Minds On
Parts of an expression

Examine the following expressions:
- What do they mean?
- How are they similar? Different?
- Which is the variable (the part that changes), and which is the constant (the part that stays the same)?
- A coefficient is a number multiplied by a variable. Do either of the expressions have a coefficient? If so, what is it? If not, how do you know?
Record your ideas digitally, orally, or in print.
Press ‘Reveal’ to reveal a sample answer.
means one more than four times a number.
means 8 more than a number.
First, I would gather like terms and simplify which means I would do:
which means one more than a number.
They are similar because they are all a variable plus a number.
They are different because:
The first has a number multiplied by the variable.
The second is just the variable plus a number.
The third at the start looks like it has two variables until you simplify it, then it is like the second expression.
They all also have different variables.
x, n and y are the variables. They could be any number. The +1, +8 and +1 are the constants.
If a coefficient is a number multiplied by a variable, then:
has a coefficient of 4.
Action
Adding and subtracting monomials
In algebra, we can use variables to help us represent and solve math problems.
In algebra, when we want to add and subtract variables, we must ensure that the variables are identical. Variables can be added and subtracted with variables and constants can be added with constants.
For example, if we want to add variables:
They can be added because they are both numbers with the variable n. A variable on its own has a 1 in front but we do not need to place it.
So, in total there are
The following model can explain. Let variables n be represented with squares and constants be represented with circles. The squares can be added with the squares and the circles can be added with the circles.
The same rules apply to subtracting monomials.
Simplify the following addition and subtraction of monomials digitally, orally, or in print, or record a detailed description.
Press ‘Answers’ to reveal answers to the questions.
Consolidation
Monomial word problems
Create and simplify monomial expressions for each of the following. Record your response digitally, orally, or in print, or create a detailed description:
- Record an expression that represents the perimeter of the rectangle. Simplify the expression.
- Write an expression that represents the perimeter of the triangle. Simplify the expression.
- Side 1:
- Side 2:
- Side 3:
- A mountain climber climbed 6x + 5 up a mountain. An hour later they walked down
3x + 1. How far up the mountain are they now?
- A caterer bought 7 bananas (b) and 2 oranges for the week. She ate 3 bananas and 1 orange. What is left?
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.