involving geometric figures. ·
Geometrical figures can be used to reproduce a
drawing at a different scale. 
Essential
Questions: ·
How can percent help you understand situations involving money? ·
How can I use proportional relationships to solve ratio and percent
problems? ·
What are the types/varieties of situations in life that depend
on or require the application
of ratios and proportional reasoning? • In what situations is an understanding of proportional reasoning
crucial? • What characteristics define the graphs of all
proportional relationships? • How can I use geometric figures to
reproduce a drawing at a different scale? ·
How can geometry be used to solve problems about
realworld situations, spatial relationships, and logical reasoning? ·
How does Geometry help us describe realworld objects? 
