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This document contains notes from a math class lesson on the surface area and volume of spheres. It includes the objectives of being able to apply the formulas for surface area and volume of spheres. Examples are provided for students to calculate the surface area and volume of various spheres given measurements like diameters and radii. Students are assigned homework problems applying these concepts.
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12.6 notes
The document discusses surface area and volume formulas for spheres. It provides examples of calculating the surface area of spheres with given diameters, as well as the volume of spheres and other objects like snow cones that can be modeled as spheres. Students are assigned homework problems applying these formulas to calculate surface areas and volumes.
4.3 notes
This document discusses the Side-Side-Side (SSS) theorem for proving triangle congruence. It states that if three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent. The document provides an example of two triangles, ΔABC and ΔDEF, where the sides are labeled as equal. It also discusses using Angle-Angle-Angle (AAA) to show similarity, not congruence, of triangles. The homework assignment is problems #5-19 odd, 24, 26 on page 236.
7.6 notes
This document contains instructions for solving various mathematical formulas by transforming them to solve for different variables. It provides examples of transforming formulas for area, perimeter, rate, distance, and temperature by solving for variables like length, rate, time, and Celsius. The goal is to practice transforming formulas to solve for the desired unknown variable.
Conversions notes
This document provides information and examples about converting between different units of measurement for length, weight, liquid, time, and dry measurements. It includes questions asking students to convert between inches and feet, miles and feet, fractions of an inch, and measurements in inches. Tables are provided defining relationships between units for weight, liquid, time, and dry measurements.
10.1 notes
This document discusses tangent properties of circles. It defines various circle terms like radius, diameter, chord, secant, and tangent. It presents theorems for tangents including that a tangent is perpendicular to the radius and tangent segments from outside the circle are congruent. It provides examples applying these theorems to find missing side lengths. The document instructs the reader to draw and label examples of circle terms on a worksheet.
Slugging % & era notes
This document contains notes from a student on baseball statistics including batting average, slugging percentage, earned run average (ERA), and winning percentage. It provides the formulas for calculating batting average, slugging percentage as hits or home runs plus bases per at bat, ERA as earned runs times 9 over innings pitched, and winning percentage as games won over total games played. The student took these notes on April 8th while working on baseball statistics homework.
12.2 notes
This document discusses the surface area formulas for prisms and cylinders. For prisms, the surface area is calculated as the perimeter of the base multiplied by the height plus two times the area of the base. For cylinders, the surface area is calculated as two times pi times the radius times the height plus two times pi times the radius squared. The document provides examples of applying these formulas and assigns homework problems calculating surface areas of various prisms and cylinders.
12.5 notes
The document discusses finding the volume of pyramids and cones. It provides the formulas for calculating volume of a cone as 1/3πr^2h and volume of a pyramid as 1/3Bh, where B is the area of the base and h is the height. Examples are given to practice applying these formulas, such as finding the volume of ice cream in a cone or the area of the base of a trapezoidal pyramid given its volume and height.
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12.6 notes
The document discusses surface area and volume formulas for spheres. It provides examples of calculating the surface area of spheres with given diameters, as well as the volume of spheres and other objects like snow cones that can be modeled as spheres. Students are assigned homework problems applying these formulas to calculate surface areas and volumes.
4.3 notes
This document discusses the Side-Side-Side (SSS) theorem for proving triangle congruence. It states that if three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent. The document provides an example of two triangles, ΔABC and ΔDEF, where the sides are labeled as equal. It also discusses using Angle-Angle-Angle (AAA) to show similarity, not congruence, of triangles. The homework assignment is problems #5-19 odd, 24, 26 on page 236.
7.6 notes
This document contains instructions for solving various mathematical formulas by transforming them to solve for different variables. It provides examples of transforming formulas for area, perimeter, rate, distance, and temperature by solving for variables like length, rate, time, and Celsius. The goal is to practice transforming formulas to solve for the desired unknown variable.
Conversions notes
This document provides information and examples about converting between different units of measurement for length, weight, liquid, time, and dry measurements. It includes questions asking students to convert between inches and feet, miles and feet, fractions of an inch, and measurements in inches. Tables are provided defining relationships between units for weight, liquid, time, and dry measurements.
10.1 notes
This document discusses tangent properties of circles. It defines various circle terms like radius, diameter, chord, secant, and tangent. It presents theorems for tangents including that a tangent is perpendicular to the radius and tangent segments from outside the circle are congruent. It provides examples applying these theorems to find missing side lengths. The document instructs the reader to draw and label examples of circle terms on a worksheet.
