Patterned

A very significant Pre-math concept for kids to understand is patterns. Patterns are easy to make with anything you have on hand (fork, spoon, spoon, fork, spoon, spoon, etc), and can provide hours of entertainment for you and your child.

Work with your child on creating an extending patterns. Take turns starting a pattern and finishing it. For example, maybe you start a pattern first, then have your child extend it, then let your child start a pattern, and you extend it.

You should also help your child be able to start a pattern that you state. For example, you say “Can you make me a pattern that goes fork, knife, fork, knife?” And your child should be able to display that pattern for you.

I am working on creating some fun use-at-home math games and manipulatives that should be available soon.

Are there any concepts you would specifically like to have manipulatives for?

If you have questions, you can ask them in the comments, email me, ask on Facebook, or on Twitter. I am on Facebook and Twitter live from 3:00-3:30 pm Mon-Thurs MDT.

you know more math than you think

Do you ever feel like math is a foreign language?

Think about how it feels to learn another language, or to be in a place where people are speaking a language you don’t understand.

Now think about how a child learns to speak their mother tongue (the language their parents speak). If a child is exposed to a language from the time they are born, and if someone interacts with them on a regular basis in that language, the child will eventually learn to speak that language. Are children born speaking a language? Maybe baby talk – but mostly they just cry.

Turns out, the ability to learn math is programmed in us similar to the way the ability to learn a language is programmed in us.

You can read about a study that was done on this subject here.

In the article, they mentioned that a lot of Euclidean Geometry (lines, space, shapes – all that basic stuff) concepts were “innate” in members of a remote tribal community in the Amazon who had no formal training in geometry. They got as many answers right about geometry as formally educated Americans.

Something that was interesting, however, was that younger children (5 and 6 years old) didn’t know the answers. The researchers weren’t sure why, but I have a hypothesis.

Since math is similar to a foreign language, and young children don’t often understand the concepts of grammar, it make sense that they also wouldn’t understand the concepts of math especially if math has not been “spoken” to them regularly. This goes back to the principle of teaching “pre-math” skills by exposing young children to concepts like classifying, sorting, number conservation, counting, etc.

If you want your child to understand math concepts better, speak math with them! Try to make it a point to “speak math” with your child every day. Whether it is by sorting and classifying, or by talking about shapes around you, or multiplying a recipe, or talking about how “steep” the stairs are, speak math with the children in your life!

How do you “speak math” with the children in your life?

If you have questions, you can ask them in the comments, email me, ask on Facebook, or on Twitter. I am on Facebook and Twitter live from 3:00-3:30 pm Mon-Thurs MDT.

Pre-Math: One of These Things

Sometimes as parents, and as teachers, we discount the things that children do as they play that help them learn math skills. We can encourage children to do things that develop good “math brains” without making them sit down and look at flash cards or do worksheets (I know a lot of kids love flash cards and worksheets, but we need to expand our horizons a little!)

One very important math concept and skill is that of sorting. In a previous post about combining like terms, I talked about how combining like terms was a lot like sorting laundry or marbles, or anything else than can be sorted and grouped.

Children like to sort and group naturally. My son will sort his toy cars by color, my daughter loves to help put the dishes in their correct places.

When our children practice sorting during play, or while helping mom and dad around the house, they are learning valuable math skills that will play a part in whether or not they are easily able to grasp the concept of things like combining like terms later in school.

Another part of sorting is being able to classify objects. In the picture above where my children are sorting laundry, they wouldn’t be able to sort the laundry unless they knew what set of classifications we were using to sort. Are we sorting kid’s clothes and grown-up’s clothes? Are we sorting every color? In our case, we were sorting according to “light” colors, “dark” and “ bright” colors, and “whites” – which meant that I had to explain what each of those classifiers meant.

When my children understood the classifiers, they were able to sort. Being able to classify objects (especially in different ways – like I said above) is also very significant and an important ability for children to develop so they will be successful in math skills later on. They have to be able to classify math “objects” such as numbers, coefficients, variables, exponents, etc.

Another game to play is “One of these things is not like the others” where you have a group of objects, and one object is not like the others. In this game, you are classifying objects, but you are also teaching the concept of “one” (which might seem like an easy concept, but trust me – you probably don’t actually understand “one”, even as an adult. I didn’t fully understand what “one” meant until I was finished with my undergraduate studies).

Try to find ways to help your children classify and sort objects. Try to make it a fun game that has to do with your life (sorting silverware or laundry, classifying cars when you are driving “Can you see a red car? How about a red truck? What about a blue truck?”). As your children learn to classify and sort objects, and as they do it on a daily basis, their brains will be gearing up to understand much more complex mathematical situations as they grow up.

What ways do you teach your children how to classify and sort? Do you feel like you are able to teach your children math concepts?

If you have questions, you can ask them in the comments, email me, ask on Facebook, or on Twitter. I am on Facebook and Twitter live from 3:00-3:30 pm Mon-Thurs MDT.

Combining Like Terms – Sorting Letters

Did you ever play sorting games as a little kid? If you fold your own laundry, then you should be a pro at sorting – pants, shirts, socks, sweaters.

Combing like terms is just like sorting laundry, or marbles (as illustrated in my sorry attempt at drawing marbles).

When we have “letters” (also known as variables) in an expression we often want to combine them so that we have an easier expression to look at.

Think of it like having a pile full of different color marbles (like in the illustration above). Let’s look at an example:

2x + 4y – 3xy + 7y – 5x + 2xy

Let’s look at the different “color” marbles we have (that is, the different “terms”)

We have x’s, y’s, and xy’s (the xy’s are their own type of term, because xy is not the same as x or y).

Now we combine the things that are “like” – We have 2x and –5x, so that is –3x. We have 4y and 7y, so that is 11y. Finally, we have –3xy and 2xy, which is –xy.

Our “simplified” expression is –3x +11y –xy.

Because of the commutative property of addition, we can write the expression in any order we want to.

-3x – xy + 11y
11y – 3x – xy

etc, etc

Here are some practice problems for combining like terms (also known as “simplifying expressions”)

Simplify the Expressions by combining like terms

1.

2.

3.

4.

5.

(Pre-Math Tip! Play sorting games with your preschooler. You may not realize it now when you are sorting blocks and dishes and beads, but your preschooler is building the foundation for basic algebra skills like being able to combine like terms!)

If you have questions, you can ask them in the comments, email me, ask on Facebook, or on Twitter. I am on Facebook and Twitter live from 3:00-3:30 pm Mon-Thurs MDT.