Foundations of Mathematical Thinking · Junior Infants

Active learning ideas

Ratio and Proportion

Active learning works for ratio and proportion because young children build number sense through physical actions and visual comparisons. Handling objects helps them move from abstract ideas to concrete understanding of quantities and relationships. Early ratio work relies on touch, sight, and movement to make comparisons meaningful long before symbols like 2:1 appear.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Number - N.1.7

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

Activity 01

• Jigsaw
• 20 min · Pairs

Pair Matching: Block Ratios

Pairs receive 10 linking blocks in two colors. First, create 1:1 (five each color), then 2:1 (seven one color, three the other). Children count, compare, and swap to balance. Discuss who has more and why.

Differentiate between a ratio and a fraction.

Facilitation Tip

For Pair Matching, circulate and ask each pair, 'How many red blocks do you have for every blue block?' to reinforce ratio language.

What to look for

Provide students with a collection of 6 red and 6 blue counters. Ask them to make two groups, one with only red counters and one with only blue counters, and then state how many red counters they have and how many blue counters they have. Observe if they can accurately count and state the quantities of each color.

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Activity 02

• Jigsaw
• 30 min · Small Groups

Small Group Sharing: Fruit Division

Groups of four get 12 play fruits. Share in ratios like 1:1 between two bowls, then 3:1. Rotate roles: divider, checker, recorder. Draw or stamp the shares.

Analyze how proportional reasoning is used in scaling recipes or maps.

Facilitation Tip

In Small Group Sharing, model fair division by taking turns placing one fruit at a time into each person's bowl.

What to look for

Present two different arrangements of toys, for example, one with 3 dolls and 2 teddy bears, and another with 6 dolls and 4 teddy bears. Ask students: 'Which group has more dolls? Which group has more teddy bears? Do the groups have the same number of dolls compared to teddy bears?' Listen for their reasoning and use of comparative language.

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Activity 03

• Jigsaw
• 25 min · Whole Class

Whole Class: Human Line-Up

Line up boys and girls to show class ratio. Count and compare totals. Adjust by adding teddy bears to make 1:1. Chant the ratio and predict changes if one child leaves.

Construct a problem that requires finding an unknown value in a proportion.

Facilitation Tip

During Human Line-Up, stand behind students and silently count aloud as they move to emphasize the counting process.

What to look for

Give each child a small bag with 4 small objects. Ask them to share the objects equally between two friends. On a piece of paper, they should draw how many objects each friend received. This checks their understanding of equal sharing.

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Activity 04

• Jigsaw
• 15 min · Individual

Individual Drawing: Pattern Scales

Each child draws two patterns: five circles to five squares (1:1), then ten circles to five squares (2:1). Color and label 'more' or 'same'. Share one with a partner.

Differentiate between a ratio and a fraction.

Facilitation Tip

For Individual Drawing, provide dotted grids to help children align and count their pattern scales accurately.

What to look for

Provide students with a collection of 6 red and 6 blue counters. Ask them to make two groups, one with only red counters and one with only blue counters, and then state how many red counters they have and how many blue counters they have. Observe if they can accurately count and state the quantities of each color.

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

A few notes on teaching this unit

Teachers use concrete objects to build intuitive understanding before introducing symbols. Avoid rushing to written work; let children explore through play and discussion first. Research shows that repeated hands-on experiences with varied groupings help children internalize proportional reasoning. Model curiosity by asking, 'What do you notice about how the groups compare?' and give time for responses.

Successful learning looks like children using comparative language naturally, such as 'more', 'less', or 'the same' while handling sets of objects. They should begin to notice and describe how parts relate to each other, not just count totals. Children should attempt to adjust quantities when asked to make equal or proportional groups.

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Watch Out for These Misconceptions

• During Pair Matching, watch for children assuming all groups must be equal. The correction is to ask, 'What if we put two yellow blocks with every one green block? Show me.'

  During Pair Matching, redirect by saying, 'Count how many yellow blocks you have for each green block. Is that a fair share? How could we describe this group differently?'.

• During Small Group Sharing, watch for children adding the total number of fruits instead of comparing the parts. The correction is to ask, 'How many apples does each friend have compared to bananas? Use your hands to show me.'

  During Small Group Sharing, hold up a bowl and say, 'Here is one friend's share. How many apples and bananas are in this one bowl together? Now, how many apples are there for every banana?'.

• During Human Line-Up, watch for children thinking the longer line always has the larger ratio. The correction is to ask, 'Does this line have the most children, or does it have the most girls for every boy?'

  During Human Line-Up, pause the line and ask, 'If we count how many girls stand next to each boy, what do you notice about this side compared to that side?'.

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Methods used in this brief

• Jigsaw