Representing Numbers to 20

Active learning works for representing numbers to 20 because young learners need to connect abstract quantities to concrete visuals before symbols feel meaningful. When children build numbers themselves using counters, ten frames, and sketches, they move from counting one-by-one to seeing groups of ten, which builds flexible number sense.

• Year 1
• Mathematics
• 4 activities
• 15 min–30 min

Learning Objectives

1. Demonstrate how to represent numbers up to 20 using ten frames and counters.
2. Compare the effectiveness of using concrete objects versus pictorial representations for showing numbers up to 20.
3. Design two distinct visual representations for the number 19.
4. Explain the composition of teen numbers (e.g., 14 is one ten and four ones) using manipulatives.

Stations Rotation

⏱ 25 min·Pairs

Pair Build: Ten Frame Challenges

Partners select a number card from 11 to 20. One builds it on two ten frames using counters while the other watches and describes the tens and ones. They switch roles and compare methods, noting efficiency. End with sharing one build with the class.

Prepare & details

Explain how to represent the number 14 using ten frames and counters.

Facilitation Tip: During Pair Build, listen for pairs explaining why a full ten frame plus extras makes counting faster than scattered groups.

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

Stations Rotation: Representation Stations

Set up three stations: concrete (counters in trays), pictorial (draw ten frames), and mixed (beads on strings). Small groups spend 7 minutes at each, representing three numbers and recording explanations. Rotate and discuss differences.

Prepare & details

Compare representing numbers with objects versus drawing pictures.

Facilitation Tip: For Station Rotation, circulate and ask students to compare their ten-frame arrangements aloud with peers at the next station.

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·Whole Class

Whole Class: Number Hunt Gallery Walk

Display pre-made representations of numbers to 20 around the room. Students walk in a line, pausing to copy one in their book using a different method and explain to a partner why it works. Teacher calls out numbers for focus.

Prepare & details

Design a way to show the number 19 using two different methods.

Facilitation Tip: During the Number Hunt Gallery Walk, prompt students to point out how each display shows both tens and ones, not just the total amount.

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

⏱ 15 min·Individual

Individual: Dual Method Cards

Give each student cards with numbers 13-19. They represent each twice: once with objects sketched, once pictorially. Self-check against a model, then pair up to verify and improve one representation.

Prepare & details

Explain how to represent the number 14 using ten frames and counters.

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

Start with manipulatives so students physically separate ten from ones, then move to pictorial tools like ten frames to anchor symbolic numbers. Avoid rushing to written numerals before children can explain why 17 is one ten and seven more. Research shows that children who spend time building teen numbers with ten frames develop stronger place-value foundations than those who only practice rote counting.

What to Expect

Successful learning looks like students effortlessly switching between counting scattered objects, grouping ten frames, and drawing dots or tally marks to show teen numbers. You’ll notice confident talk about tens and ones, where children explain their choices rather than just state numbers.

Watch Out for These Misconceptions

Common Misconception

During Pair Build, watch for students insisting that 14 must be shown with 14 separate counters, not a ten frame plus four.

What to Teach Instead

Ask the pair to build 14 both ways, then time how long it takes to count scattered counters versus a grouped ten frame, guiding them to notice the efficiency of grouping.

Common Misconception

During Station Rotation, watch for students dismissing abstract dot or tally marks as 'not real pictures.'

What to Teach Instead

Prompt students to sketch both realistic items and dots for the same number, then compare which sketch helps them count faster, reinforcing that symbols speed up mental math.

Common Misconception

During Number Hunt Gallery Walk, watch for students assuming all representations of 16 must look identical.

What to Teach Instead

Ask students to study three different displays of 16 and explain how each one shows one ten and six ones, even if the visuals differ, to build flexibility in representation.

Assessment Ideas

Exit Ticket

After Pair Build, give each student a number between 10 and 20 on a card. Ask them to draw the number on a ten frame using dots and write one sentence explaining their drawing, for example, 'I drew 18 as a full ten frame and eight dots because 18 is one ten and eight ones.' Collect these to check accuracy of grouping and explanation.

Discussion Prompt

During Station Rotation, present pairs with two different representations of the same number, such as 17 counters scattered versus 17 counters on two ten frames. Ask: 'Which representation makes it easier to see the tens and ones? How does each picture show the number of tens and ones?' Listen for mentions of grouping and efficiency in counting.

Quick Check

After the Number Hunt Gallery Walk, hold up a number like 12 using fingers. Ask students to show this number using two ten frames and counters at their desks. Observe which students correctly fill one ten frame and place two counters on the second ten frame, noting any who struggle with the ten-one split.

Extensions & Scaffolding

• Challenge students who finish early to represent the same number using three different tools (e.g., counters, ten frame, tally marks) and explain which they prefer and why.
• Scaffolding: Provide students who struggle with a partial ten frame already filled and ask them to add the remaining counters to reach the target number.
• Deeper exploration: Ask students to create their own teen number mystery bags with hidden quantities inside, then swap bags and represent the mystery number using two ten frames before revealing the answer.

Key Vocabulary

Ten Frame	A grid with two rows of five squares, used to visually represent numbers up to ten, and two ten frames can represent numbers up to twenty.
Counters	Small objects, such as buttons or colored discs, used to represent numbers on a ten frame or in other counting activities.
Partition	To break a number down into smaller parts, such as showing 14 as a full ten frame and four individual counters.
Pictorial Representation	A drawing or diagram that shows a number, such as drawing dots on a ten frame instead of using physical counters.