Organising a quantity of items helps us to count accurately.
Some ways of arranging a collection make it easy for us to see how many items there are in the collection, without needing to count every item.
Each group
A large quantity of small items which students can take a handful of (for example: counters, pasta, dried beans). A student handful should be around 10 to 20 items.
Each student
How big is a handful? Student sheet
Task
Introduce the idea of a ‘handful’ to the students. For example:
I had a handful of blueberries for morning tea today. I wondered afterwards: how many blueberries might have been in my handful? How big is a handful?
Present students with a large quantity of small items (e.g. counters, pasta, dried beans). Ask students to take a handful of items each.
Pose the question: How many items do you think might be in your handful? Encourage reasonable estimates, not the ‘right answer’.
Pose the task: Carefully count the items in your handful. Organise your collection in a way that makes it easy to see how many items you have.
Allow students time to count and organise their collection.
Once students have organised their collection, ask them to show their handful to someone else and compare the ways they have arranged their collections. Prompt them to consider: Which arrangement makes it easier to work out the total number of items in your collection? Why?
After comparing, students may rearrange their handful if they would like to.
Ask students to use How big is a handful? Student sheet to record the final way they arranged their handful and how many items were in their handful altogether.
Work samples
Look at how these students have arranged their handfuls.
Discuss with colleagues: What do these students know and what have they shown that they can do? Give evidence from the pictures for your statements.
Look at how these students have arranged their handfuls.
Discuss with colleagues: What do these students know and what have they shown that they can do? Give evidence from the pictures for your statements.
Ask students to display their student sheet next to their handfuls in preparation for a gallery walk.
Review the original task (Organise your handful in a way that makes it easy to see how many items you have) 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: Which arrangements make it easy to see how many are in a handful? Why?
Conduct the class gallery walk.
Gallery walk
In a gallery walk, students display their mathematical work as posters on the wall or as physical displays on tables or the floor. Everyone then moves around the classroom like they are in an art gallery, in silence or whispering with a partner. Tell students to take their time to look at and make sense of other students’ solutions.
As students move around the classroom, they can stick post-it notes next to other students’ work to give feedback or to ask questions about the mathematics they see. In Foundation, students might leave a post-it note with a tick or smiley face along with their name or initials to indicate they really like a strategy. They might leave a question mark with their name or initials to communicate they have a question to ask. Make sure you allow time at the end of the gallery walk for students to look at their post-it notes and to ask any questions they may have. It is also good to provide students with the time to add to or adjust their work based on what they have seen.
We have used a gallery walk at this point in the task so students can see different arrangements that have been used, and to reflect on which arrangements make it easy to see how many are in the different handfuls. This focus draws students back to the learning goal for this task: some ways of arranging handfuls make it easy to see how many there without needing to count.
In a gallery walk, students display their mathematical work as posters on the wall or as physical displays on tables or the floor. Everyone then moves around the classroom like they are in an art gallery, in silence or whispering with a partner. Tell students to take their time to look at and make sense of other students’ solutions.
As students move around the classroom, they can stick post-it notes next to other students’ work to give feedback or to ask questions about the mathematics they see. In Foundation, students might leave a post-it note with a tick or smiley face along with their name or initials to indicate they really like a strategy. They might leave a question mark with their name or initials to communicate they have a question to ask. Make sure you allow time at the end of the gallery walk for students to look at their post-it notes and to ask any questions they may have. It is also good to provide students with the time to add to or adjust their work based on what they have seen.
We have used a gallery walk at this point in the task so students can see different arrangements that have been used, and to reflect on which arrangements make it easy to see how many are in the different handfuls. This focus draws students back to the learning goal for this task: some ways of arranging handfuls make it easy to see how many there without needing to count.
Discuss: Which arrangements made it easy to see how many are in a handful? Why?
- Students might think about patterns that made numbers easy to count. For example, subitising patterns such as those on dice.
- Some students may use groups of 10 when there are more than 10 objects.
Ask the students to return to their own collections and rearrange their items a final time, using the strategies they have seen to make their collections easier to count.
Again, ask students to show their arrangements to someone else and compare the different ways they have arranged their collections.
Connect Phase
Focus this Connect discussion on which arrangements made it easy to see how many there were. You might make comparisons to familiar objects that are designed for easy counting or recognisable collections; for example, playing cards, dominoes, or dice. Also look at those arrangements that are not easy to quantify quickly. As a class, consider how these handfuls might be rearranged so that it is easy to see how many there are without needing to count.
Focus this Connect discussion on which arrangements made it easy to see how many there were. You might make comparisons to familiar objects that are designed for easy counting or recognisable collections; for example, playing cards, dominoes, or dice. Also look at those arrangements that are not easy to quantify quickly. As a class, consider how these handfuls might be rearranged so that it is easy to see how many there are without needing to count.