--- title: "Comparing integers" subtitle: "Number Foundations · Integers · Lesson 1" --- # Comparing integers **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Thredbo at −9 °C, Canberra at −3 °C: which is colder? Below zero, the number that looks bigger is the smaller one. :::teacher-note **In one sentence:** Students place integers on a number line, find that further left is less (so −7 < −2), and compare and order integers with < and > (AC9M7N07, node 1). **Students should be able to say:** I can put a set of integers, including negatives, in order from least to greatest. I can write a comparison between two integers with < or >. I can explain why −10 is less than −1, even though 10 is more than 1. **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 Think of temperatures: is $-7$ °C or $-2$ °C warmer? :::keep-together **Which is greater, $-7$ or $-2$?** ☐ $-2$ ☐ You cannot compare two negative numbers ☐ $-7$, because 7 is more than 2 ☐ Neither: they are both negative, so they are equal My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** −2 is greater. On the number line −2 is to the right of −7: further right is greater. −7 is further below zero, so it is less. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Further left is less :::keep-together ### Ordering on the line Here is how to put integers in order, using where each one sits on the number line. 1. $-2, \; -8, \; 3, \; 0$ — Put these in order from least to greatest. 2. $\text{place each on the line}$ — Negatives go left of zero: $-2$ is 2 left, $-8$ is 8 left. 3. $-8 \text{ is furthest left}$ — Furthest left is least, so $-8$ comes first. 4. $-8, \; -2, \; 0, \; 3$ — Read the line from left to right. 5. $-8 < -2$ — Between two negatives, the one further from zero is less. **Which is true?** ☐ $-5 = -1$ ☐ $-5 < -1$ ☐ $-5 > -1$ ::: :::teacher-note **Answer:** $-5 < -1$ −5 is further left than −1, so −5 < −1. ::: :::keep-together ### Find the mistake **Ari puts four numbers in order. Click the line where the reasoning goes wrong.** ``` 1 Put these in order from least to greatest: −2, −8, 3, 0 2 The numbers without signs are 2, 8, 3 and 0. 3 8 is the biggest of those, so −8 is the greatest negative. 4 Least to greatest: −2, −8, 0, 3 ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: 8 is bigger than 2, but −8 is further below zero than −2, so −8 is less. The order is −8, −2, 0, 3. ::: :::keep-together ### Either side of −3 **Less than $-3$, or greater than $-3$?** Groups: Less than −3, Greater than −3 - −6: {{field-15}} - −1: {{field-15}} - 0: {{field-15}} - −10: {{field-15}} - 2: {{field-15}} - −4: {{field-15}} ::: :::teacher-note **Answer:** −6 → Less than −3; −1 → Greater than −3; 0 → Greater than −3; −10 → Less than −3; 2 → Greater than −3; −4 → Less than −3 ::: :::typical ## One change at a time **Between two negatives.** Each task changes one thing. First: drag $P$ to a number between $-8$ and $-4$. **Temperatures.** The same idea in degrees. Warmer means further right. **Zero and the negatives.** Zero is greater than every negative number. **Further from zero.** When is the number further from zero the smaller one? Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Compare and order :::keep-together ### Which sign? **Which sign goes in the gap? $-6 \;\square\; -9$** ☐ $<$ ☐ $>$ ::: :::teacher-note **Answer:** $>$ −6 > −9: −6 is to the right of −9. ::: :::keep-together ### In order **Which list is in order from least to greatest?** ☐ $-9, -4, 0, 2, 5$ ☐ $0, -4, -9, 2, 5$ ☐ $-4, -9, 0, 2, 5$ ::: :::teacher-note **Answer:** $-9, -4, 0, 2, 5$ Left to right on the line: −9, −4, 0, 2, 5. ::: :::keep-together ### Colder **At 6 am it was $-5$ °C in Cooma and $-8$ °C in Perisher. Which was colder?** ☐ Perisher ☐ Cooma ::: :::teacher-note **Answer:** Perisher −8 < −5, so Perisher was colder. ::: :::keep-together ### Review **Review: what number is 4 places to the left of 1 on a number line?** Answer: {{field-15}} ::: :::teacher-note **Answer:** -3 From 1, four places left: 0, −1, −2, −3. ::: ## Make: a surprising pair Find a pair where the less number has the bigger size without its sign. The sentence under the line tells you which is less. Stretch: write three temperatures below zero, then put them in order from warmest to coldest. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Put in order from least to greatest: 4, −6, 0, −1, −10.** {{lines-3}} ::: :::teacher-note **Answer:** −10, −6, −1, 0, 4. :::