Slugging % & era notes
This document contains notes from a student on baseball statistics including batting average, slugging percentage, earned run average (ERA), and winning percentage. It provides the formulas for calculating batting average, slugging percentage as hits or home runs plus bases per at bat, ERA as earned runs times 9 over innings pitched, and winning percentage as games won over total games played. The student took these notes on April 8th while working on baseball statistics homework.
12.2 notes
This document discusses the surface area formulas for prisms and cylinders. For prisms, the surface area is calculated as the perimeter of the base multiplied by the height plus two times the area of the base. For cylinders, the surface area is calculated as two times pi times the radius times the height plus two times pi times the radius squared. The document provides examples of applying these formulas and assigns homework problems calculating surface areas of various prisms and cylinders.
12.5 notes
The document discusses finding the volume of pyramids and cones. It provides the formulas for calculating volume of a cone as 1/3πr^2h and volume of a pyramid as 1/3Bh, where B is the area of the base and h is the height. Examples are given to practice applying these formulas, such as finding the volume of ice cream in a cone or the area of the base of a trapezoidal pyramid given its volume and height.
9.3 notes
This document contains notes from a geometry class on reflections. It includes the definitions of a line of reflection and the coordinate rules for reflecting points across the x-axis, y-axis, lines y=x and y=-x. It also states that a reflection is an isometry and provides the reflection matrices used to calculate the reflected image of a point by multiplying the matrix and the coordinates of the pre-image point. The document records the student working through homework problems on reflections.
12.1 notes
Students were instructed to make two solids by naming and coloring a base, folding faces, gluing edges, and displaying the solids. They were then asked to classify solids as prisms or pyramids based on the shape of the base. Finally, homework was assigned to complete problems 3 through 27 of odd numbers on page 798.
7.4 notes
The document outlines an agenda for a math class that includes writing equations. It provides three word problems asking students to write equations to determine: 1) the original price of a puppy that was $21 less than original price and bought for $48, 2) the number of miles driven for a two-day van rental that cost $79.46 with a $29.95 per day fee plus $0.12 per mile, and 3) the original price of a sweater that was on sale for $48 at 20% less than the original price. Students are assigned homework problems from page 360, numbers 1 through 11.
3.1 notes
The document defines and describes various types of lines and angles. It defines parallel lines as lines that do not intersect and are coplanar. Skew lines do not intersect and are not coplanar. A transversal is a line that intersects two or more lines at different points, and can be used to define corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. The document also presents the parallel postulate and perpendicular postulate.
7.5 notes
This document contains notes from a math class on solving two-step inequalities. It includes the date, objective of the lesson which is solving two-step inequalities, examples of inequalities to solve, and a word problem involving an inequality about the maximum number of hikers an expedition can support given weight limits of food and equipment. The document appears to be a teacher's notes and worksheets for students covering solving two-step inequalities.
8.4 notes
The document discusses different types of quadrilaterals:
- Parallelograms have both pairs of opposite sides parallel.
- Rhombuses have four equal sides.
- Rectangles have four right angles.
- Squares are both rhombuses and rectangles, with four equal sides and four right angles.
Theorems state that a quadrilateral is a rhombus if its diagonals are perpendicular, or if each diagonal bisects a pair of opposite sides. A quadrilateral is a rectangle if its diagonals are parallel.
4.5 notes
The document discusses different postulates and theorems that can be used to prove triangles are congruent, including:
1) Angle-Side-Angle (ASA) - If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
2) Angle-Angle-Side (AAS or SAA) - If two angles and the non-included side of one triangle are equal to two angles and the non-included side of another triangle, then the triangles are congruent.
3) Angle-Angle-Angle (AAA) only proves triangles are similar, not congruent. Side-Side-Angle (SSA
10.3 notes
The document appears to be notes from a math class on February 28th, 2014 about chord properties. It includes instructions for students to complete a bellwork activity individually without sharing answers. The class will later split into groups to learn different theorems - group A will cover theorem 10.3, group B theorem 10.4, and so on. The document provides space for each group to take notes. At the end, it reminds students to complete homework problems #3-19 odds from page 667.
7.1 & 7.2 notes
The document discusses the Pythagorean theorem and its converse. It provides examples of using the theorem to find the length of a hypotenuse or the area of a triangle. It also lists several Pythagorean triples and explains how to determine if a triangle is a right triangle using the converse of the theorem. The homework assignment is to complete all problems on the worksheet except problems 7-9 dealing with the converse and problem 21 which is extra credit.
