At a glance. One lesson of about 60 minutes. Students sort variables into nominal, ordinal, discrete and continuous, then see why a count has gaps and a measurement does not.
Calculator: no calculator. Nothing here needs one. The skill is deciding what kind of thing was recorded.
What students will learn
Know
- Categorical data is words (nominal or ordinal); numerical data is numbers (discrete or continuous).
- Discrete data is counted; continuous data is measured.
- A number used only as a name is categorical.
Understand
- The type of data decides which calculations and which graphs make sense.
- A finer instrument gives a closer reading of a continuous variable but never an exact one.
- How data is recorded can change its type: a height can become short, medium or tall.
Do
- Classify a variable using the two questions.
- Explain a classification in a sentence, naming the test used.
- Decide how many values a discrete variable can take over a range.
MYP assessment criteria
Wording paraphrased. What this lesson gives you evidence for, and what to look for:
- Criterion A. Knowing and understanding: naming the type and kind of each variable (questions 1 to 6 and 9).
- Criterion B. Investigating patterns: the clock figure. Ask students to predict the reading at the next finer step before sliding, and to state the pattern in the number of steps from 14 to 15.
- Criterion C. Communicating: justifying a classification in a full sentence, using the words counted, measured, order and name (question 7 and the what-if).
- Criterion D. Applying mathematics in real-life contexts: the canteen notebook and the pencil-case and bakery records (the hook and the worked examples).
The one thing to do with the figure
Ask for a prediction before the first slide. “Which column of the canteen notebook could you add up?” Take answers, then send the variables through the path one at a time and ask the room for the branch before you move the slider.
Stop at the bus route number and ask why a number goes down the words branch. In the second figure move the clock from coarse to fine and keep the goals line in view: it never gains a point between 2 and 3.
A possible order
| 5 min | Warm-up from the student page, in silence, then answers. |
|---|---|
| 10 min | Hook and the first figure. Predict the branch for each variable before sliding. |
| 10 min | Key idea and the warn card on numbers used as names; the second figure on counted and measured. |
| 10 min | Worked example on the pencil case; students finish the faded bakery example in pairs. |
| 5 min | Question 1, the check. If many choose A, go back to the second figure. |
| 15 min | Your turn, Levels 1 to 3, at each student's own pace. |
| 5 min | Exit ticket, question 9, on paper or on screen. |
The answers
| Warm-up | 9.04; 6; 7/20. |
|---|---|
| Worked example | Discrete; continuous; nominal; ordinal. |
| Faded example | Baking time: continuous; kind of loaf: nominal; crust: ordinal. |
| 1. Continuous data | B, the length of a river. A is a count (discrete); C is nominal; D is ordinal. |
| 2. Nominal data | A, categorical nominal. B needs an order; C and D need numbers. |
| 3. Spot the numerical data | 3. Items 1, 3 and 5. |
| 4. Ordinal data | B, categorical ordinal. A ignores the order; C and D treat words as numbers. |
| 5. Count the continuous variables | 4. Items 1, 4, 7 and 8. |
| 6. Discrete data | B, numerical and discrete. A confuses counting with measuring; C and D treat a count as words. |
| 7. Type depends on how it is recorded | B. A says nothing is lost; C says the order is lost, but it is kept; D calls the words numbers. |
| 8. Values a discrete variable can take | 8. 0 to 7 inclusive. |
| 9. Match the type | B. A counts pages (discrete); C is a name (nominal); D has an order (ordinal). |
What each wrong answer tells you
| They give | What it usually means | What to do |
|---|---|---|
| A in question 1 | Treated a count of petals as a measurement because it is a number. | Ask whether there can be 4.6 petals. If not, there is a gap between neighbours, so it is counted. |
| C or D in question 1 | Went for words or grades because they feel like a measure of quality. | Ask what number each answer is: a blood group or a grade has none. |
| B in question 2 | Heard “categories” and chose ordinal without checking for an order. | Ask: can you put salt, paprika and cheese from least to most? If not, no order. |
| 4 in question 3 | Counted the house number as numerical because it is digits. | Ask whether you would ever add two house numbers. A name is not an amount. |
| 2 in question 3 | Believed numerical means counted, so left out the wingspan. | Name both kinds of number: counted gives discrete, measured gives continuous. |
| A in question 4 | Missed the order never, sometimes, often, daily. | Ask which of two answers shows more reading. If one does, there is an order. |
| 6 or 2 in question 5 | Counted all numerical items, or counted the discrete ones. | Write C for counted and M for measured beside each numerical item, then count the M's. |
| A in question 6 | Thought any number is continuous. | Ask whether a hen can lay 4.6 eggs. |
| A, C or D in question 7 | Missed that words replaced numbers, or thought the order was gone. | Ask: can you say how much taller one plant is? Which type of data allows that? |
| 7, 25 or 6 in question 8 | Subtracted 7 − 0, used the number of students, or left out the ends. | List 0, 1, 2 up to 7 in a line and count the entries. |
| A, C or D in question 9 | Mixed up counted with measured, or treated a name as a count. | Run each option through the two questions on the path. |
Questions worth asking
- Is a postcode numerical? No. It is written with digits but works as a name. Listen for “you would not add two of them”.
