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Adding with an Unknown Quantity

In this post, we’re going to explain what adding with an unknown quantity is and why it’s taught during the first years of Elementary school.

Some people think it’s strange that children are taught such an important variable, like an unknown quantity, in addition problems shortly after the children have just started to get used to adding horizontally. Perhaps it seems rushed.

In order to understand it, we’re going to go through some examples that will require us to use addition with and without an unknown quantity in order to solve them.

Adding without an Unknown Quantity

“My grandpa had a hen and bought another four hens at the market. How many hens does my grandpa have now?”


Adding with an Unknown Quantity

“In my fridge, there were 3 cartons of orange juice. My dad left to go grocery shopping and must have come back with one more because now there are 4 cartons. How many cartons of orange juice did my dad bring back?”


By looking at the problems separately, it’s easy to see that solving a problem is more difficult when the unknown quantity is one of the numbers that we are adding instead of the answer, but it’s solvable.

Later on, with more complex numbers, students will solve these problems by using subtraction (35 + ? = 67 becomes 67 – 35 = ? ), but for now, they use simple numbers.

The point is for them to solve this question: “What number do I need to add to 3 in order for it to be 4?”

By doing so, they’re amplifying their understanding of addition and at the same time, improving their mental math. Ultimately, they’re “studying” what addition is from a different perspective. We’re helping them to not get boxed into thinking that addition problems only look like this: 1 + 4 =?

To work with addition with unknown quantities, we use visual aids here at Smartick. We utilize objects that help children visualize the situation and motivate them to answer, such as “how many astronauts do you have to add to three astronauts so that there will be 4 astronauts?”

AddingIf you want to practice these kinds of problems, and more, go to Smartick and try it for free.

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