Build, Represent, Explain Numbers

Overview

Students investigate whole numbers to at least 10,000 using place-value equipment, number lines and expanded notation. They build on prior understanding of ones, tens and hundreds to explain how the position of a digit affects its value, compare numbers, and justify their thinking with mathematical language.

Learning intentions

• WALT represent whole numbers to at least 10,000 in different ways.
• WALT explain the value of each digit using place-value language.
• WALT compare numbers and justify which is greater or less.
• WALT use mathematical representations as evidence for our thinking.

Success criteria

• I can build or draw a number using thousands, hundreds, tens and ones.
• I can write a number in standard, word and expanded notation.
• I can place and compare numbers on a number line.
• I can explain which number is greater using place-value evidence.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge learners and deepen mathematical understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: relevant challenge connected to learners’ existing textbook and classroom content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: opportunities for learners to reason, represent and communicate beyond routine calculation.
• Mathematical practices: noticing structure, choosing representations, explaining strategies and responding to another learner’s reasoning.

Lesson structure (45 minutes)

1. 0–5 min · Hook: What number am I? Teacher displays a mystery number clue on the mystery-number opening slide: “I have 4 digits. My thousands digit is 3. My hundreds digit is 2 more than my tens digit. My ones digit is 5.” Students think, solve independently, then compare answers with a partner. Reveal 3,?; clarify that more than one answer may be possible and ask what extra clue would make it certain.

2. 5–13 min · Make the place value visible. Teacher models 4,306 with place-value equipment and on the place-value modelling slides, connecting each digit to its value: 4 thousands, 3 hundreds, 0 tens and 6 ones. Record 4,306, four thousand three hundred and six, and 4,000 + 300 + 6. Students build 2,580, draw or record their representation, and explain the zero in the tens place to a partner.

3. 13–22 min · Represent it three ways. Teacher distributes the number representations and comparison worksheet and models the first example, using equipment or a quick sketch before writing. Students complete three teacher-selected numbers, representing each in digits, expanded notation and on a number line. Pause to ask: “Which representation makes the value of the hundreds easiest to see?” and select two different strategies to share.

4. 22–34 min · Partner challenge: Build, change, explain. Teacher displays challenge instructions on the partner challenge slides and gives each pair place-value equipment and number cards or teacher-called numbers. Partner A chooses or receives a number between 1,000 and 9,999; Partner B builds it, writes its expanded form and places it approximately on a number line. Partner A changes one digit and asks, “Which number is greater now? How do you know?” Students swap roles and complete at least two rounds, explaining their comparison using “first I compared the…, then I compared the…”.

5. 34–40 min · Reasoning discussion. Teacher presents two comparison prompts on the reasoning discussion slides, such as 4,098 and 4,890, then 7,205 and 7,250. Invite pairs to show evidence using equipment, expanded notation or a number line. Students agree or disagree respectfully, identify the first place value that differs, and improve an explanation such as: “4,890 is greater because both numbers have 4 thousands, but 8 hundreds is greater than 0 hundreds.”

6. 40–45 min · Exit task and next steps. Teacher displays the exit instructions on the exit-task slide and students independently complete the final section of the number representations and comparison worksheet: compare 6,407 and 6,470, circle the greater number, represent both in expanded notation, and justify the answer with place-value evidence. Collect responses to identify who needs further support with zero as a place holder, expanded notation or comparing from the greatest place.

Resources

• the number sense teaching deck
• the number representations and comparison worksheet
• Place-value equipment: thousands, hundreds, tens and ones blocks or place-value discs
• Individual or paired number lines marked from 0 to 10,000
• Mini-whiteboards and pens
• Number cards or teacher-prepared numbers from 1,000 to 9,999
• Pencils and highlighters
• One place-value chart per pair

Assessment

• Listen during modelling and partner work for accurate use of thousands, hundreds, tens and ones and for explanations that compare the first differing place.
• Check worksheet representations for consistency between digits, expanded notation, equipment and number-line position.
• Use the exit task to group students for next learning: reteach place value with concrete materials, practise comparing numbers, or extend reasoning with numbers containing zero and multiple possible representations.

Differentiation

• Support learners with a labelled place-value chart, concrete equipment, pre-marked number lines and sentence frames: “___ is greater than ___ because…”.
• Limit supported numbers initially to three or four digits, then introduce 10,000 when the learner is ready. Say numbers aloud and display them in large, clear print for learners who need visual or language support.
• For EAL learners, explicitly model and revisit “digit”, “value”, “thousands”, “expanded notation”, “greater than” and “less than”; allow drawing, pointing and oral rehearsal before written explanations.
• Extend confident learners by asking them to create two different numbers that satisfy a set of clues, find the smallest and greatest possible numbers, or explain why comparing the greatest place first is an efficient strategy.