Interpreting Graphs I can interpret information from graphs I know to check the axes to determine the quantities being measured and the scale

Filling flasks 1 Start by explaining that the we 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. As the first flask fills up the graph of depth against time will be drawn. Ask pupils to tell you how many cm are filled each second for the flask. Ask pupils to predict the slope of the graph for the new flask compared to the previous flask. Ask pupils to justify why they think the graph will be steeper or less steep than before. Continue for each flask in turn. Establish the depth in the narrowest flask will increase the fastest and therefore produce the steepest graph. The depth in the widest flask will increase the slowest. Ask pupils to explain why all the line pass through the origin. Ask pupils to explain why the lines are straight. Ask pupils to 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?

Filling flasks 2 Start by explaining that the we 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. As the first flask fills up the graph of depth against time will be drawn. Ask pupils to predict the shape of the next graph before it is drawn, justifying their explanations. Establish that the wider the flask is at a given point the loner it will take for the water to increase in depth. Continue for each flask in turn. Ask pupils to explain why all the line pass through the origin. Ask pupils to 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? Ask pupils if we can use the graph to work out the capacity of each flask.

Interpreting the shapes of graphs Smudger eats a bar of chocolate. This graph shows how the mass of the chocolate bar changes as it is eaten. 150 50 100 10 20 30 40 60 70 80 90 Eating a bar of chocolate Mass of chocolate (g) Time (seconds) Discuss the graph and ask the following questions: What do the vertical portions of the graph represent? What do the horizontal portions of the graph represent? How many bites did it take to finish the bar? What was the weight of the biggest bite? How long did it take Jessica to eat the first bite? What is the original weight of the chocolate bar? How long did Jessica take to finish the chocolate bar in seconds/ in minutes and seconds?

Interpreting the shapes of graphs This graphs shows how the temperature of the water in a pan changes when frozen peas are added. Time Temperature of water Ask a volunteer to point to the point on the graph that shows when the peas are added to the water. Discuss trends in the graph. Ask pupils to describe what is happening in the portion of the graph that slope downwards. Ask also what is happening in the portion of the graph that slopes upwards. Ask pupils to describe what is happening at each turning point in the graph.

Which graph is correct? 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? Mass of sponge (g) Volume of water (cm3) Graph A Graph B Graph C Graph D Ask pupils to justify their choice of graph to fit the situation.

Sketching graphs 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. Time (minutes) Temperature (oC) The temperature graph for beaker A looks as follows: How would the graphs for beakers B and C compare to this? Ask pupils to describe what the graph for beaker A shows. Agree that it shows the water cooling rapidly and then cooling more slowly. Ask pupils how the graphs for beakers B and beaker C will differ from the one shown. Use the next slide to sketch these different graphs. Beaker A

Sketching graphs Use the pen tool to sketch the graph of beaker A cooling down. Ask volunteers to sketch the graphs of beaker B and beaker C. Remind pupils that the three beakers all start at the same temperature.

Matching graphs to statements Establish that if something is rising rapidly over time it will have a steeper and steeper gradient. If something is falling rapidly it will have a steeper negative (or downward) gradient. If something is rising or falling steadily then the graph will be straight. Ask pupils what a horizontal section of graph would represent. Each of the graphs in this example illustrates trends rather than accurate information.

Distance-time graphs 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? time distance The slope of the line tells us the average speed. Ask pupils to tell you what is happening at the places where the line is horizontal (the object is not moving). Ask pupils what it means if the graph slopes downwards (the object is moving in the opposite direction). Stress that a straight line in a distance-time graph indicates constant speed. What would it mean if the line was curved? A curved line would indicate acceleration or change in speed over time. The steeper the line is, the faster the speed.

Label the distance-time graph Use this activity to discuss the meaning of different parts of the graph. The correct positions are: A, accelerating; B, moving slowly at constant speed; C, moving rapidly away from the starting point at constant speed; D, not moving; E, moving at constant speed towards the starting point; F, decelerating.

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. You could ask one volunteer to vary the speeds of the swimmers and another to provide a race commentary, stating when one swimmer overtakes another, for example.

FOR EACH SECTION OF THE GRAPH! Information Graphs On information graphs, always look to see What information each axis gives (label) and What one square represents (scale) When describing a graph you need to state: The distance moved (travelled) The time taken to move The speed (rise/run) The direction of travel (away from or towards) FOR EACH SECTION OF THE GRAPH!