Proportions & Unit Rate 7 th Grade Math. 1. Melanie and Valerie went shopping last week. Melanie bought twice as many shirts as Valerie. If Valerie bought.

Slides:

Advertisements

Similar presentations

Ratios and Proportional Relationships Test Review

Advertisements

7.RP - Analyze proportional relationships and use them to solve real-world and mathematical problems. 1. Compute unit rates associated with ratios of.

Unit Rate Review From Ratios to Rates.

Identifying and Representing Proportional Relationships

{ 8-1: Ratios and Equivalent Ratios IWBAT read and write ratios and equivalent ratios.

02 – 4a Unit Rates PA Grade 7, Math Anchor M07.A-R Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and.

Proportions, Ratio, Rate and Unit Rate Review

Unit Rate Review. Vocabulary Review A ratio is a comparison of two quantities by division. ̶17 out of 20 students, or A rate is a special type of ratio.

Ratio Notes A ratio is a comparison of two numbers by division. Each number in a ratio is called a term. Ratios can be written three ways and SHOULD ALWAYS.

Writing and Solving Proportions. Proportions Proportion is an equation stating that two ratios are equivalent. Proportional are two quantities that form.

Identify, write, and graph an equation of direct variation.

Constant of Proportionality

Direct Variation What is it and how do I know when I see it?

Direct Variation What is it and how do I know when I see it?

Solving Proportions by Creating Equivalent Ratios Wednesday, October 07, 2015 We are learning to…use proportional reasoning to solve problem situations.

Interpreting the Unit Rate as Slope

Representing proportional relationships with equations.

1 Math Solving Proportions. 2 Vocabulary ► Proportion—an equation that shows that two ratios are equivalent. ► Cross Product—the product of the numerator.

Topic 1 Ratios and Proportional Relationships. Lesson Rates A ratio that compares two quantities with different kinds of units is called a rate.

Proportions. Proportion – two equal ratios 1 = 4 3 = = 21 a = c 8 24 b d.

Ratio, Rate, Proportion, and Percent. Ratio  Comparison of two numbers by division  Can be written three different ways 4 to 9 4 :

4.5 Direct Variation What is it and how do I know when I see it?

P ATTERNS AND P ROPORTIONAL R ELATIONSHIPS. D IRECT P ROPORTION The table below is a linear function. X1234 Y One way to describe the function.

Reduce the following ratios: 18 to : 32 9 to

DO NOW. OBJECTIVE : SWBAT Solve problems involving proportional relationships Convert between measurement systems using unit rates and using proportions.

Solving Proportions. 2 ways to solve proportions 1. Equivalent fractions (Old) Cross Products (New)

Directions: 1. Circle ALL crayons. 2. Determine how many crayons you have. 3. Determine how many markers you have. There are crayons for every markers.

Unit 3, Lesson 6 Constant of Proportionality and Writing Direct Variation Equations.

6.RP - Understand ratio concepts and use ratio reasoning to solve problems. 1. Understand the concept of a ratio and use ratio language to describe a.

Unit 1 Ratios and Unit Rates Unit 1 Ratios and Unit Rates.

RP Unit 1a: Ratios & Proportional Reasoning. Greatest Common Factor A factor is a number that you multiply by another number to get a product. Example:

When comparing two objects of the same proportion... Proportional Relationships Proportion: a statement that two ratios are equal.

Warm Up. Chapter 4 Solving & Applying Proportions.

Direct Variation Section 1.9.

Equivalent Ratios Problem Solving

8-5 6 th grade math Rates. Objective To use rates to solve problems Why? To know how to convert miles per hour, miles per gallon, revolutions per minute,

LESSON How can you use tables, graphs, and equations to represent proportional situations? Representing Proportional Relationships.

4.7 PROPORTIONAL RELATIONSHIPS I CAN IDENTIFY PROPORTIONAL RELATIONSHIPS AND FIND CONSTANTS OF PROPORTIONALITY BY USING PROPORTIONS.

Unit 5 Test Review Chapter 1 Lessons 1-8.

+ Directly Proportional. + Directly proportional: as one amount increases, another amount increases at the same rate. Hence, the straight line when we.

Vocabulary ratio: a comparison of two numbers through division often expressed as a fraction. Proportion: An equation that states that two ratios are equal.

What do you guess?. # of hours you studyGrade in Math test 0 hour55% 1 hour65% 2 hours75% 3 hours95%

Proportional and Non- Proportional Relationships using Tables Objective: I will determine proportional and non-proportional relationships using tables.

A proportion is an equation stating that two ratios are equal.

Ratios, Rates, and Proportions. Ratios Ratios are used to make comparisons. Ratios can be written in three different ways: ◦ Using the word “to” ◦ As.

Direct Variation: What is it and how do I know when I see it? Do Now: Find the slope of the line that contains the points (-3, 5) and (6, -1).

Direct Variation If two quantities vary directly, their relationship can be described as: y = kx where x and y are the two quantities and k is the constant.

7.RP.2 Analyze proportional relationships and use them to solve real-world and mathematical problems. Recognize and represent proportional relationships.

What is it and how do I know when I see it?

