# كتاب الطالب الرياضيات منهج انجليزي الصف السادس Reveal الفصل الأول 2022-2023

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كتاب الطالب الرياضيات منهج انجليزي الصف السادس Reveal الفصل الأول 2022-2023

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 'earned 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 Vinegar (c), Olive Oil (c), 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-ccordinate 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 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, Salad Dressing

#### Learn Use Graphs to Compare Ratio Relationships

Ratios for ingredients in dog food vary among companies that manufacture it. Company A advertises 25 grams Of protein for every cup of dog food. The relationship between protein and cups of dog food for two other companies is shown in the table and graph

How can you compare the ratios of protein to cups of dog food for the three companies

The ratios for each of the three companies is shown using a different representation. To compare them, you can use the same representation for each, such as a graph

The ratios for Company C are already graphed. For Company A, you can generate equivalent ratios to find the ordered pairs (1, 25), (2, 50), and (3, 75)

For Company B, the ordered pairs are (2, 44), (3, 66), and (4, 88)

Draw a dotted line through the points to determine which relationship has the steepest graph The graph for Company A is the steepest, and the graph for Company B is steeper than the graph for Company C. This means that Company A has the greatest ratio of protein to cups of dog food

#### Example 1 Use Graphs to Compare Ratio Relationships

Paulo's Pizzeria advertises 24 pepperonis on every 12-inch pizza. The relationship of pepperonis to pizza size for two other pizzerias is shown in the table and graph
Slice of Pie

Which pizzeria advertises the greatest ratio of pepperonis to pizza size

To compare the three ratios. use the same representation for each, such as a graph. The ratios of pepperonis to pizza size for The 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 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 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

#### 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 labei 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 I Use a double number line

Step l 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. låbel 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 I Free sale on all reams of paper. A ream of peper 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

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 wondering about

How can you approach the task ? What strategies can you use