Number: Time for tea
View Sequence overviewQuantities can be compared to find which has more and which has less.
Number names have a stable order which allows objects to be counted in order.
Whole class
A container of enough assorted tea party items for the whole class (e.g. cups, cutlery, plates, serviettes, forks, spoons)
A number line showing numbers 1-20 on a long paper strip/large paper sheet
Word wall from previous tasks
Number line with sticky notes attached from previous task
Each group
A4 sheet of paper to make a group checklist
Small box of tea party items—include a selection of items for students to refer to as they plan their placemats
Each student
A3 sheet of paper
Task
Review the number line with sticky notes created in the previous lesson.
Revise: Last time, we each drew our own placemat showing what we would need for a class party. We learnt that everyone did not draw the same number of tea party items on a placemat. Some of us had more items than others on our placemat, and some of us had less items than others. We used the number line to stick our numbers on, to show who had the same as others, more than others and who had less than others.
Show students the container of tea party items, and recap what some of the items are.
Discuss how at tea parties, everyone usually has the same items on their placemat. When the items on each placemat match, it's easier to plan and prepare for the tea party!
Ask students to think about:
- what items they will need for their tea party.
- how they can agree about what to have on each placemat.
- how they can check that they have the same number of items on a placemat.
You may want to model or represent some of the students’ suggestions that arise during this discussion, using tea party items, diagrams, and the word wall.
Pose the task: Each group is going to draw placemats so that everyone in your group has the same number of tea party items on their placemat.
Organise students into groups of different sizes (for example, 2, 3, 4, or 5 students), as later in this task, students need a range of numbers to count and compare the number of people and items in different groups.
Provide each group with a small box of tea party items and each student with a sheet of A3 paper to draw their placemat.
In their groups, students decide what tea party items will go on each placemat. Using the decisions made by their group, students select these tea party items from the small box of tea party items. They draw one item (e.g. plate, cup) at a time on their placemat.
Invite students who are finding it hard to get started or who need some ideas to go on a Spy walk, to give them chance to quietly observe their peers’ work and to get back on track.
- How many placemats does your group need? How do you know?
- This connects the act of counting the items with the number of items counted.
- How do you know you have enough placemats?
- This connects matching the number of placemats with the number of students.
- How many items do you have on your placemat? How can you be sure that you have counted them accurately?
- Subitising (recognising small numbers of items at a glance) or counting (using counting principles to keep track of the count) to find how many.
- What do you notice about the numbers on your list? How do you know that you have enough items for everyone?
- This connects the quantity that has been counted with the numbers used to represent this amount.
When the group has finished their placemats, all group members should have the same tea party items on their placemat. Ask students to count the items on their own placemat and compare this number with their group, to check that they all have the same number of items.
Provide each group with a sheet of A4 paper and ask them to write their names at the top of the sheet. This page will be used to make a group checklist of how many of each tea party item they need.
Ask students to count how many of each tea party item they need for their group and write the number and name of each item on their sheet. For example, a group of four students will write four cups. They repeat this for the other items on their placemat: four plates, four serviettes, four spoons etc.
Students who have completed their lists can also count how many tea party items their group has on every placemat altogether.
Consider:
- Do students count with one-to-one correspondence?
- Do students recognise the last number counted is the total in the count (cardinal principle)?
- Do students recognise that the order items are counted in does not affect the total (order irrelevance principle)?
- How do students compare their placemats to check they each have the same number of items? (use subitising or count all)
- Do students recount to check, or do they write a number?
Select a pair of students from each group to share their placemats and checklists during the Connect phase.
Counting and quantifying
Counting may seem simple to us as teachers, but it actually involves two distinct yet connected skills (Van de Walle, Karp, & Bay-Williams, 2013):
- Reciting the standard sequence of counting words in the correct order.
- Matching each counting word to one object in a set so that every item is counted once and only once.
The ability to connect the act of counting objects with the total number of items in a collection forms the essential foundation for all later mathematical learning (Clements & Sarama, 2007).
Research highlights how important our role is in this process. Children need “...repeated, often massive, experience and demonstrations, modelling, or scaffolding from adults in learning counting competencies” (Clements & Sarama, 2007, p. 476).
