Your name: Helin Wang
School, grade & course: Eric Hamber, Math 8
Topic of unit (NOTE: This should be a unit you will actually be teaching on practicum!):
Understanding Percent, Ratios, Rates, and Proportional Reasoning
(1) Why do we teach this unit to secondary school students? Research and talk about the following: Why is this topic included in the curriculum? Why is it important that students learn it? What learning do you hope they will take with them from this? What is intrinsically interesting, useful, beautiful about this topic? (150 words)
This unit is foundational because percent, ratios, rates, and proportional reasoning appear everywhere in students' daily lives-prices, discounts, taxes, recipes, maps, data, and comparisons. These ideas form core mathematical tools for financial literacy, scientific thinking, and data interpretation. The BC Curriculum includes these topics because they help students understand multiplicative relationships, develop number sense, and recognize patterns across different representations. Strong proportional reasoning predicts success in later mathematics, including algebra, linear functions, and statistics.
This content is also intrinsically interesting and beautiful: percent offers a consistent "out of 100" lens for comparison; ratios reveal hidden relationships in nature, art, and culture; proportions show how scale governs the structure of buildings, canoes, and snowshoes across Indigenous nations. By the end of the unit, students should feel confident switching between representations, interpreting real-world situations, and using proportional thinking flexibly and confidently.
(2) A mathematics project connected to this unit: Plan and describe a student mathematics project that will form part of this unit. Describe the topic, aims, process and timing, and what the students will be asked to produce, and how you will assess the project. (250 words)
Project Title: "Understanding Our World Through Percents and Proportions"
Aim:
Students investigate a context of their choice where percent, ratios, rates, or proportional reasoning play a meaningful role (e.g., sports stats, clothing discounts, climate data, music tempo ratios, recipe scaling, Indigenous canoe proportions, or art scaling). The goal is to integrate mathematics with personal interest, community relevance, and real-world interpretation.
Process & Timing:
The project unfolds over four class days plus at-home work.
- Day 1: Students brainstorm contexts and choose a topic. Teacher provides exemplars.
- Day 2: Students gather real data, organize it into tables, and decide which mathematical tools apply (percent change, ratios, rate comparisons, proportional scaling, etc.).
- Day 3: Students create visual representations such as percent bar models, ratio tables, double-number lines, scaled diagrams, or percent growth charts.
- Day 4: Students produce a final product and practice explaining their reasoning. Students then submit a polished two-page report, poster, or digital slideshow.
Final Product Requirements:
1. At least two mathematical representations (e.g., percent change + ratio table, or scale diagram + proportional equation).
2. A written explanation that justifies why the mathematics fits the situation.
3. A reflection on how the math helped them understand the context better.
Assessment:
Rubric includes accuracy, clarity of reasoning, use of multiple representations, communication, and reflection. Emphasis is on understanding, not perfection.
(3) Assessment and evaluation: How will you build a fair and well-rounded assessment and evaluation plan for this unit? Include formative and summative, informal/ observational and more formal assessment modes. (100 words)
Assessment will be balanced across formative, summative, observational, and performance-based modes. Formative assessments include warm-ups, whiteboard checks, exit slips, and mid-lesson conferences to target misconceptions. Observational assessment happens during partner and group work, especially in open-ended problem-solving tasks. Summative assessments include a chapter test, the culminating project, and selected practice problems that model exam-style questions. Students also complete self-assessment checklists to reflect on progress with key competencies. Throughout the unit, assessment prioritizes reasoning, flexible strategy use, and understanding rather than procedural memorization
Elements of your unit plan:
a) Give a numbered list of the topics of the 10-12 lessons in this unit in the order you would teach them.
Lesson | Topic |
1 | Chapter 8 Get Ready – Understanding Percent |
2 | Chapter 8.1 Understanding Large and Small Percents |
3 | Chapter 8.2 Fractions, Decimals, and Percents |
4 | Chapter 8.3 Percent of a Number |
5 | Chapter 8.4 Combined Percents & Percent of a Percent |
6 | Chapter 8.5 Percent & Financial Literacy |
7 | Chapter 8 Unit Review |
8 | Chapter 7 Get Ready – Ratios, Rates, and Proportional Thinking |
9 | Chapter 7.1 Ratios |
10 | Chapter 7.2 Rates |
(11) | Chapter 7.3 Using Proportional Reasoning |
(12) | Chapter 7 Unit Review |
b) Write a detailed lesson plan for three of the lessons which will not be in a traditional lecture/ exercise/ homework format. These three lessons should include at least three of the following six elements related to your mathematical topic. (And of course, you could include more than three!)
