Make the Whole

Overview

Students revisit known addition and subtraction facts, then use them to find complements to 10, 20 and 100. The warm-up moves from familiar facts to Year 3 number knowledge, with students explaining strategies such as counting on, using known facts and bridging through a tidy number.

Learning intentions

• WALT find the missing number needed to make a whole of 10, 20 or 100.
• WALT use addition and subtraction facts to solve missing-number equations.
• WALT explain and check a strategy for finding a complement.
• WALT work cooperatively to match equations and answers.

Success criteria

• I can complete equations such as 34 + __ = 100.
• I can match an addition equation with its missing complement.
• I can explain how I checked my answer.
• I can use a known fact or bridge through a tidy number.

Curriculum links

• Mathematics and Statistics — Number: recall and apply addition and subtraction facts.
• Mathematics and Statistics — Number: find missing parts and complements within 100.
• Mathematics and Statistics — Mathematical practices: notice patterns, choose efficient strategies and justify thinking.
• Mathsteasers: use higher-order thinking and explanation to deepen mathematical understanding.
• Key competencies: thinking, relating to others, participating and contributing.

Lesson structure (10 minutes)

1. 0–1 min · Hook. Display the question “What number is missing: 34 + __ = 100?” using the opening complement question. Students silently decide what they would add and show a possible answer with their fingers or on mini-whiteboards.

2. 1–3 min · Connect to known facts. Teacher briefly revisits the progression 7 + 3 = 10, 17 + 3 = 20 and 34 + __ = 100, using the progression from 10 to 20 to 100. Students solve each equation and identify whether they counted on, used a known fact or bridged through a tidy number.

3. 3–4 min · Model a strategy. Teacher models 34 + __ = 100 by bridging through 40: 34 + 6 = 40, then 40 + 60 = 100, so the complement is 66. Record the matching subtraction, 100 − 34 = 66, and students explain why both equations check the same answer.

4. 4–7 min · Pair card hunt. Teacher places or hands out mixed equation and complement cards, explaining the task with the make-the-whole card hunt instructions. Students work in pairs, or one group of three, to find matches for totals of 10, 20 or 100, then record each match and the strategy used on the make-the-whole recording sheet.

5. 7–9 min · Check and explain. Teacher selects two matches, including one complement to 100, and asks pairs to justify them using the prompts on the strategy discussion prompts. Students compare answers with another pair and check by adding the two parts or subtracting the known part from the whole.

6. 9–10 min · Exit check. Display “58 + __ = 100” and “__ + 7 = 20” on the final exit questions. Students record both answers and one short strategy on the bottom of the make-the-whole recording sheet, then hold their work up for a quick teacher scan.

Resources

• the make-the-whole warm-up and card-hunt deck
• the make-the-whole recording sheet
• the editable make-the-whole task cards
• Mini-whiteboards and pens
• Prepared addition-equation and complement cards
• Pencils
• Timer
• Visualiser or board

Assessment

• Listen for whether students identify the missing part rather than treating the blank as an operation symbol.
• During the card hunt, check recorded matches and ask: “How do you know?” Look for counting on, known facts, bridging through a tidy number or checking with subtraction.
• Use the two exit questions to identify students who can find complements to 20 and 100 independently.

Differentiation

• Support students with a number line to 100, tens-and-ones partitioning and the sentence frame: “I know ___ + ___ = ___, so ___ + ___ = ___.”
• Allow students who need concrete support to build the whole with counters or use a hundred chart before recording the equation.
• Pair students strategically and give the group of three clearly allocated roles: finder, checker and recorder.
• Challenge confident students to find two different strategies for the same complement, write the related subtraction equation and create a new “make 100” card for a partner.