--- title: "Changing one thing at a time" subtitle: "Linear relations · Rules, tables and graphs · Lesson 12" --- # Changing one thing at a time **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A scientist testing a plant changes the light, but not the water. In a formula, that is how you find what each letter does. :::teacher-note **In one sentence:** Students vary one variable at a time in V = lwh, d = st and A = s², write the results as a table and describe the effect (AC9M7A06, nodes 1 and 2). **Students should be able to say:** I can change one variable and hold the others still. I can describe in words what happens to the output. I can say which variable has the biggest effect, and why. **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 Keep l and w the same. :::keep-together **A box has $l = 2$, $w = 3$ and $h = 2$, so $V = 12$. What is $V$ when $h$ is doubled to 4 and the rest stay the same?** ☐ 12 ☐ 14 ☐ 16 ☐ 24 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 24. V = 2 × 3 × 4 = 24: doubling one factor doubles the product. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## A fair test :::keep-together ### The pattern in the table **With $l = 2$ and $w = 3$, $V$ is 6, 12, 18 when $h$ is 1, 2, 3. By how much does $V$ go up for each extra 1 in $h$?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 6 V goes up by 6 each time, which is l × w = 2 × 3. ::: :::keep-together ### A fair test? **Tom wants to know what h does to V. Click the line where his test stops being fair.** ``` 1 Tom wants to know what h does to V = lwh. 2 He sets l = 2, w = 3 and h = 1, so V = 6. 3 Then he changes h to 2 and w to 4, so V = 16. 4 V went from 6 to 16, so doubling h made V go up by 10. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: he changes w as well as h, so he cannot tell which caused the change in V. Change h alone: V = 2 × 3 × 2 = 12. ::: :::keep-together ### What to change **To find the effect of $w$ on $V = lwh$, what should you do?** ☐ Change w and h together ☐ Change w only, and keep l and h the same ☐ Change l, w and h together ☐ Change l and h only ::: :::teacher-note **Answer:** Change w only, and keep l and h the same Isolate one variable at a time: that is a fair test. ::: :::typical ## Other formulas **Find the speed.** Hold the time at 3. **Both double.** **Side and area.** **The biggest change.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Vary and describe :::keep-together ### Find V **$V = lwh$ with $l = 2$, $w = 3$, $h = 4$. What is $V$?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 24 2 × 3 × 4 = 24. ::: :::keep-together ### Change w **Now change only $w$, from 3 to 4. What is $V$?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 32 2 × 4 × 4 = 32. ::: :::keep-together ### Change t **$d = st$ with $s = 60$ km/h. The time doubles from 2 to 4 hours. What is $d$ now, in km?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 240 60 × 4 = 240 km, double the 120 km for 2 hours. ::: :::keep-together ### Review: substitution **Review: $P = 2l + 2w$ with $l = 6$ and $w = 4$. What is $P$?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 20 2 × 6 + 2 × 4 = 12 + 8 = 20. ::: ## Make: a test of your own Now write a table (on paper or in a spreadsheet) that varies $h$ from 1 to 6 for your box, and describe in a sentence what happens to $V$ as $h$ goes up. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **In V = lwh with l = 2, w = 3, h = 4, h goes to 8 and nothing else changes. What is V?** {{lines-3}} ::: :::teacher-note **Answer:** 48: 2 × 3 × 8, double the 24 it was. :::