1. Too many grades of D or F in math? Hanlonmath

2. Kids only get one chance at receiving a good education, we are working to ensure they get it! Hanlonmath

3. Today Today’s presentation focuses on what we can do to help struggling students, students living in poverty, become successful in their study of mathematics. Hanlonmath

4. MLL In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments in which the altitude is the geometric mean of the lengths of the two segments. Hanlonmath

5. Geometric Mean Hanlonmath

6. Geometric Mean Proportion - Proportions equal fractions Hanlonmath

7. Equivalent Fractions Hanlonmath

8. MLL Math Language Learners Hanlonmath

9. Vocabulary & Notation There is no more single important factor that affects student achievement than vocabulary and notation Hanlonmath

10. Vocabulary Find the degree of the monomial 4x 2 y 3 z 5 Hanlonmath

11. Vocabulary Best Bet? –Bet A Probability of winning is 3/5 –Bet B Odds of winning 3 to 5 Hanlonmath

12. Language Acquisition Double meanings area volume operation power mean feet product Hanlonmath

13. MLL Solve Find the roots Find the zeroes Find the value of the variable that makes the open sentence true Hanlonmath

14. Speaking Oral recitation Speaking Working in pairs (groups) Hanlonmath

15. Oral Recitation Language Acquisition Teaches students how to learn Embeds in short tem memory Hanlonmath

16. Classroom Oral Recitation Procedure – Adding/Subtracting Fractions 1.Find a common denominator 2.Make equivalent fractions 3.Add/Subtract numerators 4.Bring down denominator 5.Reduce Hanlonmath

17. Classroom Oral Recitation Quadratic Formula Hanlonmath

18. Rules in Mathematics Don’t make sense! Hanlonmath

19. Math Rules! Division by Zero Dividing Fractions Rules for Exponentials Rules for Integers Hanlonmath

20. Understanding What does “do you understand” really mean? Hanlonmath

21. Understanding Divide Fractions –Flip & Multiply Hanlonmath

22. Understanding ax + b = c 4x + 2 = 30 5x – 4 = 3x + 16 2(3x– 4) – 2 = 4x + 10 x/3 – x/4 = 6 (x – 4)/2 + (x + 3)/5 = x – 5 Hanlonmath

23. Axiom The more math you know, the easier math gets! Hanlonmath

24. Way of Thinking Math is more than just a body of knowledge, it is a way of thinking that affects the way we live. Hanlonmath

25. Decisions Computation;4 x 13 x 25 –Algorithm (rule) –Properties of Real Numbers Hanlonmath

26. Decisions Finding a common denominator –Multiply denominators –Write multiples –Factor Tree, LCM –Reducing Method Hanlonmath

27. Decisions Systems of Equations –Graphing –Substitution –Linear Combination –Cramer’s Rule Hanlonmath

28. Decisions Quadratic Equations –Zero Product Property –Completing the Square –Quadratic Formula –Rational Root Theorem Hanlonmath

29. The more math you know, the easier math gets! Hanlonmath

30. Answering the Question What are you doing to help my child learn? Hanlonmath

31. Organizing Student Learning Preparation really matters! Instruction, Concept Development-Linkage Note Taking Homework Test Preparation Assessment Student-Teacher Relationships My Kid Standard Hanlonmath

32. What are you doing to improve instruction? Hanlonmath

33. What are you doing to help my child learn? Hanlonmath

34. Good News! Teachers are already employing many of the best practices needed to increase student achievement. Hanlonmath

35. Best practices Note taking Homework Tests Hanlonmath

36. Components of an Effective Lesson Before presenting a lesson, refer to the assessment blueprint for the unit. Introduction Daily Reviews Daily Objective Concept and Skill Development and Application Guided / Independent / Group Practice Homework Assignments Closure Long-Term Memory Review Hanlonmath

37. Its about you! Use the DATA Hanlonmath

38. Increasing Student Achievement No simple answer- what works is work Hanlonmath

39. Success on Success Hanlonmath

40. Success on Success First Test – Important for confidence! –Grade Distribution Success on Success –Teach students how to learn effectively and efficiently. –Concentration times Hanlonmath

41. Studying Reading Thinking Reflecting Organizing Writing Analyzing Visualizing Reviewing Remembering Recalling Hanlonmath

42. Student-Teacher Relationships 1.Treat your students the way you want your own children treated. 2.Build success on success. 3.Talk to your students. Be friendly. 4.Talk positively to your students about their opportunity to be successful. 5.Call home early with information and good news. 6.Make testing as much a reflection of your instruction as their studying. Hanlonmath

