Mathematics · Year 1 · Number Sense and Place Value · Autumn Term

Representing Numbers to 20

Extending the use of concrete objects and pictorial representations to show numbers up to 20.

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

About This Topic

Representing numbers to 20 extends students' number sense by combining concrete objects, such as counters or beads, with pictorial tools like ten frames and dot cards. In Year 1, children partition numbers into tens and ones, for example showing 14 as a full ten frame plus four more counters. This practice aligns with KS1 Number and Place Value standards, helping students visualise quantity beyond rote counting.

Within the Autumn Number Sense and Place Value unit, this topic connects counting sequences to structured representations, fostering subitising skills and comparisons between methods. Students explain their choices, such as why ten frames clarify teen numbers better than scattered objects, building fluency in describing quantities.

Active learning shines here because manipulatives make abstract partitioning tangible. When children build, swap, and justify representations in pairs or groups, they gain confidence, correct errors through peer feedback, and retain concepts longer than through worksheets alone.

Key Questions

1. Explain how to represent the number 14 using ten frames and counters.
2. Compare representing numbers with objects versus drawing pictures.
3. Design a way to show the number 19 using two different methods.

Learning Objectives

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

Before You Start

Counting to 20

Why: Students must be able to count reliably to 20 to represent these numbers.

Representing Numbers to 10

Why: Prior experience with ten frames and counters for numbers up to 10 provides a foundation for extending this to teen numbers.

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.

Watch Out for These Misconceptions

Common Misconception

Teen numbers like 14 need 14 separate objects with no grouping.

What to Teach Instead

Ten frames reveal the structure of 10 + 4, showing teens as a ten and extras. Hands-on building in pairs lets students test scattered versus grouped arrangements, discovering through trial how grouping aids quick recognition.

Common Misconception

Pictures must show realistic items, not dots or frames.

What to Teach Instead

Abstract symbols like dots in ten frames represent quantity efficiently. Group sketching activities encourage experimentation, where peers critique and refine drawings, helping students see that symbolic reps speed up mental maths.

Common Misconception

All representations look the same for a number.

What to Teach Instead

Multiple methods highlight flexible thinking. Station rotations expose variety, with discussions clarifying that while value stays constant, visuals differ, building adaptable number sense through collaborative comparison.

Active Learning Ideas

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.

25 min·Pairs

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.

30 min·Small Groups

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.

20 min·Whole Class

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.

15 min·Individual

Real-World Connections

• Toy store displays often arrange small items like building blocks or toy cars in groups of ten and then additional items to show quantities up to 20, helping customers visualize how many they are buying.
• Bakers use trays with spaces for a dozen cookies and then add individual cookies to show orders for numbers slightly over twelve, like 14 or 19 cookies.

Assessment Ideas

Exit Ticket

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.'

Discussion Prompt

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?'

Quick Check

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.

Frequently Asked Questions

How to represent 14 using ten frames in Year 1?

Fill one ten frame completely with counters for the ten, then place four in a second frame. Students verbalise 'ten and four more makes fourteen.' Practice with partners reinforces this by having one build while the other counts aloud, solidifying place value basics for numbers to 20.

How does active learning support representing numbers to 20?

Active approaches with manipulatives and peer talk turn passive recognition into deep understanding. Children manipulate counters on ten frames, justify to partners, and rotate stations, correcting misconceptions on the spot. This builds subitising, confidence, and retention far beyond static images, aligning with concrete-pictorial-abstract progression.

Compare objects versus pictures for numbers to 20?

Concrete objects let students feel quantity and partition physically, ideal for initial grasp. Pictorial reps like ten frames promote visual fluency and mental images for quick recall. Sequence activities from objects to drawings, with students comparing speed and clarity in group reflections to appreciate both.

Activities for showing 19 two different ways Year 1?

Use ten frames: one full and nine in another, or tally marks with a ten bundle and nine singles. Pair tasks where students create both, explain pros like speed for frames, then gallery walk to vote on clearest. This develops flexible representation skills key to place value.