7th Grade Math Chapter 4 Proportional Relationships Name: ___________________________
Period: _______
Common Core State Standards CC.7.RP.2 - Recognize and represent proportional relationships between quantities. CC.7.G.1 -
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing.
Scope and Sequence Day 1
Lesson 4-1
Day 11
Lesson 4-5
Day 2
Lesson 4-1
Day 12
Lesson 4-5
Day 3
Lesson 4-2
Day 13
Lesson 4-6
Day 4
Lesson 4-2
Day 14
Lesson 4-6
Day 5
Lesson 4-3
Day 15
Lab 1
Day 6
Lesson 4-3
Day 16
Lab 2
Day 7
Quiz
Day 17
Review Day 1
Day 8
Lesson 4-4
Day 18
Review Day 2
Day 9
Lesson 4-4
Day 19
Test
1
IXL Modules SMART Score of 80 is required Due the day of the exam
Lesson 1
Lesson 2
Lesson 3
Lesson 4-5
Lesson 6
7.J.1
Understanding ratios
7.J.4
Compare ratios: word problems
7.J.5
Unit rates
7.J.6
Do the ratios form a proportion?
7.J.7
Do the ratios form a proportion: word problems
7.J.2
Equivalent ratios
7.J.3
Equivalent ratios: word problems
7.J.8
Solve proportions
7.J.9
Solve proportions: word problems
7.X.13
Similar figures: side lengths and angle measures
7.X.14
Similar figures and indirect measurement
7.J.13
Scale drawings and scale factors
2
Lesson 4-1 Rates Warm-Up
Objective: Learn to write ratios and find and compare unit rates, such as average speed and unit price. A ratio is a comparison of two quantities using ____________. The ____________ of the terms is important. Ratios can be written to compare part to part, part to whole or whole to part.
3
Examples: Writing Ratios Use the table to write the ratio.
Cats to rabbits
Dogs to total number of pets
Total number of pets to cats
Birds to total number of pets
Snakes to birds
Total number of pets to hamsters
A rate is a ratio that compares two quantities measured in ____________ units. A unit rate is a rate whose ____________ is 1 when written as a fraction. To change a rate to a unit rate, first write the rate as a fraction and then divide both the numerator and denominator by the ____________.
4
Examples: Finding Unit Rates Find the rate. A Ferris wheel revolves 35 times in 105 minutes. How many minutes does 1 revolution take?
Sue walks 6 yards and passes 24 security lights set along the sidewalk. How many security lights does she pass in 1 yard?
A dog walks 696 steps in 12 minutes. How many steps does the dog take in 1 minute?
To make 12 smoothies, Henry needs 30 cups of ice. How many cups of ice does he need for one smoothie?
An average rate of speed is the ratio of distance traveled to time. The ratio is a rate because the units being compared are ____________.
5
Examples: Finding Average Speed Danielle is cycling 68 miles as a fundraising commitment. She wants to complete her ride in 4 hours. What should be her average speed in miles per hour?
Rhett is a pilot and needs to fly 1191 miles to the next city. He wants to complete his flight in 3 hours. What should be his average speed in miles per hour?
A unit price is the price of one ____________ of an item. The unit used depends on how the item is sold.
Examples: Consumer Math Application A 12-ounce sports drink costs $0.99, and a 16-ounce sports drink costs $1.19. Which size is the best buy?
A 1.5 gallon container of milk costs $4.02, and a 3.5 gallon container of milk costs $8.75. Which size is the best buy?
6
Lesson 4-2 Identifying and Writing Proportions Warm-Up
Objective: Learn to find equivalent ratios and to identify proportions. Equivalent ratios are ratios that name the same ____________. An equation stating that two ratios are ____________ is called a proportion .
If two ratios are equivalent, they are said to be ____________ to each other or in proportion .
7
Examples: Comparing Ratios in Simplest Forms Determine whether the ratios are proportional. 24 72 51 , 128
150 90 105 , 63
54 72 63 , 144
135 9 75 , 4
Examples: Comparing Ratios Using a Common Denominator
Directions for making 12 servings of rice call for 3 cups of rice and 6 cups of water. For 40 servings, the directions call for 10 cups of rice and 19 cups of water. Determine whether the ratios of rice to water are proportional for both servings of rice.
Use the data in the table to determine whether the ratios of beans to water are proportional for both servings of beans.
You can find an equivalent ratio by multiplying or dividing both terms of a ratio by the ____________ number. 8
Examples: Finding Equivalent Ratios and Writing Proportions Find a ratio equivalent to each ratio. Then use the ratios to find a proportion. 3 5
28 16
2 3
16 12
9
Lesson 4-3 Solving Proportions Warm-Up
Objective: Learn to solve proportions by using cross products. For two ratios, the ____________ of the numerator in one ratio and the denominator in the other is a cross product. If the cross products of the ratios are equal, then the ratios form a ____________.
Examples: Solving Proportions Using Cross Products Divide. 9 15
= m5
6 7
m = 14
10
It is important to set up proportions correctly. Each ratio must compare ____________ quantities in the ____________ order. Suppose a boat travels 16 miles in 4 hours and 8 miles in x hours at the same speed. Either of these proportions could represent this situation.
Examples: Problem Solving Application
If 3 volumes of Jennifer’s encyclopedia takes up 4 inches of space on her shelf, how much space will she need for all 26 volumes?
John filled his new radiator with 6 pints of coolant, which is the 10 inch mark. How many pints of coolant would be needed to fill the radiator to the 25 inch level?
11
Lesson 4-4 Similar Figures and Proportions Warm-Up
Objective: Learn to use ratios to determine if two figures are similar. Similar figures are figures that have the same ____________ but not necessarily the same ____________. The symbol ~ means “is similar to”. Corresponding angles of two or more similar polygons are in the same relative ____________. Corresponding sides of two or more similar polygons are in the same relative ____________. When naming similar figures, list the corresponding angles in the ____________ order.
12
Examples: Determining Whether Two Triangles Are Similar Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar.
Examples: Determining Whether Two Four-Sided Figures are Similar Tell whether the figures are similar.
13
Lesson 4-5 Using Similar Figures Warm-Up
Objective: Learn to use similar figures to find unknown lengths. Indirect measurement is a method of using ____________ to find an unknown length or distance in ____________ figures.
Examples: Finding Unknown Lengths in Similar Figures Find the unknown measures in the similar figures.
14
Examples: Measurement Application The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle.
The rectangle on the left is similar in shape to the rectangle on the right. Find the width of the right rectangle.
15
Examples: Estimating with Indirect Measurement City officials want to know the height of a traffic light. Estimate the height of the traffic light.
The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle.
16
Lesson 4-6 Scale Drawings and Scale Models Warm-Up
Objective: Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale. A scale drawing is a ____________ two-dimensional drawing of an object. Its dimensions are related to the dimensions of the ____________ object by a ratio called the scale factor . A scale model is a ____________ three-dimensional model of an object. A scale is the ratio between two sets of ____________. Scales can use the same units or different units.
17
Examples: Finding Scale Factor Identify the scale factor.
Examples: Using Scale Factors to Find Unknown Lengths A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is 51 . Find the size of the photograph.
18
Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is 1.5:1. Find the size of the dollhouse.
Examples: Measurement Application On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles?
On a road map, the distance between Dallas and Houston is 7 inches. What is the actual distance between the cities if the map scale is 1 inch = 50 kilometers?