43. Student-Teacher Relationships 6.Teach your students how to study effectively and efficiently (visual, audio, kinesthetic, concentration time). 7.Tell them you like them. 8.Go over expectations explicitly and give examples. 9.Build trust, make sure they know you are there for them by telling them you are. 10.Tell them you want them to succeed. 11.Continually answer the question; “What am I doing to help my students learn?” Hanlonmath

44. Contradictory Rules Hanlonmath

45. Learning Students learn best when they are given feedback on their performance and praised for doing things well Hanlonmath

46. Unsuccessful Students Hanlonmath

47. STAR System 3 Stars – on the test unchanged, no computation, no manipulation 2 Stars – on the test, changes in numbers 1 Star – allows variability, so curriculum is not narrowed Hanlonmath

48. The Phone Conversation Introduction Pleasure teaching your son/daughter, nice young man/lady Explanation, how I intend to help your child succeed – Instruction –Clear instruction, linkage, memory aids –Notes, * system, very prescriptive –Homework, comes from notes & instruction –Oral recitation, procedures & formulas –Practice tests, * system –Study/flash cards –Reviews Hanlonmath

49. The Phone Conversation Permission to use those strategies/consequenes Parental help –Know when tests are scheduled –Examine student notebooks –Use flashcards to help study Hanlonmath

50. Content & Pedagogy Hanlonmath

51. 1st Essential - Instruction Hanlonmath

52. Instruction Teach for understanding –Its not a matter of if students will forget information, it’s a matter of when they will forget –Students should be able to reconstruct knowledge over time Hanlonmath

53. Preparation Creation of a practice test and choosing examples before instruction begins suggests that teachers prepared for the unit; knowing where students traditionally experience difficulty and having resources and strategies ready to address those difficulties. Hanlonmath

54. Preparation Practice test Cover curriculum appropriately (rigor) Grades - Fair & Portable Benchmarked Unit questions reflect questions on: –Curriculum –Unit –HSPE –Semester exams –College Entrance exams (ACT & SAT) Hanlonmath

55. Balance Vocabulary & Notation Concept Development & Linkage Memorization of Important Facts & Procedure Applications Appropriate Use of Technology Balance in mathematics has been defined as: Balance should be reflected in assessments and in the delivery of instruction. Hanlonmath

56. Time on Task Stake and local school districts usually determine the classroom time available to teachers and students. However, regardless of the quantity of time allocated to classroom instruction, it is the classroom teacher and school administrator who determine the effectiveness of the time allotted. According to a survey conducted by the American Association of School Administrators, teachers identify student discipline as the single greatest factor that decreases time on task in the classroom. Generally, teachers with well- managed classrooms, have fewer disciplinary problems. These classrooms typically have teachers who have established rules and procedures are in the classroom when the students arrive, and begin class promptly. They reduce the “wear and tear” on themselves and students by establishing procedures for make- up work, they arrange their room to accommodate their teaching philosophy and style, and they develop routines that increase overall efficiency. The benefits of establishing these classroom procedures and routines become apparent as the total time on task approaches the allocated time. Hanlonmath

57. Time on Task When teachers begin class immediately, students view them as better prepared, more organized and systematic in instruction, and better able to explain the material. Students also see these teachers as better classroom managers, friendlier, less punitive, more consistent and predictable, and as one who values student learning. Routines like beginning class immediately, reviewing recently taught material, orally reciting new material, having students take notes, and ending the class by reviewing important definitions, formulas, algorithms, and the daily objective keep students engaged and on task. Quality time on task is not a “silver bullet” that can cure all the problems facing education. However, it can play an important role in increasing student achievement. Hanlonmath

58. Content - Instruction What you teach affects student achievement How you teach it affects student achievement Hanlonmath

59. Subtraction 5 – 115 – 68 – 814 – 6 13 – 59 – 215 – 97 – 1 14 – 516 – 94 – 410 – 4 6 –212 – 410 – 36 – 3 Hanlonmath

60. When will I ever use this? Pythagorean Theorem Parabola Circumference Hanlonmath

61. Knowledge, Interest, & Enthusiasm Hanlonmath

62. Systems Hanlonmath

63. Functions C = 10 +.05m y = 10 +.05x y =.05x + 10 y = (1/20)x + 10 Hanlonmath

64. Use simple straight forward examples that clarify what you are teaching. Do not get bogged down in arithmetic. Hanlonmath

65. Multiplication by 11 by 25 Hanlonmath

66. Leading the department Leaders make sure all department members know what and how material is assessed and what a good answer looks like. Leaders make sure all members teach and assess the standards on high-stakes tests. Hanlonmath

