Foundations of Mathematical Thinking · Junior Infants

Active learning ideas

Algebraic Problem Solving: Word Problems

Active learning works for algebraic word problems because young children connect abstract symbols to real objects and stories. Acting out problems with toys or drawings makes the unknown quantity visible, transforming '3 - ? = 1' from a puzzle into a clear situation where counters or fingers can show the gap between what was there and what remains.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Algebra - A.1.12

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 25 min · Whole Class

Story Circle: Duck Pond Addition

Read a word problem about ducks swimming to a pond. Children use toy ducks or counters to build the starting amount, add more, and write or draw the number sentence like 4 + 3 = ?. Discuss as a group why addition fits. End with children creating their own duck stories.

Analyze the key information in a word problem to form an equation.

Facilitation Tip

During Duck Pond Addition, model aloud how to turn 'some ducks flew away' into subtraction by moving counters off the pond and saying, 'Now there are fewer, so we take away.'

What to look for

Present a simple word problem, such as 'There are 4 birds on a branch. 2 more birds fly to the branch. How many birds are there now?' Ask students to use counters to show the problem and then write the number sentence (e.g., 4 + 2 = 6).

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 02

• Problem-Based Learning
• 20 min · Pairs

Pairs Puzzle: Missing Snacks

Give pairs picture cards showing snacks before and after eating. They identify totals and missing parts, like 5 cookies - 2 eaten = ?, using real snacks or drawings to solve. Pairs explain their equation to another pair.

Justify the choice of variable and operations when setting up an algebraic model.

Facilitation Tip

In Missing Snacks, circulate and gently ask pairs, 'Which number in your story is hiding? How will the objects show you that missing number?'

What to look for

Read a word problem like 'Leo had 5 toy cars. He gave 3 to his friend. How many cars does Leo have now?' Ask: 'What is the unknown number we need to find?' 'What math operation should we use, and why?' 'Does your answer make sense?'

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 03

• Problem-Based Learning
• 30 min · Small Groups

Small Group Hunt: Toy Shop Problems

Hide number cards around the room with word problem clues, like 'Shop has 6 cars, sells 4, how many left?'. Groups find cards, act out with toy cars, form subtraction sentences, and share solutions.

Evaluate the reasonableness of a solution in the context of the original problem.

Facilitation Tip

For Toy Shop Problems, provide baskets labeled 'bought' and 'left' so students physically group toys to see the operation needed.

What to look for

Give each student a card with a word problem. Ask them to draw a picture representing the problem and write the number sentence. For example, for 'Sarah had 6 stickers and lost 2. How many are left?', they might draw 6 stickers, cross out 2, and write 6 - 2 = 4.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 04

• Problem-Based Learning
• 15 min · Individual

Individual Draw and Solve: Family Sharing

Each child draws a picture for a sharing word problem, like 'Dad shares 8 sweets equally with 2 children. How many each?'. They use blocks to model division as repeated subtraction and write the sentence.

Analyze the key information in a word problem to form an equation.

Facilitation Tip

During Family Sharing, ask students to whisper the number sentence to you before they draw, then match their drawing to their sentence to catch mismatches early.

What to look for

Present a simple word problem, such as 'There are 4 birds on a branch. 2 more birds fly to the branch. How many birds are there now?' Ask students to use counters to show the problem and then write the number sentence (e.g., 4 + 2 = 6).

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach algebraic problem solving by first focusing on understanding the story before writing anything. Use think-alouds to model how to identify the unknown and choose an operation based on whether items join or leave. Avoid rushing to symbols; let students experience the problem with objects first. Research shows that young learners benefit from repeated, varied exposure to the same problem types with different contexts, which builds flexible thinking rather than rote procedures.

Successful learning looks like students translating word problems into number sentences with an unknown, solving with concrete materials, and explaining why their answer fits the story. They should also adjust their approach when an answer doesn't match the context, showing they are thinking beyond just the numbers.

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Watch Out for These Misconceptions

• During Duck Pond Addition, watch for students who always add all numbers even when ducks leave the pond.

  Gather students and ask them to act out a 'leaving' story with toy ducks. Move ducks off the pond while narrating, 'When ducks fly away, we subtract. Count how many are gone to find the missing number.'

• During Missing Snacks, watch for students who assume the unknown is always the largest number in the problem.

  Have pairs compare their counters and drawings side by side. Ask, 'Is your missing number bigger than the total you started with? How do the objects prove that?'

• During Toy Shop Problems, watch for students who solve the problem without checking if the answer fits the real situation.

  After solving, ask students to role-play the problem with props. For example, if their answer is 10 apples for 3 ducks, set out 10 apples and 3 ducks, then ask, 'Does this make sense? What should we change?'

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Methods used in this brief

• Problem-Based Learning