Divide With Confidence

Overview

Students revisit the written algorithm for dividing a four-digit number by a two-digit number, focusing on place value, estimating, recording each quotient digit, and checking with multiplication. The lesson is a short re-instruction session that builds on students’ prior understanding of multiplication facts and division with one-digit divisors.

Learning intentions

• WALT divide a four-digit number by a two-digit number using a written method.
• WALT use estimation to decide how many times the divisor will fit.
• WALT record quotient digits in the correct place-value columns.
• WALT check a division answer using multiplication and the remainder.

Success criteria

• I can divide from left to right, using place value to decide what to divide.
• I can estimate, multiply, subtract and bring down in the correct order.
• I can place each quotient digit above the correct column.
• I can check that my answer is reasonable and use multiplication to verify it.

Curriculum links

• Mathematics and Statistics — Number: applying multiplicative thinking and written strategies to division.
• Mathematics and Statistics — Number: using place value, estimation, multiplication and division relationships.
• Mathematics and Statistics — problem solving: explaining, checking and communicating mathematical thinking.
• Mathsteasers: developing higher-order thinking and challenge through non-routine mathematical questions.

Lesson structure (20 minutes)

1. 0–3 min · Hook and diagnose. Teacher displays 3,276 ÷ 24 and asks, “Before calculating, about how large should the answer be?” Students estimate independently, then briefly compare with a partner. Open with the estimation question and note common estimates on the board.

2. 3–8 min · Re-instruct the algorithm. Teacher uses the same example to model the cycle: estimate, divide, multiply, subtract, bring down, and repeat. Emphasise that the first quotient digit is written above the thousands/hundreds section being divided, not simply above the first digit; model 32 ÷ 24, then bring down 7 to make 87, followed by 3,276 ÷ 24 = 136 remainder 12. Students track each step on their worksheet and explain why 24 cannot fit into 3 but can fit into 32. Refer to the worked long-division example.

3. 8–12 min · Guided practice. Teacher works through 4,368 ÷ 18 with the class, pausing after each stage for students to predict the next quotient digit and check the multiplication. Students complete the matching example on the guided long-division practice sheet and show a partner where each quotient digit belongs. Use place-value language such as “4 thousands, 3 hundreds, 6 tens and 8 ones”.

4. 12–17 min · Independent practice and feedback. Teacher directs students to complete two problems: 5,184 ÷ 24 and 6,735 ÷ 32, including remainders where appropriate. Students use the written scaffold on the independent practice questions; they must estimate first and check at least one answer using divisor × quotient + remainder. Teacher circulates, checking alignment of quotient digits and intervening with the prompt, “What number are you dividing now?”

5. 17–20 min · Plenary and exit check. Teacher displays 2,496 ÷ 16 and asks students to write the first quotient digit and explain why it belongs in that place. Students complete the short exit response on the final check question, then share one error to avoid. Reveal the completed structure using the plenary and checking slide.

Resources

• the long-division re-instruction deck
• the guided long-division practice sheet
• Whiteboard and markers
• Student exercise books and pencils
• Place-value chart displayed or drawn on the board
• Multiplication fact charts for students who need them
• Calculators for checking only, if available

Assessment

• During modelling, listen for students’ explanations of why the divisor is first compared with 3, then 32, and monitor whether quotient digits are aligned correctly.
• During independent practice, check estimation, the repeated divide–multiply–subtract–bring-down cycle, and whether remainders are smaller than the divisor.
• Use the final check question to identify students needing another guided example; collect or photograph worksheets for evidence of strategy and accuracy.

Differentiation

• Support students with a place-value chart, a clearly boxed sequence of “divide, multiply, subtract, bring down”, multiplication facts, and a partially completed first problem. Allow verbal rehearsal with a partner before recording.
• For students who confuse place value, cover unused digits and reveal the dividend one section at a time, asking, “What number are we working with now?”
• Provide an optional calculator check after the written method, not before, so students can compare and correct their reasoning.
• Extend confident students by asking them to create a four-digit dividend with a two-digit divisor that gives a remainder of 7, then prove that their answer is correct. Support EAL learners with visual arrows, consistent gestures and the sentence frame: “The divisor fits ___ times into ___ because ___ × ___ = ___.”