http://math.pmhclients.com/index.php/site/index/ en jeff@shosholoza.org Copyright 2010 2010-03-12T15:05:00-08:00 http://math.pmhclients.com/index.php/site/hl_class_63/ http://math.pmhclients.com/index.php/site/hl_class_63/#When:15:05:00Z Lesson Title Lesson 21: Looking Closely (1) Overview Today students continue to examine functions from a very close perspective. They see that when viewed closely enough, all smooth continuous functions become essentially linear. Textbook Sections Vocabulary function independent variable dependent variable with respect to rate of change limit derivative explicit equation implicit equation Key Attitudes Willingness to work as a group to help meet individual and group goals. Enduring Understandings Change is fundamental to understanding functions. Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral). Essential Question What does a function look like when viewed very closely? Do all functions behave like this? How can an equation for the line which approximates a function at a given point be created? Key Knowledge How to zoom using a GDC. Finding the limit of a function graphically, numerically, and algebraically. Key Skills I can explain what it means for a function to be locally linear. I can determine if a function will have a local linearization. I can find the local linearization of a function, if it exists. Turn-In (#-1) § (Txt. p.) Handouts No Handouts Posted Assignment PS 21 and any other previous work. Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word. 2010-03-12T15:05:00-08:00 http://math.pmhclients.com/index.php/site/math_7_class_126/ http://math.pmhclients.com/index.php/site/math_7_class_126/#When:15:04:00Z Lesson Title Investigation 3: Patterns of Similar Figures Overview In today’s class students continue to work with Rep-tile. Textbook Sections Problem 3.2 (Txt. p.29) Building with Rep-tiles Vocabulary similar corresponding sides corresponding angles segment ratio perimeter Key Attitudes Willingness to work as a group to help meet individual and group goals. Enduring Understandings Change is fundamental to understanding functions. Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral). Essential Question How can transformations be described mathematically? How do different shapes compare to each other? What is required for two shapes to be similar? Key Knowledge Certain properties of a shape are maintained when a shape is enlarged or reduced. Key Skills I can visually determine if two shapes are similar. Turn-In (#-1) No Homework Handouts No Handouts Posted Assignment No Homework Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word. 2010-03-12T15:04:00-08:00 http://math.pmhclients.com/index.php/site/sl_class_63/ http://math.pmhclients.com/index.php/site/sl_class_63/#When:15:04:00Z Lesson Title Lesson 19: Optimization (2) Overview In today’s class students continue to develop their ability to use calculus to determine the optimal solution to a variety of applied problems. Textbook Sections Vocabulary function independent variable dependent variable with respect to rate of change limit derivative difference quotient derivative from first principals Key Attitudes Willingness to work as a group to help meet individual and group goals. Enduring Understandings Change is fundamental to understanding functions. Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral). Essential Question What has to be true about the value of a derivative in order to have a maximum or minimum value? If the derivative of a function is zero, does this always represent a maximum or minimum? What information does the first derivative give me about the original function? What information does the second derivative give me about the original function? Key Knowledge The derivative of a function can be used to find the optimal solution to a problem. If the derivative of a function changes sign around a critical point, the function is said to have a local (relative) extremum at that point. If the derivative changes from positive (increasing function) to negative (decreasing function), the function has a local (relative) maximum at the critical point. If the second derivative is positive at a point, the graph is concave up. If the second derivative is positive at a critical point, then the critical point is a local minimum. If the second derivative is negative at a point, the graph is concave down. If the second derivative is negative at a critical point, then the critical point is a local maximum. An inflection point marks the transition from concave up and concave down. The second derivative will be zero at an inflection point. The second derivative may be used to determine local extrema of a function under certain conditions. If a function has a critical point for which f′(x) = 0 and the second derivative is positive at this point, then f has a local minimum here. If, however, the function has a critical point for which f′(x) = 0 and the second derivative is negative at this point, then f has local maximum here. This technique is called Second Derivative Test for Local Extrema. Key Skills I can make and label a diagram to represent a situation. I can identify the key variables in a situation. I can mentally model what is going on in a situation. I can create equations relating the key variables in a situation. I can create an equation between the two main variables in a situation. I can find and use a derivative to determine an optimal solution for a situation. I can use multiple representations to determine if a function has a relative maximum or a relative minimum on a given interval. I can use multiple representations to determine if