A collection of ones can be grouped together to form a unit.
Whole class
Lolly Shop PowerPoint
Each group
A large quantity of Unifix or interlocking cubes (ideally 2cm). Each group of 2-3 students needs at least 120 cubes.
Each student
Packing lollies Student sheet
Task
Use Lolly Shop PowerPoint to establish the context of Ms Fizz and her Lolly Shop:
Ms Fizz owns a very popular lolly shop. She sells lots of different lollies. Sometimes there are so many lollies in her shop it is hard to keep track of them all.
Ms Fizz needs to organise her lollies to make it easier to work out how many there are altogether. She needs our help!
Explain to the students that they will be provided with interlocking cubes representing the lollies in Ms Fizz's shop.
Pose the task: Organise your lollies so that it is easy to work out how many there are. How many lollies do you have altogether?
Provide groups of 2-3 students with a large quantity of Unifix or interlocking cubes (at least 120 cubes). Allow students time to organise and count their collection of lollies in any way they choose.
Provide students with Packing lollies Student sheet and ask them to create a diagram of how they organised and counted their collection.
Ask students: Can you explain how you’ve organised your lollies? How does this strategy help you work out how many lollies you have?
- Not equal sized groups or using ones – Students may recognise that groups are helpful but use groups that are not equal in size. These students will likely count the total in ones. Prompt students to think about how they might make counting easier using groups.
- Creating equal-sized groups – Students may stack the cubes in small groups, such as twos or fives.
- Do students count the cubes, or do they use measurement to ensure that the same number of cubes are in each stack? The more cubes that are in a stack the more likely it is that students measure using direct comparison. Ask students why measuring is helpful in this context.
- Do the students skip count the groups to find the total, or do they determine the total by counting in ones (not utilising the group structure)? Prompt students’ inquiry by asking them to think about how the group structure can support efficient counting.
- Groups of 10 – Students may group in tens. Ask students to consider whether tens are the most helpful way to group. Are tens more or less helpful than twos or fives? Why?
Work samples
Students can record their count in any way that they choose. Look at how these students have chosen to record their work.
Discuss with colleagues: What is it that these students have shown that they can do? Give evidence from the work samples for your statements.
Students can record their count in any way that they choose. Look at how these students have chosen to record their work.
Discuss with colleagues: What is it that these students have shown that they can do? Give evidence from the work samples for your statements.
Differentation
Differentiate this task by carefully choosing the number of lollies (cubes) that students are asked to count. For example, students who are still building their counting skills might be given a smaller collection of cubes, and those who are more fluent counters can be given a larger collection.
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 lollies (cubes) that students are asked to count. For example, students who are still building their counting skills might be given a smaller collection of cubes, and those who are more fluent counters can be given a larger collection.
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 display their student sheet next to their cubes in preparation for a gallery walk.
Review the task that was posed and ask students to think about what they expect to see as they complete the gallery walk. Ask students to consider the following questions as they look at others’ work:
- What do you notice that is the same? What do you notice that is different?
- How many lollies are in each collection? Which strategy/strategies do you find most helpful for working out the total in the collection? Why?
Conduct the class gallery walk.
At the end of the class gallery walk, allow students time to read and reflect on any post-it notes left on their work. They may rearrange their cubes if they would like to. Ask students to record any changes they make on their student sheet.
Looking at the work of others
In a gallery walk the role of the students is to critically view and review others’ mathematical activity. They need to think more broadly than the strategy they have personally used, as they consider how their thinking fits with the representations of thinking used by others in the class.
In this gallery walk, students are asked to consider how strategies are similar and different, and also which strategy/strategies are the most helpful when determining the total. It is likely that most students have used groups to organise the count. We want students to recognise that when using equal-sized groups, some group sizes are more helpful than others.
In a gallery walk the role of the students is to critically view and review others’ mathematical activity. They need to think more broadly than the strategy they have personally used, as they consider how their thinking fits with the representations of thinking used by others in the class.
In this gallery walk, students are asked to consider how strategies are similar and different, and also which strategy/strategies are the most helpful when determining the total. It is likely that most students have used groups to organise the count. We want students to recognise that when using equal-sized groups, some group sizes are more helpful than others.
Gallery walk
In a gallery walk, students move around the classroom like they are in an art gallery, in silence or whispering with a partner. Students use post-it notes to post comments and questions about the mathematics they see. They should be encouraged to take their time to respectfully read and respond to the work of others.
In a gallery walk, students move around the classroom like they are in an art gallery, in silence or whispering with a partner. Students use post-it notes to post comments and questions about the mathematics they see. They should be encouraged to take their time to respectfully read and respond to the work of others.
Ask students to reflect on the gallery walk and the different strategies they saw.
Discuss:
- What do you notice that is the same? What do you notice that is different?
- Similarity may be evident in the use of equal-sized groups. Difference may be seen in the size of these groups. There will also be difference in the number of groups that were made and the total in each collection.
- How many lollies are in each collection? Which strategy/strategies do you find most helpful for working out the total in the collection? Why?
- Equal-sized groups can be used as a counting unit. This is an efficient way to count large collections.
- Do you have any advice for Ms Fizz on how she might organise her lollies?
- Some ways of counting are easier than others. For example, it is easier to count a large quantity by fives rather than by threes. The power of ten may emerge in this discussion.
Connect phase
This Connect discussion focuses on the idea that a collection of ones can be grouped together to form a unit. The use of multiple equal-sized groups, or units, allows for a large quantity of items to be skip counted.
It is important to note that the size of the unit impacts the ease and efficiency of skip counting. When working with large quantities, twos will be easier than threes for most students, and fives will be easier again as there are less groups to count. Tens are easier still. Grouping in tens also mirrors the place value structure of our number system, which is the focus of the next task.
This Connect discussion focuses on the idea that a collection of ones can be grouped together to form a unit. The use of multiple equal-sized groups, or units, allows for a large quantity of items to be skip counted.
It is important to note that the size of the unit impacts the ease and efficiency of skip counting. When working with large quantities, twos will be easier than threes for most students, and fives will be easier again as there are less groups to count. Tens are easier still. Grouping in tens also mirrors the place value structure of our number system, which is the focus of the next task.