Task cards are such a great way to incorporate practice into your math classroom. My differentiated rational functions task cards resource is a great way to give students voice and choice in their learning, while providing an opportunity for challenge!
To check out a FREE unit of differentiated task cards CLICK HERE!
Simplifying Rational Expressions
The first skill that students will probably learn is how to simplify a rational expression. The problems are broken down as follows:
- Easy: a monomial divided by a monomial
- Medium: a monomial divided by a binomial, or vice versa
- Hard: all numerators and denominators are either binomials or trinomials that must be factored in order to simplify
Adding and Subtracting Rational Expressions
Since the skills are quite similar I combined adding and subtracting into one resource.
- Easy: All problems have a common denominator and do not simplify after being added or subtracted.
- Medium: Most problems only need one of the rational expressions to be multiplied in order to get a common denominator.
- Hard: Both rational expressions must be multiplied in order to get a common denominator. Some additional simplification may be necessary after performing the addition or subtraction.
Multiplying and Dividing Rational Expressions
Again, as with adding and subtracting, I combined the two operations into one resource. Students need to be careful to check whether they are multiplying or dividing in each problem!
- Easy: a rational expression multiplied or divided by another rational expression, where both are a monomial divided by a monomial
- Medium: some denominators and numerators contain trinomials that must be factored in order to perform the operation and simplify
- Hard: all problems contain either binomials or trinomials with a leading coefficient greater than 1 that must be factored in order to perform the operation and simplify
Graphing Rational Functions
This one is a BIG resource because there are lots of characteristics to list! I’ve included a version with slant asymptotes and another version without slant asymptotes.
- Easy: none of the rational functions contain holes, and they all have a horizontal asymptote
- Medium: some problems have holes, and some have multiple vertical asymptotes
- Hard: the problems require factoring and simplifying, and the graphs may include holes and multiple vertical asymptotes
Solving Rational Equations
Lastly, we learn to solve rational equations, although you could teach graphing last if you wanted!
- Easy: a single rational expression equal to a single rational expression (all could technically be solved by cross multiplication)
- Medium: rational expressions are either added or subtracted on one side of the equation, but no extraneous solutions arise
- Hard: just like the medium level, except some of the solution sets include extraneous solutions that must be excluded
To learn more about how I introduce graphing rational functions click here! If you use any of these resources in your classroom let me know how it goes in the comments or connect with me on social media!
Don’t forget, you can get a FREE unit of differentiated task cards by clicking HERE!
Happy teaching,
Natasha