Mixed Skill Challenge

Learning Objectives

• Recognise and explain the connection between addition and subtraction as inverse operations; apply to partition numbers and find unknown values in number sentences. - Extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator. - Add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator. - Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies. ## Duration 15 minutes

Class Size

1 student

Resources Needed

• Worksheet station cards with questions and prompts
• Base ten blocks or counters
• Whiteboard and markers
• Paper and pencil
• Calculator (optional)
• Manipulatives for visual models (e.g., small objects for grouping)
• Timer or clock

Lesson Structure and Activities

Introduction (2 minutes)

• Quick warm-up: Ask the student to recall known addition and subtraction facts to 20.
• State the focus: “Today, you will work through different challenge stations solving problems that use addition, subtraction, and problem-solving skills. You'll explain your thinking as you go.”
• Explain that at each station the tasks become a little more challenging and will ask the student to use different strategies, including reasoning and calculations.

Station 1: Number Sentences and Inverse Operations (4 minutes)

• Task: Use part-part-whole diagrams and bar models to represent addition and subtraction problems.
• Questions start at simple facts and progress to unknown values:
• Simple: (16 + 8 =?)
• Intermediate: Find the missing number: (24 - \square = 8)
• Advanced: “Peter had some money, spent $375, now has $158. How much did Peter start with?” Represent as a number sentence and solve.
• Encourage the student to explain how each number relates to the problem and how addition and subtraction connect.

Station 2: Efficient Mental Strategies for Larger Numbers (4 minutes)

• Task: Solve addition and subtraction problems by partitioning and regrouping without a calculator.
• Start with two-digit additions, progressively moving to three-digit numbers:
• Easy: (56 + 37 =?) (Teach partitioning tens and ones)
• Medium: (214 + 325 =?) (Use place value groups)
• Hard: (485 + 365 =?) (Use non-standard partitioning, e.g., by subtracting to make easier sums)
• Facilitate the student to verbalise mental steps; model parts-jottings if needed.

Station 3: Problem-Solving with Mathematical Modelling (5 minutes)

• Task: Solve practical problems involving addition, subtraction, and multiplication using bar models and number sentences.
• Example problems:
• “I had 75 tomatoes and picked some more, now I have 138. How many did I pick?”
• “There are 4 tomato plants. Each has 6 tomatoes. How many tomatoes in total?”
• “A prize of $36 is shared equally among 4 people. How much does each get?”
• Encourage making bar models and explaining solution choice: addition, multiplication, or division.
• Prompt reflective questions: How do you know your answer is reasonable? What strategies helped?

Conclusion and Reflection (1 minute)

• Ask the student to summarise the strategies they used and which concepts were easiest or hardest.
• Praise effort and highlight progress from simple to complex tasks.
• Emphasise the importance of reasoning and discussing methods to deepen understanding.

Assessment and Feedback

• Observe the student’s ability to represent problems with models.
• Listen to explanations for reasoning about inverse operations and calculation choices.
• Check accuracy and efficiency in computations.
• Provide immediate feedback on strategies and encourage self-correction where needed.
• Use questioning to deepen thinking rather than just giving solutions.

Alignment with Australian Curriculum (Version 9)

• This lesson directly supports Number and Algebra content:
• AC9M3A01 supports understanding addition and subtraction as inverse operations with number sentences.
• AC9M3A02 focuses on developing mental strategies for larger number computations.
• AC9M3N03 develops concrete calculation skills using place value and partitioning for multi-digit operations.
• AC9M3N06 engages students with mathematical modelling for practical problem-solving in additive and multiplicative contexts.
• The activities encourage reasoning, problem-solving, and communication of mathematical ideas, key proficiencies in the Australian Curriculum.
• The lesson is scaffolded to progress from foundational skills to more complex application, promoting a move from a C to an A level of understanding through mixed-skill challenge stations.

This approach provides a rich, varied engagement with key Year 3 mathematical content, personalised for a single student while promoting deep conceptual and applied understanding within a concise 15-minute timeframe.