Partition Numbers to Add

Overview

In this 25-minute small-group lesson, 8 Year 4 students use place value to add two- and three-digit numbers by partitioning. They represent numbers, explain their thinking, and compare partitioning with another efficient strategy.

Learning intentions

• WALT partition numbers into hundreds, tens and ones.
• WALT add parts separately and recombine them to find a total.
• WALT explain how place value helps us add efficiently.
• WALT listen to and respond respectfully to different mathematical ideas.

Success criteria

• I can partition a number into hundreds, tens and ones.
• I can add the parts accurately and recombine them.
• I can record a number sentence and show my thinking.
• I can explain why my strategy works.

Curriculum links

• Exploring and using mathematical ideas through active investigation and problem-solving.
• Developing confidence and competence with number, quantity and relationships.
• Communicating mathematical thinking using words, drawings, materials and symbols.
• Learning through responsive, reciprocal relationships and respectful participation.

Lesson structure (25 minutes)

1. 0–3 minutes – Notice and wonder

Open with the hook and learning intention slides. Display: “How could we solve 47 + 35 without counting every one?” Invite students to think silently, then share a quick idea with a partner. Establish that there may be more than one sensible strategy.

2. 3–8 minutes – Model partitioning

Use the place-value modelling slides and the place value partitioning strategy mat under the teacher’s demonstration. Build 47 and 35 using place-value representations, then partition:

47 + 35 = (40 + 7) + (30 + 5) = (40 + 30) + (7 + 5) = 70 + 12 = 82.

Ask: “What did we add first? Why is it helpful to keep tens with tens and ones with ones?” Emphasise that 12 ones can be regrouped as 1 ten and 2 ones.

3. 8–12 minutes – Guided practice

Display the examples on the guided practice slides. Solve 26 + 43 and 58 + 27 together. Invite students to suggest each step while the teacher records the partitioned equation. Check that students can explain the regrouping in 58 + 27: 50 + 20, then 8 + 7 = 15.

4. 12–20 minutes – Partner problem-solving

Give each pair the partitioning addition practice worksheet. Students solve four problems, such as 34 + 25, 46 + 38, 127 + 42 and 153 + 126. They must show partitioning, calculate the total, and circle one problem they can explain.

Keep the partner task and discussion prompt slides visible. Pair students strategically and circulate, asking: “How did you partition?” “What does this part represent?” and “Can you check your answer another way?” Students may use the strategy mat or drawings if needed.

5. 20–23 minutes – Share and compare

Return to the strategy comparison slides. Select two students to explain different examples. Compare partitioning with a vertical or open-number-line method without presenting one method as the only correct approach. Discuss how place value is visible in both strategies.

6. 23–25 minutes – Exit reflection

Use the plenary slide. Students complete the final box on the worksheet: solve 72 + 19 by partitioning and finish the sentence, “Partitioning helps me because…”. Invite two students to share. Collect worksheets for assessment.

Resources

• the complete addition and partitioning slide deck
• the partitioning addition practice worksheet
• the place value partitioning strategy mat
• Place-value blocks or counters
• Mini-whiteboards and pens
• Pencils and erasers
• A large place-value chart
• Prepared pairs or mixed-ability seating

Assessment

• Observe whether students partition each addend accurately into hundreds, tens and ones.
• Listen for explanations that connect the calculation to place value, especially when regrouping 10 or more ones.
• Use the worksheet and exit reflection to identify students who can calculate but cannot yet explain the strategy.

Differentiation

• Support learners with place-value blocks, the strategy mat, a large place-value chart and sentence stems: “I partitioned ___ into ___ and ___.” Allow them to begin with two-digit examples.
• Work with a small teacher-led group using one problem at a time. Colour-code hundreds, tens and ones and rehearse the language orally before recording.
• Support EAL learners with visuals, gestures, partner talk and repeated vocabulary such as “partition”, “tens”, “ones”, “add” and “total”. Accept drawings and oral explanations alongside equations.
• Extend confident learners with three-digit additions involving regrouping in more than one place. Ask them to solve one problem using two strategies and justify which is more efficient.