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Writing equations with unknowns I


Writing equations

Sometimes we have all of the information we need to solve a number problem. Other times, we have some information, but perhaps not all of it. We can still write out our number problem, or equation, using letters in place of unknown numbers. These letters are called pronumerals.

The first step is to work through the written text to work out what we know, and what remains unknown. In Video 1, we'll work through some examples of this using addition and subtraction.

After watching the first video, do you think you could write the equation a different way, perhaps? What if you were asked to fill in the gaps here, what would you write in place of the question mark?

Car wash equation
180 - ? = c



You can use any letter as a pronumeral.


Multiplication and division

Just like we did above with addition and subtraction, we can write equations that involve multiplication and division. By looking at which parts of our information have been used in the equation, we can identify what needs to go in the box, to complete the equation. This is a little like writing a number problem from sentences, except we are using a letter, or pronumeral, in one place.

Let's look at how we can do this in Video 2.


Writing the whole equation!

What if you have all of the information but no equation? Yikes! It's okay, as long as you think about what it means to add, subtract, multiply or divide

Let's see how we can write some equations using the information in Video 3.


Just as we can use turnarounds with some number problems, we can often write an equation more than one way.


Worked Examples

Question 1

Farmer Noah planted $60$60 new crops in the morning. He wants to plant a total of $150$150 crops by the time the sun sets.

Let $c$c be the number of crops Farmer Noah needs to plant in the afternoon. Fill in the blanks to make an equation.

  1. $\editable{}+c=150$+c=150

Question 2

Amy has $100$100 books, which perfectly fill up her bookshelf. The bookshelf has $5$5 rows.

Let $n$n be the number of books that fit on each row. Fill in the blanks to make an equation.

  1. $100\div\editable{}=n$100÷​=n

Question 3

To get to work each morning Sandy first walks for $5$5 minutes to the bus stop, then catches a bus the rest of the way. It takes her $25$25 minutes in total to get to work.

Let $t$t be the amount of time Sandy spends on the bus. Write an equation for the situation using an addition.



Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.

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