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This document discusses trigonometric ratios and their use in right triangles. It defines the three basic trig functions - sine, cosine, and tangent - which relate angles to sides of a right triangle. Sine is defined as the ratio of the opposite side to the hypotenuse. Cosine is the ratio of the adjacent side to the hypotenuse. Tangent is the ratio of the opposite side to the adjacent side. Several examples are given of calculating trig ratios and solving for unknown sides or angles in right triangles. Angles of elevation and depression are also defined.
10.5 notes
The document discusses surface area formulas for prisms and cylinders. It defines surface area as the sum of the areas of all surfaces that enclose the solid. For prisms, surface area is calculated as the perimeter of the base multiplied by the height, plus twice the area of the base. For cylinders, surface area is the circumference of the circular base multiplied by the height, plus twice the area of the circular base. Examples are given to demonstrate how to apply these formulas.
12.6 notes
This document contains a lesson on spheres that includes:
1) Objectives about applying the volume and surface area formulas for spheres and developing problem-solving skills
2) Examples of calculating the surface area and volume of various spheres and hemispheres
3) Word problems involving spheres that require using the volume formula
4) An assignment to complete problems #4-22 on page 842 of the homework that are even numbers.
Geom12point6 97
This document provides information about calculating the surface area and volume of spheres. It defines key terms related to spheres such as radius, diameter, center, and hemisphere. It gives the formulas for calculating the surface area (S=4πr^2) and volume (V=4/3πr^3) of spheres. Examples are provided to demonstrate how to use the formulas to find the surface area of a baseball and the radius of a ball bearing given its original volume as a cylinder.
9 2 Notes (D2 A)
This document provides instructions and questions for students regarding the area formula for regular polygons and circles. It begins by asking students to explain why the area formula for regular polygons works using a square diagram. It then provides example problems for students to find the area of regular polygons like pentagons and hexagons, as well as circles. It asks students to work with partners on homework questions and provides sample raffle problems related to these concepts. It concludes by providing two exit slip problems for students to work on with a partner - one finding the area of a regular polygon in terms of pi and one finding the area of a circle to the nearest hundredth.
12.6 notes
This document contains a lesson on surface area and volume of spheres. It includes objectives of understanding volume formulas for spheres and applying 3D thinking skills. There are examples of calculating surface area and volume of various spheres and hemispheres with given radii or diameters. Students are assigned even problems from page 842 numbers 4 through 22 as homework.
12.4 notes
This document provides instruction on calculating the volume of prisms and cylinders. It defines volume as the amount of space inside an object. To find the volume of a prism or cylinder, students are told to find the area of the base and multiply it by the height of the object. Formulas for calculating the volume of prisms and cylinders are provided, with the key being to identify the base shape and insert its area formula. Examples of prism and cylinder volume problems are given for students to work through.
Day 7 area of a circle
The document is about finding the area of circles. It explores rearranging a circle into a parallelogram shape to relate the circumference and radius to the base and height of the parallelogram. This leads to the formula for the area of a circle being πr^2. Examples are given of calculating the area when given the radius or diameter. It also explores the relationship between the circumference and area, deriving the formula A=C^2/4π.
12.3 notes
This document contains notes on finding the surface area of pyramids and cones. It provides the formulas for calculating surface area of regular pyramids as one-half of the perimeter of the base times the sum of the slant height and apothem. For cones, the surface area formula is given as the area of the base plus the radius times pi times the slant height. The document includes examples of applying these formulas to find the surface area of various pyramids and cones.
9 2 Notes (D1) B
This document contains a math lesson on circles and regular polygons. It includes examples of calculating the area and circumference of circles and finding side lengths, radii, areas, and perimeters of regular polygons. Students are asked to work through sample problems and show their work. A raffle assignment provides additional practice problems to solve involving circles and polygons.
Strafford Volleyball Apparel
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Ch 12 unit schedule
This document outlines the Geometry 2016 Chapter 12 unit on 3D shapes that will be covered from April 11th to April 29th. It includes the chapter sections and topics to be covered each day, such as different types of prisms and pyramids, as well as the homework assignments and assessments including quizzes, tests, and a study guide.
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9.3 notes
This document contains notes from a geometry class on reflections. It includes the definitions of a line of reflection and the coordinate rules for reflecting points across the x-axis, y-axis, lines y=x and y=-x. It also states that a reflection is an isometry and provides the reflection matrices used to calculate the reflected image of a point by multiplying the matrix and the coordinates of the pre-image point. The document records the student working through homework problems on reflections.
