Go to Collaborative Learning Go to FLAG Home Go to Search
Go to Learning Through Technology Go to Site Map
Go to Who We Are
Go to College Level One Home
Go to Introduction Go to Assessment Primer Go to Matching CATs to Goals Go to Classroom Assessment Techniques Go To Tools Go to Resources




Go to Tools overview
Go to Tool search
Go to Tools sorted by discipline
Go to Tools sorted by technique


Tools - Math 'Plausible Estimation' Estimates for a Million Tasks, Set #1 (solutions)



Estimates for a Million, Set #1 (solutions)
Estimating for Amazing Facts: Set #2 (solutions) || Set #3 (solutions)
Estimates for the USA, Set #4 (solutions)

Malcolm Swan
Mathematics Education
University of Nottingham
Malcolm.Swan@nottingham.ac.uk

Jim Ridgway
School of Education
University of Durham
Jim.Ridgway@durham.ac.uk


The aim of this assessment is to provide the opportunity for you to:
  • develop a chain of reasoning that will enable you to estimate quantities to an appropriate degree of accuracy
  • choose suitable units for your estimate
  • communicate the assumptions upon which your estimate is based.



  1. Breathing
    How many days would it take you to breathe a million times?

Solution:
Assumptions

You breathe once every 4 seconds.


Reasoning

Calculation:

4,000,000 seconds is about 46 days.

Answer: About 50 days.








  1. Paper Clips
    Suppose a chain is made from a million paper clips. How far will it stretch?
    Choose suitable units for your answer.

    A picture of 4 paper clips strung together

Solution:
Assumptions

Each paper clip is about 4 cm in length.


Reasoning

Calculation:

4,000,000 cm = 40 km (or about 25 miles)

Answer: About 40 kilometres or 25 miles.








  1. The brick wall
    Suppose you use a million household bricks to build a wall four feet high. How long would the wall be? Picture of a man laying bricks to build a wall


Solution:
Assumptions

A brick is about 3 inches high and 9 inches long.


Reasoning

Calculation:

The wall will be (4 feet ÷ 3 inches) = 16 bricks high

This means that the wall will be (1 million ÷ 16) 62,500 bricks in length

= 62,500 x 9 inches

= 8.9 miles.

Answer: Just under 9 miles.
(Maybe with mortar it would be just over 9 miles)








  1. The dripping faucet
    A faucet drips a million times. How many buckets will it fill? Picture of a dripping faucet


Solution:
Assumptions

A bucket holds about 8 liters.

A drip has a diameter of 2 mm


Reasoning

Calculation:

The volume of a drip is given by

    4/3 Greek letter pi (1)3 ≈ 4 mm3

A million drips will therefore have a volume of
4 x 106 mm3 = 4 liters

Answer: About one half a bucket.








  1. Writing a million
    How long would it take you to write out all the numbers, from one to a million?

    Remember that some numbers have more digits than others!

    Picture of a pencil twisted into a question mark


Solution:
Assumptions

You can write down 2 digits per second


Reasoning

Most ( 90%) of the numbers have 6 digits.

So we need to write down nearly six million digits.

This would take nearly 3 million seconds = 35 days (approx)

Answer: 35 days, working day and night.








Estimates for a Million, Set #1 (solutions)
Estimating for Amazing Facts: Set #2 (solutions) || Set #3 (solutions)
Estimates for the USA, Set #4 (solutions)


Got to the top of the page.



Introduction || Assessment Primer || Matching Goals to CATs || CATs || Tools || Resources

Search || Who We Are || Site Map || Meet the CL-1 Team || WebMaster || Copyright || Download
College Level One (CL-1) Home || Collaborative Learning || FLAG || Learning Through Technology || NISE