Give students the Binomial Expansion Worksheet. Have them work in pairs to complete problems 1-3. These problems ask the students to expand an increasing number of binomials (2, 3, then 4). The purpose of this activity is to review binomial expansion and to show the need for a quicker method. Students will attempt to answer Question 4 by examining patterns they find from working on questions 1, 2, and 3. At this point, they may or may not find the correct answer. You will be discussing the patterns with them in the during phase of the lesson. You will also give them another chance to find the correct answer to question 4.
Open the PowerPoint Presentation. This presentation will progress through the patterns in the binomial expansion. These patterns, along with Pascal's Triangle, will be introduced as a method for expanding any binomial. Finally, the use of combinations will be incorporated into the binomial theorem. Have students make notes and work problems from the slides in their notebook or on the Binomial Theorem PowerPoint Presentation Notes Handout if notebooks are not used.
Slide 1: Introductory Slide. Be sure to explain to students that we need a quicker and more efficient method for finding a binomial expansion.
Slide 2: This slide contains the answers to the worksheet questions 1 - 3. Question 4 will be answered in slide 9.
Slide 3: In this slide, you will discuss patterns and the first and last term of the expansion. These are always the first and last term of the binomial raised to the power of the binomial.
Slide 4: The discussion of the sum of the exponents of each term in the expansion is included on this slide. Students should see that the sum of the exponents of each term is always the exponent of the binomial.
Slide 5: The exponents of the first binomial term are discussed on slide 5. The exponents always begin at the binomial exponent and decrease to 0 in the expansion.
Slide 6: The exponents of the last binomial term are discussed on slide 6. The exponents begin at 0 and increase to the binomial exponent.
Slide 7: Ask students to make some conjectures about the coefficients. You want students to realize the coefficients are from Pascal's Triangle.
Slide 8: This slide presents Pascal's Triangle, you can use it to introduce this to your students, if necessary.
Slide 9: Ask the students to return to question 4 on the worksheet and find the expansion. The answer is provided when you click.
Slide 10: Provides another example for students to try.
Slide 11: Presents an example that has a coefficient in the binomial.
Slide 12: Now we need to transition to the Binomial Theorem using combinations. Point out to students that at times we don't want to have to write all the rows of Pascal's Triangle to find our expansions. Make sure they know that the numbers in the triangle are simply a set of combinations. The formula for a combination is included.
Slide 13: Students are presented with an example using combinations.
Slide 14: This slide contains a problem for students to work. Answers are included.
Ask students to complete the Exit Ticket before leaving class.