This counting collections activity engages students in predicting and then identifying the number of lollies dispensed by a vending machine.
Students can estimate the size of a collection using number sense in a real-world context. Collections can be grouped and counted reliably and accurately. Students can record their estimation and count using words, numbers and pictures.
Counting collections promotes number sense, and is an essential foundation for students to be successful mathematicians. Recent literature (e.g. Boaler, 2008) suggests that flexible grouping practices best supports equitable opportunities for student learning.
It is important to share the mathematical focus with students. This task provides students with opportunities to wonder about how many there are in a collection. Students will use prior mathematical and contextual knowledge to estimate how many, before seeing the collection in its entirety and counting it. The progression in the sophistication of students’ thinking when asked to count a collection of objects goes from counting in ones, to counting in groups.
Consider the mathematical language your students are likely to use when grouping and counting and the language you want to develop. Provide the students with opportunities to work collaboratively, to record and share their thinking and their counts. Student agency is promoted if students have choice over their own counting and recording methods.
Rather than suggesting particular solutions or counting methods to students, teachers can use enabling prompts to support students who require assistance. Extending prompts can be offered when students have completed the task to build more sophisticated strategies and understandings.
- Video: part one (mp4, 35MB)
- Video: part two (mp4, 42MB)
- Images of hand closed and open to show lollies
Part One
This task encourages students to wonder about quantity in an engaging context, and promotes mathematical curiosity and inquiry.
- Show part one of the video.
- Encourage students to estimate and record how many lollies are in the closed hand using numbers, words and pictures.
Considerations when planning for the task introduction include:
What do students understand about relative magnitude of numbers?
What real life pictures do students have to enable them to visualise quantities?
What key mathematical ideas and language do teachers need to clarify with students in order for them to engage with the task?
- While the students are recording their estimations, listen to their mathematical thinking and language.
- If students are struggling to get started enabling prompts can be offered, but only when students have had sufficient time to struggle with the problem.
Examples include:
Do you think there are more or less than the fingers on your hand?
Pretend these counters are the lollies.
- Extending Prompts can be offered if students finish quickly or find the task easy. They encourage higher order thinking and generalisation within the same task.
Examples include:
How else could you record your estimation?
How reasonable do you think your estimation is?
If it is not exactly correct do you think it is likely to be more or less? Why?
Part Two
- Show part two of the video.
- Ask students to record their count and compare this with their estimation.
Where possible allow students to image the collection rather than giving individual students a photo of the lollies. - Possible enabling prompts include:
Use this photo of the collection to help with your recording.
Pretend these counters are the lollies. - Possible extending prompts include:
These lollies cost $1. I wonder how many lollies we might get for …
Do you think we would get exactly the same lollies every time?
What may change? - Record students' thinking.