Download 2011-2012 Geometry Ch 7 assignments

Geometry Ch 7
Class website (lesson handout and homework answers): http://PassGeometry.weebly.com
To receive full credits, you must copy/summarize the question, copy diagrams with fidelity,
and show work. Graphing must be done on graph paper.
A graphing calculator is required in class (and for homework).
5 full tutoring sessions = 10% on a test, or 3 HW passes
You must know: radical numbers; how to multiply binomials, e.g.  2 x  3 x  5 ; and solve
quadratic equations ( x2  5x  36  0 ). Otherwise, come to tutoring during the first week.
Lesson 1--Aim: Applying the Pythagorean Theorem and simplifying radicals (Section 7.2)
HW #1: P436 – 438: 3–4, 6, 9–11, 17, 24–25, 26*, 34*(challenge = extra credit)
Lesson 2--Aim: How do we classify triangles by their angles using their sides? (Section 7.2)
HW #2: P444 – 445: 3–4, 7, 15–18, 25, 27, 28, 34*(challenge).
Lesson 3--Aim: What is the ratio of the side lengths of a 45-45-90 triangle? (Section 7.4)
HW #3: P461 – 462: 1, 3 – 5, 11, 14, 21
Lesson 4--Aim: What is the ratio of the side lengths of a 30-60-90 triangle? (Section 7.4)
HW #4: P461 – 463: 6, 8 – 10, 12, 13, 15, 16, 18, 20, 24
Lesson 5--Aim: What are the properties associated with altitudes within right triangles? Day 1 (Section
7.3)
HW #5: P453 – 455: 3 – 4, 14, 16, 17, 22, 28
Lesson 6--Aim: What are the properties associated with altitudes within right triangles? Day 2 (Section
7.3)
HW #6: P453 – 455: 13, 15, 18, 21, 23, 27*(Challenging)
Lesson 7--Aim: What are the properties associated with altitudes within right triangles? Day 3 (Section
7.3)
HW #7: Finish Worksheet
Practice Test
At the end of this unit, you should be able to
1) apply Pythagorean Theorem to verify that a triangle is right
2) use Pythagorean Theorem to verify that a triangle is not right. When the triangle is not right,
determine if it is acute or obtuse.
3) know that in a right triangle when an altitude is drawn from the right angle to its opposite side, it
creates three similar right triangles resulting in three Geometric Means theorems.
a) (CD)2  AD( BD)
b) ( BC )2  DB( AB)
c) ( AC )2  AD( AB)
4) know which Geometric Mean theorem is appropriate to find the missing side length in problems.
5) know the relationship between the sides of a isosceles right triangle (45-45-90) and apply it in
problems to find the missing side length
6) know the relationship between the sides of a 30-60-90 triangle and apply it in problems to find the
missing side length
Ch 7 Uniform Unit Test
(Must be taken on or before Feb. 14, due to Midwinter Recess)
Common Core Standards Addressed
G-SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle
divides the other two proportionally, and conversely; the Pythagorean Theorem proved
using triangle similarity.
G-SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures.
G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.
Methods of Differentiated Instructions
Revolution K-12, a student-driven online learning platform, is used to differentiate instruction for all
students in class and subject areas.
All students are held to the Common Core-aligned standards. Teacher performs formative assessments
through lessons to check student understanding, including cold-calling, student board work, and exit
tickets. Teacher circulates room to perform further formative assessments and to guide small groups and
individuals.
Lower-performing students are grouped heterogeneously with higher-performing students using
assessment data, interests, and work habits, to encourage student-to-student engagement and learning.
They are also provided guided notes and graphic organizers to build schemas.
English Language Learners are paired with students who are fluent in English, and given extra time.
Vocabulary is pronounced several times and accompanied by alternative words or phrases that are
simplified. Visual aids, including pictures, Smart boards, and manipulatives, help students make clear
connections to the text.
Students with Special Needs are grouped with helpers and given instructions or assessments with
simplified language or extra time. Color-coding on the Smart board help illustrate steps required to solve
a problem. Hands-on activities are provided to help construct student learning.
Gifted/Honor students are given challenge problems during lessons, homework, and summative
assessments, which earn extra credits. They are expected to complete the whole worksheet, and are
given challenge (e.g. open-ended) problems that develop higher-level thinking.
Geometry Ch 8
Class website (lesson handout and homework answers): http://PassGeometry.weebly.com
To receive full credits, you must copy/summarize questions, copy diagrams, and show work.
