Internet Explorer is not a fully supported browser. For the best experience, please use Chrome or Firefox.

Sara Davick

##
Visual Patterns and Algebraic Expressions

**Grades:**
6th Grade,
7th Grade,
5th Grade

**Subjects:**
Math

**Student Instructions**

1. Study the pattern on the first page.
2. What will come next if the pattern is continued?
3. Use the to show what case 3 would look like if the pattern continued.
4. Use the boxes to answer the questions on pages 3 and 4. Think about the meaning of the words "variable" and "constant". How do you see those in your patterns? How can you use a variable and a constant to write a variable expression that represents the pattern?
Follow these steps for each pattern.

**Teacher Notes (not visible to students)**

Students should have previously been shown and/or given a definition for the terms: variable, constant, and variable expression. I use this activity following the activity titled: "Introduction to Variable Equations."
The patterns all begin with a shape that grows with each case. The growing pattern allows students to visually see a constant and recognize it is the part that never changes. The growing pattern gives students a visual representation of a variable as the number that changes depending on the situation or the "case".
This is my adaptation of an example from Jo Boaler who warns that in U.S. classrooms variables are often introduced by first asking students to solve for "x" which can lead to the idea that a variable is one set number instead of the idea that it varies or changes depending on the situation. She encourages using visual patterns to help students see that variables represent a pattern of growth instead of thinking that a variable is a set number that satisfies "x".
In my classroom, I give students colored cubes to first build the patterns physically and then represent them with a diagram on SeeSaw, and finally with a written expression.
Pattern One: 3x + 4
Pattern Two: 2x + 3
Pattern Three: 4x + 1