a function is concave up or concave down on a given interval. I can use multiple representations to determine if a function has an inflection point on a given interval. Turn-In (#-1) PS 18 Handouts No Handouts Posted Assignment PS 19 and or Past Paper Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word. 2010-03-12T15:04:00-08:00 http://math.pmhclients.com/index.php/site/math_6_class_126/ http://math.pmhclients.com/index.php/site/math_6_class_126/#When:15:03:00Z Lesson Title Investigation 5: Side-Angle-Shape Connections Overview Students continue investigating flipping and turning triangles. Textbook Sections Problem 5.1 (Txt. p.52) Flipping and Turning Triangles Vocabulary tiling regular polygon polygon pentagon hexagon octagon angle ruler precisely vertex Key Attitudes Willingness to work as a group to help meet individual and group goals. Enduring Understandings Change is fundamental to understanding functions. Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral). Essential Question How can transformations be described mathematically? Key Knowledge Flipping means to turn a shape over. Turning means to rotate a shape around a given point. Key Skills I can determine the number of ways a shape can be turned and or flipped in order to fit into a missing hole in a pattern. Turn-In (#-1) ACE p.57 #1, 6 Problem 5.1 A-- How many ways do you think there really are? Get convinced! Handouts No Handouts Posted Assignment No Homework Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word. 2010-03-12T15:03:00-08:00 http://math.pmhclients.com/index.php/site/hl_class_62/ http://math.pmhclients.com/index.php/site/hl_class_62/#When:14:11:00Z Lesson Title Mock Exam Paper 3 Overview Textbook Sections Vocabulary function independent variable dependent variable with respect to rate of change limit derivative explicit equation implicit equation Key Attitudes Willingness to work as a group to help meet individual and group goals. Enduring Understandings Change is fundamental to understanding functions. Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral). Essential Question How can transformations be described mathematically? How can transformations be described mathematically? What has to be true about the value of a derivative in order to have a maximum or minimum value? Key Knowledge Flipping means to turn a shape over. Certain properties of a shape are maintained when a shape is enlarged or reduced. The derivative of a function can be used to find the optimal solution to a problem. Key Skills I can determine the number of ways a shape can be turned and or flipped in order to fit into a missing hole in a pattern. I can visually determine if two shapes are similar. I can make and label a diagram to represent a situation. Turn-In (#-1) § (Txt. p.) Handouts No Handouts Posted Assignment Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word. 2010-03-11T14:11:00-08:00 http://math.pmhclients.com/index.php/site/math_7_class_125/ http://math.pmhclients.com/index.php/site/math_7_class_125/#When:14:10:00Z Lesson Title Investigation 5: Side-Angle-Shape Connections Overview Students continue investigating flipping and turning triangles. Textbook Sections Problem 5.1 (Txt. p.52) Flipping and Turning Triangles Vocabulary tiling regular polygon polygon pentagon hexagon octagon angle ruler precisely vertex Key Attitudes Willingness to work as a group to help meet individual and group goals. Enduring Understandings Change is fundamental to understanding functions. Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral). Essential Question How can transformations be described mathematically? Key Knowledge Flipping means to turn a shape over. Turning means to rotate a shape around a given point. Key Skills I can determine the number of ways a shape can be turned and or flipped in order to fit into a missing hole in a pattern. Turn-In (#-1) Will It Tile? Worksheet- Back Side Grid Sums 4 Handouts No Handouts Posted Assignment ACE p.57 #1, 6 Problem 5.1 A-- How many ways do you think there really are? Get convinced! Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word. 2010-03-11T14:10:00-08:00 http://math.pmhclients.com/index.php/site/sl_class_62/ http://math.pmhclients.com/index.php/site/sl_class_62/#When:14:10:00Z Lesson Title Lesson 19: Optimization (1) Overview In today’s class students complete the work from our last meeting regarding the transformation of function. Then they use their newly developed ability for making inferences from a function to determine the optimal solution to problems. Textbook Sections Vocabulary function independent variable dependent variable with respect to rate of change limit derivative difference quotient derivative from first principals Key Attitudes Willingness to work as a group to help meet individual and group goals. Enduring Understandings Change is fundamental to understanding functions. Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral). Essential Question What has to be true about the value of a derivative in order to have a maximum or minimum value? If the derivative of a function is zero, does this always represent a maximum or minimum? What information does the first derivative give me about the original function? What information does the second derivative give me about the original function? Key Knowledge The derivative of a function can be used to find the optimal solution to a problem. If the derivative of a function changes sign around a critical point, the function is said to have a local (relative) extremum at that point. If the derivative changes from positive (increasing function) to negative (decreasing function), the function has a local (relative) maximum at the critical point. If the second derivative is positive at a point, the graph is concave up. If the second derivative is positive at a critical point, then the critical point is a local minimum. If the second derivative is negative at a point, the graph is concave down. If the second derivative is negative at a critical point, then the critical point is a local maximum. An inflection point marks the transition from concave up and concave down. The second derivative will be zero at an inflection point. The second derivative may be used to determine local extrema of a function under certain conditions. If a function has a critical point for which f′(x) = 0 and the second derivative is positive at this point, then f has a local minimum here. If, however, the function has a critical point for which f′(x) = 0 and the second derivative is negative at this point, then f has local maximum here. This technique is called Second Derivative Test for Local Extrema. Key Skills I can make and label a diagram to represent a situation. I can identify the key variables in a situation. I can mentally model what is going on in a situation. I can create equations relating the key variables in a situation. I can create an equation between the two main variables in a situation. I can find and use a derivative to determine an optimal solution for a situation. I can use multiple representations to determine if a function has a relative maximum or a relative minimum on a given interval. I can use multiple representations to determine if a function is concave up or concave down on a given interval. I can use multiple representations to determine if a function has an inflection point on a given interval. Turn-In (#-1) § (Txt. p.) Handouts No Handouts Posted Assignment PS 18 Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word. 2010-03-11T14:10:00-08:00 http://math.pmhclients.com/index.php/site/math_6_class_125/ http://math.pmhclients.com/index.php/site/math_6_class_125/#When:14:09:00Z Lesson Title Investigation 5: Side-Angle-Shape Connections Overview Students continue investigating flipping and turning triangles. Textbook Sections Problem 5.1 (Txt. p.52) Flipping and Turning Triangles Vocabulary tiling regular polygon polygon pentagon hexagon octagon angle ruler precisely vertex Key Attitudes Willingness to work as a group to help meet individual and group goals. Enduring Understandings Change is fundamental to understanding functions. Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral). Essential Question How can transformations be described mathematically? Key Knowledge Flipping means to turn a shape over. Turning means to rotate a shape around a given point. Key Skills I can determine the number of ways a shape can be turned and or flipped in order to fit into a missing hole in a pattern. Turn-In (#-1) Will It Tile? Worksheet- Back Side Grid Sums 4 Handouts No Handouts Posted Assignment ACE p.57 #1, 6 Problem 5.1 A-- How many ways do you think there really are? Get convinced! Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word. 2010-03-11T14:09:00-08:00 http://math.pmhclients.com/index.php/site/algebra_2_class_62/ http://math.pmhclients.com/index.php/site/algebra_2_class_62/#When:14:15:00Z Lesson Title 3.2.1 How can I find the equation? Overview Today student will continue to work on using their knowledge of linear equation to help develop algebraic strategies for finding linear and exponential functions. They will also learn more about working with roots and exponents. Textbook Sections 3.2.1 (Txt. p.143) How can I find the equation? Vocabulary interest simple interest compound interest Key Attitudes Willingness to work as a group to help meet individual and group goals. Enduring Understandings Change is fundamental to understanding functions. Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral). Essential Question How does it grow? How is the rate written as a percent? As a decimal? How is it the same or different? How can I find an equation for an exponential situation? Key Knowledge Exponential growth is caused by a constant multiplication. Key Skills I can find an equation for an exponential function when given a graph, a table, or a situation. Turn-In (#-1) 3-81 to 3-83 Handouts No Handouts Posted Assignment 3-84, 3-85, 3-95 to 3-99 Quiz Corrections Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word. 2010-03-10T14:15:00-08:00 http://math.pmhclients.com/index.php/site/math_7_class_124/ http://math.pmhclients.com/index.php/site/math_7_class_124/#When:14:14:00Z Lesson Title Investigation 3: Patterns of Similar Figures Overview Today students begin to study “Rep-tiles”, a shape whose copies can be put together to make a larger, yet similar, shape. Textbook Sections Problem 3.2 (Txt. p.29) Vocabulary similar corresponding sides corresponding angles segment ratio perimeter Key Attitudes Willingness to work as a group to help meet individual and group goals. Enduring Understandings Change is fundamental to understanding functions. Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral). Essential Question How can transformations be described mathematically? How do different shapes compare to each other? What is required for two shapes to be similar? Key Knowledge Certain properties of a shape are maintained when a shape is enlarged or reduced. Key Skills I can visually determine if two shapes are similar. Turn-In (#-1) ACE p.33 #1-4 Handouts No Handouts Posted Assignment ACE p. 33 #5-7 GroundWorks Grade 7 Reasoning with Data: What Do You Mean 4 Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word. 2010-03-10T14:14:00-08:00