Variables

A variable is a letter or a symbol that is used in place of an unknown amount or quantity.

* + 4 = 12

* is the variable. We don’t know what number is missing yet so it holds the place.

A variable can also be used when the number missing isn’t just one number.

4 + 6 = # + *

# and * are the variables in this case.

In this question, we know that 4 + 6 = 10.

We know that both sides of the equal sign need to be equal to the same amount.

So, we need to find two numbers that when added together have a sum of 10.

We can show this as a part-part-whole relationship, using a part-part-whole model.

What are some numbers that could go under the 10? Record your ideas in a notebook or a method of your choice.

Press ‘Answer’ to reveal the answer to this problem.

Answer

A baker has begun baking a new type of cookie.

The baker sold 7 cookies, then 4 more.

How many were sold in all?

We can write an addition statement with a variable

The variable will take the place of the number we don’t know.

C is used for the unknown number of cookies.

7 + 4 = C

We can also use a Part-Part-Whole model to solve.

We don’t know the whole (that’s C).

We would add 7 + 4 to find C.

The next day the baker sold 5 cookies, then some more, selling 12 in total.

An addition statement would look like 5 + C = 12.

This time, we are missing one of the parts. C is one of the parts in our part-part-whole model.

Your turn!

Respond to the following questions. Record your ideas in a notebook or a method of your choice.

1. What addition sentence would you write if the baker sold 3 cookies, then 6 more? We want to find out how many were sold in total?
2. What will you use as a variable? Will you use a C for cookies? How would you show this on a part-part-whole model?
3. Write a cookie problem of your own that includes a variable.

Part-Part-Whole relationship

In the Minds On section, we looked at a Part-Part-Whole model to find missing numbers in an addition problem.

A variable can take the place of an unknown, and sometimes, there can be more than one unknown.

The baker sold some cookies in the morning, and some cookies in the afternoon. The baker sold 42 cookies all together.

Use a part-part-whole model to show one possible answer. The whole is 42, but both of the parts are unknown. You can use your notebook or another method of your choice.

Press ‘Answer’ to reveal the a possible answer for this question.

Answer

Try This!

A teacher is passing out glue sticks.

There are 20 glue sticks in a box.

Each student gets one glue stick.

After the teacher passes out all the glue sticks, there is only one left in the box.

We can represent this problem using a variable.

20 − J = 1

What does the J stand for?

How could you represent this on a part-part-whole model? You can use your notebook or another method of your choice.

How many students are in the class? How do you know?

Press ‘Answer’ to reveal the answer to this problem.

Answer

Who has mail?

A letter carrier is very busy delivering mail.

The amount of mail that the letter carrier delivers at each stop is variable.

At the first stop the carrier delivered 2 pieces of mail.

At the second, 5.

At the third, 3 pieces of mail.

At the fourth, some mail.

By the fifth house, 15 pieces of mail were delivered.

1. Describe how a variable could be used in this mail delivery problem.
2. How could you find how many pieces of mail were delivered on the 4th day?
3. Could you use a part-part-whole model to help you find the answer?

Record your ideas in a notebook or a method of your choice.

Think about your learning

Select the correct answer, then press “Check Answer” to see how you did.

Reflection

How do you feel about what you have learned in this activity?  Which of the next 4 sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.

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