Independent and Dependent Variables Worksheets
When we are working on an experiment to determine if one factor affects another, we often try our best to keep all the conditions the same and only manipulate one factor at a time and track if changes to that factor made a difference at all. The variable that we control, and change is called the independent variable. The variable that we observe, and track is called the dependent variable. If the experiment or scenario goes according to plan the independent variable will influence the dependent variable in some way. It (independent) could make it make the dependent variable increase, decrease, or in some rare cases even stay stable. I find a good way to help children remember this is to teach them that the independent is the cause and that the independent is the effect. Another thing to remember with this unit is the placement of the variables on a graph. The independent is always found on the horizontal (x) axis and the dependent is placed on the vertical (y) axis. These worksheets and lessons will help students navigate one of the more tricker portions of the algebra curriculum. Students are asked to use two different variables in the same expression or equation.
Aligned Standard: Grade 6 Expressions and Equations - 6.EE.C.9
- Making Pastries Step-by-step Lesson- The amount of math problems found in a kitchen never cease to amaze me.
- Guided Lesson - You start to have to play with two variable sets in this lesson.
- Guided Lesson Explanation - When you look at the problems the way I do here, they seem simple.
- Practice Worksheet - I tried to make these problems more about the setup than the actual calculations.
- Matching Worksheet - A nice way to wrap up the section. Clear cut problems.
- Answer Keys - These are for all the unlocked materials above.
This would be the first transition students make to using algebra in story based problems.
- Homework 1 - The equation below shows the number of cupcakes Garcia has made as it relates to the number of days she has spent making the cup-cakes. c = 5d The variable d represents the number of days spent making cup-cakes, and the variable c represents the number of cup-cakes.
- Homework 2 - The below equation represents how many pages are in a book that Eric is reading and how it depends on the number of pages he reads daily.
- Homework 3 - This equation shows how the total number of mosquitoes born is related to the number of days in a season.
Playing cards start making an appearance here.
- Practice 1 - The variable r represents rounds, and the variable t represents the time taken to complete a round. How many rounds can he complete in a 5 minutes?
- Practice 2 - The equation shows how much furniture a carpenter makes as related to the number of days he has. f = 5d
- Practice 3 - The variable a represents ace cards, and the variable o represents other cards. How many ace cards are there if there are 48 other cards?
Math Skill Quizzes
I made everything in multiple choice format here to provide students a little bit of a prompt.
- Quiz 1 - The variable d represents dolls, and the variable w represents the number of days to make dolls. How many dolls can Rita make in a 5 days?
- Quiz 2 - The variable t represents total amount, m represents the number of mangoes and c represents the number of cucumbers. If John buys 12 items and 3 were mangoes, how many cucumbers did he buy?
- Quiz 3 - The above equation shows the time (min.) needed to bake a cake as related to the number of cakes being baked.
How to Use Variables to Represent Two Quantities in An Equation?
In sixth grade, the students learn to solve word problems that include the use of multiple variables in them. By this time, the students have an idea about solving algebraic equations and calculating the value of the unknown variable but working with two that are brand new to students. If both variables are the same, we learn to combine like terms and carry on with business as usual with the rest of the problem. When those variables differ, it gets more complicated, and we learn to restate each variable as the other.
A lot of kids find the variable word problems challenging and are scared to deal with them. However, these word problems are not that difficult, and the use of variables actually makes solving word problems simple and easy. Let’s talk a look at a well-grounded problem to illustrate this.
Example: Alison and Ben have 50 cents in total. Alison has 10 cents more than ben. If Ben's share is 20 cents, what is Alison's share?
Step 1 - Create Sentences That Act as Instructions
The first step is to highlight the keywords in the world problem and organize the data. We will diagram the math sentences into equations. I’ll state all the variables in word form for now. We will eventually progress to using symbols in their place.
Alison's share + Ben's share = 50
Alison's share = Ben's share + 10
Step 2 - Restate Variables as Symbols
To make the word problem easy, you need to introduce coordinating variable symbols into the solution. You can choose any symbols of your liking. I will stay boring and use the traditional symbols (x, y).
We will let Ben's share be "x."
We will let Alison's share be "y."
Step 3 - Incorporate Variables into Sentences Created
Replace the symbols with the math word sentence we first created that modelled the problem from step 1.
x + y = 50
y = x + 10
Step 4: Solve for the Unknowns
As we know Ben's share (20), since it was given in the original problem. We can incorporate that value into these equations that we have generated and find out Alison's share. We are just placing one equation into the other to isolate a single symbol, in this case,
y = 20 + 10 = 30
Alison's share is 30 cents.