كتاب الطالب Interactive Student Edition الرياضيات Reveal الصف السادس منهج انجليزي الفصل الأول
I Can... represent a collection of equivalent ratios as ordered pairs and graph the ratio relationship on the coordinate plane
Learn Ratios as Ordered Pairs
You previously learned how to create a ratio table and extend it by finding equivalent ratios. You can also represent a ratio relationship by creating a table of ordered pairs and graphing the ordered pairs on the coordinate plane
To make a simple salad dressing, you can use 3 cups of olive oil for every cup of vinegar. You can then add herbs, salt, and /or pepper for seasoning. This ratio relationship is shown in the table
Each pair of equivalent ratios can be expressed as an ordered pair. The X-coordinate represents the number of cups of vinegar. The y-coordinate represents the number of cups of olive oil
Recall that to graph a point, start at the origin. Move right along the x-axis the number of units indicated by the x-coordinate. From that location, move up along the y-axis the number of units indicated by the y-coordinate. Place a dot at that location
The graph illustrates the ratio Salad Dressing relationship of the cups of olive oil to the cups of vinegar in the salad dressing
What do you notice about the graphed points ? You might notice that to travel from each point to the next point, you move up 3 units and to the right 1 unit. These are the same numbers in the ratio of 3 cups of olive oil for every 1 cup of vinegar
Which pizzeria advertises the greatest ratio of pepperonis to pizza size
To compare the three ratios, use Pizza Size (in.) the same representation for each, The Pizza Place such as a graph. The ratios of Paulo's Pizzeria pepperonis to pizza size for The Slice of Pie Pizza Place are already graphed
For Paulo's Pizzeria, use scaling to write the ordered pairs (8, 16), (10, 20), (12, 24), (14, 28), and (16, 32) to represent the ratio relationship. For Slice of Pie, the ordered pairs are (10, 15), (12, 18), and (14, 21)
Draw dotted lines through the points. The graph for The Pizza Pizza Size (in.) Place is the steepest, and the graph for Paulo's Pizzeria is steeper than the graph for Slice of Pie. This means that has the greatest ratio of pepperonis to pizza size, in inches, followed by and then Check Refer to Example 1. A fourth pizzeria, Pizza Café, advertises 14 pepperonis for every 8-inch pizza. Graph the ratio relationship for Pizza Café on the graph above. Which pizzeria, Pizza Café or Slice of Pie, advertises the greater ratio of pepperonis to pizza size? Justify your response
Show your work Go Online You can complete an Extra Example online
Learn Use Double Number Lines and Equivalent Ratios to Solve Ratio Problems
The manager of a small hotel determines that it takes 30 loads of laundry to clean the towels and sheets of the hotel's rooms each day. A large bottle of laundry detergent contains 150 ounces and the label indicates that the contents of the bottle can clean 75 loads. How many ounces of detergent are needed to clean the hotel's towels and sheets each day
You can represent this ratio relationship and solve the problem by using double number lines and equivalent ratios
Method 1 Use a double number line
Step 1 Draw a double number line
The top number line represents the number of loads of laundry. The bottom number line represents the number of ounces of detergent needed
Mark the ratio of loads to detergent (75: 150). Mark and label equal increments to show 30 loads
Step 2 Find the equivalent ratio
There are 5 equal sections. Because 150 = 5 = 30, label equal increments of 30 on the bottom number line
The value on the bottom number line that corresponds with 30 loads is 60 ounces of detergent
So, 60 ounces of detergent are needed each day
Apply Inventory
The manager of an office supply store decides to hold a Buy 2. Get 1 Free sale on all reams of paper. A ream of paper holds 500 sheets of paper. The sale is held for one week and a total of 154 reams of paper were sold (not including the ones given away for free). If each ream of paper cost the store $4.50, how much money did the store lose by giving away the free reams of paper
1 What is the task
Make sure you understand exactly what question to answer or problem to solve. You may want to read the problem three times. Discuss these questions with a partner
First Time Describe the context of the problem, in your own words
Second Time What mathematics do you see in the problem
Third Time What are you wonderin about
How can you approach the task ? What strategies can you ue
What is your solution
Use your strategy to solve the problem Show
How can you show your solution is reasonable
Write About It! Write an argument that can be used to defend your solution
use any strategy to solve each problem
I. Mr. Anderson is ordering pizzas for a class pizza party. Pizza Place has a special where he can buy 3 large pizzas for $18.75. At Mario's Pizzeria, he can buy 4 large pizzas. for $22. If he needs to buy 12 pizzas, how. much will he save if he buys the pizzas from Mario's Pizzeria instead of Pizza Place (Example 1)
. Melissa is buying party favors to make gift bags. Supplies LTD sells a 5-pack of favors for $11.25 and Parties and More sells a 3-pack of favors for $8.25. At these rates, how much will she save if she buys 15 favors from Supplies LTD than Parties and More (Example 1)
A bakery makes 260 donuts in 4 hours. At this rate, how many donuts can they make in 6 hours ? (Example 2)