Minds On
Area relationships
A rectangle is a quadrilateral with 4 right angles.
A square also has 4 right angles.
A rectangle with base 4 cm and height 1 cm is the same as a rectangle with base 1 cm and height 4 cm.
The two rectangles are congruent. Is every square a rectangle? Is every rectangle a square?
Consider the following picture. What shape is each design?
What math words do you associate with squares?
Action
Part A: Working with squares
You will need:
- grid paper
- access to the Mathify whiteboard
- square tiles, paper to draw tiles, or items that can be a substitute for tiles.
If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the fillable document.
Press the ‘TVO Mathify' button to access this interactive whiteboard and the ‘Activity’ button for your note-taking document. You will need a TVO Mathify login to access this resource.
TVO Mathify (Opens in new window) Activity (Open PDF in a new window)Choose 3 areas from the following list and use the tiles to make as many different rectangles as you can with that area.
- 4 square units
- 6 square units
- 8 square units
- 9 square units
- 12 square units
- 16 square units
- 20 square units
- 25 square units
Understanding square roots and perfect squares
When we multiply a number by itself, we square the number.
For example: The square of 4 is 4 × 4 = 16
We write: 4 × 4 = 42
So, 42 = 4 × 4 = 16
We say: Four squared is sixteen.
16 is a square number, or a perfect square.
One way to model a square number is to draw a square whose area is equal to the square number.
When we look for a number that can be multiplied by itself to get another number, we are looking for the square root.
The square root of 16 is 4. √16=4.
The square root of a number that gives a whole number is a perfect square.
The square root of a number that gives you a decimal number is not a perfect square.
Examples of perfect squares: 1, 4, 9, 25, 100
Examples of non-perfect squares: 2, 11, 15, 27, 30
Find the square root of the numbers you did with the grid paper in the action section activity.
Part B: Designing an outdoor living space
The Quansah family wants to design new landscaping for their backyard. They want to include an area for a vegetable garden and an area for their patio table. The family wants each design to be a square.
The design should include:
- a vegetable garden. The garden is divided into congruent square plots.
- design the garden showing the side lengths of each plot.
- the family wants a fence around the whole garden area. What length fencing might they possibly need?
The family wants to include a square patio for their table. The concrete slabs are 2m by 2m each. How many slabs are needed? Sketch the patio area.
Sketch and label the designs for the backyard. Explain how you use square roots in your calculations.
Consolidation
Designing a children’s play area
The Quansah family also want to include a play area for their children. They are undecided about the design, but they want it to involve squares to match the rest of the landscaping.
So far, your landscaping design includes: a vegetable garden, an area for the Quansah family's patio table, and a fence that runs along the perimeter of the whole garden area
Next, design, sketch and label the play area for the family. Explain how you use square roots in your calculation.
Reflection
As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.
I feel...
Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.
When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.
Press ‘Discover More’ to extend your skills.
Discover MoreExplain how to use perfect squares to estimate the square root of a non-perfect square. Use an example in your explanation.
Connect with a TVO Mathify tutor
Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.
TVO Mathify (Opens in new window)
Learning goals
We are learning to…
- identify and represent perfect squares and determine their square roots, in various contexts
Success criteria
I am able to…
- show the relationship between the area of a square and the square root of a number
- evaluate a square root and calculate the result
- use perfect squares to calculate the square root of non-perfect square numbers