Estimation is a key skill for all students to learn. You use this skill more in everyday life than most mathematical concepts. It allows one to check the validity of possible outcomes and gauge the reasonability of everyday life. It is a key to good judgement, and there are many ways to exercise this skill. Here are a few:
- Estimation Jar – An old standby for estimating number and volume, but one of the reasons this works so well is that it can be modified in so many ways. You can have different items in a jar (cookies, beans, pennies, jelly beans – though I’d recommend something not edible). Make it a contest. Give an award for the best or most creative thought process and explanation of how the calculated the number.
- Google Maps or Google Earth – Population Density. (This is a good activity also in that the point is not the final answer, but the reasoning and the presentation of the reasoning.) Have students pic a city or town to look over and make some guesses as to how many houses per square mile there are in that area. How many might there be if the town was 50 square miles? 100? How many people would you guess live there? (How many people per house? What type of housing is there? Single Family? Many Unit?).
- Estimating Length – Give groups different lengths of string (8 inches or less) and have groups estimate how many of their “units” (which if you are brave, you can encourage them to name) equal the length of the item. Create a class chart. A follow up exercise could be creating ratios between the created “units”. (In this case you don’t want them to use rulers to compare).
- Online Estimation Game (different math concepts – the one on length might be interesting for non-visual learners)
In these, think about offering them strategies, ways to make EDUCATED or REASONABLE guesses. List all variables you can think of which may change the answer. Use measuring tools (or create your own). Compare elements to things you know (use a “middle man”). Show your work. Use a calculator.
“I have measured out my life with coffee spoons…”
from “the Love Song of J. Alfred Prufrock.”
A poetic math activity.
This is only one line in this poem, but one it has always striked me as one of the most powerful. There are so many ways to measure your life, to mark time, to define yourself. (Ok, so this one isn’t as inspirational as laughs created or children saved, but to each his own or her own, right?)
For this exercise – it is very simple – identify and calculate:
How do you measure your life?
- hours of tv?
- kisses from loved one?
- ice cubes?
- religious ceremonies?
- cars that you’ve passed by?
- minutes awake? (minutes asleep?)
- books read?
- number of innoculations?
- great runs?
- lines of code?
1. Identify: To start this activity, I might ask students to journal a list of activities that define them. What do your friends say about you? What would your parents or siblings say if they were asked?
2. Estimate: Ask students to think one activity and calculate how many times they have done this. For example – glasses of milk. If you had approximately one glass of milk per day(defined as 8 ounces) between 4 and 15 years old that would be 365 glasses of milk per year x 12 years = 4,380. And for 0-4, maybe it is the equivalent to 3 glasses a week which would equal 624 glasses. Total, it would be approximately 5,004 glasses of milk or 40,032 ounces. Have students show their work to describe their choices. Ask them to consider when this might vary and why and find ways to compensate for this in their calculation.
3. Project forward: Calculate the quantity of your life defining activity for when you are 25, 50, 80, and 95 years old. Do you think your activity will be consistent over time? How will it vary? When? Why? How will you account for this in your estimation?
- Create a graph to show visually your estimation for your life from birth to age 95.
- What things do you expect will change the trend? Why? How did you account for this in your calculations? Show these on the chart with specific points and explanations.
- Write a paragraph analyzing your estimation. When you see this, what do you think? Is it exciting? Disturbing? Does it lead you to ask any more questions? What do you think we should be doing more or less of as a society? Is there anything as humans you think we should monitor and measure to aspire to do more or to do less?