Graphs, Double Line Graphs, Bar Diagrams More Ratio Tools Graphs, Double Line Graphs, Bar Diagrams

What Will We Accomplish? We will compare ratios after graphing the data on the coordinate plane. We will use a variation of a bar diagram to solve problems. We will use a double number line to solve ratio problems.

Graphing Data on the Coordinate Plane We will combine our knowledge of ratios and graphing to graph ratio information for comparisons. You are going to run a cattle ranch this year! You know that every 6 cows needs 5 acres of land on which to graze. One of your family members, however, wants to raise sheep. Six sheep can graze on just two acres. Let’s fill out the charts that set up ratios between the animal and the land. We will then use colors to graph the different points for the sake of comparison.

Kara’s dog eats 3 lbs of dog food every two weeks. Joe’s dog eats 4 lbs. each 3 weeks. Graph the data. Kara’s Dog Joe’s Dog 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Pounds of Dog Food Week x Pounds y 2 3 4 6 9 8 12 Week x Pounds y 3 4 6 8 9 12 16 After 10 weeks, whose dog has eaten more? How much more? Kara’s dog had eaten 2 more lbs. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Weeks

Two friends save money each week. Marcus saves $10 each week Two friends save money each week. Marcus saves $10 each week. David saves $15. Graph the data and compare the ratios for each boy’s savings. $10 (1,10) $20 (2, 20) $30 (3, 30) $40 (4, 40) $15 (1,15) $30 (2, 30) $45 (3, 45) $60 (4, 60) How much more money than Marcus will David have after 6 weeks?

Double number lines allow you to compare ratios. Two sets of data are arranged above and below a number line. Entering the changing data allows you to compare ratios and make predictions. 270 x 7 = 1890 calories 270 810 Calories Scoops | | | | | | | | 0 1 2 3 4 5 6 7 Set up the number line and enter what we are given. 3 Now let’s find the unit rate. 810 3 = 9 9 10 3 =270 𝑝𝑒𝑟 𝑠𝑐𝑜𝑜𝑝

The Mason family can drive 145 miles on 4 gallons of gas The Mason family can drive 145 miles on 4 gallons of gas. Use a double number line to fine the miles per gallon as well as how many miles they could travel on 6 gallons. 145 ÷ 4= 36 ¼ 36 ¼ (6) 217.5 145 miles gallons | | | | | | | | 0 1 2 3 4 5 6 7

Using Bar Diagrams to Compare Ratios Devon drive 171 miles in 3 hours. Logan drove 177 miles in 3 hours. At these rates, how many more miles can Logan drive in 7 hours than Devon? Devon Logan 171 miles 177 miles 1 hour 1 hour 57 miles 59 miles 2 x 7 = 14 There are two approaches……… 7(59 – 57) = 7(2) = 14  (59 x 7) – (57 x 7) = 413 – 399 = 14

Your Turn Predict the number of blue squares in a quilt with 11 green squares if there are 4 green squares in a quilt with 68 blue squares. Talk about this in your group. Start with what you know! Yes, there are several ways to answer this. You are to create a bar diagram. 68 blue squares 𝑏𝑙𝑢𝑒 𝑔𝑟𝑒𝑒𝑛 = 68 4 = 17 𝑏𝑙𝑢𝑒 1 𝑔𝑟𝑒𝑒𝑛 1 green 1 green 1 green 1 green 17 blue Now we use the 17 per green to answer the question about a quilt with 11 green squares. 11 x 17= 187

Accomplishments? We have solved problems with ratios and rates using graphs, double number lines and bar diagrams. Is saying rate and ratios redundant? I think so.