Graphing must be done on graph paper. Ask before you need it, or print graph paper from
http://mathbits.com/mathbits/studentresources/graphpaper/graphpaper.htm
5 full tutoring sessions = 10% on a test, or 3 HW passes
To retake ch8 test, you must attend at least one tutoring session before the week of the test.
This chapter requires at least 8 flash (index) cards with your name, worth 10% on the unit test.
On the front of each index card, write the name of a figure: quadrilateral, parallelogram, rhombus,
square, rectangle, trapezoid, isosceles trapezoid, and kite. On the back, write or illustrate its definition
and properties. Can be used also on quizzes, homework, and class work. Start after lesson #10.
Lesson 8—Aim: How do we find the angle measures in polygons? (Section 8.1)
HW #8: P510 – 512: 3, 8, 12, 14, 15, 18, 27*. *challenging
Lesson 9—Aim: What are the properties of a parallelogram? (Section 8.2) 2 Days
HW #9: P518 – 519: 4, 7, 10, 15, 23 – 28, 30, 34; Flash cards
Lesson 10—Aim: How do we prove that a quadrilateral is a parallelogram? Day 1 (Section 8.3)
HW #10: P526 – 527: 3 – 6, 8, 10, 15, 16, 18, 20, 21
Lesson 11—Aim: How do we prove a quadrilateral is a parallelogram? Day 2 (Section 8.3)
HW #11: P526 – 527: 11, 12, 25, 26
This homework assignment must be done on graph paper or no credit.
Lesson 12—Aim: What are the properties of rectangles, squares, and rhombus? (Section 8.4) 2 Days
HW #12: Flash cards & P537-538: 25 – 29, 32 – 34; (Day 2) Finish worksheet.
Lesson 13—Aim: How do we prove a quadrilateral is a rhombus or a rectangle? (Section 8.4)
HW #13: P537 – 538: 38 – 41, 44 – 49
Lesson 14—Aim: How do we prove a quadrilateral is a rhombus or a rectangle? (Section 8.4)
HW #14: Finish worksheets
This homework assignment must be done on graph paper or no credit.
Lesson 15—Aim: What are the properties of a trapezoid? (Section 8.5)
HW #15: P546 – 547: 7 – 8, 14, 26, 30, 32*. *challenging
Lesson 16—Aim: How do we prove a quadrilateral is a trapezoid or an isosceles trapezoid? (Section
8.5)
HW #16: P546 – 547: 3 – 4, 6, 15
Questions 3–4 must be done on graph paper or no credit.
Lesson 17—Aim: What are the properties of a kite? (Section 8.5)
HW #17: P547: 19, 21, 23
P555: 18-20
Ch 8 Review/Uniform Unit Test
BEFORE test review day, identify topics to concentrate on for review.
1) find the missing measure of an exterior angle of a polygon when all other exterior angles are given.
2) find the missing measure of an interior angle of a polygon when all other interior angles are given
3) know the definition and properties of a parallelogram and apply them to find the missing segment
length or angle measure in parallelogram.
4) know how to show a quadrilateral is a parallelogram.
5) prove a quadrilateral is a parallelogram using coordinate proof.
6) find the missing vertex when given three vertices of a parallelogram,
7) know the definition and properties of a rectangle, a square and a rhombus, and use them to solve
problem involving these special quadrilaterals
8) prove a quadrilateral is a rectangle using coordinate proof.
9) prove a quadrilateral is a square using coordinate proof.
10) prove a quadrilateral is a rhombus using coordinate proof.
11) know the definition and properties of a trapezoid and an isosceles trapezoid
12) prove a quadrilateral is a trapezoid or an isosceles trapezoid using coordinate proof.
13) know and apply the Mid-segment theorem for isosceles trapezoids.
14) know and apply the property of a kite
Common Core Standards Addressed
G-CO.3
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and
reflections that carry it onto itself.
G-CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent,
opposite angles are congruent, the diagonals of a parallelogram bisect each other, and
conversely, rectangles are parallelograms with congruent diagonals.
G-GM.3 Apply geometric methods to solve design problems (e.g., designing an object or structure
to satisfy physical constraints or minimize cost; working with typographic grid systems
based on ratios).
Methods of Differentiated Instructions
Revolution K-12, a student-driven online learning platform, is used to differentiate instruction for all
students in class and subject areas.
All students are held to the Common Core-aligned standards. Teacher performs formative assessments
through lessons to check student understanding, including cold-calling, student board work, and exit
tickets. Teacher circulates room to perform further formative assessments and to guide small groups and
individuals.
