Review for Test on Topic 4 Systems of Linear Equations and Inequalities.

Ben participated in a school wide Valentine's celebration today.

4-5 Systems of Linear Inequalities – We continued to practice graphing linear inequalities to solve systems of linear inequalities on the same coordinate plane. Then we learned to solve real-world problems by using systems of inequalities.
Assignment: For homework complete assigned problems.

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.

4-5 Systems of Linear Inequalities – We combined the understanding of systems of linear equations and the graphing of linear inequalities to solve systems of linear inequalities on the same coordinate plane. We discovered that the overlapping region is the solution. We also learned to write systems of inequalities by analyzing a graph.
Assignment: For homework complete assigned problems.

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.

Today Ben and I worked on the properties of multiplying and dividing exponents. We started with using his desk and the expo marker to work the problem 4^3*4^(-1) (that is 4 to the third power times 4 to the -1 power). We reviewed the rule: multiplying like bases -> add powers. So that gave us 4^2. Then we evaluated that as 16. We practiced several examples like 4y^3*3y^2=12y^5. Ben started picking up on the concept. Then I introduced division. I asked him, "If we multiply like bases and add powers, then when we divide like bases, what do you think we do?" He answered, "Subtract." That led us into a discussion about the rules of inverses. We then moved to the white board and I wrote problems for him to try on his own. He worked them aloud, asking great questions along the way.

4-4 Linear Inequalities in Two Variables – We practiced graphing solutions to linear inequalities in two variables. Then we practiced representing constraints with inequalities and interpreting solutions as viable or nonviable options in a modeling context.

Today Ben and I began a new Chapter on exponents. I looked at the material in the textbook and realized its far too advanced for where Ben is at right now. During his MAPs test I realized he did not have the basic understandings for exponents. So instead of using the text book as a guide, we are going to take a step back and scaffold the content so he can gain a proper foundation. We started with the rule that when you are multiplying like bases, you add the exponents. I explained to him that 3^2*3^3 (that's 3 squared and 3 cubed) really means (3*3)(3*3*3) so we can see that we have 3^5. Instead of writing it out each time, we use the property that we can add the powers. Then I gave Ben a series of problems with increasing difficulty. He made a few mistakes as he worked, but was able to make corrections. He did well on this new concept to him.

Testing and 4-4 Linear Inequalities in Two Variables – We learned that the graph of a linear inequality in two variables shows the solutions of the inequality as a half-plane above or below the boundary line. Then we learned that the boundary line is included in the solution when the inequality symbol is less than or equal to or greater than or equal to. The boundary line in an inequality is excluded when the inequality symbol is less than or greater than.
Assignment: For homework complete assigned problems.