Perimeter

Consider the following conversations among two students about calculating the perimeter of a quadrilateral:

Student A says that to calculate the perimeter of a quadrilateral you need to add up all of the sides.

Student B says that you can just multiply one side by 4.

Variables

Algebra uses letters of the alphabet to represent unknown parts of an equation.

These letters are known as variables.

They are used in the same way as symbols, such as hearts, stars, triangles, or happy faces.

In this episode of Homework Zone, explore variables with Teacher Ms. Liu. Consider what Teacher Ms. Liu notes about the variable g.

If we repeat the same letter, every time we see that letter in that equation or expression, it has to represent the same thing.

If $g=1,$

then $g-g+g$

would be the same as saying $1-1+1.$

Teacher Ms. Liu also reminds us that “substituting” is another way to say “taking the place of.”

Evaluating expressions

In the Minds On section, you were asked whether Student A, Student B, or both are correct.

Student A may have been describing a square. Their expression could be $4s$.

Student B may have been describing a rectangle. Their expression might be $2b+2h$.

If the length of one side of Student A’s square is 15 units, you can use the expression to determine the perimeter, or the distance around the square by substituting the values into the expression.

4s

= 4(15) which means 4 × 15

= 60

The square is 60 units around.

How about Student B’s rectangle?

If the base length (b) of a rectangle is 5 units and the height (h) 2 units, we can determine the perimeter of the rectangle by substituting the values into the expression.

2b + 2h

= 2(5) × 2(2)

= 10 + 4

= 14 units

Your turn

Evaluate the following expressions, where s = 6, b = 5 and h = 8. Record your answers using a method of your choice.

• 5s
• 4b
• 2h + 2b
• b + h
• 10s

Click ‘Answer’ to check your solutions.

Answer

Writing and evaluating expressions

Consider the following pentagon and answer the questions that follow.

1. Write an expression to describe the perimeter of the shape above. Note that all sides are equal. Make sure to use a variable to represent any unknown value.
2. What letter did you use for the variable? Why?
3. If the perimeter of this shape is 90, find the length of one side. Can you use your expression to justify your thinking?
4. Why is using a variable necessary in question 1?

You can use the following fillable and printable Pentagon document to record your answers. You may also use your notebook or a voice recorder.

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.