

Unit 1 Ratios
and Proportional Relationships Grade
7 Math 


Unit
Length and Description: 20 days In this
unit, students extend their understanding of ratios from Grade 6 to include
ratios of fractions and unit rates as complex fractions. Students decide
whether two quantities are in a proportional relationship, identify constants
of proportionality, and represent proportional relationships by equations.
They graph proportional relationships and understand the unit rate informally
as a measure of the steepness of the related line, called the slope. They can
also distinguish proportional relationships from other relationships.
Students develop an understanding of proportionality and use proportional
relationships to solve singlestep and multistep problems. These skills are
then applied to real‐world
problems, including scale drawings as students analyze proportional
relationships in geometric figures. Students solve problems about scale
drawings by relating corresponding lengths between the objects or by using
the fact that relationships of lengths within an object are preserved in
similar objects. 

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 7.NS.A.3 Solve realworld and mathematical problems involving the four
operations with rational numbers. 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.2 ·
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.). ·
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. ·
I
can represent proportional relationships by writing equations. ·
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 mean in
terms of a specific situation. 7.RP.A.3 ·
I
can recognize situations in which proportional relationships apply. ·
I
can apply proportional reasoning to solve single and multistep ratio
problems. 7.NS.A.3 ·
I
can solve realworld and mathematical problems involving complex fractions. 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: ·
Reasoning
with ratios involves attending to and coordinating two quantities. ·
A ratio
is a multiplicative comparison of two quantities. ·
Forming a
ratio as a measure of a realworld attribute involves isolating that
attribute from other attributes and understanding the effect of changing each
quantity on the attribute of interest. ·
A number
of mathematical connections link ratios and fractions: °
Ratios
are often expressed in fraction notation, although ratios and fractions do
not have identical meaning. °
Ratios
are often used to make “partpart” comparisons, but fractions are not. °
Ratios
can often be meaningfully reinterpreted as fractions. ·
Ratios
can be meaningfully reinterpreted as quotients. ·
A
proportion is a relationship of equality between two ratios. In a proportion,
the ratio of two quantities remains constant as the corresponding values of
the quantities change. ·
If one
quantity in a ratio is multiplied or divided by a particular factor, then the
other quantity must be multiplied or divided by the same factor to maintain
the proportional relationship. ·
A rate is
a set of infinitely many equivalent ratios. ·
Scale
drawings and scale models are used to represent objects that are too large or
too small to be drawn or built at actual size. ·
The scale
gives the ratio that compares the measurements of the drawing or model to the
measurements of the real object. ·
The
measurements on a drawing or model are proportional to the measurements on
the actual objects. 
Essential
Questions: ·
What
are the types/varieties of situations in life that depend on or require the
application of ratios and proportional reasoning? ·
How
can a complex fraction be simplified? ·
What
is the difference between a unit rate and a ratio? ·
What
is a proportion? ·
Why
are multiplicative relationships proportional? ·
How
are equivalent ratios, values in a table, and ordered pairs connected? ·
What
characteristics define the graphs of all proportional relationships? ·
How
can you show that two objects are proportional? ·
How
are proportional and nonproportional relationships
alike? How are they different? ·
What
is the constant of proportionality? ·
How
is unit rate related to rate of change? ·
How
can you use different measurements to solve reallife problems? ·
How
does geometry help us describe realworld objects? 
