Numbers you count and numbers you measure

By the end of this lesson you can tell counts (3 mangoes) from measurements (1.4 kg), and say why both are numbers.

Why it matters

Before you work with a number, you need to know where it came from. A nurse counts how many tablets are left, but measures a baby's weight. If you mix the two up, you can end up with an answer like "2.6 tablets", which makes no sense.

The idea in plain words

Meet Lucía. Lucía teaches two classes, 5A and 5B, at a school in Bogotá, Colombia. She asked all 30 pupils the same questions, and typed the answers into a table. You will use her table all through this module.

Some of Lucía's questions have number answers. But the numbers come in two kinds.

Counting. "How many brothers and sisters do you have?" You find the answer by counting, one by one: one, two, three. The answer is always a whole number. Nobody has 2.5 sisters.

Count: a number you find by counting things one by one. It is always a whole number: 0, 1, 2, 3 ...

Measuring. "How many minutes does it take you to get to school?" You find the answer with a tool, here a clock. The answer could have parts, such as 20 and a half minutes. Lucía's pupils rounded to whole minutes, but the time itself could be in between.

Measurement: a number you find with a tool, such as a clock, a scale or a ruler. It can have parts, such as 1.4 kg.

A quick test: could the answer sensibly be "and a half"? If yes, it is probably a measurement.

Both are numbers, so you can add them up and compare them. Knowing which kind you have tells you what an answer can look like.

See it done

Data: class-survey.csv, Lucía's survey (synthetic: made up for this course). One row is one pupil.

First, open it. Bring it into Google Sheets just as you did in lesson 1.5: File, Import, Upload, choose class-survey.csv. This time set Import location to Insert new sheet(s), so Amara's data stays in its own tab. Then View, Freeze, 1 row.

Question: in Lucía's table, which number columns are counts and which are measurements?

1. List the columns with numbers in them. Look along row 1 and down a few rows. The number columns are pupil_number, age, travel_minutes and siblings.
2. Put pupil_number aside. It is a name tag, not an amount. (Lesson 2.6 is all about this.)
3. Ask the "how was it found?" question for each. - siblings: found by counting brothers and sisters. A count. - travel_minutes: found with a clock. A measurement. - age: found from a date of birth and a calendar, then rounded down to whole years. Time is measured, so age is a measurement that we keep as whole years.
4. Check with the "half" test. 20.5 minutes makes sense. 1.5 siblings does not. The test agrees.

travel_minutes was measured with a clock. siblings was counted. Notice the empty box in row 7: it comes back in lesson 2.5.

Your turn, with help

Go back to Amara's tab. Is the quantity column a count or a measurement?

Hint: how did Amara find the number? Could a customer buy "and a half" a pineapple from her?

Show the answer

A count. Amara counts the fruits as she hands them over: 1, 2, 3, 4. She sells whole fruits, so the answer is always a whole number.

Your turn, alone

Say whether each is a count or a measurement.

1. The number of goals in a football match.
2. How much rain fell in Accra today, in millimetres.
3. The height of a pupil, in centimetres.
4. The number of buses that stop outside a school in one hour.

Check your answers

1. Count (goals are counted one by one).
2. Measurement (a rain gauge measures it, and 3.5 mm makes sense).
3. Measurement (a tape measure, and 141.5 cm makes sense).
4. Count.

Watch out

• Answers that cannot exist. If you work out "2.6 siblings" for one pupil, something went wrong. Counts for one thing are whole numbers. (An average over many pupils can have parts. You will meet averages later.)
• Rounded measurements look like counts. Lucía's minutes are all whole numbers, but only because pupils rounded them. Ask how the number was found, not just how it looks.
• Forgetting the units. "20" means nothing until you know it is 20 minutes, not 20 kilometres. Good column names carry the unit, such as travel_minutes.

Say it back

1. What is a count?
2. What is a measurement?
3. Is "weight of a bag of rice in kg" a count or a measurement?

Show the answers

1. A number found by counting one by one. Always a whole number.
2. A number found with a tool. It can have parts.
3. A measurement.

What is next

Lucía's table also has columns like favourite_fruit and travel_mode. They hold words, not numbers. Can you work with words? Can you find the "average fruit"? Next lesson.