Coordinate AlgebraReal Life Graphs (Submit When Completed)

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Title: Real Life Graphs

Standard(s):MCC9‐12.F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. ★ _(Focus on linear functions.)

MCC9‐12.F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. ★ (Focus on linear functions.)

Learning Goals:★Construct functions arising from real-life problems, and plot and interpret their corresponding graphs.★Model relationships between quantities by looking at graphs.★Sketch graphs showing key features given a verbal description of the relationship.

Description:In this online interactive activity, you will be guided through lessons that involve creating, reading, and interpreting graphs. You will need to take Cornell notes on the information that you do not understand. The contents of this lesson follow:

Contents: I. Reading GraphsII. Plotting GraphsIII. Conversion GraphsIV. Distance- Time GraphsV. Interpreting Graphs

To Begin, Please Logon to KS3 Mathematicswww.swanshurst.org/.../A6%20 Real - life %20 graphs %201.ppt

I. Reading Graphs

Graphs can be used to illustrate any function or formula containing two variables. This graph on slide 3 compares two types of tariff (tax) offered by a mobile phone company: The ‘Pay as you go’ tariff (shown in blue) has no monthly charge and charges a fixed amount per minute.

a. Drag the moving point on the graph to work out the cost per minute.

b. The ‘Monthly’ tariff (shown in red) has a fixed monthly charge and charges calls at fixed amount per minute. Drag the moving point on the graph to work out the monthly charge and the cost per minute.

c. What is the significance of the point where the two lines cross?

d. Which tariff is cheaper?

e. Do the intermediate points (point in between each whole value) have any practical significance?

f. Create a formula to describe the “Pay As You Go” tariff (tax)

g. Create a formula to describe the “Monthly” tariff (tax)

II. Plotting Graphs

Slide 5 Plotting Graphs Using a Table of Values:

Coordinate AlgebraReal Life Graphs (Submit When Completed)

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a. Can you create a formula (rule) linking c, the cost, with d, the number of days?

b. Slide 5: What kinds of graph will this produce? Hint: describe the shape. Use appropriate terminology.

c. Slide 5: When we are plotting a graph it is very important to know which variable depends on the other. This tells us which variable will go along the horizontal axis and which variable will go along the vertical axis. When we are plotting graphs of functions, for example, the value of y depends on the value of x.

Slide 6 Choosing a Scale:d. Describe a suitable scale for the range of units in this problem. (number of days, Cost in £).

Slide 7 Drawing the Axes & Slide 8 Plotting the Points:e. As you view slide 7 & 8 describe all of the components a graph must include to completely represent a situation.

f. When is it appropriate to join the points on a graph?

Slide 9 & 10 Science Experiment:a. Describe why mass of object moving down the ramp is the independent variable and Time taken for object to move down the ramp is the dependent variable.

b. Do the intermediate points (all of the points between the ordered pairs given) have any practical significance?

c. How could we make the graph more accurate?

d. Should each point be joined together using straight lines or should we use a line of best fit?

e. Would it make sense for the line to meet the horizontal axis?

f. How are the variables related?

g. How long it would take for an object of mass 225 grams to slide down the slope?

h. How long it would take for an object of mass 300 grams to slide down the slope?

i. What mass would we use if we wanted the object to side down the slope in 10 seconds?

III. Conversion GraphsSlide 12 Plotting a Conversion Graph

Suppose we would like our graph to convert up to £200 to 300 euros. We need some coordinates to plot and so the first thing we should do is draw a table of values. Let’s find four points.

What’s the minimum number of points needed to create a linear graph? Is it a good idea to have a few more points to plot, to ensure accuracy?

Coordinate AlgebraReal Life Graphs (Submit When Completed)

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We want our graph to convert up £200, where would we place £200 on our graph? Click to reveal 200 in the table.

£200 equals 300 euros. Click to reveal this too.

Now let’s choose some intermediate amounts that are easy to convert. For example, £20, £100 and £160. We can then put the corresponding number of euros underneath. Click to reveal the values in the table.

This gives us four points that we can plot on our graph. Click to reveal these.

How do we choose appropriate scales for the axes?

Looking at our grid we have room to use 20 squares to represent £200 along the horizontal axis. How much will each square represent?

III. Conversion Graphs continued…

Slide 13 Conversion Graphs – Money

Drag the point along the line to demonstrate a variety of Franc to Pound and Pound to Franc conversions.Would it make sense to have negative values?

Slide 14 Conversion Graphs – temperature

Most conversion graphs are straight lines passing through the origin. What does this mean?

Does the Celsius – Fahrenheit conversion graph show a proportional relationship?

IV. Distance – Time GraphsSlide 16 Distance-time graphs

a. What is happening at the places where the line is horizontal?

b. What does is mean if the graph slopes downward?

c. What would it mean if the line were curved?

Slide 17 Label the Distance-time graph:

Label the distance-time graph by dragging the descriptions to the appropriate letter.

Coordinate AlgebraReal Life Graphs (Submit When Completed)

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Slide 18 Olympic Swimmers:This animation shows a distance-time graph being plotted in real time. Start by choosing a different starting speed for each swimmer and pressing go. Change the speed of the swimmers as the race progresses and note what happens on the graph. To make a swimmer stop altogether change his speed to 0.

Provide a race commentary for your race.__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

V. Interpreting GraphsSlide 20 Filing Flasks 1:

You are going to produce a graph of the depth of water in a flask as it fills with water. Note that the water flows out of the tap at a constant rate.a. What relationship is shown in the graph?

b. How many cm are filled each second for the red flask?

c. Predict the slope of the graph for the…Green flask.Blue flask.Pink flask.Orange flask.

d. Justify why they think the graph will be steeper or less steep than before.Green.Blue.Pink.Orange.

e. Explain why all the lines pass through the origin.

f. Explain why the lines are straight.

g. Explain what would happen if the water from the tap did not flow out at a constant rate. For example, in real life the rate of the water coming out of the tap would speed up as the tap is turned on. How would this affect the shape of the graph?

Slide 21 Filling Flasks 2Repeat questions a through g for this experiment.

Homework Practice: Slide 22 Interpreting the Shapes of Graphs

h. What do the vertical portions of the graph represent?i. What do the horizontal portions of the graph represent?j. How many bites did it take to finish the bar?k. What was the weight of the biggest bite?l. How long did it take Jessica to eat the first bite?m. What is the original weight of the chocolate bar?n. How long did Jessica take to finish the chocolate bar in seconds/in minutes and seconds?

Coordinate AlgebraReal Life Graphs (Submit When Completed)

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Homework Practice: Slide 23 Interpreting the Shapes of Graphs What is happening in the

portion of the graph that slopes downwards?

What is happening in the portion of the graph that slopes upwards?

What is happening at each turning point in the graph?

Homework Practice:

Homework Practice:

Homework: Describe what the graph for beaker A shows. How the graphs for beakers B and beaker C will differ from the one shown. Use the next slide to sketch these different graphs.

Each of the graphs in this example illustrates trends rather than accurate information. Match each graph with the correct statement.

Coordinate AlgebraReal Life Graphs (Submit When Completed)

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