A collection of ones can be grouped together to form a unit.
Whole class
reSolve Garden PowerPoint
Each group
A large quantity of items to represent ‘seeds’ (for example: counters or dried beans)
Each student
At least one ‘seed packet’ (for example: snap lock bags, brown paper bags, or envelopes). Each packet should be labelled with a different number between 25 and 99.
How many seeds? Student sheet
Task
Using the reSolve Garden PowerPoint, establish the context of the reSolve Garden:
Mr Sprout the gardener is organising all his seeds. He is putting the seeds into packets. Each packet has a number of seeds clearly written on the front. Mr Sprout needs to make sure that he puts exactly the right number of seeds in each packet. Mr Sprout needs our help!
Provide each student with loose seeds (e.g. counters or dried beans) and a seed packet (e.g. snap lock bags, brown paper bags, or envelopes) with a 2-digit number clearly written on the front. Explain that the number written on each packet represents the number of seeds that need to be placed into that packet.
Pose the task: Count out the correct number of seeds to put into your seed packet.
Differentiation
Differentiate this task by carefully choosing the number of seeds that each student is asked to count. For example:
- students who are still building their counting skills might be given a seed packet with a smaller two-digit number
- those who are more fluent counters can be given a seed packet with a larger two-digit number.
Differentiating the task in this way gives all students the opportunity to engage in the main mathematical activity of the task, and communicates that everyone has an important part to play in building the collective learning of the class.
Differentiate this task by carefully choosing the number of seeds that each student is asked to count. For example:
- students who are still building their counting skills might be given a seed packet with a smaller two-digit number
- those who are more fluent counters can be given a seed packet with a larger two-digit number.
Differentiating the task in this way gives all students the opportunity to engage in the main mathematical activity of the task, and communicates that everyone has an important part to play in building the collective learning of the class.
Ask students to count out their seeds, ready to pack into their seed packet. They can organise and count in any way they choose.
Use a Fishbowl to look at some of the different ways students are organising their counts. Encourage those watching to notice how students use grouping to ensure that they have the correct number of seeds.
Following the Fishbowl activity, allow students additional time to reorganise and recount their seeds based on what they have learnt from others if they choose.
Provide students with How many seeds? Student sheet and ask them to create a diagram of how they organised and counted their seeds.
Ask students: Do you have the right number of seeds to go into your seed packet? How do you know?
No organisation – Students who do not organise their count may find it hard to keep track of their count and may miss some seeds or double count others. Prompt students to think about how they might arrange the seeds to make counting easier.
Using ones – Lining up seeds facilitates counting in ones. Do these students keep track of their count, and are they saying numbers in the correct sequence? Prompt students to think about how they might arrange the seeds to make counting easier.
Creating groups – Students may organise their seeds into small groups such as twos, fives, and tens.
- Does each group contain the same number of seeds? Prompt students’ inquiry by asking them to think about how they might arrange their groups to ensure each group has the same number of seeds.
- Do students skip count their groups to find the total number of seeds, or do they determine the total by counting in ones instead of utilising the group structure? Prompt students’ inquiry by asking them to think about how the group structure can support efficient counting.
Organised groups – Organising each group of seeds makes it easy to see the number of seeds in each group. For example, students might arrange their seeds using subitisable patterns. Once students have counted the total number of seeds to go into their packet, there may be some seeds that do not form a complete group. Prompt students' inquiry by asking them to think about how they might deal with these seeds.
Coming soon: Key mathematical ideas
Students are asked to record their count in any way that they choose. Look at how these students have represented their work.
Discuss with colleagues: What do these students know and what have they shown that they can do? Give evidence from the work samples for your statements.
Students are asked to record their count in any way that they choose. Look at how these students have represented their work.
Discuss with colleagues: What do these students know and what have they shown that they can do? Give evidence from the work samples for your statements.
Fishbowl
We have used a Fishbowl at this point in the Explore phase so that students can see and learn from how other students in the class are organising and counting their collections.
Invite students to form a class Fishbowl around a variety of different counting strategies—some complex, some more simple. This communicates to students that all strategies are valued and that there is opportunity to learn from everyone in the class.
We have used a Fishbowl at this point in the Explore phase so that students can see and learn from how other students in the class are organising and counting their collections.
Invite students to form a class Fishbowl around a variety of different counting strategies—some complex, some more simple. This communicates to students that all strategies are valued and that there is opportunity to learn from everyone in the class.
Select some students who changed their counting strategy after the Fishbowl activity, and invite them to share their working with the class. Specifically focus on those who changed from counting in ones or using different-sized groups to using equal-sized groups.
Ask these students: What was the first strategy that you used? What was the second strategy that you used? Why did you choose to change your counting strategy after looking at what others were doing?
After selected students have shared, ask students to return to their seeds and to count the seeds using one or two of the different grouping strategies that were shared.
Discuss as a class: Which strategy did you find most useful for counting out the right number of seeds to put into your seed packet? Why?
Discuss how it is easier to count seeds that are organised into units of equal-sized groups.
Connect phase
Focus this Connect phase on the idea that a quantity can be organised into equal-sized groups. Making equal-sized groups of two or five means that it is easy to skip count the total. This idea is extended in the next task to making equal-sized groups of ten.
Focus this Connect phase on the idea that a quantity can be organised into equal-sized groups. Making equal-sized groups of two or five means that it is easy to skip count the total. This idea is extended in the next task to making equal-sized groups of ten.
Learning together
A class is a community of learners who are working together to build shared mathematical understandings. We learn from each other as we listen to and make sense of how others solve problems. This idea of a community learning together is reinforced in two ways through this Connect phase:
- Asking those who changed their strategies after the Fishbowl to share their working and the reason that they changed their strategy; and
- Providing additional time for students explore some of the different strategies shared in the Connect phase and then asking students to reflect on which strategy they found most helpful.
A class is a community of learners who are working together to build shared mathematical understandings. We learn from each other as we listen to and make sense of how others solve problems. This idea of a community learning together is reinforced in two ways through this Connect phase:
- Asking those who changed their strategies after the Fishbowl to share their working and the reason that they changed their strategy; and
- Providing additional time for students explore some of the different strategies shared in the Connect phase and then asking students to reflect on which strategy they found most helpful.