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Literal Eq Notes
Literal Eq NotesMr. Hohman
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Solving literal equations involves finding the value of a variable in terms of other variables or constants. Examples of solutions to literal equations include x = 3y - a, y = 4 + x/r, and solving equations such as 3x - 4y = 7, dx - 2y = 3z, y = mx + b, or by + 2 = c/3 for the variable on one side of the equal sign.Solve Eq Notes 01
Solve Eq Notes 01Mr. Hohman
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The document provides instructions for students to learn how to solve basic addition and subtraction equations. It includes 5 examples of equations for students to practice solving, such as r + 16 = -7 and 8 = m - 3. The steps demonstrated include drawing a line to separate the equation, then adding or subtracting values from both sides to isolate the variable. The goal is for students to be able to solve one-step equations using these fundamental arithmetic operations.Literal Eq Example 01
Literal Eq Example 01Mr. Hohman
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This math worksheet contains 3 problems: 1) Find the value of x if y is 5, 7, or 10 with no other information given; 2) Solve the equation 2x - 4 = y + 3 for x, where y could be any value; 3) Solve for r in an equation with no other details provided.workshop zakelijk twitteren voor MVO Nederland
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Workshop voor de communicatie afdeling van MVO nederland op 1 april 2011, over hoe zij twitter zakelijk (beter) kunnen inzetten voor hun doelstellingen.Student Response System In A Math Classroom Ietc
Student Response System In A Math Classroom IetcMr. Hohman
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This document summarizes a presentation about using student response systems, also known as "clickers", in a math classroom. It discusses two specific response systems - TurningPoint and SMART Response - and how the teacher uses the systems for pre-assessments, instruction, review activities, and assessments with feedback. Examples are provided of multiple choice and numerical response questions displayed on slides. The document aims to demonstrate how response systems can increase interactivity, participation and feedback in the math classroom.Solve Eq Notes 02
Solve Eq Notes 02Mr. Hohman
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This document discusses how to solve equations using addition and subtraction properties of equality. It explains that to solve an equation means to isolate the variable on one side. It then introduces the addition property of equality, which states that if a = b, then a + c = b + c, meaning any number can be added to both sides of an equation without changing whether it is true. Several examples are worked through to demonstrate adding and subtracting various numbers from both sides of an equation. Finally, the subtraction property of equality is presented similarly.Translate And Fraction Example 01
Translate And Fraction Example 01Mr. Hohman
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The document contains 3 math word problems to translate into equations: 1) x - 18 = 12, which can be written as x = 30. 2) 85 - 5x = 10, which can be written as 5x = 75 so x = 15. 3) 4x + 15 = 83, which can be written as 4x = 68 so x = 17.
ICTM 2010
ICTM 2010Mr. Hohman
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Dave Hohman discusses different SMART technologies for the classroom including the SMART Board, SMART Slate, and SMART Response system. The SMART Board is an interactive whiteboard that allows teachers to use digital tools and save lessons. The SMART Slate is a cheaper alternative that runs the same software. SMART Response is a student response system that provides instant feedback through individual clickers or self-paced tests, giving teachers data to shape instruction.Function vs not function
Function vs not functionMr. Hohman
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The document discusses functions and non-functions through several examples of relations between x and y values. It provides tables and graphs of relations that illustrate functions, such as a y value being mapped to only one x value, as well as non-functions where a single x value is mapped to multiple y values or a y value is not mapped to any x values at all.Solve Eq Example 01
Solve Eq Example 01Mr. Hohman
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This math problem involves solving two equations for the variable x. The first equation is x - 3 = 5, which can be solved to get x = 8. The second equation is 2(x - 4) = 2, which can be solved to get x = 6. Since x cannot equal both 8 and 6, the system of equations has no solution.Chapter 3 Quiz 1 Review
Chapter 3 Quiz 1 ReviewMr. Hohman
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The document summarizes key concepts in geometry including alternate interior angles, same side interior angles, corresponding angles, parallel lines, and perpendicular lines. It asks questions about which angles are equal, supplementary, or perpendicular when given information about parallel or perpendicular lines. It also asks how many lines can be drawn through a point that are parallel or perpendicular to a given line.Review Chapter 2
Review Chapter 2Mr. Hohman
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This cumulative review covers chapters 1 and 2, with 17 multiple choice questions testing the reader's understanding of the key events, characters, and ideas discussed in those chapters. The questions cover a range of details and ask the reader to think critically about cause-and-effect relationships, character motivations and themes in the chapters.1 5 Postulates And Theorems Relating Points, Lines Filled In
1 5 Postulates And Theorems Relating Points, Lines Filled InMr. Hohman
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The document outlines several postulates and theorems relating points, lines, and planes in geometry:
Postulate 5 states that a line contains at least two points, a plane contains at least three non-collinear points, and space contains at least four points not all in one plane.
