Houston County School System Mathematics

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1 Student Name: Teacher Name: Grade: 6th Unit #: 4b Unit Title: Analyzing Quantitative Relationships Approximate Start Date of Unit: January 4 Approximate End Date (and Test Date) of Unit: January 19 I can plot pairs of values that represent equivalent ratios on the coordinate plane. 1. The most common women s shoe size in the U.S. is reported to be an 8 1. A shoe store uses a table like the one below to decide how many pairs of size 8 1 shoes to buy when it places a shoe order from the shoe manufacturers. Total Pairs of Shoes Being Ordered Pairs of Size 8 1 to Order a. What is the ratio of the number of pairs of size 8 1 shoes the store orders to the total number of pairs of shoes being ordered? b. Draw a coordinate plane. Plot the values from the table on a coordinate plane. Label the axes. Then use the graph to find the number of pairs of size 8 1 shoes the store orders for a total order of 15 pairs of shoes.. There are pints in one quart. Fill in the missing values. 3. The graph shows the hours worked and total pay for Paul s part-time job.

2 4. Mrs. Baker poured a cup of hot chocolate and set it on the table to cool. She recorded the temperature of the hot chocolate every 10 minutes. Here is her data: a. Plot the values from the chart. Hot Chocolate Temperature b. Does the graph show a ratio? How do you know? Elapsed Time in Support your answer from the table and the graph. Temperature Minutes I can analyze and describe patterns that arise from mathematical rules, tables, and graphs. 5. Claire and Kate are entering a cup stacking contest. Both girls have the same strategy: stack the cups at a constant rate so that they do not slow down at the end of the race. While practicing, they keep track of their progress, which is shown below. Claire: Kate: c = 4t, where t represents the amount of time in seconds and c represents the number of stacked cups a. A. At what rate does each girl stack her cups during b. the practice sessions? c. B. Kate notices that she is not stacking her cups fast enough. What would Kate s equation look like if she wanted to stack cups faster than Claire?

3 6. Bryan and ShaNiece are both training for a bike race and want to compare who rides his or her bike at a faster rate. Both bikers use apps on their phones to record the time and distance of their bike rides. Bryan s app keeps track of his route on a table, and ShaNiece s app presents the information on a graph. The information is shown below. Bryan: Hours Miles a. At what rate does each biker travel? Explain how you arrived at your answer. ShaNiece: 7. Victor was having a hard time deciding which new vehicle he should buy. He decided to make the final decision based on the gas efficiency of each car. A car that is more gas efficient gets more miles per gallon of gas. When he asked the manager at each car dealership for the gas mileage data, he received two different representations, which are shown below. Vehicle 1: Gallons of Gas Miles Legend Vehicle : Supreme a. If Victor based his decision only on gas efficiency, which car should he buy? Provide support for your answer. b. After comparing the Legend and the Supreme, Victor saw an advertisement for a third vehicle, the Lunar. The manager said that the Lunar can travel about 89 miles on a tank of gas. If the gas tank can hold 17 gallons of gas, is the Lunar Victor s best option? Why or why not?

4 8. James can read 1 pages in 4 minutes. a. Complete the following table: Time to Read b. Plot the values from the data table. Draw a line that best fits the data points, extending it beyond the first and last data points. c. Use the graph to find the number of pages that can be read in 1 minute. Circle this point on the graph. Pages Read Time in Minutes 4 I can define independent and dependent variables. I can use variables to represent two quantities in a real-world problem that change in relationship to one another. I can write an equation to express one quantity (dependent) in terms of the other quantity (independent). 9. Joshua spends 5 minutes of each day reading. Let d be the number of days that he reads, and let m represent the total minutes of reading. Determine which variable is independent and which is dependent. Then, write an equation that will model the situation. Make a table showing the number of minutes spent reading over 7 days. 10. Charlotte reads 4 books each week. Let b be the number of books she reads each week, and let w be the number of weeks that she reads. Determine which variable is dependent and which is independent. Then, write an equation to model the situation, and make a table that shows the number of books read in under 6 weeks. 11. The table below shows the relationship between the number of cans and the weight of those cans in ounces. Cans Weight (in ounces) a. What are the dependent and independent variables of this relationship? Dependent variable Independent variable b. Write an equation to represent the weight (W) for any number of cans (c). c. Use your equation to determine how much will 10 cans weigh (in ounces).

5 I can analyze the relationship between the dependent variable and independent variable using tables and graphs. I can relate the data in a graph and table to the corresponding equation. 1. Each week Quentin earns $30. If he saves this money, create a graph that shows the total amount of money Quentin has saved from week 1 through week 8. Write an equation that represents the relationship between the number of weeks that Quentin has saved his money, w, and the total amount of money in dollars that he has saved, s. Then, name the independent and dependent variables. Write a sentence that shows this relationship. 13. It takes one gallon of gas for Mr. Kraft to drive 1 miles in his truck. Mr. Kraft starts making a chart to show the number of miles, m, that can be driven based on a number of gallons of gas, g. 14. The table shows the relationship between the number of pineapples bought and the total cost. Number Bought Total Cost 10 $5 15 $ $50 30 $75 a. Fill in the missing spaces in Mr. Kraft s chart. b. Write an equation to show the relationship between the gallons of gas, g, and the number of miles driven, m. Write an expression to find the total cost of buying any number of pineapples. Use data from the chart to explain your answer. 15. Maria is selling candy bars to raise money for her band trip. Each candy bar sells for $1.50. Use the graph paper to show a relationship between the number of candy bars Maria can sell and how much money she will receive? a. Write an equation to show total money earned (M) based on number of candy bars sold (b). b. Use your formula to show how much money Maria will receive if she sells 7 candy bars. c. If Maria needs to earn $ for her band trip, what is the minimum number of candy bars she will need to sell?