Representing Numbers to 20

Active learning helps students grasp the concept of representing numbers to 20 by engaging multiple senses and learning styles. When students manipulate objects, draw pictures, and discuss their ideas, they connect abstract numerals to concrete quantities in lasting ways. This hands-on approach builds fluency and confidence with numbers beyond ten.

• Year 1
• Mathematics
• 4 activities
• 20 min–40 min

Learning Objectives

1. Design multiple representations for numbers up to 20 using concrete materials, drawings, and numerals.
2. Compare different visual and numerical representations of the same quantity up to 20.
3. Explain the equivalence between different representations of a number up to 20.
4. Identify the numeral that corresponds to a given quantity represented by objects or pictures.
5. Classify representations of numbers based on whether they accurately depict a specific quantity.

Stations Rotation

⏱ 25 min·Pairs

Pairs: Ten Frame Showdown

Pairs receive cards with numbers 11-20 and ten frames. One partner builds the number using counters on the frame; the other draws it and writes the numeral. Partners switch roles, then compare their work to find matches. Discuss why both show the same number.

Prepare & details

Design multiple ways to show the number 15 using objects and drawings.

Facilitation Tip: During Ten Frame Showdown, circulate and ask pairs to explain how their arrangement matches the numeral, reinforcing the connection between grouping and notation.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 30 min·Small Groups

Small Groups: Representation Relay

Divide class into groups of four. Each student represents a number up to 20 using objects, pictures, numerals, or fingers. Pass to next student who creates a different representation. Groups race to complete five numbers and justify equivalences.

Prepare & details

Compare different representations of the same number.

Facilitation Tip: For Representation Relay, assign each small group a specific number to ensure focused practice and quick feedback during the rotation.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 40 min·Whole Class

Whole Class: Number Line Gallery

Students create posters showing three ways to represent numbers 10-20. Display around room for a gallery walk. In pairs, visit posters, note similarities, and vote on most creative representation. Debrief as class.

Prepare & details

Justify why different representations can still mean the same quantity.

Facilitation Tip: Set clear expectations for the Number Line Gallery by providing examples of varied representations so students understand the range of acceptable responses.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 20 min·Individual

Individual: My Number Journal

Each student picks five numbers to 20 and draws or pastes three representations per page: objects, picture, numeral. Add a sentence justifying one match. Share one page with partner.

Prepare & details

Design multiple ways to show the number 15 using objects and drawings.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Teaching This Topic

Teach this topic by moving from concrete to pictorial to symbolic representations, giving students time to explore each stage. Avoid rushing to numerals before students grasp the quantities they represent. Research shows that students learn best when they build, draw, and discuss their thinking before abstracting it. Use questioning to push their reasoning, asking them to explain why different representations show the same number.

What to Expect

Students will confidently create and compare multiple representations of numbers up to 20 using counters, ten frames, drawings, and numerals. They will justify their choices and recognize that different forms can show the same quantity. Collaboration and discussion will deepen their understanding of number composition.

Watch Out for These Misconceptions

Common Misconception

During Ten Frame Showdown, watch for students who separate the numeral 15 into 1 and 5 when explaining their arrangement. Redirect them by asking, 'How many counters are in the full ten frame? How many are outside? How does that match the numeral 15?'

What to Teach Instead

During Ten Frame Showdown, students often see the numeral as separate digits. Have pairs physically place counters on the ten frame to show ten and five, then write the numeral 15 beside it. Ask them to explain how the grouped counters match the written number.

Common Misconception

During Representation Relay, watch for students who assume that different-looking pictures mean different numbers. Redirect them by asking, 'How do you know these all show the same amount?'

What to Teach Instead

During Representation Relay, provide each group with three different representations of the same number. Ask them to sort the cards and explain why they belong together, using counters to verify equivalence if needed.

Common Misconception

During Number Line Gallery, watch for students who rely only on counting one-by-one to confirm the amount. Redirect them by asking, 'Can you see the number without counting? What other ways can you tell how many there are?'

What to Teach Instead

During Number Line Gallery, ask students to subitize the quantities in the representations. Provide dot cards or ten frames to help them recognize the numbers instantly, then discuss how these patterns match the numeral.

Assessment Ideas

Quick Check

After Ten Frame Showdown, provide students with a collection of 16 counters and a blank ten frame. Ask them to arrange the counters to show 16 and explain how their arrangement matches the numeral 16.

Discussion Prompt

During Representation Relay, show students three different representations of the number 14: a group of 14 loose counters, counters arranged as a full ten frame and 4 more, and a drawing of 14 hearts. Ask, 'Which of these shows the same amount as the others? How do you know? Can you draw another way to show 14?'

Exit Ticket

After My Number Journal, give each student a card with the numeral '18'. Ask them to draw a picture that shows 18 objects and write one sentence explaining why their drawing represents the number 18.

Extensions & Scaffolding

• Challenge students to represent the same number in three different ways using materials of their choice after completing the Representation Relay.
• For students who struggle, provide pre-printed ten frames with dots already arranged for them to match numerals during Ten Frame Showdown.
• Deeper exploration: Have students create a poster showing all the ways to represent 19 using counters, ten frames, tally marks, and numerals, then present their findings to the class.

Key Vocabulary

Ten Frame	A grid with two rows of five squares, used to visually represent numbers up to 10 and help with composing and decomposing numbers.
Numeral	A symbol or figure that represents a number, such as 1, 2, or 15.
Representation	A way of showing or expressing a number, using objects, pictures, or written symbols.
Quantity	The amount of something, represented by a number.
Compose	To make a number by joining smaller numbers or groups of objects together.
Decompose	To break a number down into smaller numbers or groups of objects.