Throughout this task sequence, students are given many opportunities to hear, use, and apply number words in meaningful contexts where numbers represent real quantities. For example, when students count the items for a tea party, one by one, and we explain that the last number they say shows the total number of items, they begin to understand that numbers tell us how many there are.
References
Clements, D. H., & Sarama, J. (2007). Early childhood mathematics learning. Second handbook of research on mathematics teaching and learning, 1, 461-555
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson.
Counting may seem simple to us as teachers, but it actually involves two distinct yet connected skills (Van de Walle, Karp, & Bay-Williams, 2013):
- Reciting the standard sequence of counting words in the correct order.
- Matching each counting word to one object in a set so that every item is counted once and only once.
The ability to connect the act of counting objects with the total number of items in a collection forms the essential foundation for all later mathematical learning (Clements & Sarama, 2007).
Research highlights how important our role is in this process. Children need “...repeated, often massive, experience and demonstrations, modelling, or scaffolding from adults in learning counting competencies” (Clements & Sarama, 2007, p. 476).
Throughout this task sequence, students are given many opportunities to hear, use, and apply number words in meaningful contexts where numbers represent real quantities. For example, when students count the items for a tea party, one by one, and we explain that the last number they say shows the total number of items, they begin to understand that numbers tell us how many there are.
References
Clements, D. H., & Sarama, J. (2007). Early childhood mathematics learning. Second handbook of research on mathematics teaching and learning, 1, 461-555
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson.
Spy walk
A spy walk is used here so that if students or the group are struggling for ideas, they can take the opportunity to notice how other students are planning their group placemats or their group list that could spark new thinking.
To make the walk purposeful, prompt students to notice:
- What do you notice about the number of students and the number of placemats on the table?
- How many of each item are on the table?
- Is the number of each item the same as the number of students in the group? Why do you think that is?
Such guidance supports deeper noticing and helps students to bring back specific insights and learn from the collective thinking of the class. When they return to their work, they do so with fresh insights and the chance to revise, extend, or refine their responses.
A spy walk is used here so that if students or the group are struggling for ideas, they can take the opportunity to notice how other students are planning their group placemats or their group list that could spark new thinking.
To make the walk purposeful, prompt students to notice:
- What do you notice about the number of students and the number of placemats on the table?
- How many of each item are on the table?
- Is the number of each item the same as the number of students in the group? Why do you think that is?
Such guidance supports deeper noticing and helps students to bring back specific insights and learn from the collective thinking of the class. When they return to their work, they do so with fresh insights and the chance to revise, extend, or refine their responses.
The purpose of this Connect phase is for students to:
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Display a number line showing numbers 1-20.
Invite a student from each group to share and discuss their group list, focusing on:
- the number of students in their group.
- the number of placemats.
- what items are on their placemats.
- how many of each item the group needs.
Ask:
- What do you notice about the numbers in each group?
- Why do you think this has happened?
- Which number is more than/less than the number of items in your group?
- Do any groups have the same number of items?
Ask the student to show where this number fits on the number line, either using a sticky note or by circling where it goes on the number line.
Prompt students to pay attention to where their group number is on the number line and to notice where it sits in relation to other group numbers. This is to anchor their discussion and reasoning about ‘more than, same as or less than’.
Ask why the groups need different numbers of tea party items compared to other groups (as there are different numbers of students in the groups).
Guide students to connect the number of students in a group with the number of each item in a group, in order to help them connect the number they marked on the number line with the number of students, the number of cups, plates etc.
Here, there is an assumption that each student will choose to have one of each item on their placemats.
If students have included two plates each, two cups etc., you need to discuss how there will be a larger number of items on the placemats for this group than for groups who have included one of each item.
Pragmatically, if some groups of students have more than one of each item on their placemats, there might not be enough tea party items for every student.
Discuss how students counted themselves and made sure they each had the same items on their placemats. When they counted the number of each item on their placemat, they found it was the same as the number of students in their group.
Explain: We can count to find how many students are in a group. We can compare the number of students in a group with the number of each tea party item on their placemat. A group with four students needs four of each item but a group with three students needs three of each item. The number of each item needs to match how many students there are.
Keep the number line with the sticky notes as it is, to refer to during the next task.