The song, "Hip to be Square" by Huey Lewis and the News is a great way to introduce this lesson. Have the song playing while students brainstorm in groups of three or four everything they know about squares. When the song is finished, or after about 3 minutes, have groups share their thoughts about squares. This can be done by drawing a square on your board with the word square in it. Outside of the square, separate your board into sections equaling the number of groups you have. Have a representative from each group come to the board to share their groups ideas. Guide students to talk about the area of a square and how to find it. A video tutor can be used to help find the area of a square. This should only take about 10 minutes.
Distribute graph paper. Have students draw the smallest square possible. This is just one of the squares on the graph paper. They can show this by coloring in the square. Talk about the dimensions and area of the square. This is a 1 by 1 square with an area of one square unit. Then have students find the next largest square possible. Color this square a different color from the original square. Students should add a square to the original square to determine if this now makes a new, larger square. Since it is not a square, students need to add another square and another until you again have a square. The fewest number of small squares that can be added is 3. This is a 2 by 2 square with an area of four square units. Have students continue to create squares in their groups using this same method. Students need to create at least 15 squares. This will give the perfect squares through 15. The first few have been included on the square root attachment. Have students make a table that shows side lengths and area of the squares. Ask students to determine a relationship between side lengths and area of squares. This will take at least 20-30 minutes.
Once all groups have finished working, call on a volunteer to begin the class summarization. Ask students to share the side lengths and area of one of their squares with the class. Have each group do this, making sure all groups are participating. This should be displayed on the board or on a piece of chart paper. Once all 15 squares have been posted by groups, ask for a response to the relationship between the side lengths and the area (sides squared is the area). Give all groups the opportunity to share their findings.
The teacher will now relate the activity to square roots. A square root is the inverse of squaring a number. For instance, the square root of 9 is 3, the square root of 36 is 6. Have students work on the square root worksheet attached.