Number: Time for tea
View Sequence overviewItems can be sorted and classified according to similarities and differences between them.
To keep track of the count, each item must be counted only once.
The last number counted represents how many in the whole count.
Whole class
A container of enough assorted tea party items for the whole class (e.g. cups, cutlery, plates, serviettes, forks, spoons)
Large sheet of paper or cards for recording vocabulary for word wall
Each group
Small container for sharing out the assorted tea party items from the big container
Sticky notes
Task
Introduce the container of tea party items to sort and classify (for example: cups, plates, spoons, serviettes...).
Set the scene: I found this box in our classroom cupboard, and it has lots of different things in it. What do you think these are and when would we use them?
Pick out one item at a time and ask students for suggestions of what it is.
After you have viewed a number (eight or so) of the tea party items, ask students to predict how many items might be in the box. Write suggested numbers on the board and ask students why they predicted this number. Use language of lots, many, quite a large number, enough, more than one and familiar number names to describe the quantity within.
Discuss: There are too many things for me to sort this box on my own so I need your help! We are going to work in groups to sort all the items in the box so that we can see what is there and what we might use some of these things for.
Invite students to suggest how they could sort the different items you have already taken from the box. For example, they may suggest by colour, by what they are made from or by what they are, etc.
As students provide suggestions for categories, record these to start developing a ‘word wall’. Words will be added throughout the sequence to build the students’ vocabulary.
Model how to sort the items into categories, using the items you have already shown students from the box. For example group the cups together, group the plates together, etc. When you have sorted these items, model counting the number of items in each category and recording these numbers on sticky notes.
Pose the task: You are now going to sort the items in the box into categories and count how many are in each category. You will put the number on a sticky note next to each group of items you have sorted.
Mathematical vocabulary
In Foundation, it is important to introduce vocabulary informally through meaningful, realistic everyday experiences. By exploring mathematical ideas in concrete ways students develop concrete thinking, and language enables them to express and share these experiences.
Through the context of sorting a box of items, students encounter both mathematical and non-mathematical vocabulary. The context of finding a box of ‘stuff’ provides a realistic context for sorting and counting these items. Using the vocabulary (such as cup, plate, serviette, spoon) enables students to talk about what they are sorting and counting.
Students may already be familiar with the number names, through reciting the number sequence and counting, but may not understand the connections between the different ways a number may be represented as a collection of items, a numeral or number word. They need extensive experiences exploring and enacting these ideas in tandem with using the vocabulary. The context of this sequence provides multiple opportunities for students to enact and experience counting items while growing non-mathematical and mathematical vocabulary naturally through class discourse orchestrated by the teacher.
Specialised mathematical vocabulary, such as lots, many, enough, more than, less than, the same, similar, different is only meaningful when students are able to connect these words with concrete experiences which embody these concepts. Therefore, providing students with tangible physical experiences (such as sorting and counting items) and using mathematical language as they do this, supports students to form connections between these experiences and the mathematical ideas, to communicate their understanding.
Vocabulary for this task:
- Number names: one, two, three...
- Quantities: lots of, many, enough, more/less than, same as, similar, different...
- Tea party words: cutlery (fork, spoon, knife), placemat, cup, napkin...
In Foundation, it is important to introduce vocabulary informally through meaningful, realistic everyday experiences. By exploring mathematical ideas in concrete ways students develop concrete thinking, and language enables them to express and share these experiences.
Through the context of sorting a box of items, students encounter both mathematical and non-mathematical vocabulary. The context of finding a box of ‘stuff’ provides a realistic context for sorting and counting these items. Using the vocabulary (such as cup, plate, serviette, spoon) enables students to talk about what they are sorting and counting.
Students may already be familiar with the number names, through reciting the number sequence and counting, but may not understand the connections between the different ways a number may be represented as a collection of items, a numeral or number word. They need extensive experiences exploring and enacting these ideas in tandem with using the vocabulary. The context of this sequence provides multiple opportunities for students to enact and experience counting items while growing non-mathematical and mathematical vocabulary naturally through class discourse orchestrated by the teacher.
Specialised mathematical vocabulary, such as lots, many, enough, more than, less than, the same, similar, different is only meaningful when students are able to connect these words with concrete experiences which embody these concepts. Therefore, providing students with tangible physical experiences (such as sorting and counting items) and using mathematical language as they do this, supports students to form connections between these experiences and the mathematical ideas, to communicate their understanding.
Vocabulary for this task:
- Number names: one, two, three...
- Quantities: lots of, many, enough, more/less than, same as, similar, different...
- Tea party words: cutlery (fork, spoon, knife), placemat, cup, napkin...
Share out the container of tea party items into smaller boxes. Organise students into groups of 4-6 and provide each group with a box of items and sticky notes.
Allow students some time to sort their items in their group. Encourage them to notice similarities and differences between items, which help them decide how to sort into different categories. Students should then count how many items are in each category, record the number on a sticky note, and put the sticky note next to the items.
- What did you notice that was similar/different about the items that helped you sort them into categories?
- Here encourage students to notice that there are cups, plates, serviettes etc.
- How many do you have in each category? How do you know?
- How did you make sure you kept track as you counted?
- How can you record how many on the sticky note?
- How do students sort items into categories? Do they sort them based on item type (plate, cup etc.), or do they sort based on colour, size, material?
- Do students arrange the items in a way that makes them easy to see and count?
- Do students demonstrate one-to-one correspondence as they count the items? For example, do they use their fingers to touch or keep track as they count “1, 2, 3 cups”?
- Do students recognise that the arrangement of objects does not affect how many there are (order irrelevance principle) when you ask them to recount the objects in another way?
- Do students restate the last number counted as the number of items in the whole collection (cardinal principle)?
