Commentary: Which Operation Gives the Biggest Result?
Students
often have poor number sense about multiplication and division with numbers
less than one. I made up an activity
which was a lot of fun: students formed teams of three or four. Each team had a small whiteboard, marker, calculators,
and an eraser. The questions had many
variations. For one type, I’d pull four
numbers out of a hat, and students would have to choose two and an operation to
form the largest or smallest result. For
example, if the numbers are 0.2, ,
12.6 and 1.4, then the largest result is formed by
;
however, if we change 1.4 to 6.4, the largest result would be
. For another variation, I’d give students a
template, e.g.
and a list of ten numbers, and they’d choose
which numbers to put in the boxes to make the largest or smallest answer. I’d give each problem a point value, and the
team that got the highest or lowest answer, as directed, got the points (some
had points for second place too). This
activity was very “un-Wheelock,” which was fun … I was surprised at how much
the students enjoyed competing; we’re not supposed to be about that…and of
course, there were prizes.
I got this
idea from an article in the Association of Women in Mathematics newsletter; I
need to check the reference; I don’t have the article anymore. The authors did the four number version of
the activity with younger kids with only natural numbers and then had them make
an algorithm before they got the numbers … e.g. for numbers greater than 1
we’ll do this, for zeroes we’ll etc. I
tried this with my class, but things get complicated when we expand past natural
numbers; for example, is bigger than both
and
. I made this graph on a spreadsheet, which is
a bit crude, but had the advantage of using a tool my students knew. After the activity, they were able to easily
make sense of this rather complicated graph.
I printed out several sheets and taped them together, with the caption
below, which has more information. 7/05
To Caption Doc File PDF File Home