Lesson 1 — Understanding Percent (Get Ready)
Integrated Theme: Indigenous perspectives on sharing, community ratios; visual arts through percent grids
Pedagogical Goals:
- Build conceptual meaning of percent as "out of 100."
- Connect percent to visual models and community-based proportional relationships.
- Introduce Indigenous perspectives on representing parts of a whole (e.g., resource sharing, community distribution).
Materials:
Hundred grids, colored pencils, chart paper, Indigenous-designed visual patterns (non-sacred), sticky notes.
Timing & Sequence:
1. Welcome + Background Knowledge Check (5 min)
Quick whiteboard prompt: "What does 50% mean? How do you know?"
2. Indigenous Context Mini-Story (10 min)
Teacher shares a non-sacred example:
- In many Indigenous communities, resources are shared proportionally (food, fish allocation, community duties).
- Percent grids help represent "equal sharing" visually.
Students discuss: How does representing parts of a whole help communities make fair decisions?
3. Visual Arts Activity - Designing Percent Tiles (20 min)
Students shade 100-square grids to create pattern tiles (inspired by beadwork, basket patterns, or weaving).
Each tile must represent:
- one "simple" percent (e.g., 25%),
- one "fractional" percent (e.g., 7%),
- one "mixed" percent (e.g., 3.5%).
4. Thinking Classroom Activity (15 min)
Groups at vertical surfaces classify pre-made grids into categories:
- "greater than 50\%,"
- "between 1% and 10 %"
- "fractional,"
- or "uncertain."
Students justify visually.
5. Consolidation (5 min)
Students write one sentence: "Percent helps us compare because..."
Assessment:
Observations during group work; completed percent tiles; exit slip on percent meaning.
Lesson 5 - Combined Percents & Percent of a Percent
Integrated Theme: History of percent in trade; arts through multiplicative patterns
Pedagogical Goals:
- Understand percent of a percent.
- Recognize historical contexts of interest rates and trade percentages.
- Visualize multiplicative relationships through geometric patterning.
Materials:
Area models, double grids, Renaissance trade examples, pattern blocks.
Timing & Sequence:
1. Historical Hook (10 min)
Short story:
- Merchants in 15th-century Italy used "per cento" to calculate goods, tax, and interest.
- Percent of a percent appeared in compound fees.
Students ask: "Why would merchants need percent of a percent?"
2. Percent-of-a-Percent Modelling (15 min)
Use area models to show:
- 40 % of 50 %
- 30% of 65%
Students create area-model art tiles showing multiplicative layering.
3. Thinking Classroom Challenge (20 min)
Vertical groups solve three tasks:
1. A store takes 70 % of the price, and a designer gets 30 % of that.
2. A population decreases by 20 % then increases by 20 %.
3. GST + PST combined.
Groups choose strategies: decimals, grids, or ratio reasoning.
4. Whole-Class Discussion (10 min)
Emphasize: percent changes are multiplicative.
Assessment:
Exit slip: "Why doesn't a 20% increase cancel a 20% decrease?"
Teacher notes from group reasoning.
Lesson 11 - Using Proportional Reasoning
Integrated Theme: Indigenous technologies (canoe design, snowshoes), art scaling
Pedagogical Goals:
- Deepen understanding of proportional relationships.
- Explore how proportional reasoning shapes Indigenous technologies.
- Use open-ended problem-solving.
Materials:
Images of Indigenous canoes/snowshoes (non-sacred), grid transparencies, ratio tables, whiteboards.
Timing & Sequence:
1. Indigenous Context Story (10 min)
Share an example:
- Many First Peoples designed canoes using proportional systems (length-to-width ratios, balance, glide efficiency).
- Snowshoes use proportional scaling to distribute weight on snow.
Ask: Why is proportion essential for stability and movement?
2. Art + Scaling Activity (15 min)
Students scale a canoe/snowshoe outline by a factor (e.g., 1:4) on grid paper.
Discuss: What happens to area when dimensions scale?
3. Thinking Classroom Problem Set (25 min)
Groups solve open-ended tasks at vertical boards:
- "Design a canoe $20 \%$ longer but with the same proportions."
- "A snowshoe is scaled down for a youth-what must stay proportional?"
- "Create two proportional and one non-proportional table-explain differences."
4. Reflection (5 min)
Students write: "Proportional reasoning helps design..."
Assessment:
Observational notes; accuracy of scaled drawings; group explanations.
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