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AGENDAS FOR THE WEEK: February 10th – February 14th MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY Review Objective(s): SWBAT *Review interval notation, finding intersections and unions of intervals, and linear inequalities. Formative Assessment Objective(s): SWBAT *Testing for understanding of Interval Notation, Intersections and Unions, and Linear Inequalities. NGSSS: MA.912.A.3.4: Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution. NGSSS: MA.912.A.3.4: Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution. CCSS: MACC.7.EE.2.4b: Solve word problems leading to inequalities of the form px+q>r or px+Q<r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. MACC.912.A-CED.1.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, MACC.912.A-REI.2.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. CCSS: MACC.7.EE.2.4b: Solve word problems leading to inequalities of the form px+q>r or px+Q<r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. MACC.912.A-CED.1.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, MACC.912.A-REI.2.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Go over yesterday's homework. Go over yesterday's homework. (5 Minutes) Engage: Display the first slide of the Power-Point with the (10 Minutes) Engage: Display the first slide of the Power-Point with Pass out the Quiz: The quiz will test the students on interval notation, intersections and unions, and linear inequalities they learned about this week. When they Interval Notation Objective(s): SWBAT *Use interval notation. *Learning new vocabulary. Intersections and Unions Objective(s): SWBAT *Find intersections and unions of intervals. Linear Inequalities Objective(s): SWBAT *Solve linear inequalities (one variable). NGSSS: N/A CCSS: N/A NGSSS: N/A CCSS: N/A NGSSS: MA.912.A.3.4: Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution. MA.912.A.3.5: Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities. CCSS: MACC.7.EE.2.4b: Solve word problems leading to inequalities of the form px+q>r or px+Q<r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. MACC.912.A-CED.1.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, MACC.912.A-REI.2.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. P Pass back and go over last Friday's Quiz. (5 Minutes) Engage: Display the first slide of the Power-Point with a 2 Go over yesterday's homework. (5 Minutes) Engage: Display the first slide of the Power-Point with interval notations (1,4) and [2,8] and ask L problems that have graphs on number lines and ask students what they think the graphs mean. the students what the graphs have in common and how they differ. inequality 2x + 5 < 17 and ask the students to solve it. After ask them write the solution in interval notation. a real-world word problem. The students should solve the two inequalities, graph them, write the solutions in interval notation. (5-10 Minutes) Explore: Display Explore slide of the Power-Point with problems asking students how they could graph the 2 different situations. (5-10 Minutes) Explore: Display Explore slide of the Power-Point with 2 graphs and ask students what they have in common and what they have that is different. Then ask how they could write that using interval notation. (5-10 Minutes) Explore: Display the Explore slide of the Power-Point with a linear inequality word problem asking the students to solve the inequality and graph it. (40 Minutes) Elaborate: Give the students their review worksheet. The worksheet covers all of the concepts learned this week, which include: Interval notation, set-builder notation, graphing an interval, finding the intersection or union of sets, and solving linear inequalities. Any problems the students do not finish in class should be completed for homework. (25-35 Minutes) Explain: Go over the answers to the problems on the Explore slide. After going over the answers ask the students if they know what interval notation is. ** It is a form of notating the solution sets of inequalities. ** Discuss how it is used to represent an interval for an inequality. Do examples. A ** Examples from Power-Point: Given the problem -2 < x < 3 and the corresponding graph. Given the problem -2 ≤ x ≤ 3 and the corresponding graph. Given the problem -2 < x ≤ 3 and the corresponding graph. ** Discuss how the brackets and parentheses determine if they use the symbols <, or ≤. Have the students guide the teacher through 3 problems. ** Examples from Power-Point: Given (-1,4] what will the (20-25 Minutes) Explain: Go over the answers to the problems on the Explore slide. After going over the answers ask the students if they remember what intersections and unions are in mathematics. ** Intersections are the set of elements common to both set A and set B. Unions are the set of elements in set A or in set B or in both sets. ** Since intervals represent sets we can find their intersections and unions. The steps to find the intersections and unions of two intervals are: 1) Graph each interval on a number line. 2) a. For intersections, take the portion of the number line that the two graphs have in common. 2) b. For unions, take the portion of number line representing the total collection of the numbers in the two graphs. Do 2 examples, to help solidify the concept. Have the students (25-30 Minutes) Explain: Go over the answers to the problems on the Explore slide. After going over the answers discuss inequalities and how multiplying and dividing by negative numbers changes the direction of the signs in the problem (called the Negative Multiplication Property of Inequality). Do 2 examples with students. ** Examples from Power-Point: 3 – 2x ≤ 11 [Answer: -4 ≤ x] -2x -4 > x + 5 [Answer: x < -3] ** Ask students how is solving inequalities similar to solving equations. Ask them how it is different. Discuss how to solve linear inequalities containing fractions. Do 2 examples with the students. ** Example from Power-Point: x+ 3 x− 2 1 ≥ + 5 3 4 [Answer: x ≤ 14] finish they must sit quietly at their seat. They may work on homework or assignments for other classes, read a book, or just sit quietly. graph look like? Given [2.5, 4] what will the graph look like? Given (-4, ∞ ) what will the graph look like? ** Discuss that there is a second way that is often used as well called set-builder notation. Show example of set-builder notation. ** Example from Power-Point: for -2 < x < 3 the notation would be {x|-2 < x < 3}. Thus the graph, the interval notation and the set-builder notation all represent the same thing. ** Have the students lead the teacher through the 3 previous examples changing the interval notation to set-builder notation. ** Example from Power-Point: Given (-1,4] what will the setbuilder notation be? [Answer: {x| -1 < x ≤ 4}] Given [2.5, 4] what will the set-builder notation be? [Answer: {x| 2.5 ≤ x ≤ 4}] Given (-4, ∞ ) what will the set-builder notation be? [Answer: {x| -4 < x < ∞}] ** Display slide with table showing the different kinds of notations and their graphs. Inform the students the table can be found on page 174 in their textbook. guide the teacher through the problem. ** Examples from Power-Point: Given [1,3], (2,6) graph and write in interval notation what the union and intersections are. Given (-3,1], [0,5) graph and write in interval notation what the union and intersections are. ** (10 Minutes) Elaborate: (Optional) Give students worksheet that uses intersections and unions with real-world examples. Have them graph and write the sets using interval notation. x− 4 x− 2 5 ≥ + 2 3 6 [Answer: 13 ≤ x] ** (10-15 Minutes) Elaborate: (Optional) Give the students worksheet that has 3 linear inequalities and a word problem on it. The students will need to make a graph and give the inequalities solutions in interval notation. (10 Minutes) Elaborate: Give students worksheet. Any parts they don't finish in class should be finished for homework. N Resources: Evaluate and Summary: Homework is the Worksheet called Interval Notation Practice. Evaluate and Summary: Homework is from the textbook Page 185, #s 15-26 Evaluate and Summary: Homework is from the textbook Page 185, #s 27-41 odd only Evaluate and Summary: Study for tomorrows quiz on section 1.7! Finish review worksheet from class. Evaluate and Summary: Quiz on Section 1.7 Objectives 1-3 today! Elaboration/Homework Worksheets Power-Point Power-Point Power-Point Review Worksheets Power-Point Quizzes