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.

• 1st Year
• Foundations of Mathematical Thinking
• 4 activities
• 20 min–35 min

Learning Objectives

1. Compare quantities up to 20 using comparative language such as 'more than', 'less than', and 'equal to'.
2. Order sets of objects and numbers up to 20 from smallest to largest and largest to smallest.
3. Explain the relationship between a number's position on a number line and its value relative to other numbers.
4. Identify situations where comparing quantities is more useful than knowing the exact count.

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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

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.

Prepare & details

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

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Exit Ticket

After Partner Match-Up, provide students with two sets of counters, for example 8 red and 12 blue, and ask them to write one sentence comparing the sets using 'more than' or 'less than.' Then, ask them to sketch a simple number line showing where 8 and 12 would be placed.

Quick Check

During Ten Frame Races, 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.

Discussion Prompt

After Human Number Line, present this 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?' Listen for students to explain situations where relative size matters more than exact counts.

Extensions & Scaffolding

• Challenge: Ask students to create their own number line walk for a partner, stepping out a sequence like 3, 15, 8, and 20 while stating each step aloud.
• Scaffolding: Provide number cards with ten frame images for students to order before moving to numerals alone.
• Deeper: Introduce comparison symbols (<, >, =) using pipe cleaners or playdough to form the shapes between ordered numbers.

Key Vocabulary

More than	Indicates a larger quantity or value. For example, 7 is more than 5.
Less than	Indicates a smaller quantity or value. For example, 3 is less than 9.
Equal to	Indicates that two quantities or values are the same. For example, 10 is equal to 10.
Number line	A visual representation of numbers in order, used to compare values and understand their relationships.