Exploring Numbers

Overview

In this lesson students represent, partition, and compose numbers up to 20 using physical manipulatives, drawings, and simple number sentences. This is Lesson 1 of 8, starting the unit by building number sense and flexible ways to see “how many” and “how it’s made”.

Learning intentions

Students will:

• represent numbers to 20 using counters and base-ten blocks (or link cubes)
• partition numbers to 20 into two parts in different ways
• compose numbers to 20 by combining two groups
• explain their thinking using “I have ___ because ___” statements

Success criteria

Students can:

• show a number (to 20) with the correct amount of objects
• split a number like 13 into two parts (e.g. 10 and 3, 9 and 4) using manipulatives
• draw and label two parts and the whole number
• write or say a simple addition sentence for “two parts make a whole” (within 20)

Curriculum links

• Number and place value: developing understanding of whole numbers to 20 through counting, representing, and comparing quantities
• Part-whole relationships: partitioning numbers and composing numbers using concrete and pictorial representations
• Mathematical communication: using diagrams, words, and simple number statements to explain reasoning
• QLD Mathematics progression emphasis: building from concrete to pictorial to symbolic representations (foundational number sense)

Lesson structure (60 minutes)

1. 0–5 min · Welcome and warm-up. Teacher displays 1–10 picture cards and asks students to show that number on mini-whiteboards or with fingers; students respond chorally and then show with their own counters.

2. 5–15 min · Teacher modelling: “Make the number.” Teacher models choosing a number card (e.g. 12), showing how to represent it with counters, then drawing a quick dot array/ten frame drawing; students follow along using their own set and copy the drawing in their book.

3. 15–27 min · Guided practice: partition with two parts. Teacher picks a number (e.g. 15) and demonstrates partitioning into two groups using two colours of counters (or two sets of blocks), emphasising “part + part = whole”. Students work in pairs: choose a card 11–20, make the number, then record two different partitions using drawings (and labels such as “10 and 5”).

4. 27–38 min · Move and match (rotation activity). Teacher sets up three stations around the room:

• Station A: Build-to-match (make the number on a card)
• Station B: Split-to-match (show two parts for the number)
• Station C: Draw-to-match (complete a partly drawn ten frame/dot diagram) Students rotate every 3–4 minutes, using counters for A and B, and drawing for C; teacher circulates with prompts: “What two parts did you use?” “Can you show another way?”

5. 38–48 min · Share and compare strategies. Teacher selects 2–3 student examples (kept anonymous if possible) and asks the class to compare: “Which partition is the same whole?” “How do you know?” Students discuss using sentence starters, then teacher records one or two partitions on the board.

6. 48–55 min · Symbol connect: write a number sentence. Teacher demonstrates converting one partition into a simple addition statement (e.g. 12 = 10 + 2) and emphasises it matches the drawing and objects. Students choose one partition from their page and write the matching sentence (with support frames for students who need it).

7. 55–60 min · Exit ticket. Teacher hands out a quick task: “Show 17. Draw two parts. Write a number sentence.” Students complete independently; teacher collects for immediate feedback.

Resources

• Number cards 11–20 and 1–10 (picture or dot-card style)
• Counters in two colours, link cubes or base-ten blocks (one set per student or per pair)
• Ten frames (printed) and blank paper for drawings/dot arrays
• Student recording sheets (partition diagrams with space for two parts and the whole)
• Mini-whiteboards and markers (or scrap paper) for warm-up
• Anchor chart templates: “Make it / Split it / Combine it”
• Station signs and timer (for rotation)

Assessment

• Formative checks during warm-up: correct representation of numbers with fingers/objects
• Guided practice observation: listen for accurate partitioning (whole matches the original number) and correct part identification
• Exit ticket review:
• whole number shown correctly (to 20)
• two-part partition drawn clearly
• simple number sentence matches the two parts

Differentiation

• Support:
• Provide sentence starters: “I have ___ because ___.” “My parts are ___ and ___.”
• Use partially completed ten frames/diagrams for drawing tasks
• Offer additional scaffolds: students may choose partitions that match “10 + ___” first
• Extension:
• Ask for a third partition for the same whole number, and challenge: “Can you find all the different ways?”
• Encourage students to explain why different partitions still make the same whole
• EAL/SEN considerations:
• Keep language consistent across activities (“whole”, “part”, “two parts make a whole”)
• Allow verbal responses paired with gesture or pointing to counters
• Use visual cues (two colours, arrows, and colour-coded labels) to reduce reading load