67. Different Ways to Measure the Same Standard Hanlonmath

68. Finding Measures of Central Tendency 1.Find the mean of the following data: 78, 74, 81, 83, and 82. 2.In Ted’s class of thirty students, the average on the math exam was 80. Andrew’s class of twenty students had an average 90. What was the mean of the two classes combined? 3.Ted’s bowling scores last week were 85, 89, and 101. What score would he have to make on his next game to have a mean of 105? Hanlonmath

69. Finding Measures of Central Tendency 4.One of your students was absent on the day of the test. The class average for the 24 students present was 75%. After the other student took the test, the mean increased to 76%. What was the last student’s score on the test? 5.Use the graph to find the mean. Hanlonmath

70. I can’t teach __________ because my kids don’t know _____________ Hanlonmath

71. Show them how - Linkage Introduce new concepts using familiar language Review and reinforce Compare and contrast Teach in a different context Hanlonmath

72. + Polynomials Hanlonmath

73. 6 7 2=6(100) + 7(10) + 2(1) 6 10 + 7 10 + 2 2 6 n + 7 n + 2 2 6x + 7x + 2 2 Hanlonmath

74. 5 3 2+3 4 1 = 8 7 3 (5 +3)(100) +(2 + 1)(1) = + (3 + 4)(10) (8)(100) + (3)(1) = + (7)(10) (800) + (3) =+ (70) Hanlonmath

75. 213 = 9 8 7 (4 +3+2)(100) + (2+2+3)(1) =+ (1+6+1)(10) (9)(100) (900) + 362 412+ (7)(1) =+(8)(10) + (80) + (7) =+ 123+271 = 8 9 6 (1 +5+2)(100) + (3+2+1)(1) =+ (2+0+7)(10) (8)(100) (800) 502 + (6)(1) =+(9)(10) + (90) + (6) =+ Addition - Left to Right Hanlonmath

76. (5x + 3x + 2) + (3x + 4x + 1) 22 = 8x + 7x + 3 2 5 3 2+3 4 1 =8 7 3 (5x + 3x ) + (3x + 4x) + (2 + 1) 22 Hanlonmath

77. Add / Subtract Rational Expressions Hanlonmath

78. 1 + 3 1 2 2 6 5 6 3 6 +

79. 1 + 3 1 2 = 5 6 1 + 4 1 5 = 9 20 1 + 3 1 4 = 7 12 Hanlonmath

80. 1 + 3 1 5 = 8 15 Hanlonmath

81. 2 + 3 1 5 = 13 15 3 + 10 2 3 = 29 30 Hanlonmath

82. 3 + 4 1 5 = 20 + 4 1 3 5 = 19 Hanlonmath

83. 2 + X 3 Y = XY 2 + X 3 Y = 2Y + 3X XY Hanlonmath

84. A + B C D = AD + BC BD A C + B D = Hanlonmath

85. 3 + x-1 2 x+3 = (x-1)(x+3) 3 + x-1 2 x+3 = (x-1)(x+3) 3(x+3) + 2(x-1) Hanlonmath

86. Relations & Functions Hanlonmath

87. Functions Special relation in which no 2 ordered pairs have the same 1st element. Hanlonmath

88. Menu Hamburger ……….4 Hotdog ……………3 Sandwich …………5 00 Hanlonmath

89. 4 00 (H, )(Hd, ) (S, ) 3 00 5 H, Hd, S,4 00 3 5 4 H, Hd,( S), 3 00 5 Hanlonmath

90. .50 1, 2, 3, 1 00 1 50.50 (1, ) (2, ) (3, ) (10, ? ) 1 00 1 50 Cold Drinks Hanlonmath

91. .50 1, 2, 3, 1 00 1 50.50 (1, ) (2, ) (3, ) (10, ? ) 1 00 1 50 C = n x.50 =.50n or y = x 1212 Hanlonmath

92. 50 (1, ) (4, ) 2 00 1 (2, )1 50 (3, ) 1 75 (4, ) Hanlonmath

93. Functions Special relation in which no 2 different ordered pairs have the same 1st element. Hanlonmath

94. Multiplication Hanlonmath

95. 3 2 6 7 2 6 4 3 2 2 1 x 3x + 6 x + 2 x + 3 2 x + 2x 2 x + 5x + 6 Hanlonmath

96. (x + 3) (x + 2) = x + 5x + 6 2 (x + 4) (x + 5) = x + 9x + 20 2 (x + 10) (x + 5) = x + 15x + 50 2 Hanlonmath

