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Activities for Studying Patterns & Relationships in Math

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Did you know that math patterns and relationships can be taught in the classroom using simple things such as beads? Learn how in this lesson, along with how little items such as paperclips can be used to teach relationships.

Beads and Patterns

In this lesson, we'll take a look at several activities you can do to help teach your students various mathematical patterns and relationships that exist in the real world. A mathematical pattern is a sequence that follows a specific rule such as 1, 2, 1, 2, … and 1, 1, 2, 3, 5, 8, etc. A mathematical relationship tells you how to process numbers to get a particular answer. For example, to find out how many points each test question is, you divide the total number of points of the test by the number of questions on the test.

We'll begin by looking at patterns by playing with beads.


pattern and relationship activities


To do this activity, you'll need beads of different colors. To make the pattern 1, 2, 1, 2, etc. with beads, you'll need beads in two colors. For example, if you have yellow and orange beads, you can place one yellow bead followed by 2 orange beads, then you start over by placing one yellow bead and two orange beads. You keep repeating until you get a nice long strand going where you can clearly see the pattern. You can then have the students turn these strands into wind chimes by tying a bell to them and hanging them in a bunch outside.

You can use these beads to create any pattern you like. The students will find it interesting as they build these patterns, and they see that they can visually continue the pattern. You can then teach your students to translate that visual continuation of the pattern back into math numbers. For example, you can have your students make the pattern 2, 4, 6, 8, 10, etc. with various colored beads. Some students may soon realize that each change of color means an additional 2 beads. You can then have your students write this down in math terms and continue the pattern 2, 4, 6, 8, 10, 12, 14, etc.

Numbers and Patterns

Another activity you can do to teach patterns is that of having your students explore various mathematical sequences. To do this activity, you can show your students several different mathematical sequences such as even numbers, odd numbers, and then the Fibonacci sequence. Ask your students to first look at these sequences to see if they can see a pattern. Some students may be able to tell you the pattern right away while others may take more time. You can then talk about each sequence and show them the pattern. For the even and odd numbers, you can show how they skip by twos on the number line. For the Fibonacci sequence, you can show them how these numbers show up in the natural world such as in the number of flower petals. The Fibonacci sequence begins with two 1's, then each successive term in the sequence is the addition of the two previous terms: 1, 1, 2, 3, 5 .... After showing your students these sequences, ask your students to continue the sequence and add more terms themselves. Then, ask your students to create sequences of their own.

Multiplication and Relationships

To teach mathematical relationships, you can use multiplication as one activity. To do this activity, you start with a pile of identical toys. You give each of your students a pile of toys. You then show them what happens when you multiply by 1. When you multiply by 1, it means you have just one group. So, if your group has 3 items, then multiplying by 1 means you still have the same group, so your answer is 3. Now, ask your students to create a group of 1. You then ask your students how many items they have when they multiply by 1. The answer should be 1. Now, ask your students to create a group of 2, then a group of 3, etc. and ask them what multiplication by 1 means each time.

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