--- title: "Reading a graph" subtitle: "Linear relations · Rules, tables and graphs · Lesson 4" --- # Reading a graph **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Weather maps, phone battery meters and sports stats all use graphs. Before you can use one, you need to read it: which number is on which axis? :::teacher-note **In one sentence:** Students read values from graphs of real data, starting from either axis, and say what a point means in a sentence with units (AC9M7A04, node 1). **Students should be able to say:** I can say what a point on a graph of real data means, with units. I can find a value on one axis and read the matching value from the other. I can tell the graph's variables from its axis labels. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict Which axis is the first number read from? What are the units of each number? :::keep-together **A graph shows temperature (°C) up the side and time (h) along the bottom. One point on it is $(15, 24)$. What does that point say?** ☐ At 24 hours the temperature is 15 °C ☐ At 15 hours the temperature is 24 °C ☐ It is 15 °C for 24 hours ☐ The temperature went up by 15, then by 24 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** At 15 hours the temperature is 24 °C. The first number is read along the bottom axis (Time), the second up the side (Temperature), just as when you plotted points. (At 24 hours the temperature is 15 °C swaps the axes.) ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Reading values :::keep-together ### Temperature Here is how to read a graph, step by step. 1. $\text{Axes: Time (h) across, Temperature (°C) up}$ — Check the labels first. 2. $\text{Time} = 9 \text{ h}$ — Find the value you know on its own axis. 3. $(9, \; ?)$ — Go up from 9 to the line. 4. $\text{Temperature} = 14 \text{ °C}$ — Read across to the other axis. 5. $\text{At 9 h the temperature is 14 °C.}$ — Say it in a sentence, with the units. **What is the temperature at 9 hours?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 14 At 9 h the line is at 14 °C, so the point is (9, 14). ::: :::keep-together ### The highest point **At what time (in hours) is the temperature highest?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 15 The highest point is (15, 24): the temperature is highest at 15 h. ::: :::keep-together ### Find the mistake **Priya reads the temperature at 6 hours from the graph. Click the line where she goes wrong.** ``` 1 Read the temperature at 6 hours. 2 Find 6 on the Time axis. 3 Go up to the line. 4 Read across: the line is at 9, so at 9 hours the temperature is 6 °C. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 4 Line 4: the line is at 9 when the time is 6, and 9 is read up the side, so it is the temperature. At 6 hours the temperature is 9 °C. Priya swapped the two numbers. ::: :::typical ## Other graphs **Fuel.** Each task loads a new graph. Read the axis labels first. **A flat line.** **Below zero.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Read the graph :::keep-together ### The time **What is the temperature at 21 hours?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 16 At 21 h the line is at 16 °C: the point is (21, 16). ::: :::keep-together ### The fuel **How much fuel is left after 300 km, in litres?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 14 At 300 km the line is at 14 L: the point is (300, 14). ::: :::keep-together ### Which sentence? **A graph of cost ($) against time (hours) has the point $(4, 30)$. Which sentence is true?** ☐ 30 hours cost $4 ☐ 4 hours cost $30 ☐ The cost went up by $4 over 30 hours ::: :::teacher-note **Answer:** 4 hours cost $30 The first number is the time (4 hours) and the second is the cost ($30). ::: :::keep-together ### Review **Review: find $y = 4x + 1$ when $x = 3$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 13 y = 4 × 3 + 1 = 12 + 1 = 13. ::: ## Make: tell a story with a graph The points move up and down only. Then answer: what does your graph say about the battery at 4 hours? Stretch: draw a graph where the battery falls quickly at first, then slowly. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A graph of height (cm) against age (years) has the point (12, 150). What does it say?** {{lines-3}} ::: :::teacher-note **Answer:** At 12 years the height is 150 cm. :::