This course covers two classic families of arithmetic problems. In time and work you learn to think in terms of one day's work, then handle people working together, joining and leaving partway, working on alternate days, sharing wages fairly by the work each person did, and comparing workers who are twice or three times as good. You also count labour in man-days and man-hours for teams of men, women and boys. In boats and streams you set up downstream and upstream speeds, recover the speed of the boat and of the current, and solve harder round-trip questions with quadratic and simultaneous equations.
Middle Years
Arithmetic Applications (Level 2)
Time and work, from one day's work to teams that change, sharing wages and comparing workers, followed by boats and streams: downstream and upstream speeds and the equations they lead to.
- 7 lessons
Overview
Lessons
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Time and work: the basics
One day's work, more workers taking less time, people working together, finding one worker's time from a pair, and three workers given in pairs.
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Work done in stages
Jobs where someone joins or leaves partway: splitting the time line into stages, finding the remaining work, and people working on alternate days.
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Sharing wages for work
Dividing payment in the ratio of the work each person did, when everyone works the whole time and when they work different numbers of days, and finding daily wages.
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Comparing efficiency
Turning statements like twice as good, thrice as good and half as much again into ratios of time or daily work, and solving the resulting problems.
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Men, women, boys and hours
Counting labour in man-days and man-hours, converting between men, women and boys, group earnings, and teams that shrink as the job goes on.
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Boats and streams: the two speeds
Downstream speed x + y and upstream speed x − y, finding the speed in still water and of the current, and times for journeys on a river.
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Boats and streams: harder problems
Round trips with a given total time, a quadratic equation for the speed of a motor boat, and two trips solved as simultaneous equations.
Practice papers
Ten question papers that follow the lessons in order. Each has 20 questions for 50 marks (1 hour 30 minutes), with a key sheet and worked solutions.
MCQ tests
Ten tests of 25 multiple-choice questions (30 minutes each). Answer them on the page and check your score, or download the PDF with its key and solutions.
Class notes
Arithmetic Applications (Level 2)
Typed from the teacher's handwritten class slides, 17 pages.
Download the notes (PDF, 604 KB)