This lesson will assist students in understanding proportions. Use of ratios and rates from the previous lesson will be continued in the set up and use of proportions. Students will demonstrate their understanding of proportion by using ratio reasoning.
The use of proportions is important because it will give students knowledge of utlilizing the concepts learned in real-life. Some of the tasks students will be able to perform are solving geometric and measurment problems, calculate recipes, driving distances, and costs. Students will be able to use proportional reasoning at work and home.
Prerequisites for this lesson are understanding ratios and rate from the previous lesson. Also, students need to have a good understanding of mulitplication.
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Lesson Objectives
At the end of this lesson, students will be able to set-up real-life proportional problems given context and calculate the missing piece of a proportion problem using ratio reasoning.
Student Target
“I can
set up proportional problems involving professional and personal situations."
calculate the missing piece of a proportion problem using ratio reasoning."
CCR Focus Standards
Number and Ratios - Level D
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
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. (Also see 7.G.1 and G.MG.2)
Algebra and Functions - Level D
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. [Also see 7.RP.2b]
Supporting Standards
Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
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.
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. (Also see 8.EE.5)
Standards for Mathematical Practice
Make sense of problems and persevere in solving them. (MP.1)
Model with mathematics. (MP.4)
Look for and express regularity in repeated reasoning. (MP.8)
KYAE Employability Standards
E.7 Accurately analyze information and respond appropriately.
E.9 Analyze self-performance to better understand strengths and areas for improvement.
