1 / 27

KS3 Mathematics

KS3 Mathematics. A6 Real-life graphs. A6 Real-life graphs. Contents. A. A6.2 Plotting graphs. A. A6.1 Reading graphs. A6.3 Conversion graphs. A. A6.4 Distance-time graphs. A. A6.5 Interpreting graphs. A. Graph of monthly mobile phone charges. A6 Real-life graphs. Contents.

aquarius
Download Presentation

KS3 Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. KS3 Mathematics A6 Real-life graphs

  2. A6 Real-life graphs Contents • A A6.2 Plotting graphs • A A6.1 Reading graphs A6.3 Conversion graphs • A A6.4 Distance-time graphs • A A6.5 Interpreting graphs • A

  3. Graph of monthly mobile phone charges

  4. A6 Real-life graphs Contents A6.1 Reading graphs • A • A A6.2 Plotting graphs A6.3 Conversion graphs • A A6.4 Distance-time graphs • A A6.5 Interpreting graphs • A

  5. Plotting graphs – using a table of values Number of days, d 1 2 3 4 5 Cost in £, c When we plot a graph we usually start with a table of values. The values in the table usually come from a formula or equation or from an observation or experiment. For example, a car hire company charges £30 to hire a car and then £25 for each day that the car is hired. This would give us the following table of values: 55 80 105 130 155 The cost of the car hire depends on the number of days. The number of days must therefore go in the top row.

  6. Plotting graphs – choosing a scale Number of days, d 1 2 3 4 5 Cost in £, c 55 80 105 130 155 The next step is to choose a suitable scale for the axes. Look at the values that we need to plot. The number of days will go along the horizontal axis. The numbers range from 1 to 5. A suitable scale would be 2 units for each day. The cost will go along the vertical axis. The cost ranges from 55 to 155. A suitable scale would be 1 unit for each £10. We could start the scale at £30.

  7. Plotting graphs – drawing the axes 150 140 130 120 110 100 90 80 70 60 50 40 30 0 1 2 3 4 5 We then have to draw the axes using our chosen scale. We will need at least 10 squares for the horizontal axis and 13 squares for the vertical axis. When the scale does not start at 0 we must show this with a zigzag at the start of the axis. Number the axes. Cost (£) Label the axes, remembering to include units, if necessary. Always use a pencil and ruler. Number of days

  8. Plotting graphs – plotting the points Number of days, d 1 2 3 4 5 Cost in £, c 55 80 105 130 155 Use the table of values to plot the points on the graph. Cost of car hire 150 It is most accurate to use a small cross for each point. 140 130 120 110 If appropriate, join the points together using a ruler. 100 90 Cost (£) 80 70 Lastly, don’t forget to give the graph a title. 60 50 40 30 0 0 1 2 3 4 5 Number of days

  9. Science experiment Mass of object moving down ramp (grams) 100 150 200 250 Time taken for object to move down ramp (seconds) 4 7 12 17 A group of pupils are doing an experiment to explore the effect of friction on an object moving down a ramp. They attach weights of different mass to the object and time how long the object takes to reach the bottom of the ramp. They put their results in a table and use the table to plot a graph of their results.

  10. Science experiment Mass of object moving down ramp (grams) 100 150 200 250 Time taken for object to move down ramp (seconds) 4 7 12 17 We can join the points using straight lines. 20 16 Do the intermediate points have any practical significance? 12 Time taken (seconds) 8 4 How could we make the graph more accurate? 0 0 50 100 150 200 250 300 Mass of object (grams)

  11. A6 Real-life graphs Contents A6.1 Reading graphs • A A6.2 Plotting graphs • A A6.3 Conversion graphs • A A6.4 Distance-time graphs • A A6.5 Interpreting graphs • A

  12. Plotting a conversion graph A conversion graph for pounds to euros £ € Let’s plot a graph to convert pounds to euros. 300 First we need a table of values: 250 200 20 100 160 200 150 30 150 240 300 € 100 This gives us the points: (20, 30) 50 (100, 150) 0 (160, 240) 0 50 100 150 200 (200, 300) £

  13. Conversion graphs – money

  14. Conversion graphs – temperature

  15. A6 Real-life graphs Contents A6.1 Reading graphs • A A6.2 Plotting graphs • A A6.4 Distance-time graphs A6.3 Conversion graphs • A • A A6.5 Interpreting graphs • A

  16. Distance-time graphs distance 0 time In a distance-time graph the horizontal axis shows time and the vertical axis shows distance. For example, this distance-time graph shows a journey. What does the slope of the line tell us? The slope of the line tells us the average speed. The steeper the line is, the faster the speed.

  17. Label the distance-time graph

  18. Olympic swimmers

  19. A6 Real-life graphs Contents A6.1 Reading graphs • A A6.2 Plotting graphs • A A6.5 Interpreting graphs A6.3 Conversion graphs • A A6.4 Distance-time graphs • A • A

  20. Filling flasks 1

  21. Filling flasks 2

  22. Interpreting the shapes of graphs 150 Eating a bar of chocolate 100 Mass of chocolate (g) 50 0 0 10 20 30 40 50 60 70 80 90 100 Time (seconds) Jessica eats a bar of chocolate. This graph shows how the mass of the chocolate bar changes as it is eaten.

  23. Interpreting the shapes of graphs Temperature of water Time This graphs shows how the temperature of the water in a pan changes when frozen peas are added.

  24. Which graph is correct? Graph A Graph B Graph C Graph D Mass of sponge (g) Mass of sponge (g) Mass of sponge (g) Mass of sponge (g) Volume of water (cm3) Volume of water (cm3) Volume of water (cm3) Volume of water (cm3) In an experiment a group of pupils poured water onto a sponge and weighed it at regular intervals. Each time the sponge soaked up all the water. Which graph is most likely to show their results?

  25. Sketching graphs Temperature (oC) Time (minutes) A group of pupils are conducting an experiment. They fill three beakers with boiling water and record the temperature of the water over time. Beaker A has no wrapping, Beaker B is wrapped in ice and Beaker C is wrapped in insulation fibre. The temperature graph for beaker A looks as follows: How would the graphs for beakers B and C compare to this? Beaker A

  26. Sketching graphs

  27. Matching graphs to statements

More Related