Mathematical Emphasis
Investigation 1—Locating Houses and Ships on a Grid

• Using positive and negative coordinates to name and locate points on a grid
• Calculating distances on a grid based on paths along grid lines
• Exploring numerical patterns that represent geometric situations
• Connecting visual and numerical descriptions of distances on a grid

Investigation 2—Rectangles, Turns, and Coordinates

• Applying knowledge of coordinates to locate points on a computer screen
• Describing geometric figures such as rectangles and squares
• Understanding how Geo-Logo commands reflect the properties of geometric shapes
• Creating and applying patterns and mental arithmetic strategies to solve turtle geometric problems

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 solve a simpler version of the problem?
• What have you already tried? What steps did you take?
• Did you show all of your work?
• Does the answer make sense?
• How do you know your answer is correct?

Helping At Home

• Offer to solve your child’s coordinate mystery after he or she creates it. If you are unsure of how to read grid coordinates, have you child teach you!
• Play Sunken Ships with your child when he or she brings it home. Your child can teach you the rules and maybe even some good game strategies!
• Keep your eyes open for rectangles in the world around you. Work with your child to find particularly large or small (smaller than an inch on a side) rectangles, rectangles that are also squares (all sides are equal) and rectangles that are much taller than most fourth graders.

Vocabulary Terms

Axis

The horizontal or vertical reference line on a grid or graph

Coordinates

The numbers within an ordered pair

Grids

Horizontal and vertical lines forming squares on graph paper

Line segment

A piece of a line defined by the endpoints:

Negative coordinates

Numbers in ordered pairs that are to the left of 0 on the x axis or below the 0 on the y axis

Ordered pair

Two numbers (x, y) which locate a point on a grid; the first coordinate (number) is always on the horizontal axis, the second coordinate is on the vertical axis

Positive coordinates

Numbers in ordered pairs that are to the right of 0 on the x axis or above the 0 on the y axis

Quadrants

The four squares formed by the x and y axis

Turn

Rotate

Mathematics Vocabulary Web site

Mathematics Strategy—Learning and Teaching Concepts

Contrary to common belief, people frequently do not use definitions when they think, rather they use “concept images.” A concept image is a combination of all the mental pictures and properties that we associate with a concept. This is strongly influenced by everything we have learned.

For example, students may see figures only in certain “standard” positions. They think a turned square is no longer a square but is instead a diamond. They may identify this triangle as containing a right angle but believe that reversed, it becomes a left angle .

Even with standard verbal descriptions or definitions, these limited concept images tend to rule children’s thinking. Therefore students need to have many experiences with a concept. That is the reason the activities in this unit present many different examples of the concept rectangle. Children will construct meaningful concept images of a rectangle through a variety of activities and examples.

Source: Investigations in Number, Data, and Space: Sunken Ships and Grid Patterns. Dale Seymour, 1998. (Page 50)

Mathematics Game—Grid Tic Tac Toe

Materials

Grid Sheet for Tic Tac Toe board

Players: 2

Playing the Game

1. The rules of the game are standard tic tac toe rules but X and O are placed on the board by naming coordinates of points. The object is to get three in a row.



2. The first player names coordinates to place his/her X. Coordinates are counted first horizontally, and second vertically. The second player names different coordinates to place his/her O on the board.



3. The game continues in this manner, ending when one player gets three points in a row. If no one can get three in a row, the game is a draw.



4. Extension: Gameboard can be drawn in a quadrant using negative numbers.

Get to Grid Sheet for Tic Tac Toe Board (for printing)

Get to Grid Sheet with Quandrant I for Tic Tac Toe Board (for printing)