Ratios and Proportions
Proportional Relationships in Graphs

Engage

DRIVING QUESTION:red race car jumping up and down and turning

 

We will begin our lesson today by thinking about proportional relationships in graphs. Listen to the Voki below to review what we know about determining whether or not a graph demonstrates a proportional relationship.

proportional graph

Now that you have listened to the Voki explain how to determine whether or not a graph demonstrates a proportional relationship, put together the puzzle below to review this information one more time.

  

To view a clearer version of the puzzle image, hover your cursor over the blue text in the paragraph below.

 

 

 

boy stading by pencils WARM-UP . . .

Now, let's use our knowledge to determine whether or not each of the graphs below demonstrates a proportional relationship. Complete the warm-up problems below with your Livescribe pen in your math notebook. Do not forget that you can listen to the Voki again or look at the information in the puzzle image if you need help remembering how to determine whether or not each of the graphs below demonstrates a proportional relationship.

 

1.) Is this graph proportional?

graph

 

ANSWER

2.) Is this graph proportional?

graph

 

ANSWER

 

 

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Explore

In order to create graphs that represent proportional relationships, we first need to review what we know about the coordinate plane. Hover your cursor over the coordinate plane image below to review some important facts about the coordinate plane.

  

So from the picture above we learned . . .

 

team of people huddled together brainstorming LET'S THINK . . .

Now, let's play The Billy Bug Game to make sure we know how to graph points in the coordinate plane.

  • The goal of the game is to help Billy Bug find food to eat.
  • Read over the directions and click on the 'Begin' button once you are ready to play the game.
  • Click on the arrows to move Billy Bug to the location of his grub and then click on the 'Feed' button.
  • How long will it take you to feed Billy Bug ten times?

 

BILLY BUG GAME

 

 

 

 

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Explain

So far, you have already thought about identifying the graphs of proportional relationships and the coordinate plane. Now, let's put those two things together and think about creating graphs that represent proportional relationships. Look at the real life proportional relationship and table below. 

I make $9 an hour.

 

 

 

 

hourly wages table

 

How do you think we could turn this table that represents a proportional relationship into a graph? Hover your cursor over the image below when you think you know the answer to this question.

 happy face scratching his chin

In order to create a graph to illustrate this proportional relationship and table, we need to graph the ordered pairs in the table. Watch the Brainshark presentation below to learn more about how to illustrate proportional relationships in the form of graphs on the coordinate plane. Remember, you can click on the bottom right hand corner of the presentation below to view a full screen version of the presentation.

So, from the Brainshark presentation we learned . . .

Let's look at another example . . .

Create a graph to illustrate the proportional relationship below.

Your teacher wants to buy 3 pencils for each student in the class.

 

  • Create a table that illustrates the proportional relationship:

 Create a table that illustrates the proportional relationship

  • Write each row of the table as an ordered pair:

 Write each row of the table as an ordered pair

  • Plot all the ordered pairs on the coordinate plane:

 Plot all the ordered pairs on the coordinate plane

  • Connect the ordered pairs with a straight line to complete the graph:

Connect the ordered pairs with a straight line to complete the graph

 

 

 

 

algebra chalkboard CREATING PROPORTIONAL GRAPHS PRACTICE 1

Create a graph to illustrate the proportional relationship below. Click on the Graph Paper Link if you would like to download a blank piece of graph paper to use in order to create your graph.

 Each dog at the dog show has four legs.

 

CHECK MY ANSWER

 

 

 

 

algebra chalkboard CREATING PROPORTIONAL GRAPHS PRACTICE 2

Create a graph to illustrate the proportional relationship below. Click on the Graph Paper Link if you would like to download a blank piece of graph paper to use in order to create your graph.

 Each box of cookies at the grocery store costs $2.50.

 

CHECK MY ANSWER

 

 

 

algebra chalkboard CREATING PROPORTIONAL GRAPHS PRACTICE 3

Create a graph to illustrate the proportional relationship below. Click on the Graph Paper Link if you would like to download a blank piece of graph paper to use in order to create your graph.

 I can run 5 miles in an hour.

 

CHECK MY ANSWER

 

 

  

 

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Extend

Now that you know all about creating graphs to illustrate proportional relationships, let's create some graphs that illustrate the real life situations we created tables for in the Creating Proportional Tables lesson. Look at each of the real life situations and the corresponding tables below. Create a graph to illustrate each of these real life situations.

I make $9 an hour.

 

 

 

 

hourly wages table

 

CHECK MY GRAPH

 

 

 

I am driving 30 mph.

 

 

 

 

table for car problem

 

CHECK MY GRAPH

 

 

 

A cheetah can run 70 mph.

 

 

 

 

table for cheetah problem

 

CHECK MY GRAPH

 

 

 

There is half a cup of flour i nthis recipe.

 

 

 

 

table for recipe problem

 

CHECK MY GRAPH

 

 

 

 

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Evaluate

Now we are experts at creating graphs that illustrate proportional relationships! Let's complete an assignment to show how much we have learned.

Each ride at the fair costs $1.50.

 

 

checklist HAVE YOU COMPLETED EVERYTHING?

Can you answer this lesson's driving question?red race car jumping up and down and turning

 

Tasks to complete in this lesson:

proportional graphs checklist

 

 

 

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