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Teaching Compound Measures using �Ratio & Proportion

Kathryn Darwin

Deputy Subject Leader – Maths

Manor Croft Academy, Dewsbury

darwink@manorcroft.org.uk

@Arithmaticks

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Session Outline

  • The problem with triangles
  • The problem with the concept
  • Speed Calculations:
    • Prerequisites
    • Bar Models
    • Ratio tables/notation
    • Unit Changes
  • Density & Pressure
  • Other topics

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The Problem with Triangles

D

S

T

M

D

V

F

P

A

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The Problem with Triangles

John drives 60 miles in 40 minutes.

What is his average speed in mph?

D

S

T

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The problem with the concept…

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Speed Calculations - Prerequisites

  • Multiplicative relationships & direct proportion
  • Unit conversions
    • Time – Hours/Min/Seconds
      • Multiples and factors of 60
      • Multiples of the factors of 60!
    • Distance
      • Metric
      • Imperial, given conversions

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Speed Calculations - Bar Models

Katie drives 80 miles in 2 hours.

What is her average speed in mph?

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Speed Calculations - Bar Models

John drives 60 miles in 40 minutes.

What is his average speed in mph?

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Speed Calculations - Bar Models

A bus travels 105 miles in 1 and a half hours.

What is the average speed in mph?

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Speed Calculations - Ratio (Tables)

  • The key is to understand that speed is a UNIT RATIO.
  • The unit is the unit of time.

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  • E.g. We write:
    • 20mph as 20 miles :1 hour
    • 50km/hour as 50km : 1 hour
    • 4m/s as 4m : 1 second
    • 1 mile/min as 1 mile : 1 minute

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Speed Calculations - Ratio (Tables)

  • Get students to PLAY with it first…
  • What else is true?

20mph

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Speed Calculations - Ratio (Tables)

Katie drives 80 miles in 2 hours.

What is her average speed in mph?

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Speed Calculations – Ratio (Tables)

John drives 60 miles in 40 minutes.

What is his average speed in mph?

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Speed Calculations - Ratio (Tables)

A bus travels 105 miles in 1 and a half hours.

What is the average speed in mph?

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Speed Calculations - Ratio (Tables)

A taxi travels at 45mph.

How far does it travel in 2 hours?

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How far does it travel in 40 minutes?

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Speed Calculations - Ratio (Tables)

A taxi travels at 45mph.

How long will it take to travel 15 miles?

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How long will it take to travel 70 miles?

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Speed Calculations - Unit Changes

  • Get students to PLAY with it first…
  • What else is true?

5m/sec

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Speed Calculations - Ratio (Tables)

Write 15m/s in kilometres per hour

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Speed Calculations - Ratio (Tables)

Write 360km/h in metres per second

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Speed Calculations - Ratio (Tables)

  •  

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Density & Pressure

  • Pressure:�An object is placed on the ground and exerts a force of 3000N on an area of 4m²�What is the pressure in N/m2?

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What is the pressure in N/cm2?

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Density & Pressure

  • Density:�A piece of wood has a mass of 7g and a volume of 10cm³�What is the density in g/cm3? �

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What is the density in kg/m3?

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Other Topics

  • Unit conversions
  • Gradient
  • Best buys
  • Similarity in 2D & 3D
    • ‘LAV’ tables

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Questions?

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Teaching Compound Measures using �Ratio & Proportion

Kathryn Darwin

Deputy Subject Leader – Maths

Manor Croft Academy, Dewsbury

darwink@manorcroft.org.uk

@Arithmaticks