Unit 5 – Operations On Polynomials
Last updated January 3rd, 2012 at 12:48 p.m.Unit Plan
Algebra 2
10th and 11th grade
Mr. Boyer
Unit 5 – Operations On Polynomials
19 days
State Standards:
6B. 1. Determine an appropriate numerical representation of a problem situation, including roots and powers, if applicable.
2. Judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities.
6B 3. Identify, represent, and solve problems with numbers expressed in exponential, logarithmic, and scientific notations using technology.
6C. 4. Determine an appropriate number of digits to represent an outcome.
7B. 5. Determine answers to an appropriate degree of accuracy using significant digits.
8A. 6. Simplify algebraic expressions using exponential, logarithmic, and rational number techniques including more advanced factoring.
7. Justify the results of symbol manipulations including those carried out by technology.
8. Represent relationships arising from various contexts using algebraic expression.
Common Core Standards:
Standard (A-SSE.1) – Interpret expressions that represent a quantity in terms of its context.
Standard (A-SSE.1a) – Interpret parts of an expression, such as terms, factors, and coefficients.
Standard (A-SSE. 1b) – Interpret compoicated expressions by viewing one or more of their parts as a single entity.
Standard (A-SSE.2) – Use the structure of an expression to identify ways to rewrite it.
Standard (A-SSE.3) – Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Vocabulary for Unit 5 – binomial, coefficient, constant, degree, FOIL method, like terms, monomial, polynomial, power, scientific notation, synthetic division, terms, trinomial.
Daily Plans
Day 1 – Multiplying Monomials
Do an investigation as a group to find how the exponents are affected when two or more monomials are multiplied. Use the findings to develop the product rule for exponents. Compare it to the rule for multiplying coefficients. Show students on the smart board how to evaluate expressions involving exponents by using substitution. Have students do examples in pairs.
Assign: Worksheet
Day 2 - Power Rule for Exponents
Use the product rule from yesterday to derive a rule for taking a monomial involving exponents to a power. Discuss the different way that the power affects the coefficients and the exponents. Evaluate expressions both in a simplified form and in the original form to verify the rule. Do examples on the smart board.
Assign: Worksheet
Day 3 – Monomial Bingo Activity
Give students a sheet with 30 monomials to place on a bingo sheet. They will each choose 24 and place them in the squares randomly. Use computer jeopardy board to display problems for which the answers are the monomials on the given sheet. Play until each student has bingo.
Assign: Students will make their own bingo game
Day 4 – Dividing Monomials
Expand a monomial expression which involves division. Show how to eliminate like terms to simplify the expression. Use the results to define a quotient rule for monomials. Use the quotient rule to find the value of any expression to the zero power. Do examples on wipe boards in small groups.
Assign: Worksheet
Day 5 – Using Multiple Rules to Simplify Expressions
Use the quotient rule from yesterday to define negative exponents. Practice writing an expression in several different ways. Recall the order of operations for real numbers and relate it to monomial operations. Do several examples on the smart board.
Assign: Worksheet
Day 6 – Scientific Notation
Recall from Algebra 1 the definition of scientific notation. Discuss when scientific notation might be used to express numbers instead of using standard form. Practice putting numbers in scientific notation and in standard form both with and without technology. Demonstrate how to use different operation on expressions in scientific notation. Do several examples as a whole class on the smart board.
Assign: Worksheet
Day 7 – Naming Polynomials
Define degree and number of terms. List the terms for first, second, etc. degree polynomials of 1, 2, 3, or 4 terms. Have students draw an example out of a pile and name it. Then have the students make up their own examples when given a polynomial name.
Assign: Worksheet.
Day 8 – Adding and Subtracting Polynomials
Recall the characteristics of like terms. Discuss how only like terms can be added or subtracted together. Discuss examples that are written both vertically and horizontally. Do examples in sharing pairs.
Assign: Worksheet
Day 9 – Multiplying Polynomials
Recall the distributive property and the rules for multiplying monomials. Introduce the FOIL method for multiplying two binomial expressions. Discuss the use of both methods and when they should be used to multiply polynomials with various numbers of terms. Do examples on the smart board.
Assign: Worksheet
Day 10 – Mid – Unit Test Review
Day 11 – Mid – Unit Test
Day 12 – Factoring x2 + bx + c and x2 + bx - c
Recall that when multiplying two binomials, the answer is usually a trinomial. Start with the different possibilities for solutions for x2 + bx + c by using factors of c that add up to b. Then do the same for x2 + bx – c by using factors of c that subtract to give you b. When doing examples, include some trinomials that are prime. Do contests in small groups with wipe boards.
Assign: Worksheet
Day 13 – Factoring a2 – b2, a3 + b3, and a3 – b3
Show how to determine if monomials are perfect squares or perfect cubes. Discuss the patterns for factoring the difference of two squares or the sum or difference of two cubes. Do examples both with and without coefficients on the smart board.
Assign: Worksheet
Day 14 – Factoring by Grouping
Recall GCF and dividing monomials. Show how to use parentheses to group together pairs of terms in a polynomial of four terms. Use the GCF of each pair to simplify each part and then factor the results. Do examples in small groups
Assign: Worksheet
Day 15 – Factoring by Splitting the Middle Term
Factor a given problem in the form ax2 + bx + c using trial and error. Discuss the advantages and disadvantages of this method. Demonstrate the steps of factoring by splitting the middle term on the same problem. Discuss when this method would be better to use. Do examples as a whole class on smart board.
Assign: Worksheet
Day 16 – Multiple Factoring Steps
Review the different methods that we have used to factor expressions in the last week. Show how more than one method may be necessary to factor an expression into its lowest terms. Do examples as a whole group.
Assign – Worksheet
Day 17 – Long Division of Polynomials
Put a numerical long division problem on the board. Have a student come up and do the problem while another student describes exactly what they are doing in each step. Now, put a polynomial divided by a binomial on the smart board. Compare the steps to do the division to the former problem. Discuss how to write the answer including the remainder. Do examples in pairs.
Assign: Problems on the netbooks.
Day 18 – Synthetic Division
Recall yesterday’s lesson. Introduce synthetic division as a quicker method of dividing. Show how to write the answer. Have students come up and do examples on the smart board. Make sure some of the examples have missing terms and coefficients other than one.
Assign: Worksheet
Day 19 – Unit 5 Review
Day 20 – Unit 5 Test
