Rational Expression Relay

Teacher Facilitation Guide • Grade 10-11 Math

Objectives

Simplify rational expressions with like denominators using factoring and cancellation.

Duration

45 Minutes

Materials

Slide Deck, Relay Problem Cards, Reflection Paper.

The Hook (5 min)

Display the expression: \[\frac{-2(x-1)}{(x-1)}\]

Question: What does this equal? (Answer: -2)
Discussion: Why can we cancel the \((x-1)\)? (Anything divided by itself is 1). Why is this "easier" than if we had distributed the -2 first?

Video & Discussion (10 min)

Watch "Adding and Subtracting Rational Expressions With The Same Denominators". Use these pauses to check for understanding:

0:40

"Is the expression fully simplified just because we combined terms? What is the GCF here?"

2:20

CRITICAL PAUSE: "What mistake do students usually make with the minus sign in subtraction problems?" (Forgetting to distribute to the second term).

3:02

"Why can we cross out the (x-1) terms? Does this always happen in subtraction?"

Collaborative Activity: Rational Relay (20 min)

Instructions:

Divide students into groups of 4.
Student 1 (Combine): Write the problem as a single fraction using parentheses for the second numerator.
Student 2 (Distribute): Distribute the negative sign/remove parentheses.
Student 3 (Simplify): Combine like terms in the numerator.
Student 4 (Factor/Cancel): Factor the GCF or binomials and cancel to find the final result.

Relay Answer Key

Card 1

\[\frac{3x+8}{x+2} + \frac{x}{x+2}\]

1: \(\frac{3x+8+x}{x+2}\)

2: (Already Distributed)

3: \(\frac{4x+8}{x+2}\)

4: \(\frac{4(x+2)}{x+2} = 4\)

Card 2

\[\frac{7x-2}{x-4} - \frac{3x+14}{x-4}\]

1: \(\frac{(7x-2)-(3x+14)}{x-4}\)

2: \(\frac{7x-2-3x-14}{x-4}\)

3: \(\frac{4x-16}{x-4}\)

4: \(\frac{4(x-4)}{x-4} = 4\)

Card 3

\[\frac{2x^2+11x}{x+3} + \frac{15}{x+3}\]

1: \(\frac{2x^2+11x+15}{x+3}\)

2: (Already Distributed)

3: \(\frac{2x^2+11x+15}{x+3}\)

4: \(\frac{(2x+5)(x+3)}{x+3} = 2x+5\)

Card 4

\[\frac{x^2-10}{x-5} - \frac{3x+10}{x-5}\]

1: \(\frac{(x^2-10)-(3x+10)}{x-5}\)

2: \(\frac{x^2-10-3x-10}{x-5}\)

3: \(\frac{x^2-3x-20}{x-5}\)? (Revised: \(\frac{x^2-x-20}{x-5}\))

Correction for Card 4: Use \(\frac{x^2-x}{x-5} - \frac{20}{x-5}\)

Reflection (10 min)

One-Minute Paper: "Explain why we cannot cancel terms (like 'x' or '3') *before* we add/subtract the fractions together. Why must we wait until the end?"

Rational Expression Relay

Relay Teacher Guide

Relay Slideshow

Relay Problem Cards Worksheet

Rational Reflection Handout

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