Foundations of Mathematical Thinking · Senior Infants

Active learning ideas

Joining and Combining Groups

Active learning works for joining and combining groups because young children develop number sense through physical movement and manipulation of objects. Concrete experiences with sets of counters, blocks, or fingers help children internalize the concept of addition as combining rather than abstract symbols. This hands-on approach makes the abstract process of addition tangible and meaningful for Senior Infants.

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

• 15–25 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 20 min · Whole Class

Whole Class: Storytime Join

Sit in a circle and use toys or blocks. Present two groups, like 3 teddies and 4 cars, and ask children to suggest a story. Join them on the floor and count altogether as a group. Repeat with fingers for 4 add 3.

How many altogether when we join these two groups?

Facilitation Tip

During Storytime Join, model counting aloud while combining groups to build oral language and number sequence fluency.

What to look for

Present the student with two small groups of counters, for example, 3 red counters and 2 blue counters. Ask, 'If we join these groups, how many counters will we have altogether?' Observe if the student counts accurately after combining.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Experiential Learning
• 15 min · Pairs

Pairs: Finger Flash Add

Partners face each other and secretly hold up fingers for numbers up to 5. On signal, they show hands, join fingers, and count total together. Switch roles and record on mini whiteboards.

Can you tell me a story about putting 3 red blocks and 4 blue blocks together?

Facilitation Tip

For Finger Flash Add, ensure pairs alternate roles and verbalize their thinking to reinforce the connection between physical actions and numerical totals.

What to look for

Give the student a set of 4 toy cars and another set of 3 toy cars. Ask, 'Can you tell me a story about putting these cars together?' Listen for their use of vocabulary like 'join,' 'combine,' or 'altogether' and their ability to state the total.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Experiential Learning
• 25 min · Small Groups

Small Groups: Counter Bags

Provide bags with 3-5 counters each. Groups join two bags, count total using trays, and build towers matching the sum. Share one story about their joined groups with the class.

Show me on your fingers: 4 add 3 equals how many?

Facilitation Tip

In Counter Bags, circulate to ask each group to explain their combined totals aloud, using the vocabulary of joining and combining.

What to look for

Provide a worksheet with two empty circles. Instruct the student to draw 3 smiley faces in the first circle and 2 smiley faces in the second. Then, ask them to draw a line connecting the circles and write the total number of smiley faces in a third box labeled 'Altogether'.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Experiential Learning
• 20 min · Individual

Individual: Draw and Combine

Children draw two groups of objects (e.g., apples and bananas) based on teacher numbers. Draw lines to join them, count total, and label with numerals. Share drawings in pairs.

How many altogether when we join these two groups?

What to look for

Present the student with two small groups of counters, for example, 3 red counters and 2 blue counters. Ask, 'If we join these groups, how many counters will we have altogether?' Observe if the student counts accurately after combining.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Experienced teachers approach this topic by prioritizing oral language and physical manipulation over written symbols. They avoid rushing to abstract number sentences, instead allowing children to internalize the concept through repeated, varied experiences with counters, fingers, and stories. Teachers focus on building a strong foundation of number conservation and flexible thinking, where children understand that joining does not change the individual group sizes. Research suggests this concrete-to-abstract progression is essential for developing true number sense in young learners.

Successful learning looks like children confidently joining two small groups and stating the total without recounting from one. They should use oral math language such as 'join,' 'combine,' or 'altogether' naturally in their explanations. By the end of the activities, children should demonstrate flexibility in their thinking, recognizing that 3 + 2 and 2 + 3 yield the same total.

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Watch Out for These Misconceptions

• During Finger Flash Add, watch for children who insist that 3 + 2 gives a different total than 2 + 3.

  Model both combinations using fingers or counters on ten frames, then ask children to compare the totals. Emphasize that the order of joining does not matter by physically moving the groups and discussing the consistent total.

• During Counter Bags, watch for children who recount from one when joining two groups.

  Guide children to identify the larger group first, then model counting on from that number. Use a number line or finger chain to reinforce starting from the larger addend and reducing cognitive load.

• During Storytime Join, watch for children who believe joining changes the individual group sizes.

  Demonstrate with blocks, separating and rejoining the groups while asking children to verify that each group maintains its original size. Encourage peer explanations to reinforce number conservation.

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Methods used in this brief

• Experiential Learning