--- title: "Counting and measuring" subtitle: "Data and chance · Data · Lesson 1" --- # Counting and measuring **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** How many siblings do you have? How long does it take you to run 100 m? One answer is always a whole number; the other could be anything in between. :::teacher-note **In one sentence:** Students sort numerical variables into discrete (counted) and continuous (measured), place a measured value between whole numbers on a dot plot, and see that measurements are always rounded to some precision (AC9M7ST01, node 1). **Students should be able to say:** I can say whether numerical data is discrete (counted) or continuous (measured). I can explain why a measurement is always rounded, and choose a sensible precision. **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 Ask of each one: is it counted, or measured? :::keep-together **Which of these could have the value $152.5$?** ☐ A person's height in cm ☐ The number of pages in a book ☐ The number of goals in a season ☐ The number of students in a school My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** A height in cm. Heights are measured, so they can be any value (152.5 cm, or 152.47 cm with a better ruler). The others are counted: whole numbers only. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Counted or measured :::keep-together ### Counted or measured Here is how to tell the kinds apart. 1. $\text{siblings: } 0, 1, 2, 3$ — Counted: separate values, no values in between. **Discrete.** 2. $\text{height: } 152.5\text{ cm}$ — Measured: any value in a range. **Continuous.** 3. $152.5 \approx 152.47\ldots$ — A measurement is rounded to the precision of the instrument (here 0.1 cm). 4. $\text{shoe size: } 7, 7.5, 8$ — Fixed steps with nothing in between: discrete, even with halves. Sort each one: discrete or continuous? **Discrete or continuous?** Groups: Discrete (counted), Continuous (measured) - Number of pets: {{field-15}} - Mass of a backpack in kg: {{field-15}} - Goals scored in a match: {{field-15}} - Time to solve a puzzle: {{field-15}} - Daily rainfall in mm: {{field-15}} - Number of letters in a name: {{field-15}} ::: :::teacher-note **Answer:** Number of pets → Discrete (counted); Mass of a backpack in kg → Continuous (measured); Goals scored in a match → Discrete (counted); Time to solve a puzzle → Continuous (measured); Daily rainfall in mm → Continuous (measured); Number of letters in a name → Discrete (counted) Counting gives separate values (discrete); measuring gives any value in a range (continuous). ::: :::keep-together ### Find the mistake **Ava decides what kind of data shoe size is. Click the line where her reasoning goes wrong.** ``` 1 Shoe sizes in our class: 7, 7.5, 8, 8.5, 9. 2 Shoe size has decimals in it. 3 So shoe size is continuous data. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: shoe sizes come in fixed steps (7, 7.5, 8, …); there is no size 7.3. Data that can only take separate values is discrete, even with halves in it. A foot length in cm would be continuous. ::: :::keep-together ### Rounded measurements **A height is recorded as $152$ cm, to the nearest centimetre. What could the real height be?** ☐ Exactly 152 cm ☐ Anything from 151.5 cm up to (but not including) 152.5 cm ☐ Anything from 152 cm to 153 cm ::: :::teacher-note **Answer:** Anything from 151.5 cm up to (but not including) 152.5 cm Measured values are rounded: 152 cm to the nearest cm means from 151.5 cm up to 152.5 cm. ::: :::typical ## One change at a time **Same topic, two variables.** Each task changes one thing. **Money.** **Ratings.** **Age.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Kinds of data :::keep-together ### Continuous **Which is continuous data?** ☐ The number of people on a bus ☐ The number of rainy days in a month ☐ The temperature at noon each day ::: :::teacher-note **Answer:** The temperature at noon each day Temperature is measured. ::: :::keep-together ### Discrete **Which is discrete data?** ☐ The length of a phone call ☐ The number of text messages sent in a day ☐ The mass of a phone ::: :::teacher-note **Answer:** The number of text messages sent in a day Messages are counted. ::: :::keep-together ### Precision **To compare 100 m times in a race, which precision makes most sense?** ☐ To the nearest minute ☐ To the nearest 0.01 s ☐ To the nearest 10 s ::: :::teacher-note **Answer:** To the nearest 0.01 s Runners are often a fraction of a second apart, so record hundredths of a second. ::: :::keep-together ### Review: decimals **Review: which is bigger, $14.3$ or $14.25$? Type the bigger one.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 14.3 14.30 > 14.25: compare the tenths first. ::: ## Make: your own measured data Then: if you rounded your times to the nearest second, how many different values would be left? Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Classify: (a) number of apps on a phone, (b) battery temperature, (c) screen size in inches. Explain one.** {{lines-3}} ::: :::teacher-note **Answer:** (a) discrete (counted), (b) continuous (measured), (c) continuous (measured, though sold in common sizes). :::