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# News from Mathnasium of Chester

### Make Math a Natural Language in Your Household

Oct 8, 2021

The words we use everyday are the gateway to making math accessible to children, even from a young age. How we define words, what symbols and syntax we use, and when we introduce and develop progressive levels of language are all critical to the success of our students.

At Mathnasium, we believe that our instructor’s ability to speak to students and teach math in an age-appropriate way is an essential part of what we do. We focus on teaching our instructors this “Natural Language” so they can better help your children feel comfortable using math in their everyday lives--and we want to empower you to do the same! We’ve included some of our favorite concepts below, along with some guidance on when to use these with your child.

Two Parts the Same (aka half)

When you first start talking about fractions with your child, it might be confusing for them to figure out what “half” really means. This is especially true when you think about how often you guesstimate when splitting things in half during your daily life (for example, when you share fries you probably don’t count or weigh them out to find half but take roughly half instead). The word half should bring to mind the image of two equal parts or, as we like to say, “2 parts the same.” Using this phrasing can help explain what half really means!

How Far Apart (aka subtraction)

We’ve all watched students painstakingly draw shapes on a piece of paper and then cross the shapes out one by one to solve subtraction problems. It works fine for smaller numbers, but can take an unreasonable amount of time for other problems. One way to build “Number Sense” when it comes to subtraction is to rephrase subtraction as “how far apart.” This is especially useful when the numbers are relatively close together - like with the problem 50 - 45. Drawing 50 circles and crossing out 45 of them would take f o r e v e r. Instead, ask how far apart they are and you can quickly count from 45 to 50 and realize the answer is 5! (We like to build on this skill at Mathnasium - it ends up being very useful when it comes to solving equations in algebra as well!)

Half of a Half (aka one fourth)

This phrase comes up in family discussions all the time - especially on Pizza Night! We have to mathematically calculate how to cut the pizza into equal slices, while simultaneously making sure there are the same number of slices for each person. That’s easy enough when you cut the pizza into fourths (cut it in half, then in half again to get 4 pieces) but gets harder when we aim for sixths, eights, etc. It’s easier to think about these fractions when you first think about splitting something in half and then about splitting it a second time to achieve the desired fraction.

Sameness (aka fractions, money, and anything else that uses denomination)

We’ve saved the most powerful concept for last! Here’s a question that’s asked universally at every Mathnasium: “When you add two apples and three bananas do you get five banapples?” Of course not! We intuitively know to change labels when counting items that are different, such as fruit. In fact, I doubt you even think about how denomination comes into play when you flawlessly change from saying “I have two apples in my cart” to “I have five pieces of fruit in my cart.” Would it blow your mind to find out that what you’re doing by changing words there is the exact same thing we do when adding fractions? By changing the words you use to describe your collection of items, you’re finding a common name (common denominators anyone?) so you can group those things together. According to The Law of SAMEness, you can only add or subtract things that have the same name - and this applies to more than grocery shopping. The concept of sameness applies to money, fractions, scientific notation, variables… the list goes on!

These are only a few of the concepts we use every day at Mathnasium when working with our students. We know that any child can be successful in math--it’s a matter of teaching it in a way that makes sense to them. Our mission is to teach children math so they understand it, master it, and love it because we know that math can change their lives and they can change the world!

Let us know if we can help your child with math, or if you’re looking for more ways to incorporate math into your home!