Lesson 11-5 Dividing Polynomials – We practiced dividing rational expressions. We divided polynomials by monomials. Then we divided polynomials by binomials with long division. Hudson will remember to put parentheses around the term you are subtracting to distribute the negative one through the parentheses.

Lesson 11-4 Multiplying and Dividing Rational Expressions – We simplified expressions involving the quotient of monomials. Then we identified values excluded from the domain of a rational expression. Next, we simplified expressions and complex fractions.

Lesson 11-4 Multiplying and Dividing Rational Expression – Hudson and I worked on multiplying and dividing rational expressions. We went through examples showing how to multiply rational expressions of all monomials. We discovered how to factor a quadratic expression before simplifying a product of rational expressions involving polynomials that are not monomials.

Lesson 9-2 Solving Quadratic Equations and Lesson 9-4 Solving Quadratic Equations by Completing the Square – Hudson and I worked on factoring quadratic equations and finding the zero products. This is to prepare him for a test this week. Then we worked on learning the different conjugations of the verb ir-to go and the words describing pastimes or hobbies for a Spanish test tomorrow.

Lesson 9-4 Solving Quadratic Equations by Completing the Square – Hudson learned how to complete the square to write perfect square trinomials. He solved quadratic equations by completing the square. Then we worked on simplifying algebraic expressions by factoring out the greatest common factor. Some of the homework problems involved factoring out an algebraic expression.

Lesson 11-4 Multiplying and Dividing Rational Expressions – We discovered that the process of multiplying rational expressions is similar to that of multiplying rational numbers. If possible, we simplified the rational expressions, then we multiplied the numerators and the denominators. To divide rational expressions, we multiplied by the reciprocal of the divisor, just as we would do when dividing rational numbers.

Lesson 8-9 Perfect Squares – We practiced finding the product of the sum and difference of two quantities. We factored perfect square trinomials and solved equations involving perfect squares. We were preparing for a test that Hudson has tomorrow.

I had Hudson do problems from Lesson 2-8 Literal Equations and Dimensional Analysis, 2-7 Percent of Change, 2-6 Ratios and Proportions, and 2-5 Solving equations Involving Absolute Value to prepare for his midterm exam tomorrow. We decided to do a few extra percent problems and word problems involving dimensional analysis.

Hudson is studying for his final exam covering the first semester. We solved several problems involving simplifying polynomial expressions and applying the laws of exponents. Then we multiplied and divided numbers in scientific notation. Then we worked on understanding Lesson 2-9 Weighted Averages. I went over example 1 and solved two similar problems in the practice section. I sent them to Hudson to try to solve them himself and check his procedure.

Relations and Functions – We learned to identify functions and their components in a variety of forms such as graphs, tables, and ordered pairs. Next, we learned that a relation is a function only if each element of the domain is assigned to exactly one element in the range. Finally, we identified constraints on the domain based on real-world problems.