the students walk into the room, ask them, “How
many seconds are there in a regular year?” Allow
a few minutes for students to respond. Do not judge answers.
Put the digit 1 on the board and tell them, “I’m going to start putting
zeros behind the 1, and you to tell me when to stop so we’ll know your
estimate of the number of seconds in a year.” It might be a good idea that
you and the class reach agreement on how many answers you will accept. Don’t
take a guess from each student in the class or else you will be adding zeros
for the whole period.
Begin and keep adding zeros until someone tells you to stop. Ask the class
if they want to stop there or keep going. If they want to go on, mark the
first zero in a different color and add more zeros until someone else says, “Stop.” Have
the students put commas in the appropriate places in the number and ask the
students to read the numeral they have chosen.
Tell the students, “ As a class we will now calculate the number. Anybody
have any suggestions?” Allow a few minutes for students to respond
and have them write their answers on the board. Hopefully someone will come
with the correct procedure, but they may not include the units of measure
numbers. As you go over the procedure, make sure to write in the units in
the appropriate spots and show how the units cancel out to get the answer,
that this technique is called unit analysis.
If nobody suggests the correct procedure, point out that unit analysis can be
used to compute the answer this question. Hand out Activity sheet or put it on
the overhead and have the students do the work in their notebooks.
Ask students. “Do you think the size of a country or of the number of neighbors
it has affects its status or economy? Why?” Allow a few minutes
for students to respond. Do not judge answers.
Show students the data on the United States from the Infrared Analyst's Guide
to Worldwide Environments web page. http://www.iriacenter.org/irworld.nsf/Frameset%201?OpenFrameSet&Frame=Target&Src=_
If you use the first website, the distances will be given in miles and area in
square miles. The second website uses a different format and uses metric units.
Both provide useful information.
Have students calculate the same information for their country.
Remind them that this data will be a part of the country
display so that it should be presented accurately and neatly.
(This might be information they wish to graph for their
Tell the students, “Being able to present data in an
appropriate manner is one of the standards in mathematics.
Simply having the data is not enough; you need to be able
to communicate it to others. Given the data that you found
yesterday about your country, what forms of representation
would you choose to make the data clear? Why would you choose
this form?” Allow a few minutes for students to respond.
Do not judge answers.
Have students make pie-graphs of the same information for
their country. Remind them that this data will be a part
of the country display so that it should be presented accurately
and neatly. (This might be information they wish to graph
for their country displays.)
The students reach closure as they work on the graphs for
their country displays.
The first day of this lesson will be assessed through
informal discussion of ways to apply unit analysis and
guided practice as the students do the Activity sheet.
The second day of the lesson will be assessed by guided
practice as the class as a whole finds the information
for Brazil. Individual or small group assessment can
be done by informal observation as the students do the
calculations for their country displays. The third day
will be assessed by guided practice as the class as a
whole makes the pie-graphs for Brazil. Individual or
small group assessment on the third day can be done by
informal observation as the students do the calculations
for their country displays.
Things to check with embedded assessments:
- Can students convent measurements from empirical to metric?
- Can students calculate percentages?
- Can students calculate ratios?
- Can the students measure angles in the pie-graphs