There are many times that we must estimate the quantity of a physical
attribute without any measuring tools. Do your students have these useful
Can your student use the span of their arms or hands,
or the length of their thumbs or feet to estimate sizes when they
don't have a measuring tool?
Can your students determine the approximate amount
of objects in a square container by counting the objects along the
length, width, and height of the container; then multiplying the three
Can your students use proportional reasoning to estimate
the size of objects too large to measure directly?
Have your students create a tile pattern with dots. Then ask them how
many dots there would be on a table if you were to use their tile to
resurface the table. Have them estimate things around school, such as
the number of students in the cafeteria at lunch, the height of the
flag pole, or the number of books in the library.
Jeff Wilson (Equitable Classroom Practices Institute 2000 participant)
created this estimation activity using his experience in the U. S. Army.
Stepping Up to Estimation activity (pdf
Melanie Kauffmann (1999 SMI participant, 2000 SMI guest speaker)
shares this activity she does with her classes. She poses the introductory
problem to her students, then asks them to use their new knowledge to
estimate and test food containers. She concludes this exploration with
a classroom discussion of downsizing in food packaging.
Which will hold more rice, an 8 1/2 x 11" piece of paper which
is made into a wide cylinder (the two 8 1/2 inch edges touch) or an
8 1/2 " x 11 piece of paper which is made into a tall cylinder
(the two 11 inch edges touch), or will they be the same?
measuring cups of different sizes
a variety of containers such as coffee cups, paper cones, fast food
containers (including containers for French fries and soda)
rice (enough for ~3 cups/group)
1. Look at container 1. Estimate how many scoops of rice it will take
to fill it to the top. Record.
2. Repeat step 1 for each container.
3. Students at each table compare and discuss their findings about how
shape and scale affect the number of scoops required to fill the container.
4. The instructor places the tall cylinder inside the wide cylinder
(see problem above)and fills the tall cylinder with rice. The
tall cylinder is then lifted, allowing the rice to fill the wide cylinder.
It will be noted that the wide cylinder is only about 3/4 full.
5. The instructor discusses with the students how the containers measured
in steps 1-2 appear to be similar in size but different volume; and
how this relates to the real world. For example, how do companies vary
container shape and size to their benefit?
Students independently investigate the downsizing of other products
and how the companies use shapes to entice the customer into thinking
she/he is getting more than he/she really does. The children may wish
to write letters to companies protesting deceptive packaging.
This was a favorite book of the SMI participants for teaching
Betcha! : Estimating (Mathstart , Level 3)
by Stuart J. Murphy, S. D. Schindler (Illustrator)