7-3 Multiplying Special Cases – We practiced determining the square of a binomial and finding the sum and difference of two squares. Next we practiced solving real-world problems involving the square of a binomial.
Assignment: Complete the assigned problems for homework.
7-4 Factoring Polynomials – We learned that the greatest common factor of the terms of a polynomial is the greatest common factor of the coefficients and the variable or variables, using the number of instances of the variable that are common to each term.
Assignment: Complete the assigned problems for homework.
Today Ben and I prepared for a Quiz that he will have tomorrow. We discussed how to go from radicals to exponent form. Ben used the acronym BOTI (he changed it to BOTN) to rewrite the expressions. Ben did a great job today. He only had difficulty with one problem involving a negative exponent. With a reminder, he was able to rewrite it.
7-3 Multiplying Special Cases – We learned that the product of the square of a binomial in the form (a + b) squared is always the square of the first term plus twice the product of the first and last terms plus the square of the last term. The product of a sum and a difference of two binomials in the form (a + b)(a – b) is always the difference of the two squares.
Assignment: Complete the assigned problems for homework.
Today Ben and I continued with the lesson on how to go from fraction powers to radical form, and vice versa. We started with the basics, using BOTI as a acronym to help us determine where the power goes. Ben was able to recall how to turn "the cube root of 4 to the fifth power" into "4 raised to the five thirds power". Ben practiced going from one form to the other and simplifying if possible.
Ben had a great class today. I got his attention at the beginning of class at the white board. I told him I was going to write some notes and asked if he would listen and he said sure. I showed him how to write a fraction power into a radical/root, by using an acronym "BOTI" which stands for Bottom--Out, Top--In. I showed Ben the problem 8^(2/3) and we wrote it in radical form. Then we evaluated it. Once Ben saw the pattern, I related it back to concepts Ben has previously learned (negative exponents, fractions, and decimals). Ben did very well today.
7-2 Multiplying Polynomials – We learned that polynomials can be multiplied by applying the Distributive Property or by using a table. They form a system similar to integers. We discovered that Polynomials are closed under multiplication. We practiced using the distributive property with polynomials to solve word problems. We used a table and an area model to complete the multiplication and find the quadratic equations.
Assignment: Complete the assigned problems for homework.
7-1 Adding and Subtracting Polynomials – We learned that a polynomial is a monomial or the sum or differences of two or more monomials. Polynomials can be added or subtracted by combining like terms. Polynomials are closed under addition or subtraction similar to integers. We practiced identifying the degree and number of terms of a polynomial. Then we practiced writing a polynomial in standard form. Next we practiced adding and subtracting two polynomials
Assignment: Complete the assigned problems for homework.
Ben had a good class today. We began by listening to two of his favorite songs. Then he was ready to begin. We discussed the relationship between exponents and radicals. We started with 4^2=16. I showed him how radicals and exponents are operations that undo each other. So the SquareRoot(16)=4. We practiced with more similar problems. Ben asked good questions to clarify his understanding.
