Build and Balance

Overview

In this first lesson of the five-lesson unit Number Sentences Make Sense, students explore open addition and subtraction sentences. They use concrete materials, drawings and mathematical language to find a missing number and explain why both sides of an equation are equal.

Learning intentions

• WALT complete open number sentences involving addition and subtraction of one-digit numbers.
• WALT use counters, ten-frames and part-part-whole models to solve problems.
• WALT explain how both sides of an equation can have the same value.
• WALT use a problem-solving strategy and mathematical language to justify an answer.

Success criteria

• I can find the missing number in an open number sentence.
• I can use materials or a drawing to prove my answer.
• I can explain how both sides of an equation are equal.
• I can use words such as part, whole, equals, same as and missing number.

Curriculum links

• Mathematics and Statistics — Number: use mathematical language, representations and problem-solving strategies to reason about addition and subtraction.
• Te Mātaiaho Mathematics and Statistics — Mathsteasers: use higher-order thinking questions to deepen mathematical understanding.
• Mathematics and Statistics — Number: connect concrete materials, drawings, part-part-whole models and number sentences.
• The key competencies are developed as students manage self-directed investigation, participate in mathematical discussion and explain their thinking.

Lesson structure (60 minutes)

1. 0–10 min · Warm-up: Notice and solve. Teacher displays the opening question from the introduction and warm-up slides: “Which number could go in the box: 2 + 5 = 3 + □?” and invites students to think, talk with a partner and share possible strategies. Students solve mentally or with fingers, then explain what they noticed about the two sides; avoid confirming an answer until students have justified it.

2. 10–25 min · Model: Build both sides. Teacher models 2 + 5 = 3 + □ using counters and the ten-frame mats, building each side separately and asking, “How many are there altogether?” and “What must the missing part be so both sides show the same amount?” Students help place counters, draw a part-part-whole model and record 2 + 5 = 3 + 4. Teacher explicitly demonstrates that the equals sign means “has the same value as”, not “the answer comes next”.

Repeat with one subtraction example, such as 8 − 3 = □ − 2, using a number track or counters to show that both sides equal 5. Refer to the modelling slides for the visual equations, prompts and worked examples. Emphasise that students may solve by building, counting on, using a known fact or comparing totals.

3. 25–30 min · Guided practice: Prove it. Teacher solves one example with the class, deliberately making an incorrect choice for the missing number and asking, “How can we check?” Students work with a partner to build or draw both sides, then use the sentence frame: “The missing number is __ because __ + __ and __ + __ both equal __.”

4. 30–50 min · Partner investigation: Build, record, explain. Teacher pairs students and distributes the open number sentences investigation sheet; provide counters and ten-frame mats to every pair. Students solve open sentences such as 4 + 2 = 3 + □, 1 + 7 = □ + 5, 9 − 4 = 6 − □ and 7 − □ = 2 + 1. For each, they build or draw a representation, write the missing number and explain how they checked it. Teacher circulates, asks “What does each side equal?”, “Which part is missing?” and “Can you find another way?”, recording observations of strategy use and mathematical vocabulary.

5. 50–60 min · Reflection: Convince us. Teacher displays the reflection prompts from the discussion and plenary slides: “Which strategy helped you most?” and “How do you know both sides are equal?” Selected pairs present one sentence and their proof. Students complete the final worksheet reflection: “I know my answer is correct because…” Teacher revisits the WALT and invites students to self-assess against the success criteria using a thumbs signal.

Resources

• the introduction, modelling, investigation and plenary slide deck
• the open number sentences investigation sheet
• the ten-frame mats
• Two-colour counters, approximately 10 per student
• Pencils, erasers and crayons
• Number tracks to 20
• Whiteboard and markers
• Mini-whiteboards or scrap paper
• Prepared sentence-frame cards or board prompts

Assessment

• During modelling and guided practice, check whether students interpret the equals sign as “same value as” and can represent both sides.
• During the investigation, observe whether students find the missing number, select an appropriate strategy, check their answer and explain it using mathematical language.
• Use the worksheet reflection and a brief conference with selected pairs to identify students ready for greater complexity or needing further work with number bonds and subtraction.

Differentiation

• Support learners with smaller numbers, counters, ten-frames, number tracks and a part-part-whole model. Begin with sentences where the missing number is the final addend before moving the blank to another position.
• Use guided practice with a teacher-led group. Provide sentence frames such as “Both sides equal __”, “I built __ and __”, and “The missing number is __ because __”.
• For EAL learners and students requiring language support, rehearse part, whole, equals, same, missing and altogether with gestures, visuals and partner talk before recording.
• Extend advanced learners by asking them to create several different open sentences with the same missing number, including addition and subtraction, and explain the pattern. They can investigate whether changing the order of the parts affects the total.