Problem Solving March 2004 (v 28.3)
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Shape Pictures GRADES K–2
In this activity, students trace around everyday objects to create
pictures. To prepare, teachers and students need to gather objects that
can be used to trace around to make a specific shape. For instance, a
jar lid, a can of soup, or a used CD disk might be used to trace a
circle. Other shapes to trace might include rectangles, squares,
triangles, and so on.
When many various shaped items have been gathered,
give the students the opportunity to explore tracing them. Next ask
them to trace any of the shapes to create a picture. With three
different sized circles, for example, a student might choose to make a
snowman. A triangle and a square might form a house. With older
students, ask them to then write about their picture using geometric
words and terms.
Send us examples of student work and include some information about how students approached this task.
Playground Geometry GRADES 3–5
Have students draw the different games painted on your playground onto
a piece of graph paper. Ask them to describe the geometric shapes that
make up the game. For example, hopscotch may be made up of nine single
squares, two larger rectangles (one at the beginning and one somewhere
in the center of the design), and a circle at one end.
Then ask students whether the shapes can be put
together into other designs. Have students try to redraw the shapes
into a new game. Would the rules change and how would they change?
Would the new game be fair?
Please send examples of student work (redrawn games
and new sets of rules) to the ComMuniCator. If students actually played
their new version of the game, explain how the game went and what
students thought of their new version.
Buying Cookies GRADES 6–8
This is a rewriting of a problem from the AMC 10 exam for 2001. It asks students to organize their answers carefully.
Dale
plans to buy four cookies. There are three types of cookies available:
chocolate, raisin, and peanut butter. Assuming that the bakery has a
large supply of all three kinds of cookies, how many different
groupings of cookies could Dale make? One choice might be two chocolate
cookies, one raisin, and one peanut butter. Or all four could be
chocolate. How can you be sure you’ve found all the groupings?
Be sure to ask students to explain how they arrived
at their solutions and how they know they have all of the possible
groupings. Teachers are encouraged to send examples of student work and
explanations to the ComMuniCator.
Decreasing Integers GRADES 9–12
At the UCLAMP Teacher Leader Institute last August, participants were
given a problem of the day about decreasing integers. Ask your students
to solve the following slightly modified version.
An
integer is called decreasing if each digit is less than the one to its
left. For example, 5320 is a decreasing integer but 5230 is not. How
many decreasing integers occur between 2000 and 7000? Explain your
strategy for solving this problem. Devise a technique for predicting
the number of decreasing integers beyond 7000.
Teachers are encouraged to send examples of student work and solutions to the ComMuniCator.
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This Page was last updated: Wednesday, May 12, 2004 at 10:38:36 AM
This page was originally posted: 5/12/2004; 10:33:25 AM.
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