97. (x+6)(x+4)= x 2 + 10x + 24 Hanlonmath

98. (2x + 3) (3x + 5) 6x + 8x + 15 2 Hanlonmath

99. 10x +15 2x + 3 3x + 5 2 6x + 9x 2 6x +19x +15 Hanlonmath

100. (2x + 3) (3x + 5) 2 6x + 19x + 15 Hanlonmath

101. F O I L Hanlonmath

102. 6 2 3 2 2 1 x 6 2 3 2 2 1 x 7 Hanlonmath

103. Equations of Lines Hanlonmath

104. = m y - y 1 x - x 1 y - y 1 = m (x - x 1 ) Hanlonmath

105. y - y 1 = m (x - x 1 ) Find the equation of a line passing through the point (2,3), with m = 4 y - 3 = 4 (x - 2) point - slope Hanlonmath

106. y – 3 = 4x - 8 Solve for y: y = 4x - 5 y – 3 = 4 (x - 2) Hanlonmath

107. y = mx + b y = 4x - 5 slope - intercept Hanlonmath

108. 4x – y = 5 general form Hanlonmath

109. -Introduce using familiar language -Review & Reinforce -Compare & Contrast -Teach in different context Increased Student Achievement LINKING Hanlonmath

110. Linking Fractions Decimals Percents Hanlonmath

111. Linking Pythagorean Theorem Distance Formula Equation of a Circle Trig Identity Hanlonmath

112. Linking Special products in algebra Special products in arithmetic Hanlonmath

113. Linking Quadratic Formula Completing the Square Hanlonmath

114. Linking Solving Linear Equations Order of Operations Hanlonmath

115. ax + b = c Linear equations Equations containing absolute value Radical equations Systems of equations Quadratic equations Hanlonmath

116. Area-Volume Rectangle Parallelogram Triangle Trapezoid Hanlonmath

117. Composition of Functions Linked to evaluating functions f(g(x)) –Make a purchase, pay a 7.5% sales tax and a $20 delivery fee. Hanlonmath

118. Why Linking? It’s not a matter of if students are going to forget information, it’s a matter of when. Linking concepts will allow students to reconstruct concepts and skills Hanlonmath

119. Basic Facts & Procedures Stopping to remember basic facts interrupts the flow of thought, which negatively impacts learning. Hanlonmath

120. Memorization Memorizing can help students absorb and retain information on which understanding and critical thought are based. The more sophisticated mental operations of analysis, synthesis, and evaluation are impossible without rapid and accurate recall of bodies of specific knowledge. Hanlonmath

121. It is my job to teach: Reading Writing Hanlonmath

122. Reading Assign reading Explicitly introduce vocabulary & notation Preview reading Connect reading Check understanding of reading Correct their understanding Use paper & pencil Hanlonmath

123. Organizing Student Thinking What’s the easiest way to help students to organize their thinking? Writing Hanlonmath

124. Writing Definitions Procedures Linkages Applications Compare & contrast Describe what they understand Describe difficulty experienced Describe how to solve a problem Summarize Explain Hanlonmath

125. Problem Solving Go back to definition Look for a pattern Make a table or list Draw a picture Guess & Check Examine a simpler case Examine a related problem Identify a sub-goal Write an equation Work backward Hanlonmath

126. Definitions How do you derive … –rules for logs –equations for conic sections –rules for exponentials without knowing the definitions Hanlonmath

127. Instruction Instruction check Practice test demonstrating pre- planning Test reflect other high stakes tests Understanding of instruction Hanlonmath

128. 2nd Essential - Note taking Hanlonmath

129. Researchers - #1 Memory Aid - Writing it Down Complete homework assignment Prepare for unit test Prepare for high-stakes tests Note Taking Hanlonmath

130. Rules and examples Hanlonmath

131. Title Date Objective Vocabulary & Notation Pattern Development Rule Examples Variation Hanlonmath

133. Use simple straight forward examples to clarify initial teaching! Increase difficulty later. Hanlonmath

134. Note check Student notes reflect instruction Contain title, date, objective, definitions, how to say it, pattern development, linkage, rules and exercises with developed rules White space Star * System Explanations ~ Cautions Hanlonmath

135. 3rd Essential - Homework Hanlonmath

136. Homework Homework should reflect what you say you value. –Vocabulary & Notation –Conceptual Understanding & Linkage –Basic Facts & Procedures Hanlonmath

137. Make sure students understand the concept or skill before sending home to practice Hanlonmath

138. Practice Guided Group Independent Hanlonmath

139. Homework Page 270, 1–32 odd Hanlonmath

140. Homework-Studying Reading Thinking Reflecting Organizing Writing Analyzing Visualizing Reviewing Remembering Recalling Hanlonmath

