Mathematics · Secondary 1

Active learning ideas

Rates and Unit Rates

Active learning works well for rates because students need to move between concrete examples and abstract calculations. Calculating speeds, costs, and other real-world rates helps students see the value of unit rates beyond the textbook, making the concept stick through repeated practice in varied contexts.

• MOE Syllabus Outcomes
• MOE: Rate and Speed - S1
• MOE: Numbers and Algebra - S1

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Outdoor Investigation Session
• 35 min · Small Groups

Speed Relay: Group Rate Calculations

Mark out course distances on the field. Small groups time each member's run, record data, and calculate individual and group average speeds as distance over time. Compare unit rates to find the fastest team and discuss factors affecting speed.

What does a rate tell us about the relationship between two different units of measure?

Facilitation Tip

During Speed Relay, have students measure their own distances and times to personalize the activity and increase engagement.

What to look for

Present students with two scenarios: Scenario A: A car travels 150 km in 3 hours. Scenario B: A cyclist travels 45 km in 1.5 hours. Ask students to calculate the rate (speed) for each and state which is faster.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 02

• Outdoor Investigation Session
• 30 min · Pairs

Market Hunt: Unit Price Challenge

Provide grocery flyers or set up mock stalls with priced items. Pairs select similar products, calculate cost per unit mass or volume, and identify best buys. Present findings to class, justifying choices with calculations.

How can we compare efficiency using unit rates?

Facilitation Tip

In Market Hunt, provide receipts with both total cost and weight to ensure students practice calculating unit prices accurately.

What to look for

Give students a shopping receipt showing the total cost and weight of a product. Ask them to calculate the unit rate (cost per unit weight) and write one sentence explaining what this unit rate tells them about the value of the product.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 03

• Outdoor Investigation Session
• 45 min · Small Groups

Journey Graph: Speed Analysis

Give journey data tables with distance and time points. In small groups, plot graphs, compute average and sample instantaneous speeds, and predict arrival times. Discuss where speed changes occur.

In what ways does average speed differ from instantaneous speed in a real journey?

Facilitation Tip

For Journey Graph, ask each group to present their graph and explain how they interpreted the speed at different points.

What to look for

Pose the question: 'Imagine you are planning a road trip. How is the average speed you calculate for the whole trip different from the speed shown on the car's speedometer at any given moment? When might each type of speed be more important to know?'

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 04

• Outdoor Investigation Session
• 25 min · Pairs

Heartbeat Rates: Personal Monitoring

Students measure pulse rates at rest and after exercise over fixed times. Individually calculate beats per minute, then share in pairs to compare unit rates and explore health contexts.

What does a rate tell us about the relationship between two different units of measure?

Facilitation Tip

During Heartbeat Rates, have students compare their results with classmates to see how activity affects heart rate.

What to look for

Present students with two scenarios: Scenario A: A car travels 150 km in 3 hours. Scenario B: A cyclist travels 45 km in 1.5 hours. Ask students to calculate the rate (speed) for each and state which is faster.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

A few notes on teaching this unit

Teach rates by starting with familiar contexts, like shopping or travel, before moving to graphs and tables. Use peer discussion to clarify misconceptions, such as confusing average speed with instantaneous speed. Avoid rushing to formulas; instead, let students derive unit rates through repeated examples until the concept feels intuitive.

Successful students will confidently calculate rates and unit rates from different representations, explain their meaning in context, and use them to make decisions. They will also distinguish average speed from instantaneous speed and recognize rates in everyday situations beyond motion.

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Watch Out for These Misconceptions

• During Speed Relay, watch for students who assume rate only applies to speed or motion.

  Ask students to describe their own rate calculations in terms of distance per time, then introduce a new rate, like pages read per minute, to broaden their understanding.

• During Journey Graph, watch for students who think average speed is the average of separate speeds.

  Have groups recalculate average speed by total distance and time using their graph data, then ask them to explain why averaging speeds directly does not work.

• During Market Hunt, watch for students who believe unit rates have no real-world use.

  Challenge groups to defend their best-value choices in a class debate, using their calculated unit rates to justify their decisions.

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Methods used in this brief

• Outdoor Investigation Session