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Four Methods to Solve Proportions: Methods and Examples, Schemes and Mind Maps of Pre-Calculus

Four methods to solve proportions with examples. The methods include using a double-sided number line, calculating unit rates, graphing, and writing an equation. Each method is demonstrated with a problem and its solution.

Typology: Schemes and Mind Maps

2021/2022

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Name:__________________________________________ Date:__________ Period:______
!
IMP Activity: Four Methods to Solve Proportions 1
Four Methods to Solve Proportions
Problem:
Apples are on sale for 2 lbs for $3. How many pounds can you buy for $30?
Question 1: Is this a proportional situation? Why or why not?
________________________________________________________________________________
________________________________________________________________________________
Method I: Draw a double-sided number line,
label the parts, set up a proportion and
solve.
Method II: Using any method, calculate unit
rate and then calculate how many pounds
you can get for $30.
Unit Rate:
How many pounds for $30:
Method III: Graph a point to represent the
original ratio. How many pounds can you buy
for $0? Record this additional point on the
graph and connect the two points. Extend
the line to predict how many pounds you can
buy for $30.
What is the slope of this line?
How many pounds for $30?
Method IV: Using the constant of
proportionality (unit rate), write an equation
to represent the original ratio (use d to
represent number of dollars and p to
represent number of pounds). Use this
equation to calculate how many pounds for
$30.
Equation:
How many pounds for $30:
Pounds
Dollars
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Name:__________________________________________ Date:__________ Period:______

Four Methods to Solve Proportions

Problem:

Apples are on sale for 2 lbs for $3. How many pounds can you buy for $30?

Question 1: Is this a proportional situation? Why or why not?



Method I: Draw a double-sided number line , label the parts, set up a proportion and solve. Method II: Using any method, calculate unit rate and then calculate how many pounds you can get for $30. Unit Rate: How many pounds for $30: Method III: Graph a point to represent the original ratio. How many pounds can you buy for $0? Record this additional point on the graph and connect the two points. Extend the line to predict how many pounds you can buy for $30. What is the slope of this line? How many pounds for $30? Method IV: Using the constant of proportionality (unit rate), write an equation to represent the original ratio (use d to represent number of dollars and p to represent number of pounds). Use this equation to calculate how many pounds for $30. Equation: How many pounds for $30: Pounds Dollars

Name:__________________________________________ Date:__________ Period:______ Problem:

Mary runs 5 km in 75 minutes. How long will it take her to run 2 km?

Question 2: Is this situation proportional? Why or why not?



Method I: Draw a double-sided number line , label the parts, set up a proportion and solve. Method II: Using any method, calculate unit rate and then calculate how long it will take her to run 2 km. Unit Rate: How long to run 2 km: Method III: Graph a point to represent the original ratio. How far did she run in 0 minutes? Record this additional point on the graph and connect the two points. Extend the line to predict how long it will take to run 2 km. What is the slope of this line? How long will it take to run 2 km? Method IV: Using the constant of proportionality (unit rate), write an equation to represent the original ratio (use d to represent distance and t to represent time). Use this equation to calculate how long it will take her to run 2km. Equation: How long will it take to run 2 km? Kilometers Time (mins)

Name:__________________________________________ Date:__________ Period:______ 24

Situation/Question

____________________________________________________

____________________________________________________

____________________________________________________

Unit Rate Table

Other/Equation Proportion

Situation/Question

____________________________________________________

____________________________________________________

____________________________________________________

Unit Rate Table

Other/Equation

24 s for $14. or 6 for $3.

Proportion

Name:__________________________________________ Date:__________ Period:______ Comparing Methods

  1. Which of the four methods is easiest for you? Why?
  2. What are the benefits to using each method?

ANSWER KEY

Problem: Apples are on sale for 2 lbs for $3. How many pounds can you buy for $30? Question 1: Are these data proportional or not proportional? Why or why not? Yes, the data are proportional because the ratio between pounds and the cost is constant. Method I: Draw a double-sided number line , label the parts, set up a proportion and solve. Method II: Using any method, calculate unit rate and then calculate how many pounds you can get for $30. Unit Rate (how much for 1 pound): How many pounds for $30: $ 1. 50 1 ๐‘™๐‘

Method III: Graph a point to represent the original ratio. How many pounds can you buy for $0? Record this additional point on the graph and connect the two points. Extend the line to predict how many pounds you can buy for $30. What is the slope of this line? . / How many pounds for $30? 20 lbs Method IV: Using the constant of proportionality (unit rate), write an equation to represent the original ratio (use d to represent dollars and p to represent pounds). Use this equation to calculate how many pounds for $30. Equation: ๐‘‘ = 1. 50 ๐‘ How many pounds for $30: 30 = 1. 50 ๐‘ 20 = ๐‘

Pounds Dollars 2 lbs $ x lbs $ 2 3

60 = 3 ๐‘ฅ by cross products 20 = ๐‘ฅ $. / 345

$ 6. 78 6 34 $1.50/lb

Problem: Mary runs 5 km in 75 minutes. How long will it take her to run 2 km? Question 2: Are these data proportional or not proportional? Why or why not? Yes, they are proportional. Method I: Draw a double-sided number line , label the parts, set up a proportion and solve. Method II: Using any method, calculate unit rate and then calculate how long it will take her to run 2 km. Unit Rate (how long for 1 km): 97 :;< 7 =:

67 :;< 6 =: 15 min/km How long to run 2 km: 15 ๐‘š๐‘–๐‘›๐‘  1 ๐‘˜๐‘š

Method III: Graph a point to represent the original ratio. How far did she run in 0 minutes? Record this additional point on the graph and connect the two points. Extend the line to predict how long it will take to run 2 km. What is the slope of this line? 15 How long will it take to run 2 km? 30 mins Method IV: Using the constant of proportionality (unit rate), write an equation to represent the original ratio (use d to represent distance and t to represent time). Use this equation to calculate how long it will take her to run 2 km. Equation: ๐‘ก = 15 ๐‘‘ How long will it take to run 2 km? ๐‘ก = 15 2 ๐‘ก = 30

x minutes 2 km 75 minutes 5 km Time Distance ๐‘ฅ ๐‘š๐‘–๐‘›๐‘  2 ๐‘˜๐‘š