141. Homework Read Sec. 9.4 - Expressions involving logarithms Define logarithm Write a procedure for converting logarithms to exponentials Explain why when multiplying logs with the same base, you add the logs log (AB) = logA + logB Page 270 1, 3, 6, 7, 9, 12, 13, 14, 21,23, 31 Hanlonmath

142. Homework Read Sec 9.4 - Adding Fractions Define Fraction Draw a model for adding fractions Write a procedure for adding fractions Explain the link between adding fractions and decimals Page 270 1, 3, 6, 7, 9, 12, 13, 14, 21, 23, 31 Hanlonmath

143. Homework Assignment Sheet demonstrates thoughtful preparation Hanlonmath

144. Homework check A quick look at the homework assignments suggest the care teachers take to reinforce the daily instruction to help students prepare for unit, semester and other high stakes tests. Star * System Hanlonmath

145. Reviews Recently taught material Long term review Hanlonmath

146. What do your students know? How do you know they know it? Assessing Student Work Hanlonmath

147. 1 + 4 1 3 = 7 12 Hanlonmath

148. 5 + 24 7 18 = 24 = 3 4 CD = 72 18 x 4 24 x 3 = 72 Reducing Method 18 = 3 24 4 Hanlonmath

149. 18 24 = 3 4 5 = 15 72 7 = 18 28 72 + 43 72 Hanlonmath

150. 4 th Essential – Test Preparation Hanlonmath

151. 4th Essential- Test Preparation Test what you say you value: Instruction – Assessment – Balance Questions reflecting other high-stakes tests Cumulative questions Practice tests - Parallel construction Setting a date Hanlonmath

152. Testing Testing drives instruction Hanlonmath

153. Differentiation 1355 ÷ 41 1355 ÷ 47 Hanlonmath

154. Differentiation x 2 + 7x + 12 x 2 + 7x + 2 Leads to decisions! Hanlonmath

155. Tests Test Design –Design tests that encourage study. –Test what you say you value Hanlonmath

156. Test Preparation Do you know what you are going to test your students on BEFORE you begin to teach a unit? Use the * System on notes, homework, and practice tests to to prepare for test Hanlonmath

157. Practice Tests Parallel constructed; especially for students who have not experienced success in math. Hanlonmath

158. Tests Monitor student learning Hanlonmath

159. Memory Aids Help your students remember Hanlonmath

160. ABBA Hanlonmath

161. SOHCAHTOA Hanlonmath

162. Quadratic Formula Hanlonmath

163. 5th Essential - Tests Form A ~ Form B Hanlonmath

164. Test Check Balanced assessment Cover the assigned curriculum/benchmarks Questions reflect other high stakes tests Grades are fair Grades are portable Parallel constructed Hanlonmath

165. Tests Are test results a reflection of instruction? Hanlonmath

166. Organizing Student Learning Making the connection - Instruction to Note taking to Homework to Test preparation to Tests Hanlonmath

167. Organizing Student Learning Helps students focus and study more effectively and efficiently resulting in increased student achievement Hanlonmath

168. This organization strategy leads to Transparency Credibility Trust Hanlonmath

169. Summary Student-teacher relationships ~parent communication~ 1)Understanding instruction 2)Notes that reflect & reinforce instruction 3)Homework that supports and reflects instruction 4)Test preparation 5)Parallel constructed tests Hanlonmath

170. Today What ideas would you consider using? Hanlonmath

171. What are you willing to do? Hanlonmath

172. Next steps What are you willing to do to increase student achievement? –Explicitly go over expectations with staff in August –Parental communication –Observe instruction in September/October with emphasis on “5+1” and understanding –Collect grade distributions for 1 st unit test –Conduct pre- and post- observation conferences within a week and provide meaningful suggestions, recommendations, or directions that improve instruction –Continue observations, conferences & monitor grade distributions Hanlonmath

173. Next steps What are you willing to do to increase student achievement? –Create pre tests that reflect unit and other high stakes tests –Parental communication –Introduce new concepts and skills using concept development or linkage –Be more prescriptive & directive with notes that reflect instruction –Create homework assignments that encourage study –Use star * system in notes, homework & practice tests –Create parallel constructed tests Hanlonmath

174. Recommended Next Steps Hanlonmath

175. Contact Information Bill Hanlon bill@hanlonmath.com 800.218.5482 –www.hanlonmath.comwww.hanlonmath.com –www.rpdp.net Hanlonmath