4.3 4.4 Notes A
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This document contains a math homework assignment on the topics of rates of change, slope, and graphing distance-time and speed-time relationships. It includes questions asking students to calculate slopes between points, determine average speed between points on a graph, identify which graphs represent steady, increasing, or decreasing speed, explain the relationship between slope and average speed, and determine if sets of points are collinear. It provides context, definitions, and examples to help students understand and work through the problems.
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1.6 1.7 notes a
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of line segments. It also discusses the different types of transformations - translations, reflections, rotations, and dilations - and provides examples of identifying each type of transformation using arrow notation. The homework assignments are to complete practice problems from sections 1.6 and 1.7 in the textbook, as listed.
1.6 1.7 notes b
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of segments. It also defines different types of transformations, such as translations, reflections, and rotations. Students are given homework problems applying these concepts, and examples of identifying transformations and describing them with arrow notation.
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This document contains various sections on geometry topics including working warm-up problems about writing equations involving angle pairs formed by parallel lines cut by a transversal. It also lists common core standards about transformations of geometric figures and using properties of parallel lines cut by transversals to establish facts about angles. Finally, it reminds students that their exam is on Thursday and includes a study guide they should complete without talking.
The history of pi
The document discusses the history and properties of pi (π). It describes how various ancient civilizations like the Babylonians, Hebrews, and Egyptians approximated pi. The Greeks studied pi's relationship to circles, cones, and cylinders. Over centuries, mathematicians like Machin, Euler, and Lambert improved approximations of pi and proved its irrationality. With modern computers, pi has been calculated to extreme accuracy. The document also notes how pi is
Pi
Pi is the ratio of a circle's circumference to its diameter. It is an irrational number that cannot be expressed as a fraction and its value never repeats. Throughout history, mathematicians have worked to calculate Pi to greater levels of precision, advancing from the ancient Babylonians' approximation of 3 1/8 to modern computers calculating Pi to billions of decimal places. Analytic geometry and calculus in the 17th century allowed Pi to be applied to shapes beyond just circles.
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Pi has been approximated for over 4000 years through various methods by ancient cultures. Archimedes was the first to calculate pi by using polygons to find the area between the inscribed and circumscribed shapes, determining pi was between 3 1/7 and 3 10/71. Zu Chongzhi, a 5th century Chinese mathematician, calculated pi to 355/113 through lengthy calculations using a 24,576-gon polygon. The Greek symbol π began being used in the 1700s and was popularized by Euler in 1737.
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1.6 1.7 notes a
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of line segments. It also discusses the different types of transformations - translations, reflections, rotations, and dilations - and provides examples of identifying each type of transformation using arrow notation. The homework assignments are to complete practice problems from sections 1.6 and 1.7 in the textbook, as listed.
1.6 1.7 notes b
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of segments. It also defines different types of transformations, such as translations, reflections, and rotations. Students are given homework problems applying these concepts, and examples of identifying transformations and describing them with arrow notation.
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This document contains various sections on geometry topics including working warm-up problems about writing equations involving angle pairs formed by parallel lines cut by a transversal. It also lists common core standards about transformations of geometric figures and using properties of parallel lines cut by transversals to establish facts about angles. Finally, it reminds students that their exam is on Thursday and includes a study guide they should complete without talking.
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The document discusses the history and properties of pi (π). It describes how various ancient civilizations like the Babylonians, Hebrews, and Egyptians approximated pi. The Greeks studied pi's relationship to circles, cones, and cylinders. Over centuries, mathematicians like Machin, Euler, and Lambert improved approximations of pi and proved its irrationality. With modern computers, pi has been calculated to extreme accuracy. The document also notes how pi is
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Pi is the ratio of a circle's circumference to its diameter. It is an irrational number that cannot be expressed as a fraction and its value never repeats. Throughout history, mathematicians have worked to calculate Pi to greater levels of precision, advancing from the ancient Babylonians' approximation of 3 1/8 to modern computers calculating Pi to billions of decimal places. Analytic geometry and calculus in the 17th century allowed Pi to be applied to shapes beyond just circles.
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A beautiful presentation describing the history of pi and its use and application in real life situations. It also covers calculating pi and world records about the number of digits of pi that have been calculated. Hope you enjoy and use it!!