Postulate 6 states that through any two points there is exactly one line. Postulate 7 states that through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane.
Theorems 1-1 and 1-3 state that if two lines intersect, they intersect at exactly one point and there is exactly one plane containing the lines. Theorem 1-2Chapter 4 Quiz 1 Review
Chapter 4 Quiz 1 ReviewMr. Hohman
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This document discusses whether different geometric figures are congruent. It asks if four pairs of figures are congruent without providing the figures, indicating the document is assessing a student's ability to determine congruency based on the definition of congruency.3 1 Parallel Lines And Planes Filled Out
3 1 Parallel Lines And Planes Filled OutMr. Hohman
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Parallel lines and planes are coplanar and do not intersect. Skew lines are noncoplanar and do not intersect. If two parallel planes are cut by a third plane, the lines of intersection will be parallel. A transversal is a line that intersects two or more coplanar lines. Alternate interior angles and same side interior angles are pairs of angles related to a transversal. Corresponding angles are in corresponding positions relative to two lines.2-5
2-5Mr. Hohman
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Two lines are perpendicular if they intersect at a right angle. If two lines form a right angle, or congruent adjacent angles, then the lines are perpendicular. If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.13 3 And 13 4
13 3 And 13 4Mr. Hohman
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The document is notes from a math class covering topics like coordinate planes, circles, parallel and perpendicular lines, vectors, and SPICSA. It includes definitions, formulas, and examples for these concepts. Sections 1 through 7 provide explanations and review of geometric shapes, slopes of lines, vectors, and how to add and multiply vectors. Section 8 indicates there will be practice problems from the covered materials.12 2 and 12 3
12 2 and 12 3Mr. Hohman
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This document reviews the formulas for calculating the lateral area, surface area, and volume of prisms, pyramids, cylinders, and cones. It notes that the formulas for cylinders are identical to those for prisms, and the formulas for cones are identical to those for pyramids. Some example problems are included for prisms and pyramids. The document concludes by listing page numbers from the textbook for additional even-numbered practice problems.12 1 Prisms Filled Out
12 1 Prisms Filled OutMr. Hohman
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The document defines and provides information about prisms. It states that a prism is a 3D solid with two congruent bases that are parallel planes. It also defines lateral faces and edges. The document provides formulas for calculating the lateral area and total surface area of right prisms. It gives an example of calculating the volume of a right trapezoidal prism and using the volume formula of a cube to solve an algebra problem.
Review For Cpt 11
Review For Cpt 11Mr. Hohman
油
The document contains several geometry problems asking for areas and perimeters of shapes including a hexagon, circle, triangle, isosceles triangle, and two similar quadrilaterals. It provides side lengths, areas, circumferences, and ratios but asks to calculate missing values like the area of a shaded region, length of a triangle base, and area of a larger quadrilateral.11 8 Geometric Probability
11 8 Geometric ProbabilityMr. Hohman
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The document introduces geometric probability and how to calculate the probability of a random point falling in a specific region. It explains that the probability is equal to the length of the region divided by the total length for a line, and the probability is equal to the area of the region divided by the total area for a two-dimensional region. It then indicates it will provide practice problems for students to work through.11 6 Arc Lengths And Areas Of Sectors
11 6 Arc Lengths And Areas Of SectorsMr. Hohman
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This document discusses calculating arc lengths and areas of sectors. It reviews that circumference is 2r and area is 1/2*r^2. It provides a worked example of finding the length of an arc and area of a sector with radius 5 and central angle of 60 degrees. Finally, it gives the general formulas that the length of an arc is r*慮/360 degrees and the area of a sector is 1/2*r^2*(慮/360) degrees.11 7 Ratio Of Areas
11 7 Ratio Of AreasMr. Hohman
