Patterns in Elementary Math!

This week, I'm focusing on pattern and series recognition in elementary math. My preschool students love making patterns with toys, blocks, markers, legos, art and basically anything else they can find in the classroom. This made me think...how would I go about teaching patterns and series to my future students?

I think the first step is to define what a pattern is. Using the Smartick website, I learned about various ways to teach patterns and how to create a lesson plan all about patterns and series. Smartick discussed that talking about patterns is basically talking about regularities. Regularities are everywhere and it’s a special skill to be able to recognize them. Regularities exist in natural and social phenomena, and the search for regularities is the base of science. Just by observing your surroundings, you can find groups of elements that have been set in a certain way that follow a rule. In this way, you can find patterns everywhere!

One way to teach students about patterns is to discuss repeating patterns. A pattern is a succession of elements that is formed by following a rule. My preschoolers make patterns with their legos by following a color pattern - for example, one blue lego, followed by one yellow lego, followed by a blue lego, and so on.

Below are a series of patterns and the different repetition patterns used in a first grade classroom:

The next topic would be to cover reoccurring patterns. See below:

I also find that since my preschoolers learn best by seeing, it would be helpful to incorporate different videos into a patterns and series lesson plan. I found the below to be fun, interactive ways to learn about patterns.

Counting Money

This week, I decided to take a break from fractions on focus on a new subject. Over the weekend, I asked my niece, a second-grade student, about some of the things she had learned in her math class this year. I also asked her what she enjoyed learning about and why. One thing she mentioned that I found interesting was about counting money. She said she liked this topic because everyone uses money, and it's important to understand how to count it...and I couldn't agree more!

After looking at various resources online, it seems like the counting money lesson plan starts as early as first grade. In first grade, students learn about the smaller monetary values -- such as pennies, nickels and dimes. As students progress to second grade, it seems like many of the lesson plans began to incorporate different dollars and quarters. See below for a resource that I discovered on K5 Learning.

Here's the worksheet with the answers filled in:

When looking at these worksheets and speaking to my niece, I began to wonder how to go about actually teaching this topic to elementary students. I came across this video which I thought was a great resource:

Additionally, after reading about this topic online, I came across several other activities that can be done with elementary students to familiarize them with counting money, what value different coins hold, and the different values of paper bills. One method I saw required the teacher or parent to give the child a pile of coins to sort. At this point the goal is to study the money, not count it. Have them sort the money by coins and ask them to notice how the coins are different. Point out the different faces on the coins and the variety of backs of the coins. from here, teachers or parents can explain how to tell different coins apart and how to understand what value each coin has. Teachers can also have students line up the nickels and dimes to get to $1.00 to better understand coin values. Touching each nickel as they count, they can count by fives to get to $1.00. Teachers can repeat this by putting the nickels in a pile and letting them move them as they count. Similarly, they can do the same thing with pennies or dimes!

Dividing MIXED Fractions!

This week, I'm focusing on dividing mixed fractions. It's not too difficult once you get the hang of it, but it does require an extra step from dividing regular fractions. Similar to multiplying mixed fractions, when dividing, you must first convert the fraction into an improper fraction. See below for the list of steps when dividing mixed fractions:

Step 1: Change to improper fractions
Step 2: Use the Keep, Change, Flip "KCF" method now. So, keep the first improper fraction as is. Change the operation from division to multiplication. And finally, flip the last fraction so the numerator becomes the denominator and the denominator becomes the numerator.
Step 3: Solve!
Step 4: Convert back into a mixed fraction

So, basically, in order to divide mixed fractions, you first convert each to an improper fraction. Then, switch to a multiplication problem by multiply by the reciprocal of the divisor. Simplify and convert your answer back to a mixed fraction to get your answer!

Let's try an example together:

In this example, they followed the same exact steps that are outlined above.

This video is also a great way to see the step-by-step process to divide mixed fractions. I like this video in particular because the speaker walks you through each step and explains the best way to set up the problem in order to solve it efficiently. Press play below and take a look!

I also really like this video from Khan Academy. Khan Academy is a great resource to use for many different subjects, but I find that they explain elementary math concepts very well. This video, similar to the one above, lays out the steps clearly. Both videos use the KCF method outline above!

Multiplying MIXED Fractions

This week, I'm focusing on multiplying mixed fractions. We've already gone over how to multiply regular fractions -- but mixed fractions require an extra step and can be difficult for students to grasp. Plus...as a elementary student learning about fractions...mixed fractions can look and feel intimidating! But fear not, because the process is quite straightforward and easy to perfect with some practice!

In order to reteach myself this concept, I went over to MathisFun.com. This website has been a great resource for me while trying to familiarize myself with fractions, and has provided really useful tips on how to best teach fractions to young students.

In order to multiply mixed fractions, there are three steps. See below:
1) Convert to an improper fraction (see my previous post to learn how to do this)
2) Multiply the fractions
3) Convert the result back to mixed fractions

Let's try an example!

Problem 1: Multiply 1 3/8 x 3 and convert your answer back to a mixed fraction at the end.

Ok, so the first thing that we need to do per the aforementioned instructions is to convert the mixed fraction into an improper fraction. 1 3/8 is equivalent to 11/8. A quick way to do this is to add the numerator and denominator (again, more detailed instructions for this can be found in my previous post). The problem should now read, 11/8 x 3. Once you multiple 11/8 x 3, you get 33/8 -- and now all that is left to do is to convert that improper fraction back into a mixed fraction which is 4 1/8.

See below illustration MathisFun to better understand this problem in a visual format.

Here's another example using two mixed numbers! Same concept but this time, both fractions need to be converted into improper fractions first, and then you can proceed with multiplying.

Lastly, the example below shows the step-by-step calculations required to multiply mixed fractions. Once students become familiar with multiplying mixed fractions, they may not need to visualize it every time (such as in the pizza pie illustration above). They can simply write it out and follow the steps included at the beginning of this post. See below:

In an effort to really perfect this topic, I did about 15 examples on my own. I found this resource to be very helpful in finding problem sets and providing answers / explanations. Check it out! There are tons of worksheets for students and teachers to use. The website covers a variety of mathematical topics and serves as a great educational resource!