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Pi has been approximated for over 4000 years through various methods by ancient cultures. Archimedes was the first to calculate pi by using polygons to find the area between the inscribed and circumscribed shapes, determining pi was between 3 1/7 and 3 10/71. Zu Chongzhi, a 5th century Chinese mathematician, calculated pi to 355/113 through lengthy calculations using a 24,576-gon polygon. The Greek symbol π began being used in the 1700s and was popularized by Euler in 1737.
5 8 Notes A
The document discusses geometric properties of triangles. It presents six statements about circumcenters, centroids, altitudes, and orthocenters and asks the reader to identify whether each statement is true or false. The statements concern the definitions and locations of these special points relative to triangles.
10.4 notes a
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6.2 Notes
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4 10 Notes B
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11.3 notes b
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11.6 notes
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4 7 Notes A
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- Explain how to quickly write an equation of a line given certain information using the different forms
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3.6 Notes A
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3.3 Notes A
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4 12 Notes A
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8.2 notes a
This document provides instructions to complete the square for several quadratic equations: (1) 3x^2 - 12x - 20 = 0, (2) 3x^2 - 5x = 12, (3) 2x^2 + x = 2, and (4) 4x^2 + 12x = 9. It also asks the reader to determine whether each equation will have two real solutions, one real solution, or no real solutions based on completing the square. Finally, it references making the process of completing the square more formal using the quadratic formula.
3.4 Notes B
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8 4 Notes A
This document contains:
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4.1 4.2 Notes A
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4.1 4.2 Notes A
The document provides instruction and examples for calculating slope between two points on a graph. It defines slope as "rise over run", or the change in the y-values divided by the change in the x-values between two points. Examples are given for finding the slope between points, identifying positive and negative slopes, and special cases where the slope is zero or undefined. Students are asked to provide their own examples comparing slopes and complete an exit slip with slope problems.
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10.4 notes a
The document contains questions and examples about calculating the surface area and lateral area of prisms and cylinders. It defines surface area as the total area of the outer surface of a solid figure, including both lateral and end areas. Lateral area refers specifically to the area of the figure's sides or lateral faces, and is always less than or equal to the surface area. Sample problems are provided to demonstrate how to calculate the lateral and surface areas of various prisms and cylinders using common formulas.
6.2 Notes
1. The document provides information about properties of parallelograms and examples to practice identifying and using those properties. It defines a parallelogram, lists four key properties, and provides two practice examples asking students to use the properties.
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3.2 Notes B
The document provides 3 examples of systems of equations and assigns homework problems from the textbook. Specifically, it contains 3 systems of equations using the addition/elimination method, and assigns homework from page 158 problems 6-11, 20-23, 25, 31 and Proof Worksheet #1.
4 10 Notes B
This document contains homework questions and examples about solving systems of equations using substitution. It includes:
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2) Three examples walking through the substitution method to solve systems of equations step-by-step. The examples find the intersection point of lines and solve systems algebraically.
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11.3 notes b
The document discusses calculating the area of a sector of a circle and the arc length of a section of a circle's circumference. It provides formulas for sector area as 1/2 * radius^2 * central angle in radians and arc length as radius * central angle in radians. It includes two practice problems asking to calculate the sector area and arc length given the radius, central angle, and other details. The document encourages checking in after the first two problems and provides a final deadline.
11.6 notes
The document provides instructions for students to complete homework questions and check their answers to a previous worksheet with a partner. It then explains three theorems about relationships between chords, secants, and tangents in circles. Students are instructed to work with partners on applying the theorems by presenting an example problem to the class, ensuring they show all work and explanations clearly. The document concludes by having students complete a graphic organizer summarizing the three theorems.
9 2 Notes (D2 A)
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4 7 Notes A
Day 2 Opener:
- Review problem solving linear equations from the previous day
- Introduce different forms of writing linear equations: point-slope form, slope-intercept form, standard form
- Students work with a partner to practice identifying properties of lines from their equations
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- Explain how to quickly write an equation of a line given certain information using the different forms
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2. Students complete an activity with basic rules of arithmetic and then rephrase the rules without using variables. Examples of rephrased rules are provided.
3. Additional examples work through binary operations, using properties of operations, and finding patterns in products. Homework assigned includes a mini quiz, practice problems, and studying for an upcoming test.