12.1 notes
Students were instructed to make two solids by naming and coloring a base, folding faces, gluing edges, and displaying the solids. They were then asked to classify solids as prisms or pyramids based on the shape of the base. Finally, homework was assigned to complete problems 3 through 27 of odd numbers on page 798.
7.4 notes
The document outlines an agenda for a math class that includes writing equations. It provides three word problems asking students to write equations to determine: 1) the original price of a puppy that was $21 less than original price and bought for $48, 2) the number of miles driven for a two-day van rental that cost $79.46 with a $29.95 per day fee plus $0.12 per mile, and 3) the original price of a sweater that was on sale for $48 at 20% less than the original price. Students are assigned homework problems from page 360, numbers 1 through 11.
3.1 notes
The document defines and describes various types of lines and angles. It defines parallel lines as lines that do not intersect and are coplanar. Skew lines do not intersect and are not coplanar. A transversal is a line that intersects two or more lines at different points, and can be used to define corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. The document also presents the parallel postulate and perpendicular postulate.
7.5 notes
This document contains notes from a math class on solving two-step inequalities. It includes the date, objective of the lesson which is solving two-step inequalities, examples of inequalities to solve, and a word problem involving an inequality about the maximum number of hikers an expedition can support given weight limits of food and equipment. The document appears to be a teacher's notes and worksheets for students covering solving two-step inequalities.
8.4 notes
The document discusses different types of quadrilaterals:
- Parallelograms have both pairs of opposite sides parallel.
- Rhombuses have four equal sides.
- Rectangles have four right angles.
- Squares are both rhombuses and rectangles, with four equal sides and four right angles.
Theorems state that a quadrilateral is a rhombus if its diagonals are perpendicular, or if each diagonal bisects a pair of opposite sides. A quadrilateral is a rectangle if its diagonals are parallel.
4.5 notes
The document discusses different postulates and theorems that can be used to prove triangles are congruent, including:
1) Angle-Side-Angle (ASA) - If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
2) Angle-Angle-Side (AAS or SAA) - If two angles and the non-included side of one triangle are equal to two angles and the non-included side of another triangle, then the triangles are congruent.
3) Angle-Angle-Angle (AAA) only proves triangles are similar, not congruent. Side-Side-Angle (SSA
10.3 notes
The document appears to be notes from a math class on February 28th, 2014 about chord properties. It includes instructions for students to complete a bellwork activity individually without sharing answers. The class will later split into groups to learn different theorems - group A will cover theorem 10.3, group B theorem 10.4, and so on. The document provides space for each group to take notes. At the end, it reminds students to complete homework problems #3-19 odds from page 667.
7.1 & 7.2 notes
The document discusses the Pythagorean theorem and its converse. It provides examples of using the theorem to find the length of a hypotenuse or the area of a triangle. It also lists several Pythagorean triples and explains how to determine if a triangle is a right triangle using the converse of the theorem. The homework assignment is to complete all problems on the worksheet except problems 7-9 dealing with the converse and problem 21 which is extra credit.
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This document provides examples and instructions for calculating medication dosages when converting between different units of measurement. It gives five examples of dosage problems where the amount ordered is in a different unit than what is available. For each problem, the student is directed to set up a proportion, convert units to be the same, substitute the converted unit into the proportion, cross multiply, and solve to determine the amount that should be given based on what is available. The document also provides an additional practice problem for students to work through.
Trig 1 notes
This document discusses trigonometric ratios and their use in right triangles. It defines the three basic trig functions - sine, cosine, and tangent - which relate angles to sides of a right triangle. Sine is defined as the ratio of the opposite side to the hypotenuse. Cosine is the ratio of the adjacent side to the hypotenuse. Tangent is the ratio of the opposite side to the adjacent side. Several examples are given of calculating trig ratios and solving for unknown sides or angles in right triangles. Angles of elevation and depression are also defined.
10.5 notes
The document discusses surface area formulas for prisms and cylinders. It defines surface area as the sum of the areas of all surfaces that enclose the solid. For prisms, surface area is calculated as the perimeter of the base multiplied by the height, plus twice the area of the base. For cylinders, surface area is the circumference of the circular base multiplied by the height, plus twice the area of the circular base. Examples are given to demonstrate how to apply these formulas.
