Foundations of Mathematical Thinking · 1st Year

Active learning ideas

Comparing and Ordering Numbers to 20

Active learning works well for comparing and ordering numbers to 20 because young students need repeated hands-on experiences to build trust in visual comparisons. Physical actions like matching objects, stepping on a human number line, or filling ten frames provide concrete evidence that helps students move beyond guesswork and toward accurate reasoning about quantities.

• NCCA Curriculum Specifications
• NCCA: Primary - Number

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Collaborative Problem-Solving
• 30 min · Pairs

Partner Match-Up: Comparing Sets

Pairs get two sets of counters up to 20 objects each. They match one-to-one to compare without full counting, then use 'more than' or 'less than' symbols and explain why. Switch sets after 5 minutes.

Analyze how we can prove that one set of objects is larger than another without counting every single one.

Facilitation Tip

During Partner Match-Up, have students physically line up matching counters from each set before stating which group is larger to reinforce conservation of quantity.

What to look for

Provide students with two sets of counters, for example, 8 red counters and 12 blue counters. Ask them to write one sentence comparing the two sets using 'more than' or 'less than'. Then, ask them to draw a simple number line showing where 8 and 12 would be placed relative to each other.

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

Activity 02

• Collaborative Problem-Solving
• 35 min · Small Groups

Small Group: Ten Frame Races

Groups fill ten frames with two colors of linking cubes to represent numbers to 20. Compare frames side-by-side, order three numbers, and record with symbols. Discuss strategies as a group.

Evaluate when it is more useful to know the exact number versus just knowing which is 'more'.

Facilitation Tip

In Ten Frame Races, remind groups to say the total out loud after each roll to connect subitizing with written numerals.

What to look for

Display two groups of objects on the board, one with 15 stars and another with 11 moons. Ask students to hold up fingers to show how many more stars there are than moons. Then, ask: 'Which number is greater, 15 or 11?'

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

Activity 03

• Collaborative Problem-Solving
• 25 min · Whole Class

Whole Class: Human Number Line

Students hold number cards 0-20 and position themselves on floor tape as a line. Teacher calls comparisons like 'Who is between 10 and 15?' Class verifies and discusses positions.

Explain how the position of a number on a line helps us understand its value.

Facilitation Tip

For the Human Number Line, place cards slightly apart at first so students can see the gaps and discuss what those spaces represent.

What to look for

Present a scenario: 'Imagine you have two bags of sweets. One bag has 10 sweets and the other has 5 sweets. Which bag would you choose if you wanted more sweets? Why is knowing which bag has 'more' sometimes better than knowing the exact number in each bag?'

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

Activity 04

• Collaborative Problem-Solving
• 20 min · Individual

Individual: Ordering Puzzle

Each student cuts and orders number strips 1-20 on a personal mat, then compares subsets like 7, 12, 9. Glue in place and label relationships.

Analyze how we can prove that one set of objects is larger than another without counting every single one.

What to look for

Provide students with two sets of counters, for example, 8 red counters and 12 blue counters. Ask them to write one sentence comparing the two sets using 'more than' or 'less than'. Then, ask them to draw a simple number line showing where 8 and 12 would be placed relative to each other.

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

A few notes on teaching this unit

Teach this topic by starting with physical materials students can manipulate, then gradually introduce symbolic representations like ten frames and number lines. Avoid relying solely on worksheets, as students need to see that 19 and 20 are close in value, not just look at the digits. Research shows that frequent verbal sharing of reasoning helps students internalize precise vocabulary and correct misconceptions early.

By the end of these activities, students will confidently compare sets of objects without counting each item and explain their reasoning using 'more than,' 'less than,' and 'equal to.' They will also order numbers up to 20 on a number line and justify their sequence with both visual and verbal evidence.

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Watch Out for These Misconceptions

• During Partner Match-Up, watch for students who claim a set is larger simply because the objects are spread out or grouped differently.

  Prompt students to rearrange one set into a line and the other into a pile while keeping the total unchanged, then recount both sets to verify the quantities stay the same.

• During Ten Frame Races, watch for students who think 19 is bigger than 20 because the digit 9 is larger than 0.

  Have students fill two ten frames completely to represent 20 and leave one space in the second frame for 19, then discuss how the full frames show the difference clearly.

• During Human Number Line, watch for students who assume all numbers above 10 are 'a lot more' than those under 10.

  Ask students to step from 8 to 12 while counting the gap, then repeat from 18 to 20 to highlight that some jumps between teen numbers are smaller than they expect.

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Methods used in this brief

• Collaborative Problem-Solving