- Can a continuous measurement ever be recorded exactly? In practice no: every instrument has a step. Listen for “only as exact as the clock”.
- Why might a survey writer choose ordinal words over exact numbers? Quicker and simpler to answer, but the exact differences are lost. Listen for what is gained and what is lost.
- Shoe sizes go 5, 5.5, 6 and so on. Is shoe size continuous? A foot length is continuous, but the size is recorded in separate steps, so the recorded data behaves as discrete. Accept an argued answer.
Differentiation
A way in for anyone stuck
- Give each student a card with the two questions and a copy of the path to run a finger down.
- Start with the clear cases: colour (nominal), goals (discrete), time (continuous). Add ordinal and the bus route number last.
- For counted or measured, ask: could there be a value halfway between two neighbours?
Stretch
- Question 8, then: a discrete variable runs from 3 to 12 in whole numbers. How many values? (10.)
- Invent a variable that can be recorded as continuous, discrete or ordinal depending on how it is written down, and say how.
Students learning in English as an additional language
Say each type with the question that finds it: “words or numbers?”, then “counted or measured?”. The word “categorical” is about categories, or groups. Students may use home-language words for count and measure beside the English ones.
| Word | Plain meaning | Example |
|---|---|---|
| categorical | data that is words or names, sorted into groups | colour of a kite |
| numerical | data that is numbers you can add and compare | goals in a match |
| qualitative | another word for categorical: data that describes a quality | kind of loaf |
| quantitative | another word for numerical: data that gives an amount | baking time |
| nominal | categories with no natural order | language spoken at home |
| ordinal | categories that go in a natural order | small, medium, large |
| discrete | numerical data that is counted, in separate steps | pages in a book |
| continuous | numerical data that is measured, with any value in a range | mass of a mango |
Sentence starters for explaining aloud or in writing:
- This is … data because it is … and it is ….
- The values are counted, so there is no value between … and ….
- It looks like a number, but it is only a name, so …
Two things not to say
“If it is a number it is numerical.” A route number and a shirt number are names; test by asking if adding them means anything.
“Discrete means whole numbers.” Discrete means counted in separate steps; the point is the gaps, not the digits.
Questions to set
Extra practice in three tiers, including one question from earlier work for spacing. Every answer has been checked.
1Fluency
The idea on its own, with friendly numbers. Set these first.
- ClassifyGive the type and kind of: the colour of a car; the number of doors on a car.
Categorical, nominal; numerical, discrete. - Spot the measureIs the time a plant takes to sprout counted or measured? What type is that?
Measured; numerical, continuous.
2In context
The same idea inside a situation, where the first job is deciding what to calculate.
- ContextA zoo records, for each animal, its species, its mass in kilograms, its number of offspring and its health rating (poor, fair, good). Give the type of each.
Nominal; continuous; discrete; ordinal. - Earlier work (Unit 1, lesson 7)Round 8.62 to the nearest whole number, then say which type of data a mass is.
9; a mass is continuous.
3Challenge
Reasoning, generalising and working backwards.
- ReasoningA dentist records the number of teeth with a filling for 40 patients. The data goes from 0 to 12. How many different values can it take, and is it discrete?
13 values (0 up to 12); yes, discrete. - Change the recordRavi measures the length of 50 leaves in millimetres. He then records each leaf as longer or shorter than 60 mm. What type is the new record?
Categorical, ordinal (shorter, longer): the exact lengths are lost.
Practicalities
Works on a phone or a shared screen. Nothing a student types is saved or sent anywhere.
Both figures work with the keyboard (tab to a slider, then the arrow keys) and by touch. Under each one, “Show me the steps” gives the same states in words.
No device? Print the two questions and nine variable cards; students sort the cards onto the path by hand.