Description of the lesson:
- Students test their classmates by asking them to decide which is the population and sample in each of their examples, or what the population is based on their sample. (WM: fluency, reasoning)
This is a good warm-up for students to use this time to help each other clarify the definitions of population and sample through peer feedback in their homework from last lesson.
Introduction: Review of population, census and sample
- Open cloze passage on the definitions of population, census, sample, the difference between population and sample, and the practicalities of collecting data through a census compared to a sample (AFL) (WM: reasoning, justification, fluency, understanding)
- Refer to the Google Doc for the open cloze passage and examples that will be used throughout the lesson.
- Students are in small groups and have to fill in the blanks of the passage. For the correct response, the group gets 1 point, if they answer incorrectly, the next group has a chance to answer. Every member of the group must be agree on their answer before responding, otherwise they lose 1 point. For an added element, you can add a 'hangman' so that they only have a limited amount of incorrect responses.
- Teacher uses this opportunity to address any misunderstandings from last lesson.
This activity acts as both a revision and introduction to making inferences about a population, foreshadowing the focus of the lesson. Students must work together in this game, requiring them to explain and justify their thinking to their team.
Activity: Khan Academy Quiz (ICT)
Extension: worksheet from Additional Resources (has different levels of questions; students can choose the level or teacher can assign)
Students have a turn at identifying the population and sample by themselves, exercising their fluency. If students require further explanation, a video matching the questions is available for viewing.
Activity: Making inferences from random samples
- This activity involves a number (10-20 depending on size) of coloured blocks (building blocks, lego blocks, whatever is available to you) being placed in an opaque bag so students can't see what is inside. Students randomly draw the number of blocks required to make a reasonable sample and record the colours being drawn from the bag. This becomes their sample and they must predict the contents of the bag. Note: the total number of blocks must be known to them. (WM: problem solving, reasoning)
Example: A bag has 20 evenly sized Lego pieces in it with 5 red pieces and 15 blue pieces. Students decide to draw 10 pieces and record the colours and then predict how many in the bag are red and how many are blue. The only information given to them is the total number of Lego pieces in the bag.
- This can be carried out as a whole class activity, or in small groups where each group is given their own bag of blocks. On completion, the class discusses their results and explains how they came to the answer. (WM: understanding, justification) The teacher reiterates that the blocks in the bag is the population and what they drew was a random sample, and so the results of their findings is proportional to the contents of the bag (the population). The result is an estimation; not exact.
- Teacher runs through Example 2 from the Google Doc to demonstrate how to mathematically make inferences about a population from a sample. More examples can be found in this video: https://www.youtube.com/watch?v=-PuoXV9W_HE
This activity demonstrates to students that they already know that samples are proportional to the population through their predictions, linking the mathematical concept of making inferences to their prior knowledge.
Activity: Khan Academy Quiz (ICT)
Students develop their fluency through answering questions on inferences about population by themselves using the mathematical approach outlined in the last activity. Again, if students require further explanation there is an accompanying video.
Conclusion: Kahoot! Quiz (ICT)
To end the lesson, students participate in a fan-favourite quiz format – Kahoot! recapping populations and samples once more in timed conditions.