Lower-performing students are grouped heterogeneously with higher-performing students using
assessment data, interests, and work habits, to encourage student-to-student engagement and learning.
They are also provided guided notes and graphic organizers to build schemas.
English Language Learners are paired with students who are fluent in English, and given extra time.
Vocabulary is pronounced several times and accompanied by alternative words or phrases that are
simplified. Visual aids, including pictures, Smart boards, and manipulatives, help students make clear
connections to the text.
Students with Special Needs are grouped with helpers and given instructions or assessments with
simplified language or extra time. Color-coding on the Smart board help illustrate steps required to solve
a problem. Hands-on activities are provided to help construct student learning.
Gifted/Honor students are given challenge problems during lessons, homework, and summative
assessments, which earn extra credits. They are expected to complete the whole worksheet, and are
given challenge (e.g. open-ended) problems that develop higher-level thinking.
Geometry Ch 9
Class website (lesson handout and homework answers): http://PassGeometry.weebly.com
The ch9 test review is printed on 6 pages. Do not wait till the last day to do it.
To retake ch9 test, you must attend at least one tutoring session before the test.
To receive full credits, you must copy/summarize questions, copy diagrams, and show work.
Graphing must be done on graph paper. Ask before you need it, or print graph paper from
http://mathbits.com/mathbits/studentresources/graphpaper/graphpaper.htm
5 full tutoring sessions = 10% on a test, or 3 HW passes
Lesson 18--Aim: How do we transform figures using translation? (Section 9.1)
HW #18: P576 – 577: 3, 7, 11, 31, 32A*
*Challenging: optional = extra credits
Homework must be done on graph paper or no credit.
Lesson 19--Aim: What is a reflection? Day 1 (Section 9.3)
HW #19: P593: 2–6
Homework must be done on graph paper or no credit.
Lesson 20--Aim: What is a reflection? Day 2 (Section 9.3)
HW #20: P593: 8–12
Homework must be done on graph paper or no credit.
Lesson 21--Aim: How do we perform rotations? Day 1 (Section 9.4)
HW #21: P602: 6, 12–14, 21, 23
No need to copy #6. Homework must be done on graph paper or no credit.
Lesson 21--Aim: How do we perform rotations? Day 2 (Section 9.4)
HW #21.5: Complete worksheet
Lesson 22--Aim: How do apply dilations and composition of transformations? (Section 9.7, 9.5)
HW #22: P628: 21, 23, 24
P611–612: 3, 10, 14
Homework must be done on graph paper or no credit.
Lesson 23--Aim: How do apply composition of transformations? (Section 9.5)
HW #23: P611–612: 6, 8, 9, 13, 26*
Homework must be done on graph paper or no credit.
Lesson 24--Aim: How do we identify symmetry? (Section 9.6)
HW #24: P621–622: 3–5, 13, 14, 24, 25*, 30
At the end of this unit, you should be able to:
1) recognize translation rule and apply it to transform a figure
2) identify the translation rule when given the pre-image and the image.
3) recognize reflection symbols and apply reflections across the x  axis and y  axis , a vertical line and
a horizontal line.
4) apply reflections across the line y  x, y   x and in the origin.
5) recognize the rotation symbols and apply counter-clockwise rotations of 90,180, 270 about the
origin.
6) recognize the dilation symbol and apply dilation to transform a figure.
7) apply a composition of transformations to a figure: remember to start with the transformation on the
right first.
8) know what are glide reflections and identify them
9) identify line, rotational and point symmetries
10) know the term isometry and identify the transformations that are an isometry.
11) know which transformation is a similarity transformation and which is a congruence transformation.
12) know which transformation preserves orientation and which does not.
Ch 9 Review/Uniform Unit Test
Common Core Standards Addressed
G-SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor:
a. A dilation takes a line not passing through the center of the dilation to a parallel line,
and leaves a line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G-SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to
decide if they are similar; explain using similarity transformations the meaning of
similarity for triangles as the equality of all corresponding pairs of angles and the
proportionality of all corresponding pairs of sides.
G-SRT.3 Use the properties of similarity transformations to establish the AA criterion for two
triangles to be similar.
G-CO.4
Develop definitions of rotations, reflections, and translations in terms of angles, circles,
perpendicular lines, parallel lines, and line segments.
G- CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed
figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of
transformations that will carry a given figure onto another.
