Your child is learning to count increasingly larger groups of objects. Now, you can move their thinking further by incorporating some very simple real-world problem solving.

In my post, In Early Math, Think Actions Not Operations, I discuss the way we too often focus on the operation (adding, subtracting, multiplying, dividing). Instead, we should focus on the action taking place in the story. Pre-kindergarten children haven’t yet built the foundational understanding needed to understand mathematical operations. By focusing on the action, we lay the foundation to connect the action to an operation.

When working with your pre-kindergarten child, there are four main actions you to focus on:

Joining
Separating
Grouping
Comparing

The simplest two to start with are joining and separating. I like to start with these two because the action words are very concrete to young children.

A joining problem is any problem in which you start with one quantity, get some more, and end with a larger quantity.

A separating problem is any problem in which you start with one quantity, take some away, and end with a smaller quantity.

For example:

Joining: I have 2 orange slices. My brother gives me 3 more orange slices. How many orange slices do I have now?
Separating: I have 9 blueberries. I eat 4 of them. How many blueberries are left?

In both of these examples the result is unknown because we know how much we start with, we know how much is joined or separated (the change), and now we need to figure out the resulting quantity. Both problems follow a similar and simple format for solving:

Count an original set
Join some to or separate some from the original set
Count the new amount after the action took place

You can incorporate the language of joining and separating in countless ways throughout the day! Eating is the most obvious one because your child is constantly thinking about getting more of their food (joining) and then eating their food (separating).

If you’re playing blocks, ask your child to count how many are in their tower. Then say, “Now I put 3 more blocks on your tower. How many blocks are on your tower now?”

While looking at cars in a parking lot, have your child count the number of cars in a row, and ask, “If 2 cars leave the parking lot, how many cars will be left?”

If your child struggles, don’t tell them the answer. Rather, help them act out the action. “You have 9 blueberries. Now you eat 4 of them. What happens to those blueberries when you eat them?” Your child will say something like, “They go in my tummy!” And you can respond, “Good. So are those blueberries still on your plate?” They will say no and then you can say, “Ok. So show me those blueberries going away off of your plate.”

As you work with your child, remember, problem-solving is hard. It takes time for them to build their understanding. If they don’t get the right answer today, or tomorrow, that’s ok. Praise their thinking. Praise their hard work. And try again another time.

Ready to try out some joining and separating problems with your child? Check out these example problem videos where all the setup is done for you!

Number Stories: Joining & Separating