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  This lesson provided by:  
Author:Bob Cloud
System: Auburn City
School: Drake Middle School

  General Lesson Information  
Lesson Plan ID: 26359


Hip to be Square


This lesson will guide students through the discovery of naming square roots of perfect squares.  Students will build squares and determine the side lengths to notice the relationship between the side lengths and the area of the squares.  This could be a hands-on or technology based activity. 

This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

 Associated Standards and Objectives 
Content Standard(s):
TC2 (6-8)
14. Use digital tools to generate new ideas, products, or processes.
Examples: ideas—predictions, trends
products—animation, video
processes—models, simulations

Local/National Standards:


Number and Operations
Understand meanings of operations and how they relate to one another.

Primary Learning Objective(s):

Naming square roots of perfect squares through 225.

Additional Learning Objective(s):


 Preparation Information 

Total Duration:

31 to 60 Minutes

Materials and Resources:

Graph paper, colored pencils, index cards

Technology Resources Needed:

Interactive whiteboard


Teacher prep:  Introduce the lesson by playing the song "Hip to be Square", available for download on iTunes. 

For an interactive whiteboard, teacher should have graph paper prepared.  For those not using an interactive whiteboard, teachers will need to have graph paper available.  The graph paper for demonstration could be display on a document camera or an overhead projector. 
The teacher will need to divide students into groups of three or four.  Consideration should be given to the math background of all students. 

Students need to have background knowledge of basic polygons (squares), exponents, and determining the area of a square. 


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. 

**Some files will display in a new window. Others will prompt you to download.


Assessment Strategies

While students are working, notice the types of things students are saying in their groups.  Students should mention four right angles and four congruent sides.  Students may also include parallel opposite sides and diagonals are perpindicular bisectors.  Other properties of squares may be mentioned.

Walk around the room providing encouragement as students work.  Aide students that are having difficulty creating the next square.  Ask students if adding one square could make a new square.  Ask them if adding two squares would make a new square.  Continue this process until the next square is found.  Once students are familiar with creating the squares, guide students toward the relationships between the side lengths and the area of each square.  Ask the students if there is a relationship between these.  Ask if they see any patterns occuring in the table they made.  For students struggling with this, it may become clear during the summarization of the lesson. 

Students will be sharing their discoveries as a whole group.  Students should see the connection between the side lengths and the area of the square.  Ask if this will work for squares bigger than what we worked with in our problem. 

Students will have completed the worksheet either in class or for homework.  The answers are provided on the same link as the problems.


A website students can go to for extra practice with square roots can be found here.


Reduce the number of squares that students will be responsible for. Provide an example of several of the smaller squares (1 square, 2x2, & 3x3)  ask the student to explain to you or a peer helper the concept that is being presented.

Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior

Be sure to check the student's IEP for specific accommodations.
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