I
am the Math Specialist in Region 10. It
is a small school system in Connecticut that is made up of two towns. I am the luckiest teacher because I get to
work in two great schools. Lake Garda is
in Burlington and Harwinton Consolidated is in Harwinton. Both schools are K-5. I am also lucky because I get to work with a
lot of really great teachers and kids.
This information and problems comes from Mrs. Kirkby’s fourth grade
class in Lake Garda. We are hoping to
have more classes submit problems in the future. In this problem, the class was working on
measurement. They decided to measure how
much their backpacks weighed each day.
To do this, they weighed themselves and then they put on their backpack
and weighed themselves again. They could
figure out how much the backpack weighed by comparing the two measures. We
created a spreadsheet that shows
the daily averages.
Weight with backpack – weight of person = weight of backpack
How much your backpack weighs can be important, because if your backpack is too heavy it can be unhealthy. Here is an article about choosing an appropriate one.
http://www.indianchild.com/Products/school_backpack.htm
After the kids weighed their backpacks for a whole week we looked at the data by organizing it into a spreadsheet. We noticed some things and that led to our questions.
Math
Trail Problems-
1) What was the
average weight of a backpack for each day of the week?
Answer-
Monday Tuesday Wednesday Thursday Friday
|
Daily
Average |
7.63 |
7.25 |
9.50 |
8.40 |
6.32 |
2) Wednesday is the
heaviest day and Friday is the lightest day on average. What reasons to do you think may have caused
that result?
Answer-
Although, you do not know our schedule, some logical conclusions might be:
1) We have lots of homework on Tuesday to Wednesday.
This would be a great guess and in fact it is correct. It isn’t that we have a lot of homework as much as we have Math homework. Math is the only class that has a hard cover textbook. So out backpacks weigh extra on that day because lots of the students are carrying their Math book.
2) Something special is happening on Wednesday.
This would be another great guess. Earlier in the year the students carried their instruments in their backpacks, so on the day we had band rehearsal the backpacks weighed a lot. Most of them stopped doing that before we collected data, but that would have been a very logical reason.
This article is about calculating the percent of your body weight that your backpack weighs that might be a good project for upper elementary or middle school classes.
State Standards addressed by this project.
How can collecting, organizing
and displaying data help us analyze information and make reasonable predictions
and informed decisions?
4.1 Collect, organize and display data using appropriate statistical and graphical methods.
4.2 Analyze data sets to form hypotheses and make predictions.
How do geometric
relationships and measurements help us to solve problems and make sense of our
world?
4.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure.