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Discrete or Continuous? Cards & Reasoning

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Discrete or Continuous? Cards & Reasoning

For each situation, decide whether the variable is discrete or continuous. Then give evidence from how it is obtained: is it counted, or measured? Remember that rounding or recording to a chosen precision does not necessarily change the type of variable.

Variable Sort Cards

Classify each variable and explain your choice using the context. Use terms such as count, measured, whole numbers, units and precision.

1.Card A: Sione counts the calves born on the farm during one month. Is the number of calves discrete or continuous? Give a reason.

2.Card B: Tevita records how many feed buckets are used in a day. Classify this variable and explain how it is collected.

3.Card C: Wiremu counts the cows waiting to enter the milking shed. Is this number discrete or continuous? Explain.

4.Card D: Sione counts the fence posts replaced during farm repairs. Classify the variable and state whether it is counted or measured.

5.Card E: Tevita records the number of milking sessions completed in a week. Is this variable discrete or continuous? Give evidence.

6.Card F: Wiremu counts the cows in each paddock. Classify the number of cows and explain your choice.

7.Card G: Sione records how many milk crates are loaded onto a truck. Is this a discrete or continuous variable? Why?

8.Card H: Tevita counts the sheep seen beside the farm track. Classify the number and explain how it is obtained.

9.Card I: Wiremu measures a calf’s height in centimetres. Is height discrete or continuous? Explain using the measurement.

10.Card J: Sione times how long it takes to fill a milk container, recording seconds. Classify the time and give a reason.

11.Card K: Tevita measures the temperature inside the milk chiller in degrees Celsius. Is temperature discrete or continuous? Why?

12.Card L: Wiremu measures the mass of a feed sack in kilograms. Classify the mass and identify the evidence.

13.Card M: Sione measures the distance a farm bike travels, in kilometres. Is distance discrete or continuous? Explain.

14.Card N: Tevita measures the milk in a tank in litres. Classify the amount of milk and say whether it is counted or measured.

15.Card O: Wiremu measures the length of a fence rail in metres. Is the length discrete or continuous? Give evidence.

16.Card P: Sione records the time taken to drive a tractor along a track, in minutes and seconds. Classify the time and explain.

17.Card Q: Tevita counts completed laps around a farm training track. The result is recorded in whole laps. Is the variable counted or measured, and is it discrete or continuous?

18.Card R: Wiremu records the amount of milk used for a recipe as 1, 2 or 3 litres only. Is the underlying amount discrete or continuous? Explain why the recorded options do not decide the type.

19.Card S: Sione records the chiller temperature to the nearest whole degree Celsius. Does this make temperature discrete? Explain the role of precision.

20.Card T: Tevita’s tracker displays the number of steps he takes, including a decimal estimate. Is the original number of steps counted or measured? Classify it and explain.

Compare and reason

Use examples from the cards to support each answer.

21.Choose one discrete card and one continuous card from this worksheet. For each, state the variable and give one piece of evidence explaining its classification.

22.Compare the completed laps in Card Q with the distance travelled on the farm bike in Card M. Which is a count and which is a measurement? Explain how their possible values differ.

23.A milk-tank reading is recorded to the nearest litre, then to the nearest tenth of a litre. What changes between the two readings, and does the variable’s classification change?