Methods of Differentiated Instructions
Revolution K-12, a student-driven online learning platform, is used to differentiate instruction for all
students in class and subject areas.
All students are held to the Common Core-aligned standards. Teacher performs formative assessments
through lessons to check student understanding, including cold-calling, student board work, and exit
tickets. Teacher circulates room to perform further formative assessments and to guide small groups and
individuals.
Lower-performing students are grouped heterogeneously with higher-performing students using
assessment data, interests, and work habits, to encourage student-to-student engagement and learning.
They are also provided guided notes and graphic organizers to build schemas.
English Language Learners are paired with students who are fluent in English, and given extra time.
Vocabulary is pronounced several times and accompanied by alternative words or phrases that are
simplified. Visual aids, including pictures, Smart boards, and manipulatives, help students make clear
connections to the text.
Students with Special Needs are grouped with helpers and given instructions or assessments with
simplified language or extra time. Color-coding on the Smart board help illustrate steps required to solve
a problem. Hands-on activities are provided to help construct student learning.
Gifted/Honor students are given challenge problems during lessons, homework, and summative
assessments, which earn extra credits. They are expected to complete the whole worksheet, and are
given challenge (e.g. open-ended) problems that develop higher-level thinking.
Geometry Ch 10A
Class website (lesson handout and homework answers): http://PassGeometry.weebly.com
Please ask your parents or guardians not to schedule vacations before April 12.
The unit test must be taken before spring break.
To receive full credits, you must copy/summarize questions, copy diagrams, and show work.
5 full tutoring sessions = 10% on a test, or 3 HW passes
To retake ch10A test, you must attend at least one tutoring session before the test.
Lesson 25--Aim: What are the special segments relating to circles? (Section 10.1)
HW #25: P655 – 656: 3 – 10, 15 – 17, 22
Lesson 26--Aim: What are the properties of tangents? (Section 10.1)
HW #26: P655 – 656: 20, 23, 24.
Lesson 27--Aim: How do we find the arc measure in a circle? (Section 10.2&10.3)
HW #27: P661-662: 3 – 10, 17
P667 – 668: 3 – 5, 7
Lesson 28-- Aim: What is the relationship between the inscribed angle and its intercepted arc?
(Section 10.4)
HW #28: P676 – 677: 3 – 5, 7, 10, 11, 18*, *Must show work.
Lesson 29-- Aim: What are the properties when we inscribe right triangles and quadrilaterals?
(Section 10.4)
HW #29: P676 – 677: 8, 12 – 14, 20 – 25
Lesson 30--Aim: How do we prove the angle and arc relationship when a chord and a tangent intersect
AND when two chords intersect inside a circle? (Section 10.5) (2 days)
HW #30: P683 – 685: 3, 6, 7, 9
Lesson 31-- Aim: What are the angle relationships when two segments intersect outside the circle?
(Section 10.5)
HW #31: P683 – 685: 11, 12
Spring break assignment will be graded as take-home exam. 10% deducted daily for lateness.
At the end of this unit, you should be able to
1) identify the terms secant, tangent, chord, point of tangency, radius and diameter.
2) know that a tangent is perpendicular to the radius it intersects.
3) know how to draw the common tangent to two circles
4) know the theorem that tangents to a circle originating from a common external point are congruent.
5) know the terms minor arc and major arc and that their measures come from the measure of the central
angles they intercept.
6) know the theorem that if two chords are congruent within the circle, then the arcs they intercept are
congruent as well.
7) know theorem: If one chord is a perpendicular bisector of another chord, then the first chord is a
diameter, and its converse.
8) know the difference between central angles and inscribed angles; if both inscribed angles intercept
the same arc, then they are congruent.
9) know the measure of an inscribed angle is half that of the central angle they both intercept.
10) know the theorem: A quadrilateral can be inscribed in a circle if and only if its opposite angles are
supplementary.
11) know theorem: If a tangent and a chord intersect at a point on a circle, then the measure of each
angle formed is one half the measure of its intercepted arc.
12) know theorem: If two chords intersect inside a circle, then the measure of
each angle is one half the sum of the measures of the arcs intercepted.
13) know and apply the following theorems:
Ch 10A TEST
Common Core Standards Addressed
G-GC.2
Identify and describe relationships among inscribed angles, radii, and chords. Include
the relationship between central, inscribed, and circumscribed angles; inscribed
angles on a diameter are right angles; the radius of a circle is perpendicular to the
tangent where the radius intersects the circle.