3.6 Notes A
The document contains a math raffle with questions about slope and parallel/perpendicular lines, homework questions on forms of equations of lines and writing perpendicular bisectors, and a problem about the cost of two rental car companies at different mileage fees. Students are instructed to write their name and ID on raffle tickets and raise their hand silently when done with the math raffle questions. A variety of line equation questions are provided for homework.
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This document contains math homework instructions for students. It includes exercises on solving compound inequalities and absolute value inequalities, with 3 examples of each. Students are instructed to work through the examples in pairs for 15 minutes and show their work. They also receive a raffle ticket math problem to solve and graph. The homework assigned is a worksheet with specific problems on compound and absolute value inequalities.
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3.3 Notes A
This document provides instruction and examples for calculating distance between points on a coordinate plane and working with absolute value. It defines absolute value as the distance between two numbers and shows how to solve equations involving absolute value. Sample problems are provided to practice finding distances between points, evaluating absolute values, and solving absolute value equations. Students are asked to work through examples with a partner and complete related homework problems.
4 12 Notes A
The document provides a quick review for a quiz on writing equations of lines and solving systems of equations using elimination. It includes 4 problems writing equations of lines, instructions to complete circled problems on a handout after the quiz, mentions of partner points, and 3 sample problems solving systems of equations using elimination.
8.2 notes a
This document provides instructions to complete the square for several quadratic equations: (1) 3x^2 - 12x - 20 = 0, (2) 3x^2 - 5x = 12, (3) 2x^2 + x = 2, and (4) 4x^2 + 12x = 9. It also asks the reader to determine whether each equation will have two real solutions, one real solution, or no real solutions based on completing the square. Finally, it references making the process of completing the square more formal using the quadratic formula.
3.4 Notes B
Coach Pieper has created a secret play called the Spartan Sneaky Shuffle Stop to help his team beat their rivals in the upcoming homecoming game. He needs help with the play but details of it are not provided. The document also includes homework questions about perpendicular lines, perpendicular bisectors, and the shortest distance between points and lines. Students are assigned homework and asked exit slip questions about perpendicular bisectors and relationships between lines that are perpendicular to the same line.
8 4 Notes A
This document contains:
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2. Practice problems asking students to solve right triangles and find missing measures.
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4.1 4.2 Notes A
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3. Readers are instructed to solve sample equations by listing the number trick steps and then reversing the steps through backtracking to find the solution values.
Chapter 1 rev notes (a)
This document provides homework questions and a review packet for a chapter. It lists 7 numbered sections that appear to be questions or tasks related to reviewing material from the first chapter. The document aims to help students review and reinforce their understanding of the concepts covered in the initial chapter through completing the homework and review activities.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. Students are asked to work on their vocabulary packet silently after finishing the quiz. Then the class will review geometry formulas.
3. The homework assignments are to complete problems on page 38 from section 1.5 and page 47 from section 1.6 in the textbook. These cover midpoints, distances, and the midpoint and distance formulas.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. Students are asked to work on their vocabulary packet silently after finishing the quiz. Then the class will review geometry formulas.
3. The homework assignments are to complete problems on page 38 from section 1.5 and page 47 from section 1.6 in the textbook. These cover midpoints, distances, and the midpoint and distance formulas.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. It includes examples of using the midpoint formula to find the midpoint of a segment and using given midpoints and endpoints to find missing endpoints.
3. There are also examples of using the Pythagorean theorem and distance formula to find the length of a segment between two points.
1.5 1.6 notes a
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6. Students are asked to work on vocabulary and postulates after the quiz.
2. Examples are given for finding midpoints and distances between points on a coordinate plane using formulas like the midpoint formula, Pythagorean theorem, and distance formula.
3. Homework assignments include problems from the textbook on the topics of formulas in geometry, midpoints, and distance.
2.6 2.7 notes a
1. The document provides instructions and tasks for students to complete mathematical expressions, homework questions, and a lesson on reversible and non-reversible operations.
2. Students are asked to simplify expressions, complete homework problems, and determine whether example operations are reversible by considering if the starting number can be determined.
3. The document demonstrates how to "backtrack" through a multi-step operation to find the original starting number using reversible operations.
2.5 notes b
This document contains notes and instructions for a math lesson that includes:
1) Solving expressions and evaluating them for given values.
2) Completing an in-class activity with partners to review basic arithmetic rules.
