Mathematical Emphasis
Investigation 1: Motions with Tetrominoes
•
Measuring an area by covering a flat space with square
units
•
Finding systematically all possible geometric arrange-
ments of a given number
•
Finding patterns for covering a space
•
Comparing area of rectangles with different di-
mensions
•
Describing physical motions in precise ways as a series
of slides, flips and turns
•
Comparing two shapes to decide if they are congruent
or not after using geometric motions - slides, flips, turns
- to try fitting one shape exactly on top of the other
Investigation 2: Finding Area
•
Measuring area by covering a flat space with square
units
•
Comparing the area of two shapes by determining if they
cover they same amount of flat space
•
Comparing shapes to see if they are congruent through
motions such as rotation (turns) and reflections (flips)
•
Exploring relationships among shapes: for example, a
rectangle can be cut into two triangles, each of which is
half the area of the rectangle
•
Finding the area of complex shapes by cutting them into
recognizable smaller units of area such as square units
and half units
Websites
http://cms.everett.k12.wa.us/math/Third Grade
Blokus Puzzler -
http://www.gottfriedville.net/blokus/index.htm
Grade 3
Tips for Helping at Home
•
Questions to ask:
What is it that you don’t understand (have
the student be specific)?
What about putting things in order?
Could you try it with simpler numbers?
Can you guess and check?
Does this make sense?
What can you do to explain your answer to
show others what you are thinking?
Does your answer seem reasonable?
•
Look for opportunities at home to talk about area
with your child. For example:
Do you have square tiles covering a floor or
bathroom wall? How
many squares are
there?
Suppose you make roll-out cookies with your
child. This poses a problem of area: how can
you place the cookie cutters so that you
cover the most area, and have the least
amount of dough left over? Do you have to
rotate the cookie cutter to get the best fit?
•
Download Tetrominoes to play on your computer
at home. See your teacher for the password.
http://investigations.scottforesman.com/flips.html
2 - D Geometry
Vocabulary
Area - the size a surface takes up. Measured
in square units.
Congruent - having the same size and shape
Slide - move an item in any direction without
rotating it.
Flip - reflect or turn over
Turn - to rotate around a point
Glossary
http://www.amathsdictionaryforkids.com/
Game
Arranging Chairs Puzzle
What you will need:
30 small objects to use as chairs (for example,
cubes, blocks, tiles, chips, pennies, buttons)
What to do:
1. Choose a number between 4 and 30.
2. Figure out all the ways you can arrange that
many chairs. Each row must have the same
number of chairs. Your arrangements will
make rectangles of different sizes.
3. Write down the dimensions of each rectan-
gle you make.
4. Choose another number and start again. Be
sure to make a new list of dimensions for
each new number.
Example:
All the ways to arrange 12 chairs
Dimensions
1 by 12
12 by 1
2 by 6
6 by 2
3 by 4
4 by 3
Understanding the Area of Triangles
Many of us learned about area only through memo-
rizing formulas; we often did not really understand
what or why we were multiplying. In this unit, stu-
dents learn about measuring area as “covering a flat
surface with square units.”
Finding the areas of triangles is done not by using a
formula, but by looking at the triangle in relationship
to a related rectangle.
When students are comfortable with the unit square
as 1 square unit and the small triangle as half of a
unit, they will spend time talking about the 1-unit tri-
angle.
How do you know what the area of this shape is?
Students can use their Tetromino Puzzle to help
them think about how the triangle is related to one
square unit.
First, you can think of this shape as half of a 2-unit
rectangle. Since the rectangle is 2 square units, and
the triangle is half of the whole shape, we can con-
clude that the triangle is half of 2 or 1-square units.
Another way is to cut the triangle into two pieces and
rearrange the pieces to make a unit square.
Clements, D. Investigations in Number, Data, and Space:
Flips, Turns, and Area. Dale Seymour Publications, 1998.
