This exercise works best if for homework the middle school students count the digits in their own cell phone, passport, bill code or some other number. They don’t have to show the passport or bill. They just have to count the digits.
Archive for the ‘statistics’ Category

Winter Olympics: Bad Math of Figure Skating Scores
February 22, 2018According to the fab NBC video, Mathletes, nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.
Tessa Virtue and Scott Moir win GOLD at Pyeong Chang 2018
This is a typical figure skating score card for one competitor.
The final score, however, is based on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.
……………………………………………………
Now consider the IDENTICAL SCORE CARDS
of Skater A & B:
Skater A:
Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)
7.00 + 7.00 + 7.00 + 6.75 + 7.00
……………………………………..
= 34.75/ 5 = 6.95
Skater B:
Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.
The average:
7.00 + 7.25 + 7.00 + 7.00 + 7.00
……………………………………..
= 35.25/ 5 = 7.05
Same score cards but Skater B gets a higher average score than Skater A.
Skater A is, in fact, beaten by a random number selector!!!!

Mean, Median and Coffee: Busting an Urban Myth
April 21, 2017
A Fun Maths Exercise.
Students count steps.
No units of length used.
You can find the free pdf worksheet (included below) here.
Other fun middle school math(s) worksheets in the Hot Heels series at TpT include
Unit Rates, Angles, Ratios and Algebra.
There is a lot of maths and science behind coffee sloshing in a coffee mug. ‘The human stride has almost exactly the right frequency to drive the natural oscillations of coffee’ explains fluid physicists at the University of California at Santa Barbara. You will find their full explanation here.

Lego Mean, Median, Mode
January 15, 2016Students can calculate the Mean, Median and Mode using Lego. Here is the exciting part:
The lego stacks become the graph
START with 40 LEGO BRICKS
Draw a graph of No. of Blocks Vs No. of Prongs (per block) Make sure all blocks are the same height.
Start with 40 bricks.
Sort into Stacks to create graph of
No. Prongs Vs No. Bricks
This is a close up of the stacks above.
The no. of bricks in each stack is written on top of the stack.

Dangerous Maths 1:Young drunk dead
August 26, 2015Statistics for alcohol consumption are tricky. Binge drinking gets confused with heavy drinking. If you want to stay young go to the UK. They think anyone under 35 is a youth! Some stats separate Male and Female drinking habits. Some don’t. And legal drinking ages vary. Canada is one crazy place. It has different legal drinking ages in different parts of the country.
Legal Drinking Age:
The Maths
What we are working on here is reading maths data. No lectures. The numbers speak for themselves.
Graph source here
The Challenge
Find the following information from data below. Percentage of Year 12 students or 18 year olds who binge drink in each country below.
1. Australia
Graph Source here.
2. Canada
Graph Source here.
3. UK
Graph Source here
4. USA
Graph source here
Answers- Young drunk dead
Use these % to create a bar graph comparing countries. (Answer below)
Graph drawn using Create a Graph website
Alcohol related death stats over lap other stats including death involving cars, motorcycles, bicycles, skateboards, jet skis, quad bikes, drowning, diving, stairs, supermarket trolleys and even high heels.
photo source Daily Mail
Alcohol Related Youth Death Statistics
UK1: 314
Australia2: 260
Canada3: 3,500
USA4: 4,358
- 15-34 years for 2011. Source
- 15-24 years average 1990-2002 Source
- Under 18 years of age. 1996 It is believed that as many as 83 percent of teenagers in Canada consume alcohol. Back in 1996, underage drinking was responsible for 3,500 deaths and 2,000,000 injuries. A 2002 survey found that 20 percent of eight graders had consumed alcohol within the previous month. Source
- 4,358 people under age 21 die each year from alcohol-related car crashes, homicides, suicides, alcohol poisoning, and other injuries such as falls, burns, and drowning. Source
These countries have different populations (See post below). USA population is 15 times Australia’s. 260 x 15 = 3,900. So the Aussie and US stats are in the same ball park even though the stats have been collected for different age ranges. But look at Canada. The USA population is about 9 times Canada’s. 4,358 ÷ 9 = 484 deaths. This death statistic for Canada is 10 times larger than the USA statistic per head of population. Meanwhile, the population of Canada is 1 1/2 or 1.5 times Australia’s. 260 x 1.5 = 390. Once again, the Canadian statistic is out by a factor of 10. What’s going on here?
The Bar Where You’re Too Afraid to Get Smashed
Mathspig is a party pig. But why does anyone drink themselves senseless? Many reasons, but one is they’re bored. Now here is a bar in Mathspig’s home town, Melbourne, where you better stay sober. Break out of prison in Trapt Bar. You’re in prison, you’re innocent, and no one believes you. You plot an escape with the other prisoners–because unless you break free soon, you’ll all face an unspeakable death (this prison is off the charts). At Trapt Bar and Escape Rooms, you and your teammates have 45 minutes to find clues, solve puzzles and escape before…well…let’s spare you the gruesome details.

4. Why the best figure skater doesn’t always win
January 23, 2014According to the fab NBC video, Mathletes, nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.
This is a typical figure skating score card for one competitor.
The final score, however, is based on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.
……………………………………………………
Now consider the IDENTICAL SCORE CARDS
of Skater A & B:
Skater A:
Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)
7.00 + 7.00 + 7.00 + 6.75 + 7.00
……………………………………..
= 34.75/ 5 = 6.95
Skater B:
Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.
The average:
7.00 + 7.25 + 7.00 + 7.00 + 7.00
……………………………………..
= 35.25/ 5 = 7.05
Same score cards but Skater B gets a higher average score than Skater A.
Skater A is, in fact, beaten by a random number selector!!!!

3. Stuff Ups 1
June 14, 2013You go to the doctor with lower back pain.
The doc recommends an MRI scan. A problem is identified and an operation, perhaps, recommended. But here is the problem. The back problem identified in the scan may not be the cause of the pain.
In maths this is called FALSE ATTRIBUTION.
You get all the pain – financial and physical – but no gain.
You will find a very interesting discussion of this problem The Health Report, Radio National, ABC.
Dentists suffer a higher incidence of lower back pain … Maybe from prancing around in towels in front of mirrors. Wait. That was only a small sample of 10 paid dentists.
No conclusion can be drawn.