Build, Break, Explain

Overview

Students investigate numbers to 10,000 by representing them with place-value parts, regrouping hundreds, tens and ones, and explaining how different representations show the same number. The lesson builds on prior work with place value and supports flexible mental and written calculation strategies through a higher-order number challenge.

Learning intentions

• WALT represent numbers to 10,000 in more than one way.
• WALT partition and recombine numbers using place value.
• WALT use addition and subtraction to check whether representations are equivalent.
• WALT explain and justify a mathematical strategy clearly.

Success criteria

• I can identify the value of each digit in a four-digit number.
• I can partition a number in at least two different ways.
• I can use a calculation or representation to prove my answer.
• I can explain why two representations are equivalent.

Curriculum links

• Mathematics and Statistics — Number: place value, representing, partitioning and recombining whole numbers.
• Mathematics and Statistics — Number: using additive thinking to calculate and check.
• Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathsteasers / Alignment: connecting challenge questions with relevant mathematical learning.

Lesson structure (40 minutes)

1. 0–5 min · Hook and notice. Teacher opens the number mystery hook and displays the number 3,640 alongside the question, “How many different ways can we build this number?” Students think independently, then share one possible representation with a partner.

2. 5–12 min · Model place-value thinking. Teacher uses the place-value model slides to model 3,640 as 3,000 + 600 + 40, then demonstrates alternative partitions such as 36 hundreds + 4 tens and 3,500 + 140. Emphasise that the total value remains unchanged even when regrouping occurs. Students identify the value of each digit and explain what has been regrouped.

3. 12–25 min · Main investigation. Teacher distributes the Build, Break, Explain investigation sheet and sets pairs the challenge: “Find as many correct ways as possible to represent each number, then prove that two ways are equivalent.” Students work in pairs on numbers such as 2,408, 5,070 and 8,999, recording expanded form, regrouped form, a number-line or place-value representation, and a checking calculation. Circulate and ask, “What has changed? What has stayed the same?” and “How do you know your representation is correct?”

4. 25–32 min · Compare strategies. Teacher pauses the class and uses the compare-and-justify slides to show two deliberately different representations of 4,250, including one incorrect example. Students discuss in groups of three whether each representation is correct, locate any error, and prepare a justification using a calculation or place-value explanation.

5. 32–37 min · Challenge and share. Teacher presents the final prompt on the Mathsteaser challenge slide: “I am thinking of a four-digit number. It has 6 hundreds, 4 fewer tens than hundreds, and 2 more ones than tens. What could the thousands digit be? Explain what information is still needed.” Students solve individually before sharing with a partner. Invite two or three students to explain why more than one answer may be possible.

6. 37–40 min · Exit check and reflection. Teacher displays the reflection prompt on the plenary slide and asks students to complete the final box on their worksheet: “Partition 7,306 in two different ways and prove both are equal.” Students hand in their response and state one strategy that helped them.

Resources

• the number mystery and teaching slides
• the Build, Break, Explain investigation sheet
• Whiteboard and markers
• Place-value blocks or bundled sticks, if available
• Individual whiteboards or scrap paper
• Pencils and highlighters
• Projector or interactive display

Assessment

• During modelling, ask individuals to explain the value of a digit rather than accepting a choral response.
• During pair work, check whether students preserve the total when regrouping and whether their written calculations prove equivalence.
• Use the exit response to identify students who need further support with zero as a placeholder, regrouping, or explaining mathematical reasoning.

Differentiation

• Support students with a place-value chart, concrete materials and a partially completed example. Begin with three-digit numbers before moving to four-digit numbers where needed.
• Provide sentence starters: “The ___ represents…”, “I know these are equal because…”, and “I regrouped ___ as…”.
• Pair students strategically and allow students to explain orally before recording. Use clear visual models and read all instructions aloud to support EAL learners and students with literacy needs.
• Extend confident students by asking them to find the greatest number of partitions for one number, create an incorrect representation for a partner to correct, or write their own number riddle with more than one possible answer.