Foundations of Mathematical Thinking · Senior Infants · Counting and Number Sense · Autumn Term

Sharing and Grouping

Multiplying and dividing fractions, including mixed numbers and understanding reciprocals.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.7

About This Topic

Sharing and Grouping introduces Senior Infant children to early division ideas through hands-on partitioning of concrete objects. They explore key questions like dividing 8 buttons into groups of 2, forming groups of 3 from 9 counters, or sharing stickers equally among friends. With manipulatives such as counters, buttons, and blocks, children see division as repeated subtraction or fair distribution, building confidence with whole numbers before formal operations.

This topic anchors the NCCA Counting and Number Sense unit in the Autumn Term, linking number partitioning to real-life fairness and cooperation. Children develop vocabulary like 'groups of' and 'share equally', while practicing one-to-one correspondence and counting accuracy. These experiences strengthen subitising skills and prepare for multiplication as inverse grouping.

Active learning suits this topic perfectly because physical manipulation of objects makes partitioning visible and interactive. Children collaborate to test different groupings, discuss fair shares, and adjust strategies through trial and error, which deepens understanding and reduces anxiety around division.

Key Questions

1. Can you put these 8 buttons into groups of 2?
2. How many groups of 3 can you make with 9 counters?
3. Share these stickers equally , does everyone get the same?

Learning Objectives

• Demonstrate the process of sharing a set of objects into equal groups.
• Identify the number of equal groups that can be formed from a given quantity.
• Compare the outcomes of sharing the same quantity among different numbers of recipients.
• Classify arrangements of objects as either equal sharing or equal grouping.

Before You Start

Counting and Cardinality

Why: Children need to be able to accurately count a set of objects before they can partition or group them.

One-to-One Correspondence

Why: The ability to match one object to one person or one group is essential for sharing and grouping activities.

Key Vocabulary

Share equally	To divide a collection of items so that each person or group receives the same amount. This is a key concept in division.
Groups of	To arrange items into sets where each set contains the same number of items. This relates to multiplication and division.
Fair share	Ensuring that when items are divided, everyone receives an equal portion, promoting fairness and understanding of equal distribution.
Partition	To divide a whole into smaller, equal parts or groups. This is the foundational action for understanding division.

Watch Out for These Misconceptions

Common Misconception

Sharing only works if items divide evenly with no remainder.

What to Teach Instead

Children often think leftovers mean failure; hands-on trials with remainders, like 7 cookies for 2 friends, show options like one extra or smaller shares. Group discussions reveal flexible fair strategies, building resilience.

Common Misconception

Groups must always look the same size visually, ignoring count.

What to Teach Instead

Young learners confuse visual space with quantity; using identical containers for grouping counters clarifies equal numbers fit regardless of appearance. Peer checking in pairs corrects this through recounting together.

Common Misconception

Sharing means round-robin distribution one by one only.

What to Teach Instead

Some stick to sequential giving; station activities encourage grouping first, like bundles of 3, showing efficiency. Collaborative rotations expose multiple methods, helping children choose based on context.

Active Learning Ideas

Stations Rotation: Grouping Stations

Prepare four stations with objects like buttons, counters, sticks, and beads. At each, children form specified groups, such as groups of 2 from 8 items, and draw or record results. Groups rotate every 7 minutes and share findings with the class.

40 min·Small Groups

Snack Sharing Pairs

Give pairs 12 pretend snacks like raisins or cubes. They share equally between two people, then try sharing among three by partitioning first. Pairs explain their method to another pair nearby.

20 min·Pairs

Hoop Grouping Challenge

Lay hoops on the floor outdoors or in the hall. Scatter counters inside a large area; small groups collect a set number, like 10, and sort into hoops for equal groups of 2 or 5. Record with photos or drawings.

30 min·Small Groups

Storytime Sharing Circle

Read a sharing story, then pass around objects like 9 teddies. Whole class decides how to share into groups of 3, acting it out and counting aloud together.

25 min·Whole Class

Real-World Connections

• When packing lunches for a class trip, a teacher needs to divide snacks equally among 24 children. They might put 3 cookies in each bag, creating 8 bags.
• A baker decorating cupcakes for a party must ensure each guest receives the same number of sprinkles. They might decide to put 5 cupcakes in each box, grouping the total cupcakes made.

Assessment Ideas

Quick Check

Provide each child with 10 counters. Ask: 'Can you put these into groups of 2? How many groups did you make?' Observe their ability to form equal groups and count them.

Exit Ticket

Give each child a card with a picture of 6 apples. Ask them to draw lines to share these apples equally between 3 teddy bears. Then ask: 'How many apples does each teddy bear get?'

Discussion Prompt

Present a scenario: 'I have 12 stickers to share with my friends. If I share them with 2 friends, how many does each get? What if I share them with 3 friends?' Facilitate a discussion comparing the results and using vocabulary like 'share equally' and 'groups of'.

Frequently Asked Questions

How to teach sharing and grouping to Senior Infants?

Start with concrete manipulatives like buttons and counters for partitioning into equal groups or shares. Pose key questions daily, such as 'How many groups of 2 from 8?', and model language like 'each gets'. Progress to drawings for recording, ensuring every child handles materials to build number sense intuitively.

What manipulatives best support sharing and grouping activities?

Counters, buttons, beads, and blocks work well because they are easy to grasp and count. Use everyday items like sticks or snacks for relevance. Provide trays or hoops to contain sets, preventing loss, and vary sizes to practice subitising small groups up to 10.

How can active learning help students understand sharing and grouping?

Active learning engages children physically with objects, making division concrete rather than abstract. Collaborative grouping in pairs or small groups sparks talk about strategies, like 'I made 4 groups of 2', correcting errors on the spot. Rotations and real-world sharing, such as snacks, link maths to fairness, boosting retention and enthusiasm over worksheets.

How to address remainders in early sharing lessons?

Introduce remainders gently with sets like 10 items for 3 friends. Let children explore outcomes, discussing 'What if one gets extra?' or reforming groups. Use stories of real sharing to normalise, emphasising problem-solving over perfect division, which prepares for later maths.