Embedded Files
Introduction
Introduction
In this lesson you will:
review linear relationships
determine relationships between quantities
explore dependent and independent variables
apply these ideas to a practical situation.
Activity 1 - Review of linear relationships
Activity 1 - Review of linear relationships
During this activity you will need to draw connections between the pattern, the table of values, the graph and the equation that describes the pattern.
Open the Desmos interactive in a new tab by clicking on the image below.
Complete this activity by exploring each pattern in turn, starting with the three pattern. (Use the red slider to change the pattern.)
Answer the following questions in your exercise book or folder:
Describe the pattern at the start, when n equals zero; and how is this shown in the table of values and the graph?
Describe how the pattern builds as n increases; and how is this shown in the table of values and the graph?
How are these represented in the equation?
Diagram showing the connections between the pattern, the table of values, the graph and the equation that describes the pattern.
Activity 2 - Determining relationships between quantities
Activity 2 - Determining relationships between quantities
In the previous activity the pattern or relationship was obvious. We could see it. But are there relationships between quantities which cannot be seen and are not obvious? If so, how can we represent the relationship?
Jay and Amanda have been thinking about the sales of ice-creams.
In your opinion, who is correct? And how could we find out if there is a relationship or not?
Record your thinking on these questions in your exercise book or folder.
We have collected some data showing the value of ice cream sales at different temperatures and have represented this in Desmos as a table and a scatter plot. (See the embedded website below.)
Does this data help to support Jay or Amanda’s claim? How do you know?
Record your thinking on these questions in your exercise book or folder.
Activity 3 - Dependent and independent variables
Activity 3 - Dependent and independent variables
In the scatter plot you have just been looking at on the embedded Desmos page above, ‘Temperature’ is our independent variable and has been placed on the x-axis. We are hypothesising that the number of sales will depend on how warm the temperature is, so ‘Sales’ will be our dependent variable, and is placed on the y-axis.
If we consider wage and hours worked, hours worked would be our independent variable, whilst wage would be our dependent variable. Your wage is dependent on the number of hours that you work. The more you work, the higher your wage.
For each of the following, identify the dependent and independent variables.
Activity 4 - Sugar vs calories
Activity 4 - Sugar vs calories
Is the number of calories in food dependent on the amount of sugar or fat?
Is the number of calories in food dependent on the amount of sugar or fat?
Find at least 10 items in your pantry or fridge and read the dietary label to identify the number of Calories per 100g or 100ml and the Total sugars per 100g or 100ml.
Go to the Desmos website and record your results in a table.
Complete this interactive tutorial if you need help creating tables in Desmos.
Use the zoom fit button to make sure all of your points appear on your screen.
Answer the following questions in your copy of the report template:
Looking at your table and the accompanying graph for Sugar and calories, do you believe there is any relationship between the amount of sugar and the number of calories in our food? Explain your reasoning.
Looking at your table and the accompanying graph for Fat and calories, do you believe there is any relationship between the amount of fat and the number of calories in our food? Explain your reasoning.
What do you believe has more impact on the number of calories, sugar or fat? Justify your answer.
For more information, please see the Australian guide to healthy eating.
Show all your working
Show all your working
Use this report template to record and present your work on this investigation.
Click on the button to the right to open a new tab and view the Google Doc.
Click on the Use Template button to create a copy for you to edit.
Handing in your work
Handing in your work
Don't forget to hand in the work you completed today!
Your teacher will have told you to do one of the following:
Upload any digital documents you created and any photos you took of your written work to your Learning Management system (MS Teams, Google Classroom for example).
Email any digital documents you created and any photos you took of your written work to your teacher.
Make sure you keep any hand written work you did in your exercise book or folder as your teacher may need to see these when you are back in class.
Student reflection
Student reflection
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