# Unit 4: Ratios, Rates, Proportions, and Percents (January 6-Feb 21)- Math 7th Grade Teacher Carol Brackin Math 7th Grade 19-25 Ratios, Rates, Proportions, and Percents
Standard(s) Taught

MAFS.7.RP.1.1
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 1⁄2 miles per 1⁄4
hour, equivalently 2 miles per hour.

MAFS.7.RP.1.2
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 as 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.

MAFS.7.RP.1.3
Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

MAFS.7.EE.1.2
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.”

Learning Targets and Learning Criteria

• compute a unit rate by iterating (repeating) or partitioning given rate.
• compute a unit rate by multiplying or dividing both quantities by the same factor.
• explain the relationship between using composed units and a multiplicative comparison to express a unit rate.
• use measures of lengths and areas to calculate unit rates with the given context.

a.
• analyze ratios in a table to determine if the
ratios are equivalent by finding the constant
of proportionality.
• calculate the cross product to determine if
the two ratios are in proportion (equivalent).
• graph ratios on a coordinate plane to
determine if the ratios are proportional by observing if the graph is a straight line through the origin (y = kx, where k is the slope/constant of proportionality).
b.
• calculate the constant of proportionality/unit
rate from a table or diagram.
• calculate the constant of proportionality/unit
rate given a verbal description of a
proportional relationship.
• compute the rate of change/slope from a
graph or equation (k in y=kx).
c.
• solve equations created from proportional
relationships
• write an equation from a proportional
relationship
d.
• calculate the unit rate by identifying that on a
graph when the x-coordinate is 1, the y-
coordinate is the unit rate.
• define the rate of proportionality from a
graph.
• explain that the y-coordinate divided by the
x-coordinate for every point other than the
origin equals the constant of proportionality
• explain the meaning of a point on a graph
y=kx of a real life situation

• use proportional reasoning to solve real- world ratio problems, including those with multiple steps.
• use proportional reasoning to solve real- world percent problems, including those with multiple steps, such as markups, markdowns, commissions, and fees
• solve percent problems when one quantity is a certain percent more or less than another.
• recall conversion of percents from ratio to decimal to percent form.
• solve percent of increase/decrease problems.

• explain how an equivalent expression relates to the original situation problem
• rewrite expressions to help analyze problems.
• simplify expressions
• translate situation problems to algebraic
expressions

Classroom Activities

 Notes    Page & Week    of  Study Topic of Study and Independent Practice in Class Homework 1 – 19 What is a Ratio HW #1  2 – 19 Rates & Unit Rates HW #2 3 – 20 Proportional vs. Nonproportional Relationships  HW #3 4 – 20 Solving Proportions  HW #4  – 21 Quiz 4-1 None 5 – 21 Proportion Word Problems  HW #5 6 – 21 Scale Drawings and Models  HW #6  7 – 21 Similar Figures HW #7 – skip Indirect Measurement  HW #8 – 22 Quiz 4-2  None  8 – 22 Percent Proportion HW #9 9 – 22 Percent Equation HW #10    10 -23 Computing Percents Mentally (5%, 10%, 15%, 20%) using 10% as a benchmark HW #11 -23       -23 Graphing Proportions   Quiz 4-3 None 11- 24 Discount, Mark-Up, Sales Tax, Tip HW #12 12- 24 Percent of Change HW #13 13- 25 Simple Interest HW #14 – 25 Quiz 4-4 None -25 Unit 4 Review – graphing proportions Study for DIA Assignments Due

Each study topic above has close notes (fill in the blank) with 6 to 8 guided practice problems done together as a class and corrected in class.  Then students do 10 to 12 independent practice problems which are also checked in class.  These problems can be used as models to help with the homework problems.  Each page of notes has a homework page which is due the next day class meets.

On Monday and Tuesday, 2/10, students will be learning to calculate common percentages (5%, 10%, 15%, 20%) using mental math.