Mathematics · Year 1

Active learning ideas

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.

• National Curriculum Attainment Targets
• KS1: Mathematics - Number and Place Value

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.

What to look for

Give each student a card with a number between 10 and 20. Ask them to draw the number on a ten frame using dots and write one sentence explaining their drawing, for example, 'I drew 15 as a full ten frame and five dots because 15 is one ten and five ones.'

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

Activity 02

• 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.

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.

What to look for

Present students with two different representations of the same number (e.g., 17 counters scattered on a table versus 17 counters arranged on two ten frames). Ask: 'Which representation makes it easier to see how many counters there are? Why? How does each picture show the number of tens and ones?'

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

Activity 03

• 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.

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.

What to look for

Hold up a number of fingers (e.g., 12). 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.

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

Activity 04

• 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.

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

What to look for

Give each student a card with a number between 10 and 20. Ask them to draw the number on a ten frame using dots and write one sentence explaining their drawing, for example, 'I drew 15 as a full ten frame and five dots because 15 is one ten and five ones.'

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

  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.

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

  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.

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Methods used in this brief

• Stations Rotation