Finding Unknown Values

Overview

In this final lesson of Mastering Addition and Subtraction, students solve addition and subtraction equations with missing numbers. Using balance models, counters and open number lines, they develop an understanding that the equal sign shows equivalence and explain strategies for finding the unknown.

Learning intentions

Students will:

• Represent unknown values using concrete materials and balance models.
• Solve missing-number addition and subtraction equations.
• Use inverse operations and related facts to check solutions.
• Explain how they know an equation is balanced and true.

Success criteria

• I can show an unknown number with counters or a drawing.
• I can find the missing number in an addition or subtraction equation.
• I can use addition or subtraction to check my answer.
• I can explain my strategy using mathematical language.

Curriculum links

• Number relationships and algebraic thinking: recognise, represent and solve problems involving unknown numbers in addition and subtraction.
• Equality and equivalence: understand that both sides of an equation must have the same value.
• Additive strategies: use mental strategies, partitioning, counting on, counting back and inverse operations.
• General capabilities: Critical and Creative Thinking through strategy selection; Personal and Social Capability through turn-taking, collaboration and explaining ideas.

Lesson structure (45 minutes)

1. 0–5 minutes – Welcome, hook and learning intention Open with the hook and learning intention slides. Display: □ + 6 = 14. Ask, “What number could hide in the box? How can we prove it?” Briefly explain that today students are mathematical detectives finding unknown values.

2. 5–12 minutes – Model equality with a balance Use a physical balance, two labelled containers or a drawn balance. Place 6 counters on one side and 14 on the other, then ask students what must be added to the side with 6 to make it equal. Model □ + 6 = 14, recording 8 + 6 = 14. Emphasise that the equals sign means “has the same value as”, not “the answer comes next”. Refer to the balance model slides.

3. 12–20 minutes – Guided hands-on investigation Give each student counters, two hoops or paper circles labelled “left side” and “right side”, and an equation card prepared by the teacher. Students build both sides and find the unknown by adding, removing or comparing counters. Work through examples such as 9 + □ = 15, 17 − □ = 10 and □ − 4 = 8, adjusting numbers for readiness. Prompt: “What do you know? What operation will help? How can you check?”

4. 20–32 minutes – Independent and supported practice Distribute the missing-number equations worksheet. Students solve equations using counters, drawings, number lines or mental strategies, then write a checking equation. Include a core set with numbers within 20, a Year 3 set extending to 100, and a Year 4 set involving two- and three-digit numbers. Sit beside students who need support and solve the first example together.

5. 32–39 minutes – Strategy share and error analysis Reopen the strategy and discussion slides. Select two equations from the worksheet and invite students to explain different methods, such as counting on, using the inverse operation or finding the difference. Show an incorrect example, such as □ + 7 = 12, answer 6, and ask students to identify and correct the error by testing both sides.

6. 39–45 minutes – Exit check and reflection Finish with the number sentence strip cards. Give each student one suitable strip to complete, or write an equivalent prompt on a strip if needed. Students solve, check their answer and explain it aloud or record a short explanation. Revisit the success criteria using the plenary and reflection slide and ask, “Which strategy helped you most?”

Resources

• the introduction, modelling, strategy and plenary slides
• the missing-number equations worksheet
• Counters or linking cubes
• Balance scale, two containers or a drawn balance model
• Two hoops or paper circles for equation sides
• Mini whiteboards and markers
• Pencils, erasers and highlighters
• Prepared equation cards with differentiated number ranges

Assessment

• Observe whether students maintain equality when building and solving equations.
• Confer during worksheet practice, noting strategy choice, use of inverse operations and ability to explain reasoning.
• Collect or photograph the completed number sentence and listen for accurate use of “equal”, “unknown”, “difference”, “add” and “subtract”.

Differentiation

• Support: use numbers within 20, concrete counters, colour-coded equation sides and a visual prompt: “What do I know? What is missing? How will I check?” Read equations aloud and provide one-to-one modelling.
• Year 3 access: use numbers within 100, open number lines and fact families; allow students to draw before recording a numeral.
• Year 4 extension within the lesson: use two- and three-digit equations, unknowns in different positions and equations such as □ + 38 = 105 or 146 − □ = 89.
• ADHD, Autism and EAL support: keep the low-variance sequence visible, give one instruction at a time, use a clear turn-taking routine, offer a quiet workspace or movement break, and provide sentence stems such as “I know ___ because ___.”