This activity allows students to explore the relationship among customary and/or metric units of measurement.
- How Much is a Million?
- If You Made a Million
- Ruler with customary
and metric measures
- Measuring cups:
customary and metric
- Scale(s): customary and
- Roll of pennies
- Dollar bill for each
materials, e.g., paper
clips, gum eraser,
straight pin, etc.
- Colored construction
- 8 1/2" x 11" white
paper (4 sheets per
- Glue stick
Much is a Million? worksheet
- If I had a Million? worksheet
- How Much is a Million?, by David M. Schwartz;
- If You Made a Million, by David M. Schwartz; ISBN 0590-43608-2
- The Magic of a Million, by David M. Schwartz & David J. Whitin;
Background for Teachers
This activity allows students to explore the relationship among
customary and/or metric units of measurement. There is a strong reading
and writing component to the activity. Students will measure ordinary,
readily available materials. They will then have to use their knowledge of
conversion to answer any or all of the following questions in book form:
How much? How many? or How far? Students should be encouraged to
use examples of length, volume, weight, and area using both customary
and metric units. The project should provide a valuable tool for
determining the students' understanding of measurable attributes as well
as conversions to appropriate units of measure.
Intended Learning Outcomes
4. Communicate mathematically.
5. Make mathematical connections.
6. Represent mathematical situations.
Invitation to Learn
Materials should be distributed and ready for use. Have students
brainstorm different tools of measurement and list them on the board--both customary
and metric. Read How Much is a Million? Ask the
students to journal their thoughts on "how much a million is."
- In cooperative groups,
have students measure the length of a
dollar bill. Ask, "How far would a million bills reach?" Students
should use customary and metric units of measure to calculate the
- Repeat the above procedure using other items (e.g., pennies,
pencils, paper clips, etc.). Ask the same question "How far would
a million ___ reach?" Students should have at least six different
items that they measured, calculated, and recorded their findings
on the How Much is a Million? worksheet.
- Students write about
the activity in their journals.
- Make a Millions Book. (Teacher models this
procedure as the
- Using one sheet of white paper, have the students find
mid-point of the two opposite long sides. (This is done by
folding the paper in half.)
- Tell students to make a mark on the fold
one inch down from
the top and one inch up from the bottom.
- Using their scissors, the
students make a 1/8 inch cut into the
fold at the marks. They will be removing the center part of the
page between the two marks, leaving the one inch sections
intact to keep the paper together.
- Using the other three pieces of
paper, students fold at the midpoint
of the long sides (best if all three are folded together at
- Students make a mark on one of the sheets, along the fold
inch down and one inch up (as done in step b).
- Tell the students to
cut on the fold from the top down (making
sure all three pieces are together) to the mark (may go a little
- Cut on the fold from the bottom up to mark (may go a little
- Open the pages and roll the three pieces of paper lengthwise,
inserting in the cutout section of first piece of paper. Once the
cuts in the three pieces line up with the fold of the first piece
of paper, move the cuts to slip over the parts of the first paper
that were not cut on the fold. This will keep the papers from separating,
forming a booklet.
- Once the above is completed, tell the students to
colored construction paper in half at the mid-point of the two
- Apply glue to one side of the outermost piece of the four
white sheets joined together.
- Insert the four pieces into the construction
- Once the sheet is glued on one side, apply glue to remaining
back page of the white paper. Close the booklet, letting the
back page adhere to the construction paper.
- With the book created,
students brainstorm, using their journals,
different measurements of a million they could write about and
illustrate on each of the 12 pages (exclude the pages glued to the
front and back covers). They should be thinking about using the
measurements and calculations completed in steps 1-3.
- Students complete
their Millions Book by writing and illustrating
at least six of the items measured earlier. There should be two
pages for each item measured--one page for customary and one
page for metric. Each page should include the words: "If I had a
million …, I would …" or "how far would a million … reach?"
- Read If You Made a Million.
Have the students use the If I Had A
Million? worksheet to create and replace the last two pages in the
Millions Book. This worksheet may also be used to create a
- Use volume measuring tools to measure and include volume
the books, replacing some of the linear measurement pages (e.g.,
If I have a million cups, or liters, or gallons, etc.). This could be
extended to weight also.
- Students take home a copy of
the If I Had A Million? worksheet
and discuss with family and/or friends.
- Create a measurement booklet to
explore and record ideas and
items families have measured.
- Observe students while they are working in groups
individually. Did they work well in cooperative groups? Were the
materials used properly and accurately? Could the students
present and discuss their opinions and feelings.
- Students complete the How
Much is a Million? worksheet based
on their observations and turn it in. Students must journal their
procedures, questions, and results. The students will create and
turn in a finished Millions Book.
Taylor, P.M., Simms, K., Kim, O. & Reys, R.E. (2001) Do your students
metrically? Teaching Children Mathematics. 7(5). 282-287.
Various attempts have been made to adopt the metric system in the
United States. Thomas Jefferson was the first to introduce the concept.
Today the U.S. is one of only three countries not using the metric system.
The Third International Mathematics and Science Study (TIMSS) showed
that students in the U.S. are behind in their understanding and use of the
metric system. Teachers are encouraged to use metrics in their curriculum
to develop a broader sense of measurement.
Principles and Standards for School Mathematics. (2000). Reston,
VA: The National Council
of Teachers of Mathematics.
In learning measurement, students should be actively involved,
drawing on familiar and accessible contexts. The first step is to
understand measurable attributes of objects and the units of
measurement--both customary and metric. Connection(s) must be made
to real-world applications. Students should investigate a wide variety of applications.