Investigating Sustainability

Big Idea

Mathematics is a powerful tool to model and solve real-world problems related to sustainability, empowering students to make informed decisions.

---

Lesson Overview

Year Level: Year 6
Subject: Mathematics
Duration: 60 minutes
Class Size: 20 students

---

Australian Curriculum Link

Strand: Number and Algebra
Sub-strand: Fractions and Decimals
Content Descriptor: Solve problems involving addition and subtraction of decimals, including those involving money (ACMNA128).

Proficiency Focus: Problem-Solving and Reasoning

---

Learning Intentions

• Solve multi-step word problems involving decimals within a real-world context of sustainability.
• Apply reasoning strategies to justify solutions for decimal addition and subtraction problems.

---

Success Criteria

• I can perform decimal calculations involving addition and subtraction accurately and confidently.
• I can connect decimal calculations to real-world sustainability models.
• I can explain and justify my problem-solving strategies clearly and logically.

---

Lesson Phases

Phase 1: Launch - Warm-Up (10 minutes)

Set the Scene – Waste Reduction Focus

• Begin with a quick class discussion recapping the previous lesson:
  • Reflect on the importance of tracking waste accurately using decimals.
  • Remind students how decimals provide precision in understanding real-world quantities.
• Use the homework data from their at-home waste tracking task as a hook:
  • Allow a few students to share some highlights from their waste tracking. Display sample data sets on the board if available.

Warm-Up Problem

• Provide this quick problem to get students thinking:
  “If you recorded 2.675 kg of total waste at home, and 0.854 kg was organic waste, how much of the remaining waste likely includes paper and plastic?”
• Facilitate brief student sharing of strategies to solve this subtraction problem.

Key Questions:

• Why is attention to decimal placement critical in these calculations?
• How could this data help inform efforts to reduce household waste?

---

Phase 2: Body - Application and Problem Solving (40 minutes)

Part 1: Direct Teaching (10 minutes)

• Present the class with the following problem on the whiteboard:

  _“As a part of the school’s sustainability plan, the following waste was collected for recycling last week:

  • Paper: 3.468 kg
  • Plastic: 4.120 kg
  • Organic Waste: 2.658 kg.
    What is the total weight of the waste collected for recycling?”_

• Walk the students through solving this step-by-step:

  1. Line up decimals correctly in vertical alignment.
  2. Add numbers systematically, column by column.
  3. Cross-check by estimating: Use rounding to the nearest unit (e.g., 3 + 4 + 3 = about 10).

Class Interaction

• Pause frequently to ask students for observations:
  • “Where do you think errors typically occur in decimal addition?”
  • “How does estimation help double-check our answer?”

---

Part 2: Group Work – Guided Practice (15 minutes)

• Divide the class into pairs and provide this set of problems as a worksheet:

  1. Subtraction Problem:
     “After tracking household waste from one of our students, we find that 0.924 kg of waste was not recycled out of 3.468 kg of total collected waste. How much waste was recycled?”

  2. Multi-step Problem:
     “The school aims to reduce this figure (non-recycled waste) by 1.352 kg over the next two weeks. Assuming success, how much waste will remain unrecycled?”

• Ensure that students collaborate to:

  • Align decimal points accurately in all scenarios.
  • Use strategies such as estimation or mental maths to verify results.

Differentiation

• Support for Struggling Learners: Offer scaffolded templates (pre-drawn vertical alignment for decimal operations). Work closely with struggling students to guide them step-by-step.
• Extension for Advanced Learners:
  • Pose a new challenge: “If the government awards a $3.25 grant per kilogram of recycled waste, how much grant money would our school be eligible for by recycling last week’s total?”

---

Part 3: Real-World Modelling (15 minutes)

Scenario Problem:
“The school has discussed reducing the waste it produces by targeting a consistent reduction of 0.450 kg weekly for six weeks. Calculate the total planned reduction, and determine how much waste will remain if the starting total is 11.867 kg.”

• Students work individually and then discuss their strategies in small groups.
• Encourage justification: Why did you choose to use multiplication here? Could another method also work?

---

Phase 3: Conclusion – Reflection (10 minutes)

Class Reflection Discussion:

• Pose the following questions for student reflection:
  • How does thinking with decimals help us understand sustainability?
  • What strategies for solving these problems worked best for you?
  • Can we use these calculations to inform other sustainability-related decisions?

Real-World Connection

• Conclude by discussing:
  • How schools globally use real waste data to improve sustainability initiatives.
  • Why mathematical accuracy helps us create effective action plans for environmental change.

---

Homework Task

Personal Waste Tracker:
Ask students to continue their at-home waste tracking for three more days, this time focusing on:

1. Recording waste amounts more precisely to three decimal places.
2. Calculating the percentage of each type of waste (paper, plastic, organic) in proportion to the total.
3. Writing 1-2 sentences on how their household could reduce waste further based on their data.

---

Assessment Opportunities

1. Formative: Monitor and record students’ problem-solving methods during the group work phase. Provide corrective feedback to develop decimal alignment accuracy.
2. Summative: Collect worksheets and review how accurately students applied decimal operations and explained their reasoning.

---

Materials and Resources

• Whiteboard and markers
• Pre-made worksheets with scaffolded problems
• Visual aids (bar charts of waste categories)
• Calculators (for extension activities only, optional)

---

This engaging and thought-provoking lesson balances mathematical rigour with an authentic real-world context, encouraging students to connect their learning with broader sustainability goals. It provides scaffolding for all learners while allowing for hands-on, practical application of mathematical concepts.