This is a set of worksheets designed to help students to understand in a logical fashion why we can only combine like terms. Frequently students will want to be able to combine the variable coefficients with the constants in an expression such as 6x + 4. Students will often want to combine those terms and give an answer of 10x. I came up with a method of visually demonstrating to students that combining like terms is just as simple as the sorting activities that they completed when they were in kindergarten. Generally, this is something that I would write out on my front board or project some items onto the screen. Through discussions with some fellow teachers I decided to create these pages to help others to better understand how I present this material to my students.
There is a single page pre-activity which is designed to assist student in understanding how to write what is pictured as an algebra term. Such as showing them five red dots and expecting them to be able to represent this picture as 5r. From this activity it then goes into 16 different activities where students are shown a picture containing some red dots and some blue dots and asking the students to count how many of each type of object is present. They are then asked to write what is pictured as an algebraic expression, such as 4r + 5b.
There are a variety of items that students are expected to count, such as colored circles, striped circles, dotted circles, Xs, 1s, -Xs, -1s, or money. The activities containing money are especially useful as this allows the students to determine the value by using an algebraic expression.
The last pages of the activity ask student to perform the opposite actions. They are given an algebraic expression such as 4x + 6 and are asked to draw a picture that could represent that expression.
Most of the activities involve positive numbers and addition but towards the end of the activities there are more negative numbers and some subtraction as well. As well, most of the activities are in black and white but there are two pages that are in color.