Unit 5 Test Review Chapter 1 Lessons 1-8

1-1 Rate: a ratio comparing two quantities with DIFFERENT units Written as a fraction with units on the top and bottom Unit Rate: a rate that is simplified to have a denominator of 1 Divide top and bottom by denominator to get unit rate *Put money on top when finding unit price or better deal!

1-1 Devin rode his bike around a pond 8 times in 58 minutes at a constant speed. How many minutes did it take him to ride around the pond one time?

Which size jar of jelly shown in the table has the lowest unit price? Size (oz) Cost ($) 10 1.69 16 3.19 32 5.79

1-2 Can also find unit rates with complex fractions Whatever unit you need one of (comes after per) must be the denominator! Set up the problem as a fraction with units first Then, write as normal division problem Keep, change, flip Cross-simplify if possible and multiply across LABEL final answer and make sure it is simplified!

1-2 A vehicle traveled 52 1 2 miles and used 2 1 2 gallons of gasoline. What was the rate of fuel use in miles per gallon?

1-2 Sally purchased 5 6 pound of grapes for $2.30. What is the cost of 1 pound of grapes?

1-3 Convert Rates Figure out if it is a single conversion or double If single, circle unit that stays the same and draw arrow from other unit If double, draw arrows to the units you are converting each to Set up units first! Set up units diagonal to cancel

1-3 A cheetah can run 70 miles per hour. What is this speed in feet per hour? Hint: 5280 feet = 1 mile

1-3 BW Alonzo fills buckets at a rate of 6 gallons per hour. What is the rate in quarts per minute? Hint: 4 quarts = 1 gallon When diving, a bald eagle can reach a speed of 50 miles per hour. What is this speed in feet per second? Round to the nearest hundredth if necessary. Hint: 5280 feet = 1 mile & 1 hour = 3600 seconds

1-4 Two quantities are proportional if they have a constant ratio or unit rate For relationships in which this ratio is not constant, the two quantities are nonproportional Use a table to see if quantities are proportional, show your work by writing ratios, and explain your reasoning

1-4 BW Jess walks 6.5 miles every 2 days. Is the number of miles she walks proportional to the number of days she walks? Complete the table and explain your reasoning. Days 2 4 6 Miles Walked

1-4 BW Which situation best represents a proportional relationship? Show proof and explain your reasoning. Jenny sold 3 necklaces for $9 and 4 necklaces for $11 Jim biked 4 miles in 20 minutes and 6 miles in 30 minutes Larry packed 24 dishes in 6 boxes and 54 dishes in 9 boxes Alice put 16 pieces of candy in 2 bags and 30 pieces of candy in 4 bags

1-5 Identify Proportional Relationships from a Graph It must be a straight line It must pass through the origin *Must have equal ratios Units of Time = x-axis Money = y-axis

Temperature (Degrees) 1-5 Determine whether the relationship between the two quantities shown in the table are proportional by graphing on the coordinate plane. Explain your reasoning. (half sheet) Temperature (Degrees) Celsius Fahrenheit 32 5 41 10 50 15 59 20 68

1-6 Solve proportions by finding the cross products (multiply diagonals) 𝑎 𝑏 = 𝑐 𝑑 ad = bc

1-6 Do they form a proportion? 6 7 , 36 49 7 11 , 15 23

1-6 Problem Solving Using Proportions Figure out the 2 quantities we are comparing by looking at the question—set up a units only fraction Use the information in the problem to set up the 1st fraction. Line up units going across For the 2nd fraction, put variable for what we are trying to find and get other value from question part of the problem Solve using cross products and label answer

1-6 Write and solve by using a proportion. Fifteen scoops of lemonade drink mix are needed to make five gallons. How many gallons will 6 scoops of lemonade mix make?

1-6 Write and solve by using a proportion. To determine the number of deer in a forest, a forest ranger tags 280 and releases them back into the forest. Later, 405 deer are caught, out of which 45 of them are tagged. Predict how many deer are in the forest.

1-6 A pond is being dug according to plans that have a scale of 1 inch = 6.5 feet. The maximum distance across the pond is 9.75 inches on the plans. What will be the actual maximum distance across the pond?

1-6 The table shows the amount of calories in various servings of a specific brand of yogurt. If the rate of calories per serving remains the same, how many calories would complete the table? Calories per Serving 2 220.4 5 551 9 ?

1-7 Constant Rate of Change *Focus on numbers that have the same unit 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 Simplify to a unit rate with labels *Focus on numbers that have the same unit

1-7 Use a Table The table shows the number of miles Claire drove on a trip. What is the constant rate of change? Time (hours) 2 4 6 Distance (miles) 130 260 390

1-7 Use a Graph Find the constant rate of change

1-7 Jaime and Ryan work at the grocery store. The wages earned for the weekend are shown in the table and graph. Who gets paid more per hour? Explain.

1-7/1-8 Slope = constant rate of change 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 Explain what constant rate of change (slope) represents by discussing y-value first and x-value second

1-7/1-8 The table shows the number of packages of raisins per box. Graph the data. Then find the constant rate of change of the line and explain what it represents. (half sheet) Boxes 1 2 3 4 Packages 20 40 60 80

1-8 The graph shows the average speed of two go-karts in a race. What does the point (2, 20) represent on the graph? What does the point (1, 12) represent on the graph? Find the slope of each line. What does the slope of each line represent? Which car is traveling faster? How do you know?