Order Operations Intro

Year Level

Year 10 (New Zealand Curriculum Phase 4)

Duration

60 minutes

Class size

20 students

Curriculum Alignment

Learning Area: Mathematics and Statistics
Strand: Number -> Operations
Level: Years 9–10 (Phase 4)

Key Learning Objectives:

Understand and use the order of operations to evaluate expressions involving addition, subtraction, multiplication, division, and exponents.
Use the mnemonic GEMA (Grouped, Exponents, Multiplicative, Additive) to remember the order of operations.
Explain why the order of operations is essential to avoid ambiguity in mathematical calculations.
Apply order of operations in practical and algebraic contexts.

These align with the New Zealand Curriculum Mathematics and Statistics learning progressions for Year 10, which emphasise evaluating expressions using order of operations and understanding related concepts such as exponents, grouping symbols, and operations precedence .

Key Competencies

Thinking: Use logic and reasoning to understand the order of operations.
Using language, symbols, and texts: Understanding and using correct mathematical notation and vocabulary.
Managing self: Persevering with challenging problems.
Relating to others: Discussing and explaining reasoning to peers.

WALT (We Are Learning To)

Understand the importance of order of operations in mathematics.
Recognise and apply the correct sequence of operations to simplify expressions accurately.

Success Criteria

Students will be able to:

Explain why the order of operations is necessary to avoid different answers.
Recite and use the mnemonic GEMA to solve numerical expressions.
Demonstrate the correct order when evaluating expressions containing brackets, exponents, multiplication/division, addition/subtraction.
Use visual aids and manipulatives to reinforce understanding.

Resources

Whiteboard or interactive board
Printed worksheets with clear fonts and wide spacing (dyslexia-friendly)
Colour-coded cards or manipulatives representing operations (e.g., brackets, powers, ×, ÷, +, -)
Sample expressions printed on large cards for group work
Timer or clock to manage activities
Student maths books for recording work

Lesson Outline

Time	Activity	Description	Differentiation / Notes
0–10 min	Introduction and Context	Engage students in a discussion: "Why do you think the order in which we do calculations matters?" Use simple examples like 2 + 3 × 4 done in different orders. Introduce the concept that without rules, maths would be ambiguous. Present the mnemonic "GEMA" (Grouped, Exponents, Multiplicative, Additive) on the board with examples.	Use visual colour-coded poster for GEMA mnemonic. Use clear dyslexia-friendly font.
10–25 min	Interactive Demonstration with Manipulatives	Students work in pairs with sets of coloured cards representing different operations and grouping brackets. Teacher models how to build expressions and decide which operation to perform first. Use examples that gradually increase in complexity, e.g., 6 + (2 × 3) − 4².	Support ELL and visual learners with step-by-step prompts and visual aids. Advanced learners can be challenged with expressions including nested brackets and exponents.
25–40 min	Guided Practice with Worksheet	Students individually solve a worksheet with expressions of increasing difficulty following order of operations rules. Include space for students to write why they chose a particular step first. Circulate to support students needing extra help.	Provide scaffolds such as step hints or partially completed examples for students needing support. Provide extension tasks (create own expressions and explain their order of operations).
40–50 min	Group Discussion and Explanation	Students share their problem-solving approaches and explain their reasoning on select problems from worksheet. Teacher highlights common misconceptions and reinforces correct concepts. Emphasise correct mathematical vocabulary (e.g., exponent, bracket, multiply).	Use guided questions to stimulate reflection and peer explanation. Encourage use of first or heritage languages for explanation if helpful (bilingual support).
50–60 min	Reflection and Assessment	Quick quiz: verbal or written - students explain why the order of operations is important using their own words, then solve one final expression. Collect responses for formative assessment.	Provide printed prompt cards with sentence starters ("The order of operations is important because...") and use clear spacing and fonts for dyslexia-friendly access.

Differentiation

Visual / Dyslexia-friendly: Use large print, clear fonts (e.g., sans serif), colour coding, spaced layout on materials.
Hands-on learners: Use manipulatives and physical cards to represent operations.
Support learners: Step-by-step scaffolding, use of worked examples, teacher or peer support.
Extension learners: Create own expressions including grouping and exponents, explain reasoning to class or in writing.

Key Vocabulary

Order of Operations
Brackets (Grouped)
Exponents (Powers)
Multiplication and Division (Multiplicative)
Addition and Subtraction (Additive)
Expression
Evaluate

Use vocabulary teaching techniques such as the Frayer model (definition, characteristics, example, non-example) and encourage students to use correct terms when explaining solutions.

Assessment

Formative assessment through:

Observation during manipulative and guided practice activities.
Responses to class discussion questions.
Worksheet accuracy and explanations.
Final reflection quiz explaining importance of order of operations.

Teaching Considerations

Emphasise use of one equal sign per line when solving (to avoid confusion).
Regularly check understanding by asking students to justify steps.
Use real-world or familiar contexts where possible to engage students.
Encourage persistence when students encounter challenging expressions.
Make connections to future concepts such as algebra and solving equations.

Follow-up

This is Lesson 1 of 11 in the unit "Mastering Order of Operations". Future lessons will build on this foundation with application in algebra, word problems, and exploring exceptions or common misconceptions.

This lesson plan is designed to align closely with the New Zealand Curriculum's Number and Operations strand for Year 10 students. It utilises methods emphasised in Te Mātaiaho including explicit teaching, use of mathematical language, multiple representations, and rich discussion to support conceptual understanding and proficiency 【4:15†Te Mataiaho Maths 0-

Teaching Instructions