--- title: "Describing a relationship" subtitle: "Linear relations · Rules, tables and graphs · Lesson 5" --- # Describing a relationship **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A graph tells a story about how two things change together. Telling that story in words, section by section, is how scientists and journalists use graphs. :::teacher-note **In one sentence:** Students describe how one measurement changes as the other increases, section by section, and tell the story a graph shows without reading it as a picture (AC9M7A04, node 2). **Students should be able to say:** I can describe a section of a graph as increasing, decreasing or constant. I can tell the story of a graph in order, with the measurements named. I can draw a graph that matches a story. **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 What is measured up the side? What would the line do if the cyclist stopped? :::keep-together **A graph shows a cyclist's distance from home against time. The line goes up, then is flat, then goes down. Which story fits?** ☐ Rides away, then home, then away again ☐ Rides up a hill, along the flat, then down a hill ☐ Rides away, then faster, then slower ☐ Rides away, stops for a rest, rides home My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** Rides away, stops for a rest, rides home. Up means the distance from home is increasing, flat means it is not changing (stopped), and down means it is decreasing (riding back). The graph shows distance, not the shape of the road. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Describing sections :::keep-together ### A rest Here is how to describe a graph, one section at a time. 1. $\text{0 to 2 h: } 0 \to 60 \text{ km}$ — Take one section at a time and compare its start and end. The distance increases. 2. $\text{2 to 3 h: } 60 \to 60 \text{ km}$ — The distance does not change. It is constant. 3. $\text{3 to 5 h: } 60 \to 0 \text{ km}$ — The distance decreases. 4. $\text{increases} \to \text{constant} \to \text{decreases}$ — Put the sections in order. Say it: "As time increases, the distance from home increases, then stays constant, then decreases." **Between 2 and 3 hours, which sentence is true?** ☐ As time increases, the distance from home stays constant ☐ As time increases, the distance from home increases ☐ As time increases, the distance from home decreases ::: :::teacher-note **Answer:** As time increases, the distance from home stays constant The line is flat from 2 to 3 hours: the distance is 60 km at both times, so it does not change. The cyclist has stopped. ::: :::keep-together ### Riding home **What is the cyclist doing between 3 and 5 hours?** ☐ Riding back towards home ☐ Riding away from home ☐ Riding down a hill ::: :::teacher-note **Answer:** Riding back towards home The distance from home decreases from 60 km to 0 km: the cyclist is riding back towards home. ::: :::keep-together ### Find the mistake **Omar describes the ride from 3 to 5 hours. Click the line where his reasoning goes wrong.** ``` 1 Describe the graph from 3 to 5 hours. 2 The line goes down. 3 So the cyclist rides down a hill. 4 The distance from home is getting smaller. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: the graph does not show hills. The line goes down because the distance from home is getting smaller: the cyclist is riding home. ::: :::typical ## Other stories **The bath.** Each task loads a new graph. Describe the sections before you answer. **Two walkers.** **A cooling drink.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Describe and match :::keep-together ### The ride **Which sentence describes the ride from 0 to 2 hours?** ☐ As time increases, the distance from home stays constant ☐ The cyclist rides up a hill ☐ As time increases, the distance from home increases ::: :::teacher-note **Answer:** As time increases, the distance from home increases The line goes up from 0 to 60 km: the distance from home increases. ::: :::keep-together ### A tank **Which story fits the graph?** ☐ The tank fills, then drains, then fills again ☐ The tank fills at the same rate the whole time ☐ The tank fills slowly, the water is left, then it fills faster ::: :::teacher-note **Answer:** The tank fills slowly, the water is left, then it fills faster From 0 to 3 min it rises (30 L). From 3 to 6 min it is flat (nothing added). From 6 to 9 min it rises 60 L, faster than before. ::: :::keep-together ### Review **Review: what is the temperature at 20 minutes, in °C?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 45 At 20 min the line is at 45 °C: the point is (20, 45). ::: :::keep-together ### The bath again **Between 6 and 8 minutes, the amount of water...** ☐ decreases ☐ increases ☐ stays constant ::: :::teacher-note **Answer:** decreases The line goes down from 80 L to 40 L: the water decreases (the plug is pulled). ::: ## Make: draw a bath Drag each point up or down. Then describe your graph in a sentence. Stretch: draw a bath that fills 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 a tap's water in a bucket (L) against time (min) goes up, then is flat. Describe it.** {{lines-3}} ::: :::teacher-note **Answer:** As time increases, the amount of water increases, then stays constant (the tap was turned off). :::