- Do students record the whole count as a numeral, tallies etc.?
Spotlight: Highlight examples of sorting where items are clearly sorted based on item categories, drawing attention to what the items in a category have in common (for example, they are cups, plates, spoons etc.). Consider how many are in each category, noting:
- Are the items in each category arranged so that they are clear to see and easy to count?
- Do the sticky note labels show the correct number of items counted?
- Is vocabulary from the word wall used to label a category?
Ask:
- What categories do you notice the items have been sorted into? Did you choose similar/different categories to sort your items?
- How have the items been arranged so they are easy to count? How did you organise your items to count them?
Encourage students to notice how the spotlighted items are arranged to make them easy to see, are labelled with words and/or numbers etc.
Allow students time to refine and make changes to how they have arranged and labelled their items, if they choose.
Select student groups who sorted and arranged their tea party items clearly into categories based on the item type (cup, plate etc.) to share their thinking during the Connect phase.
Spotlight
A spotlight is used here to pause student activity and highlight examples of students sorting their items into defined categories according to similarities/differences they notice. This is an opportunity for the teacher to use examples of student work to scaffold the class’s thinking, without directly telling them what they should be doing. The teacher prompts students to compare the examples with their own work and to refine their categorising and counting, by drawing attention to students’ work which:
- is clearly arranged.
- is easy to see categories and how many in each.
- includes how many in each category as numbers on sticky notes.
Following the Spotlight, students are allowed time to refine their own work, if they choose, to include some useful ideas from the examples of student work they have been shown.
A spotlight is used here to pause student activity and highlight examples of students sorting their items into defined categories according to similarities/differences they notice. This is an opportunity for the teacher to use examples of student work to scaffold the class’s thinking, without directly telling them what they should be doing. The teacher prompts students to compare the examples with their own work and to refine their categorising and counting, by drawing attention to students’ work which:
- is clearly arranged.
- is easy to see categories and how many in each.
- includes how many in each category as numbers on sticky notes.
Following the Spotlight, students are allowed time to refine their own work, if they choose, to include some useful ideas from the examples of student work they have been shown.
Counting principles
Early experiences with number, such as classifying, sorting, grouping, and ordering, provide the foundations for being able to quantify number, as well as underpinning students’ capacity to subitise and count. Counting requires connecting number names, numerals and quantities, and being able to trust the count.
There are five principles of counting which are fundamental to students being able to do this:
- One-to-one principle: Each item should be counted and named only once.
- Stable order principle: Number names are said in a conventional order.
- Cardinality principle: The final number said represents the number of items in the whole collection, as long as they are only counted once and in the conventional order.
The first three principles may be referred to as the How to count principles.
- Abstraction principle: Anything can be counted: physical items such as counters, people, toys, and non-physical items such as jumps, claps, seconds.
- Order irrelevance principle: As long as each item is counted only once, items may be counted in any order, from any starting place.
The last two principles may be referred to as the What to count principles.
The context of this task provides meaningful opportunities for students to count quantities (to ten initially) connecting number names, numerals and quantities, including zero. Repeated opportunities to count and check sets of items enables students to practice keeping track of the count, as well as to explain their reasoning. Throughout the tasks, there are opportunities for teachers to observe students applying principles of counting.
References
Gelman, R. & Gallistel, C. (1978) The Child's Understanding of Number. Cambridge, MA. Harvard University Press.
Early experiences with number, such as classifying, sorting, grouping, and ordering, provide the foundations for being able to quantify number, as well as underpinning students’ capacity to subitise and count. Counting requires connecting number names, numerals and quantities, and being able to trust the count.
There are five principles of counting which are fundamental to students being able to do this:
- One-to-one principle: Each item should be counted and named only once.
- Stable order principle: Number names are said in a conventional order.
- Cardinality principle: The final number said represents the number of items in the whole collection, as long as they are only counted once and in the conventional order.
The first three principles may be referred to as the How to count principles.
- Abstraction principle: Anything can be counted: physical items such as counters, people, toys, and non-physical items such as jumps, claps, seconds.
- Order irrelevance principle: As long as each item is counted only once, items may be counted in any order, from any starting place.
The last two principles may be referred to as the What to count principles.
The context of this task provides meaningful opportunities for students to count quantities (to ten initially) connecting number names, numerals and quantities, including zero. Repeated opportunities to count and check sets of items enables students to practice keeping track of the count, as well as to explain their reasoning. Throughout the tasks, there are opportunities for teachers to observe students applying principles of counting.
References
Gelman, R. & Gallistel, C. (1978) The Child's Understanding of Number. Cambridge, MA. Harvard University Press.
The purpose of this Connect phase is for students:
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Invite selected students to describe and explain why they organised the tea party items into the categories they chose, and ask them to model how they counted the tea party items in each category. Focus on strategies students used to count accurately.
Ask these students:
- How did you keep track of your count? (relates to one-to-one correspondence)
- Discuss strategies students used to keep track of their count, e.g. using their finger, touching each item as they count.
- Did the number of items change when you counted in a different way? (relates to the principle of order irrelevance)
- Students should recognise that it does not matter the order you count the items, the number is always the same.
- How did you know how many items you had? (relates to the cardinal principle)
- Students should recognise the last number counted indicates the total number in a collection and this is the number written to show how many.
Discuss whether others in the class used similar strategies or if they did something different. Invite students to share the name of the categories they sorted the items into.
Discuss how the box was full of items that are all used at the table for meals, and were sorted into categories of cups, plates etc. Review how students used counting to find how many were in each category.
Explain: It is important to keep track when we count to make sure that we only count each item once. We can touch each item as we count it or hold up our fingers to help us keep track. It does not matter where we start counting from as long as we only count each item once. The last item we count tells us how many we have altogether, and we can record this as a number.