## A Latin Square Deal

### Cindy BeckhamSanta Rosa District Schools

#### Description

Students use four squares of geometric design to create a pattern.

#### Objectives

The student describes, predicts, and creates numerical and geometric patterns through models (for example, manipulatives, tables, graphs).

#### Materials

-Sheet of one-inch grid paper per student OR a copy of A Latin Square grid (See Associated File)
-Copy of Latin Square Assessment per student (See Associated File)
-Crayons, fine-tip markers or colored pencils
-Dry erase board and markers or overhead with pens (at least four different colors)

#### Preparations

NOTE: To create the 9-square by 11-square grid needed to complete the Latin Square, a grid sheet of 3/4" squares (as opposed to one-inch squares) was created. This layout allows the grid to copy on 8 1/2" x 11" paper. If a true one-inch grid is desired, be sure to locate one-inch grid paper and use it instead of the Latin Square provided in the Associated File.

1. Make copies of the Latin Square grid with the Latin Square Assessment on back. (See Associated File)
2. The day before the activity, instruct students to bring in colored pencils, fine-tip markers, or crayons.
3. Prepare a grid on the board or on an overhead transparency to demonstrate how the first five rows are generated.

#### Procedures

1. Introduce the Latin Square activity by creating a pattern on the board. Use at least four different colors to make the design attractive. Each square may contain four different colors or a different color may be used in each square. If a dry erase board is not available, use an overhead projector. To create the geometric pattern, select a design for Square 1, for example, an arrow ( -&rt; ). For Square 2, make a change to Square 1. Instead of the arrow pointing to the right, make the arrow point down. In Square 3 make the arrow point to the left ( <- ). In Square 4 make the arrow point up. In other words each square is a 90-degree clockwise rotation of the previous square. The main idea that the teacher should get across to the students is that as they create their different squares, the changes should be consistent. The change does not have to be a rotation. The change just has to be consistent over the four squares. Another example would be to put an octagon in the first square, a heptagon in the second square, a hexagon in the third square, and a pentagon in the fourth square.

2. Once the design for each square is established, a key should be included at the top of the grid sheet showing the four different squares.

3. After making the key, the 9 by 11 grid is filled in the following manner.
Row 1 is made by entering squares in this order:
1, 2, 3, 4, 1, 2, 3, 4, 1
Row 2 is made by entering squares in this order:
2, 3, 4, 1, 2, 3, 4, 1, 2
Row 3 is made by entering squares in this order:
3, 4, 1, 2, 3, 4, 1, 2, 3
Row 4 is made by entering squares in this order:
4, 1, 2, 3, 4, 1, 2, 3, 4
When entering Row 5, repeat Row 1. Row 6 is the
same as Row 2. Row 7 is the same as Row 3.
Continue is this manner until the entire grid is filled.

4. Have the students complete the activity using at least four different colors.

#### Assessments

Formatively assess students' Latin Squares based on the following criteria. A score sheet is available in the associated file.

Key of 4 squares
Contains at least 4 colors
Uses 4 different squares
Correct pattern sequence
Creativity

#### Extensions

Number and display the students' designs. Cover the students' names or have them write their names on the back of the grid sheet. Have students vote in a secret ballot for their two favorite designs.

#### Attached Files

This file contains A Latin Square grid sheet and the Latin Square Assessment.     File Extension: pdf