3) Practicing the basic rules of arithmetic through examples of simplifying expressions using properties like commutative, associative, and distributive properties.
2.4 notes b
1. Students were asked to put math problems on the board from previous homework. The document then provides examples of expressions and teaches how to simplify them using order of operations and properties like the distributive property. Students are asked to simplify sample expressions involving variables.
2. The document reviews that expressions need to have "like terms" to be simplified, such as terms with the same variables. Students practice simplifying expressions with multiple variables and terms by combining like terms.
3. To conclude, students are instructed to write their name and ID number on raffle tickets and provide just the simplified answer, practicing the skills of defining a variable, writing an expression, simplifying it, and evaluating it.
2.3 notes b
This document contains instructions for students to complete various math exercises on their TI-Nspire calculators. It asks students to match expressions to steps, write an expression for the area of a rectangle, simplify an algebraic expression, evaluate expressions for different variable values, and complete an activity on their calculators worth daily work points. Students are told to work with partners but can ask other group members for help if needed and to raise their hand once finished.
2.2 notes a
1. When entering class each day, students should say hi, have their homework out, write any questions on the board, and start the opener problem.
2. The document then provides examples of algebra problems involving variables to represent unknown quantities and expressions combining variables, operators, and constants.
3. Students are instructed to complete a set of practice problems from page 94 in their workbook and have their work checked by the teacher.
8.7 notes b
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions on graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages. Finally, it addresses solving an equation like x^3 + 5x = 7x^2 - 5 by graphing and reflects on graphing techniques from prior lessons.
8.7 notes b
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions about graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages.
8.7 notes
The document discusses a 4 step process but provides no details on the actual steps or content of the process. It references numbered sections but provides no information within those sections. Overall, the document does not contain any substantive information that could be summarized due to the lack of details provided within the numbered sections.
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4.3 4.4 Notes A
- 1. Opener: Write 1 pair of points or slopes for each of the following Complete these statements: questions in your notes with your a. a positive slope and a negative slope that is steeper partner. b. a negative slope and a positive slope with the same steepness c. two pairs of points that have the same slope d. a pair of points whose slope is undefined e. a pair of points whose slope is zero 1
- 2. Homework Questions: 2
- 3. January 6th & 7th: 4.3 Rates of Change Launch: How does the pace of 8 mph that you calculated in exercise 10 relate to this graph? Speed the rate at which the location of an object changes average speed = distance time 3
- 4. Finding the average speed between points What is Tia's average speed between the following points? a. O and A b. A and B c. B and C d. O and C When was Tia traveling the fastest? Would you have been able to tell this even without the specific units labeled? How so? 4
- 5. Slope and Average The slope between two points on a distance‐time Speed graph is the ___________ ________ of travel between those two points. Partner A: Explain this theorem to your partner in your own words. Partner B: Listen carefully to see if there's anything you think that needs to be added in. Distance‐Time In which graph are you moving steadily? Speeding up Graphs gradually? Slowing down gradually? Explain. 5
- 6. Speed ‐ Time Graphs In which graph are you moving steadily? Speeding up gradually ? Slowing down gradually? Explain. Distance-Time Distance‐Time: speed is change of distance over Graphs vs. Speed- ________ interval of time Time Graphs Speed‐Time: speed is change of distance over ________ interval of time 6
- 7. Slope = Rate of What are some other examples of rate of change Change problems we can find comparing two quantities? Checkpoint! 5a.) How many miles was Ryota’s trip? How long did it Open your books to take, including the alleged nap? page 324. 5b.) Sketch two possible distance‐time graphs for Ryota’s trip. Include his nap in one graph but not in the other. 7
- 9. Collinear Points Points that all lie on the same line. Pg. 328 • • • Determining Collinearity How can you tell if three points lie on a horizontal line? What are some possible ways to determine whether On a vertical line? three points are collinear by looking at their coordinates? On any line? 9
- 10. Using Slope to Points A, B, and C are collinear if... Determine Collinearity Are the three points collinear? A (‐1,3), B (4, 15), C (14, 39) Checkpoint! Complete # 2‐5 under "For You to Do" on page 329. Be prepared to share your answers with the rest of the class. (7 minutes) 10
- 11. Homework: SAME as assignment sheet for today : Pg. 325, Pg. 330, & graphing review 11
- 12. 12