Mathematics · Year 1 · Number Sense and Counting Systems · Term 1

Representing Numbers to 20

Using concrete materials, pictures, and numerals to represent numbers up to 20.

• ACARA Content Descriptions
• AC9M1N01

About This Topic

Representing numbers to 20 helps students use concrete materials, pictures, and numerals in flexible ways. They explore numbers like 15 through counters grouped as ten and five, dot patterns on ten frames, or the written numeral 15. This directly supports AC9M1N01 by building skills to recognise and represent numbers, with a focus on quantities up to 20 in the Number Sense and Counting Systems unit. Students design multiple representations, compare them, and justify why they show the same amount.

This topic strengthens foundational number sense, including subitizing small quantities and partitioning numbers into parts. It connects to counting sequences and prepares for place value by showing how tens and ones combine. Through peer comparisons, students develop mathematical language to explain equivalences, such as why fifteen blocks match fifteen dots.

Active learning benefits this topic greatly because hands-on work with materials makes abstract numerals concrete and reveals multiple pathways to the same quantity. Collaborative tasks encourage students to share and debate representations, building confidence and deeper understanding through visible, manipulable models.

Key Questions

1. Design multiple ways to show the number 15 using objects and drawings.
2. Compare different representations of the same number.
3. Justify why different representations can still mean the same quantity.

Learning Objectives

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

Before You Start

Counting Sequences to 20

Why: Students need to be able to count reliably to 20 to understand and represent numbers within this range.

Subitizing Quantities to 10

Why: The ability to instantly recognize small quantities helps students quickly identify parts of numbers, like the 5 in a group of 15.

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.

Watch Out for These Misconceptions

Common Misconception

The numeral 15 shows two separate numbers, 1 and 5.

What to Teach Instead

Ten frame activities group ten and five clearly, helping students see the numeral as a single quantity. Pair discussions compare numeral to objects, revealing the whole. Hands-on building reinforces composition without separation.

Common Misconception

Different pictures mean different numbers.

What to Teach Instead

Gallery walks let students compare diverse representations side-by-side, spotting equivalences. Group relays build multiple forms quickly, showing flexibility. Peer justification in small groups corrects this through shared evidence.

Common Misconception

Only counting one-by-one shows the correct amount.

What to Teach Instead

Subitizing games with dot cards or ten frames build instant recognition. Collaborative matching tasks show pictures equal objects without recounting each time, fostering efficient strategies.

Active Learning Ideas

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.

25 min·Pairs

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.

30 min·Small Groups

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.

40 min·Whole Class

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.

20 min·Individual

Real-World Connections

• Cashiers at a grocery store use numerals and physical counts of items to represent the total cost of a customer's purchase, ensuring the amount matches the items bought.
• Builders use drawings and measurements to represent the quantity of materials needed for a construction project, such as ordering 15 beams or 15 bags of cement.

Assessment Ideas

Quick Check

Provide students with a collection of 15 counters and a blank ten frame. Ask them to arrange the counters on the ten frame to show 15 and draw their representation. Observe if they correctly group 10 and 5.

Discussion Prompt

Show students three different representations of the number 12: a group of 12 loose counters, counters arranged as a full ten frame and 2 more, and a drawing of 12 stars. Ask: 'Which of these shows the same amount as the others? How do you know? Can you draw another way to show 12?'

Exit Ticket

Give each student a card with the numeral '17'. Ask them to draw a picture that shows 17 objects and write one sentence explaining why their drawing represents the number 17.

Frequently Asked Questions

How do you teach representing numbers to 20 in Year 1?

Start with concrete materials like counters and linking cubes to build numbers, then transition to pictures such as ten frames and dot arrays, finally adding numerals. Use key questions to guide: design ways to show 15, compare representations, justify sameness. Align with AC9M1N01 through daily practice in flexible forms. This sequence builds from tangible to symbolic understanding over several lessons.

What activities align with AC9M1N01 for number representation?

Incorporate ten frame match-ups in pairs, representation relays in small groups, and gallery walks as a class. These hands-on tasks cover concrete, pictorial, and symbolic representations up to 20. Each activity includes comparison and justification, directly targeting curriculum proficiencies while keeping engagement high across 20-40 minute sessions.

How does active learning support representing numbers to 20?

Active learning with manipulatives and drawings makes numbers visible and touchable, helping students grasp multiple representations intuitively. Group comparisons reveal equivalences through talk and shared models, reducing errors. Individual journals consolidate learning, while whole-class shares build a community of mathematical thinkers. This approach boosts retention and confidence in AC9M1N01 skills.

What are common misconceptions in representing numbers to 20?

Students often see numerals like 15 as separate digits or believe different pictures show different quantities. They may rely solely on one-by-one counting. Address with ten frames for grouping, peer galleries for comparisons, and relays for variety. These active methods provide evidence to reshape ideas, aligning with curriculum emphasis on flexible representation.