Partitioning Makes Sense

Overview

Lesson 6 of 7 in Mastering Addition and Subtraction. Students use place value partitioning to break numbers into hundreds, tens and ones, then recombine the parts to solve addition and subtraction problems. The lesson follows a low-variance sequence: I do, we do, you do, review.

Curriculum links

• Place value: recognise the value of digits in two-, three- and four-digit numbers.
• Addition and subtraction: use efficient mental and written strategies to solve problems.
• Mathematical modelling: represent problems with materials, diagrams and equations.
• Reasoning and communication: explain strategies using mathematical language and check whether answers are sensible.

Learning intentions

Students will:

• partition numbers into place value parts.
• use concrete materials and visual models to add and subtract.
• record partitioning strategies as equations.
• explain why partitioning helps produce an accurate answer.

Success criteria

• I can partition a number into hundreds, tens and ones.
• I can use place value parts to solve an addition or subtraction problem.
• I can show my thinking with materials, a drawing or an equation.
• I can explain how I checked my answer.

Lesson structure (45 minutes)

1. 0–5 minutes – Settle, connect and state the goal Seat the four students where materials and the teacher model are clearly visible. Open with the hook and learning intention slides and display: “How can 246 be easier to work with than it first appears?” Students briefly share what they notice. State: “Today we will break numbers apart by place value, solve, and explain our thinking.”

2. 5–13 minutes – Explicit teacher model: addition Use place value blocks, bundled sticks or a place value chart to build 246 and 132. Partition each number: 246 = 200 + 40 + 6 and 132 = 100 + 30 + 2. Model adding like place values: 200 + 100, 40 + 30 and 6 + 2, then recombine to make 378. Record the matching written equation on the partitioning model slides. Think aloud: “I keep hundreds with hundreds, tens with tens and ones with ones.”

3. 13–20 minutes – Guided practice: subtraction Build 368 and remove 124 using materials. Partition and solve: (300 − 100) + (60 − 20) + (8 − 4) = 244. Ask students to point to each place value as it is discussed. Repeat with a suitable example; for Year 2, use two-digit numbers or subtraction without renaming. For Years 3–4, briefly discuss what changes when there are not enough ones or tens, without requiring formal renaming unless students are ready. Refer to the guided subtraction slides.

4. 20–31 minutes – Supported partner practice Give each student a small selection of cards from the addition strategies task cards and provide place value materials. Students solve one addition or subtraction problem at a time, first building or drawing the numbers, then partitioning and recording the calculation on the place value partitioning practice sheet. After each problem, the student explains their method to a peer or the teacher using: “I partitioned ___ into ___ because ___.” Prompt, rather than reteach, by asking: “Which place value will you combine first?”

5. 31–39 minutes – Independent differentiated practice Students complete the remaining worksheet questions independently. Suggested range: Year 2 uses two-digit addition and subtraction; Year 3 uses three-digit calculations without renaming; Year 4 uses three- or four-digit calculations, including one problem requiring regrouping if appropriate. Students may use materials, a place value chart or a drawn model. Circulate and record whether each student partitions accurately and aligns like place values.

6. 39–43 minutes – Reasoning and error analysis Open the reasoning and discussion slides. Show an incorrect example such as 235 + 124 = 2 hundreds + 5 tens + 3 ones + 1 hundred + 2 tens + 4 ones = 359. Ask students to identify the error and correct it. Students explain that ones, tens and hundreds must be combined with the same place value.

7. 43–45 minutes – Exit check and preview Ask each student to solve one brief problem orally or on a mini-whiteboard: “Partition 324 and use it to solve 324 + 145.” Use a subtraction alternative for students who need it. Revisit the reflection slide and preview Lesson 7: choosing and comparing efficient addition and subtraction strategies.

Resources

• the complete lesson slide deck
• the place value partitioning practice sheet
• Place value blocks, bundled sticks or linking cubes
• Place value chart or arrow cards
• Mini-whiteboards and markers
• Pencils and highlighters
• Small selection of addition strategy task cards
• Visual timer and quiet workspace

Assessment

• Observe whether students partition numbers correctly and combine matching place values.
• Check worksheet representations, equations and explanations for accuracy.
• Use the exit check to identify students needing further work with place value, subtraction or regrouping.

Differentiation

• Support: use two-digit numbers, colour-code hundreds, tens and ones, provide a completed example and allow students to build every number before recording.
• ADHD/autism support: use the same predictable instruction sequence for every question, provide a visual timer, limit cards on the table, offer movement or sensory breaks, and give one-step verbal directions with wait time.
• EAL/SEN: provide sentence stems, gestures and visual labels for “partition”, “hundreds”, “tens”, “ones”, “add”, “subtract” and “recombine”; accept oral explanation, drawing or pointing.
• Extension: ask students to solve the same problem using a second strategy and explain which method is more efficient and why.