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.

• Junior Infants
• Foundations of Mathematical Thinking
• 4 activities
• 15 min–30 min

Learning Objectives

1. Compare the number of objects in two or more groups using concrete materials.
2. Identify situations where quantities are combined or separated.
3. Demonstrate equal sharing of a set of objects among a specified number of recipients.
4. Construct a simple ratio by combining two distinct sets of objects in a specified relationship.

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.

Prepare & details

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.

Setup: Flexible seating for regrouping

Materials: Expert group reading packets, Note-taking template, Summary graphic organizer

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

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.

Prepare & details

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.

Setup: Flexible seating for regrouping

Materials: Expert group reading packets, Note-taking template, Summary graphic organizer

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

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.

Prepare & details

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.

Setup: Flexible seating for regrouping

Materials: Expert group reading packets, Note-taking template, Summary graphic organizer

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

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.

Prepare & details

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.

Setup: Flexible seating for regrouping

Materials: Expert group reading packets, Note-taking template, Summary graphic organizer

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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.'

What to Teach Instead

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?'.

Common Misconception

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.'

What to Teach Instead

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?'.

Common Misconception

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?'

What to Teach Instead

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?'.

Assessment Ideas

Quick Check

After Pair Matching, provide each child with 4 red and 4 blue counters. Ask them to make two groups, one with only red and one with only blue, and then tell you how many red counters they have and how many blue counters they have. Listen for accurate counting and use of the word 'to' when describing the groups.

Discussion Prompt

During Small Group Sharing, present two different arrangements of toys, for example, one with 2 dolls and 4 teddy bears and another with 4 dolls and 8 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 like 'twice as many'.

Exit Ticket

After Individual Drawing, give each child a small bag with 6 small objects. Ask them to draw how many objects each of two friends would receive if shared equally. Collect the drawings to check if children divided the total into two equal groups.

Extensions & Scaffolding

• Challenge: Provide bags with 8 objects and ask students to divide them into groups of 3 and 5, then describe the ratio using the words 'to' in a sentence.
• Scaffolding: Offer trays with two compartments for Small Group Sharing so children can physically separate objects before counting.
• Deeper: Introduce a third color in Pattern Scales, asking children to create a 1:2:3 ratio and compare their patterns with a partner.

Key Vocabulary

Ratio	A way to compare two quantities. For example, the ratio of red blocks to blue blocks might be 2 to 3.
Proportion	When two ratios are equal. For example, if 2 red blocks and 3 blue blocks is the same as 4 red blocks and 6 blue blocks.
Equal Sharing	Dividing a group of items into smaller groups so that each smaller group has the same number of items.
Grouping	Putting items together into sets of a specific size, like making groups of two or groups of three.