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The document discusses ratios between similar figures and geometric probability. It states that if the scale factor between two similar figures is a:b, then the ratio of their perimeters is a:b and the ratio of their areas is a^2:b^2. As an example, it gives two circles with a scale factor of 5:2 and calculates the area of the larger circle given the area of the smaller. It then defines probability as 1 for an event occurring, 0 for not occurring, and 1/2 for a 50% chance. It says geometric probability is calculated as a length or area to be picked over the whole length or area.11 4 Areas Of Regular Polygons
11 4 Areas Of Regular PolygonsMr. Hohman
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The document discusses calculating the areas of regular polygons. It states that the area of a regular polygon is equal to half the product of the apothem and perimeter. The apothem is the distance from the center of the polygon to the midpoint of one side, and can be calculated using trigonometric functions like tangent and cosine based on the central angle of the polygon. Formulas are provided for calculating the areas of regular pentagons and general regular n-gons.11 2 Areas Of Parallelograms, Triangles, And
11 2 Areas Of Parallelograms, Triangles, AndMr. Hohman
油
This document discusses formulas for calculating the areas of parallelograms, triangles, and rhombuses. The area of a parallelogram is calculated as A = bh, where b is the base and h is the height. The area of a triangle is calculated as A = 12bh. The area of a rhombus is calculated as A = 12d1d2, where d1 and d2 are the diagonals of the rhombus.11 1 Areas Of Rectangles
11 1 Areas Of RectanglesMr. Hohman
油
The document discusses the concept of area and provides formulas for calculating the area of different shapes. It defines area as the surface enclosed by a shape and explains that the area of a square is the length of one side squared. It also states that if two figures are congruent, their areas are the same, and that the area of a rectangle is calculated by multiplying its base by its height. Finally, it provides a proof that the formula for the area of a rectangle is base times height.More Related Content
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ICTM 2010
ICTM 2010Mr. Hohman
油
Dave Hohman discusses different SMART technologies for the classroom including the SMART Board, SMART Slate, and SMART Response system. The SMART Board is an interactive whiteboard that allows teachers to use digital tools and save lessons. The SMART Slate is a cheaper alternative that runs the same software. SMART Response is a student response system that provides instant feedback through individual clickers or self-paced tests, giving teachers data to shape instruction.Function vs not function
Function vs not functionMr. Hohman
油
The document discusses functions and non-functions through several examples of relations between x and y values. It provides tables and graphs of relations that illustrate functions, such as a y value being mapped to only one x value, as well as non-functions where a single x value is mapped to multiple y values or a y value is not mapped to any x values at all.Solve Eq Example 01
Solve Eq Example 01Mr. Hohman
油
This math problem involves solving two equations for the variable x. The first equation is x - 3 = 5, which can be solved to get x = 8. The second equation is 2(x - 4) = 2, which can be solved to get x = 6. Since x cannot equal both 8 and 6, the system of equations has no solution.Chapter 3 Quiz 1 Review
Chapter 3 Quiz 1 ReviewMr. Hohman
油
The document summarizes key concepts in geometry including alternate interior angles, same side interior angles, corresponding angles, parallel lines, and perpendicular lines. It asks questions about which angles are equal, supplementary, or perpendicular when given information about parallel or perpendicular lines. It also asks how many lines can be drawn through a point that are parallel or perpendicular to a given line.Review Chapter 2
Review Chapter 2Mr. Hohman
油
This cumulative review covers chapters 1 and 2, with 17 multiple choice questions testing the reader's understanding of the key events, characters, and ideas discussed in those chapters. The questions cover a range of details and ask the reader to think critically about cause-and-effect relationships, character motivations and themes in the chapters.1 5 Postulates And Theorems Relating Points, Lines Filled In
1 5 Postulates And Theorems Relating Points, Lines Filled InMr. Hohman
油
The document outlines several postulates and theorems relating points, lines, and planes in geometry:
Postulate 5 states that a line contains at least two points, a plane contains at least three non-collinear points, and space contains at least four points not all in one plane.
Postulate 6 states that through any two points there is exactly one line. Postulate 7 states that through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane.
