Number Connections Showcase

Overview

Lesson 15 of 15 in the unit Number Connections: Fractions, Decimals, Percentages. Students complete and present a real-life investigation, selecting representations, solving multi-step problems, explaining strategies, and reflecting on efficiency.

Learning intentions

• WALT apply fraction, decimal and percentage knowledge in an integrated context.
• WALT select representations that help us solve and explain a problem.
• WALT communicate our mathematical thinking clearly.
• WALT reflect on and compare efficient strategies.

Success criteria

• I can select an appropriate representation for the problem.
• I can solve a multi-step problem accurately.
• I can communicate my strategy using mathematical language.
• I can explain why my method is efficient, or how it could be improved.

Curriculum links

• Number: use fractions, decimals and percentages to represent, compare and calculate with quantities.
• Number: connect equivalent representations and apply additive and multiplicative thinking in familiar contexts.
• Algebraic thinking: identify relationships, follow a sequence of steps and use information to solve an unknown.
• Mathematical communication and modelling: make decisions, justify strategies, interpret results and communicate reasoning.
• Key competencies: thinking; using language, symbols and texts; managing self; participating and contributing.

Lesson structure (45 minutes)

1. 0–5 minutes – Reconnect and introduce the challenge Open with the hook and learning intentions slides. Display a prompt such as: “How could we use fractions, decimals and percentages to make a fair and realistic plan for our class?” Briefly revisit equivalent forms, estimation and choosing a useful representation. Students turn and talk about where these ideas occur in everyday life.

2. 5–10 minutes – Model decision-making Use the worked-example slides to model a short class-event budget. For example, a class has $240, spends 25% on food, $60 on equipment and shares the remaining amount between two activities. Think aloud: identify the steps, estimate first, choose a table or bar model, calculate, and check whether the answer is reasonable. Emphasise that an answer without an explanation is incomplete.

3. 10–13 minutes – Explain task choices and success criteria Distribute the Number Connections investigation worksheet. Students choose one structured investigation: planning a class event budget, analysing participation percentages, or scaling a recipe. Read the options aloud and clarify that each task must include at least two number forms, two or more steps, a representation, working and a written explanation.

4. 13–30 minutes – Investigate and confer Students work independently or in pairs, using the worksheet. Encourage them to represent information with a table, number line, bar model, diagram or equations. Circulate and ask: “What do you know?”, “What is the question asking?”, “Why did you choose that representation?” Run a small support group using the worked example, vocabulary prompts and one step at a time. Students who finish early add a constraint, such as a fixed budget limit or minimum participation target, and compare two strategies.

5. 30–38 minutes – Showcase strategies Students prepare a one-minute explanation of their solution. In groups of four, each student or pair presents the context, representation, calculation, answer and check. Peers identify one clear connection between the fraction, decimal and percentage representations and ask one mathematical question. Use the showcase discussion prompts to keep feedback focused.

6. 38–43 minutes – Whole-class comparison Invite two or three groups to share different methods. Compare representations and discuss which method was most efficient, easiest to follow or easiest to check. Highlight that different correct strategies can produce the same result, provided the reasoning is valid.

7. 43–45 minutes – Reflect and close Students complete the reflection section of the Number Connections investigation worksheet: “My most useful representation was…”, “My strategy was efficient because…” and “Next time I would…”. Finish with the reflection and closing slides and invite a few students to share one connection they now see between fractions, decimals and percentages.

Resources

• the Number Connections Showcase slide deck
• the Number Connections investigation worksheet
• Whiteboard and markers
• Pencils, rulers and coloured pencils
• Calculators, if normally available for checking rather than replacing reasoning
• Class budget, recipe or participation data prepared on the worksheet
• Vocabulary prompts: fraction, decimal, percentage, equivalent, total, remaining, increase, decrease, represent, justify, efficient

Assessment

• Observe whether students select a suitable representation, sequence the steps and connect equivalent forms.
• Collect the investigation worksheet to assess accuracy, reasoning, communication and reflection.
• During the showcase, listen for correct use of mathematical vocabulary and justification of strategy choices.

Differentiation

• Support: offer a structured budget task with smaller numbers, a worked example, a step-by-step checklist and vocabulary prompts. Work with a small group to identify known information before calculating.
• Support: allow students to use a table, bar model or number line and rehearse explanations orally with a partner before writing.
• Extension: require multiple constraints, such as staying within a budget while meeting a minimum percentage, then compare two valid strategies.
• Extension: ask students to provide a written proof or create a new challenge for a peer, including an answer and explanation.
• EAL/SEN: read task instructions aloud, highlight key information, provide sentence stems such as “I chose ___ because…” and pair students strategically. Accept labelled diagrams and oral explanation alongside written working.