Mathematical Emphasis
Investigation 1—Motions with Tetrominoes
- Measuring area by covering a flat space with square units
- Finding systematically all possible geometric arrangements of a given number of squares
- Finding patterns for covering a space
- Comparing area of rectangles with different dimensions
- 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 the same amount of flat space
- Comparing shapes to see if they are congruent through motions such as rotation (turns) and reflection (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
Tips For Helping At Home
Questions To Ask:
- What is the problem about? Tell me in your own words.
- What did you do in class to get started?
- Can you make a drawing (model) to help you figure out the problem?
- Can you solve a simpler version of the problem?
- What have you already tried? What steps did you take?
- Does your answer make sense?
- How do you know your answer is correct?
- Did you show all of your work?
Helping At Home
Part of this unit is about discovering area as a measure of flat surface. Look for opportunities at home to talk about area with your child.
- 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 leftover? Do you have to rotate the cookie cutter to get the best fit?
Vocabulary Terms
- Area
- The size of a flat surface measured in square units
- Congruent
- To be the same size and shape
- Flip
- To turn a figure over
- Slide
- To move a figure in any direction without rotating it
- Turn
- To rotate a figure in place
Mathematics Vocabulary Web site
Mathematics Strategy—Understanding the Area of Triangles
In this unit, children learn about measuring area as “covering a flat surface with square units.” It is easy to begin understanding the area of triangles as one-half of a square unit.
Once children are comfortable with the unit square as 1 square unit and the small triangle as a half of that unit, children start examining a larger triangle with an area of 1 square unit. As in the picture, children are able to think about the triangle as being half of a two square unit when picturing it using the squares.
Children will work with this concept while using Tetromino Puzzles in this unit of study.
Source: Investigations in Number, Data, and Space: Flips, Turns, and Area Dale Seymour, 1998. (Pages 37)
Mathematics Activity—Tetromino Cover-Up
Materials
Tetromino Shapes
10 by 12 Rectangle
Choose one of the Tetromino shapes. Using that shape, cover as many squares in the rectangle as you can. You can do it in several different ways.
- Use one copy of the Tetromino and trace it in the rectangle grid as many times as you can.
- Cut out many copies of one of the Tetrominoes. Arrange them on the rectangle and cover as much as you can. Can you make a whole rectangle with no spaces?
Get to Tetromino Shapes (for printing)