Theorems 1-1 and 1-3 state that if two lines intersect, they intersect at exactly one point and there is exactly one plane containing the lines. Theorem 1-2Chapter 4 Quiz 1 Review
Chapter 4 Quiz 1 ReviewMr. Hohman
油
This document discusses whether different geometric figures are congruent. It asks if four pairs of figures are congruent without providing the figures, indicating the document is assessing a student's ability to determine congruency based on the definition of congruency.3 1 Parallel Lines And Planes Filled Out
3 1 Parallel Lines And Planes Filled OutMr. Hohman
油
Parallel lines and planes are coplanar and do not intersect. Skew lines are noncoplanar and do not intersect. If two parallel planes are cut by a third plane, the lines of intersection will be parallel. A transversal is a line that intersects two or more coplanar lines. Alternate interior angles and same side interior angles are pairs of angles related to a transversal. Corresponding angles are in corresponding positions relative to two lines.2-5
2-5Mr. Hohman
油
Two lines are perpendicular if they intersect at a right angle. If two lines form a right angle, or congruent adjacent angles, then the lines are perpendicular. If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.13 3 And 13 4
13 3 And 13 4Mr. Hohman
油
The document is notes from a math class covering topics like coordinate planes, circles, parallel and perpendicular lines, vectors, and SPICSA. It includes definitions, formulas, and examples for these concepts. Sections 1 through 7 provide explanations and review of geometric shapes, slopes of lines, vectors, and how to add and multiply vectors. Section 8 indicates there will be practice problems from the covered materials.12 2 and 12 3
12 2 and 12 3Mr. Hohman
油
This document reviews the formulas for calculating the lateral area, surface area, and volume of prisms, pyramids, cylinders, and cones. It notes that the formulas for cylinders are identical to those for prisms, and the formulas for cones are identical to those for pyramids. Some example problems are included for prisms and pyramids. The document concludes by listing page numbers from the textbook for additional even-numbered practice problems.12 1 Prisms Filled Out
12 1 Prisms Filled OutMr. Hohman
油
The document defines and provides information about prisms. It states that a prism is a 3D solid with two congruent bases that are parallel planes. It also defines lateral faces and edges. The document provides formulas for calculating the lateral area and total surface area of right prisms. It gives an example of calculating the volume of a right trapezoidal prism and using the volume formula of a cube to solve an algebra problem.Review For Cpt 11
Review For Cpt 11Mr. Hohman
油
The document contains several geometry problems asking for areas and perimeters of shapes including a hexagon, circle, triangle, isosceles triangle, and two similar quadrilaterals. It provides side lengths, areas, circumferences, and ratios but asks to calculate missing values like the area of a shaded region, length of a triangle base, and area of a larger quadrilateral.11 8 Geometric Probability
11 8 Geometric ProbabilityMr. Hohman
油
The document introduces geometric probability and how to calculate the probability of a random point falling in a specific region. It explains that the probability is equal to the length of the region divided by the total length for a line, and the probability is equal to the area of the region divided by the total area for a two-dimensional region. It then indicates it will provide practice problems for students to work through.11 6 Arc Lengths And Areas Of Sectors
11 6 Arc Lengths And Areas Of SectorsMr. Hohman
油
This document discusses calculating arc lengths and areas of sectors. It reviews that circumference is 2r and area is 1/2*r^2. It provides a worked example of finding the length of an arc and area of a sector with radius 5 and central angle of 60 degrees. Finally, it gives the general formulas that the length of an arc is r*慮/360 degrees and the area of a sector is 1/2*r^2*(慮/360) degrees.11 7 Ratio Of Areas
11 7 Ratio Of AreasMr. Hohman
油
The document discusses ratios between similar figures and geometric probability. It states that if the scale factor between two similar figures is a:b, then the ratio of their perimeters is a:b and the ratio of their areas is a^2:b^2. As an example, it gives two circles with a scale factor of 5:2 and calculates the area of the larger circle given the area of the smaller. It then defines probability as 1 for an event occurring, 0 for not occurring, and 1/2 for a 50% chance. It says geometric probability is calculated as a length or area to be picked over the whole length or area.11 4 Areas Of Regular Polygons
11 4 Areas Of Regular PolygonsMr. Hohman
油
The document discusses calculating the areas of regular polygons. It states that the area of a regular polygon is equal to half the product of the apothem and perimeter. The apothem is the distance from the center of the polygon to the midpoint of one side, and can be calculated using trigonometric functions like tangent and cosine based on the central angle of the polygon. Formulas are provided for calculating the areas of regular pentagons and general regular n-gons.11 2 Areas Of Parallelograms, Triangles, And
11 2 Areas Of Parallelograms, Triangles, AndMr. Hohman
油
This document discusses formulas for calculating the areas of parallelograms, triangles, and rhombuses. The area of a parallelogram is calculated as A = bh, where b is the base and h is the height. The area of a triangle is calculated as A = 12bh. The area of a rhombus is calculated as A = 12d1d2, where d1 and d2 are the diagonals of the rhombus.11 1 Areas Of Rectangles
11 1 Areas Of RectanglesMr. Hohman
油
The document discusses the concept of area and provides formulas for calculating the area of different shapes. It defines area as the surface enclosed by a shape and explains that the area of a square is the length of one side squared. It also states that if two figures are congruent, their areas are the same, and that the area of a rectangle is calculated by multiplying its base by its height. Finally, it provides a proof that the formula for the area of a rectangle is base times height.