Proportional Relationships

Daily Problem for Tuesday 10/11/16

2-6 Ratio and Proportion Goal:

What is it and how do I know when I see it?

Constant of Proportionality

Do Now: 10/30/17

Chapter 3 Ratios and Rates

Constant of Proportionality

Lesson 4.3 Graphing Proportional Relationships

Do Now Can you Reason abstractly?

Proportions, Ratio, Rate and Unit Rate Review

Warm-up October 26, 2017 Factor: 66B + 12A – 14

Interpreting the Unit Rate as Slope

Algebra November 12, Direct Variation Objective:

You need: Pencil Agenda Scrap Paper AP log Math book Calculator

Comparing and Scaling Develop students ability to make intelligent comparisons of quantitative information using ratios, fractions, decimals, rates, unit.

Objectives Compare linear, quadratic, and exponential models.

Homework: Maintenance Sheet 15 via study island due Friday

Proportional or Non-proportional?

Additive Relationship

Presentation transcript:

Proportions & Unit Rate 7 th Grade Math

1. Melanie and Valerie went shopping last week. Melanie bought twice as many shirts as Valerie. If Valerie bought x number of shirts, which expression shows the total number of shirts that Melanie and Valerie bought? a) x ²b) x +2 c) x + 2x d) x + x 2.What is the value of the expression (x-y)(x+y) when x = 12 and y = -12? 3.Greg can ride at the rate of 24 miles to Gainesville in two hours on his bike. If he rides at the same rate, how long will it take him to ride his bike the 36 miles to the soccer field? (Set up a proportion.) 0 3

CC.7.RP.2b Identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Standard

How do I identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships? Essential Question

Ratio is … A comparison of two numbers. There are twelve girls and nine boys in a class at MTSU. Write the ratio of boys to girls in fraction form. 9 12

A Proportion is… Two ratios that are equivalent to each other. $4 for 3 folders = $8 for 6 folders =

Do these ratios form a proportion? ? Cross multiply and see if the products are equal. 2  7 = 143  4 = 12 14≠ 12 They do not form a proportion.

Find the missing part. 5w = w = 24 Cross multiply and solve the equation.

Real World Application Miles Minutes Cross multiply and solve the equation.

Unit Rate is… A ratio that has a denominator of one… showing the value of one unit. Examples: price per pound pages read in one hour pages read in one hour cups that can fit on one shelf cups that can fit on one shelf price per gallon price per gallon

Real World Application If a person walks ½ mile in ¼ hour, what is the unit rate? (miles per hour) 2 miles per hour

How do you determine the better buy using unit rates? The CHEAPER of two unit rates…(the lowest amount). Example: 2 cokes for $ cokes for $ cokes for $1.75 is cheaper so it is the better buy. ($.50 each) ($.44 each)

Write the unit rate: $30 for six books ____ for one book $5

X independent Y dependent Record your information in a table. Books Price The independent variable does not depend on anything. The dependent variable depends on the independent variable in order to find its value.

Graph It! independent dependent Books Price A straight line through the origin shows a direct proportion on a graph… As x is increasing, y is also increasing.

Proportionality The graph of a proportional relationship is a straight line that passes through the origin. Proportional quantities can be described by the equation y = kx, where k is a constant ratio... also known as constant of proportionality.

X independent Y dependent Using the form y = kx, write an equation for the information in the chart. Books Price What did you do to x to get y? 5x = y

X independent Y dependent Books Price x = y If y = kx then doesn’t k = y/x? To find the constant of proportionality, you can divide the y coordinate by the x coordinate. 5/1 = 5 10/2=5 15/3=5 20/4=5 25/5=5 30/6=5 The constant of proportionality is 5.

Constant of Proportionality Do you remember where the 5 came from? The unit rate…it is the number that you used to multiply by each x value to get each y value. Unit rate is also known as the constant of proportionality because it is the number that remains constant in each proportional situation.

Write the unit rate: Read 80 pages in 2 hours _______ pages in one hour 40

X independent Y dependent Record your information in the table. Hours Pages Is this a direct proportion? Yes…as x increases, y increases. What is the constant of proportionality? 40 Which is the dependent variable and which is the independent variable? (hours and pages)

Graph It! independent dependent Hours Pages How do you determine if the graph is a direct proportion? A straight line through the origin shows a direct proportion.

Write the unit rate: A plane travels 2250 km in 3 hours. What is the average speed? (km per hour) 750 km/hr What is the constant of proportionality? They are asking for unit rate… 750

Graph It! independent dependent Hours Km Is this a direct proportion? Yes…A straight line through the origin shows a direct proportion.

k = y/x k = 20/2 k = 10

k = 2 Write the equation for the graph above. y = 2x

Write an equation for the information in the table. Xy y = 10x What is the constant of proportionality?10

k = 5 Write the equation for the graph above. y = 5x

k = 7.5 Write the equation for the graph above. y = 7.5x

Y = 12/x No. The equation is not in the form y = kx.

k = 12.5

Closing How do you find the constant of proportionality from a: Ratio? Table? Equation? Graph? How do you determine if the proportional relationship shown is a direct proportion in a: Table?Graph?