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Similar to 12.6 notes
12.6 notes
This document contains a lesson on spheres that includes:
1) Objectives about applying the volume and surface area formulas for spheres and developing problem-solving skills
2) Examples of calculating the surface area and volume of various spheres and hemispheres
3) Word problems involving spheres that require using the volume formula
4) An assignment to complete problems #4-22 on page 842 of the homework that are even numbers.
Geom12point6 97
This document provides information about calculating the surface area and volume of spheres. It defines key terms related to spheres such as radius, diameter, center, and hemisphere. It gives the formulas for calculating the surface area (S=4πr^2) and volume (V=4/3πr^3) of spheres. Examples are provided to demonstrate how to use the formulas to find the surface area of a baseball and the radius of a ball bearing given its original volume as a cylinder.
9 2 Notes (D2 A)
This document provides instructions and questions for students regarding the area formula for regular polygons and circles. It begins by asking students to explain why the area formula for regular polygons works using a square diagram. It then provides example problems for students to find the area of regular polygons like pentagons and hexagons, as well as circles. It asks students to work with partners on homework questions and provides sample raffle problems related to these concepts. It concludes by providing two exit slip problems for students to work on with a partner - one finding the area of a regular polygon in terms of pi and one finding the area of a circle to the nearest hundredth.
12.6 notes
This document contains a lesson on surface area and volume of spheres. It includes objectives of understanding volume formulas for spheres and applying 3D thinking skills. There are examples of calculating surface area and volume of various spheres and hemispheres with given radii or diameters. Students are assigned even problems from page 842 numbers 4 through 22 as homework.
12.4 notes
This document provides instruction on calculating the volume of prisms and cylinders. It defines volume as the amount of space inside an object. To find the volume of a prism or cylinder, students are told to find the area of the base and multiply it by the height of the object. Formulas for calculating the volume of prisms and cylinders are provided, with the key being to identify the base shape and insert its area formula. Examples of prism and cylinder volume problems are given for students to work through.
Day 7 area of a circle
The document is about finding the area of circles. It explores rearranging a circle into a parallelogram shape to relate the circumference and radius to the base and height of the parallelogram. This leads to the formula for the area of a circle being πr^2. Examples are given of calculating the area when given the radius or diameter. It also explores the relationship between the circumference and area, deriving the formula A=C^2/4π.
12.3 notes
This document contains notes on finding the surface area of pyramids and cones. It provides the formulas for calculating surface area of regular pyramids as one-half of the perimeter of the base times the sum of the slant height and apothem. For cones, the surface area formula is given as the area of the base plus the radius times pi times the slant height. The document includes examples of applying these formulas to find the surface area of various pyramids and cones.
9 2 Notes (D1) B
This document contains a math lesson on circles and regular polygons. It includes examples of calculating the area and circumference of circles and finding side lengths, radii, areas, and perimeters of regular polygons. Students are asked to work through sample problems and show their work. A raffle assignment provides additional practice problems to solve involving circles and polygons.
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12.7 notes
This document contains notes from a math class on similar solids. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. It then states the Similar Solids Theorem: if two similar solids have a scale factor of a:b, their corresponding areas have a ratio of a2:b2 and their corresponding volumes have a ratio of a3:b3. Examples of homework problems involving similar solids are listed.
12.5 notes
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12.4 notes
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Indian volleyball tournament
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12.3 notes
This document contains notes and examples for calculating the surface area of pyramids and cones. It provides the formulas for finding the surface area of regular pyramids and cones. For pyramids, the surface area equals one-half the perimeter of the base times the sum of the slant height and apothem. For cones, the surface area equals pi times the radius squared plus pi times the radius times the slant height. The document includes practice problems applying these formulas to find the surface area of various pyramids and cones.
12.2 notes
The document discusses surface area formulas for prisms and cylinders. It defines surface area as the sum of the areas of all surfaces that enclose a solid. For prisms, surface area is calculated as the perimeter of the base multiplied by the height, plus twice the area of the base. For cylinders, surface area is the circumference of the base multiplied by the height, plus twice the area of the circular base. The document provides examples of applying these formulas to prisms and cylinders.
12.5 notes
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11.7 notes
This document contains notes from an 11th grade math class on the topic of geometric probability. It includes examples of calculating the probability of events based on ratios of lengths and areas, such as the probability of a driver speeding in front of a school based on the length of road in front of the school over the total road length. The homework problems assigned were problems 4-10 of the even numbers, 20-23, and 30-33 on page 774 of the textbook.
11.6 notes
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