G-GC.5
Derive using similarity the fact that the length of the arc intercepted by an angle is
proportional to the radius, and define the radian measure of the angle as the constant
of proportionality; derive the formula for the area of a sector.
G-MG.1
Use geometric shapes, their measures, and their properties to describe objects (e.g.,
modeling a tree trunk or a human torso as a cylinder).
Methods of Differentiated Instructions
Revolution K-12, a student-driven online learning platform, is used to differentiate instruction for all
students in class and subject areas.
All students are held to the Common Core-aligned standards. Teacher performs formative assessments
through lessons to check student understanding, including cold-calling, student board work, and exit
tickets. Teacher circulates room to perform further formative assessments and to guide small groups and
individuals.
Lower-performing students are grouped heterogeneously with higher-performing students using
assessment data, interests, and work habits, to encourage student-to-student engagement and learning.
They are also provided guided notes and graphic organizers to build schemas.
English Language Learners are paired with students who are fluent in English, and given extra time.
Vocabulary is pronounced several times and accompanied by alternative words or phrases that are
simplified. Visual aids, including pictures, Smart boards, and manipulatives, help students make clear
connections to the text.
Students with Special Needs are grouped with helpers and given instructions or assessments with
simplified language or extra time. Color-coding on the Smart board help illustrate steps required to solve
a problem. Hands-on activities are provided to help construct student learning.
Gifted/Honor students are given challenge problems during lessons, homework, and summative
assessments, which earn extra credits. They are expected to complete the whole worksheet, and are
given challenge (e.g. open-ended) problems that develop higher-level thinking.
Geometry Ch 10B
Class website (lesson handout and homework answers): http://PassGeometry.weebly.com
WILL NEED COMPASS FOR LESSONS 35–39
To receive full credits, you must copy/summarize questions, copy diagrams, and show work.
Graphing must be done on graph paper. Ask before you need it, or print graph paper from
http://mathbits.com/mathbits/studentresources/graphpaper/graphpaper.htm
5 full tutoring sessions = 10% on a test, or 3 HW passes
To retake ch10B test, you must attend at least one tutoring session before the week of the test.
Lesson 32--Aim: What is the segment relationship when two chords intersect inside a circle?
(Section 10.6)
HW #32: P692 – 694: 4, 5, 13, 16**
**Must show work for this multiple-choice question.
Lesson 33--Aim: What is the segment relationship when two secants intersect? (Section 10.6)
HW #33: P692 – 694: 6, 7, 8**, 14.
**challenging
Lesson 34--Aim: What is the segment relationship when a secant and a tangent intersect outside the
circle? (Section 10.6)
HW #34: P692 – 694: 9 – 11, 17.
Lesson 35--Aim: More exercises on conics
HW #35: Finish worksheet (consider it part 1 of test review)
Bring compass for next class
Lesson 36--Aim: How do we write and graph equations of circles? Day 1 (Section 10.7)
HW #36: P702 – 704: 3, 5, 9, 17.
This assignment must be done on graph paper or no credit.
Lesson 37--Aim: How do we write and graph equations of circles? Day 2 (Section 10.7)
HW #37: P702 – 704: 6 – 8. 12 – 13, 19, 24, 25, 31** **challenging
This assignment must be done on graph paper or no credit.
Lesson 38--Aim: What is locus? 2 DAYS
HW #38: Finish worksheets.
Copy the questions and show neat work on a separate sheet of paper or no credit.
Lesson 39&40--Aim: How do we find compound loci? 2 DAYS
HW #39&40: Worksheets. You must draw the diagrams neatly or no credit for just an answer.
At the end of this unit, you should be able to
1) know and apply Segments of Chords Theorem, Segment of secants theorem, Segments of Secant
and Tangent Theorem:
,
,
2) write the equation of the circle when it is given on the coordinate plane—know how to identify the
radius and center.
3) graph a circle when the equation is given.
4) write the equation of a circle when the endpoints of the diameter are given.
5) know the five fundamental loci.
6) find the compound loci by graphing each individual locus separately first.
7) apply compound loci to solve real-life problems.
Lesson 24&25– Aim: How do we solve a system of equations?
HW#24&25: Finish worksheet
Objectives: know how to graph a parabola
Know that the solutions to a system of equation are their intersections points
Know how to find the solutions graphically using a graphing calculator
Ch 10B TEST
Common Core Standards Addressed
G-GC.1
Prove that all circles are similar.
G-GC.2
Identify and describe relationships among inscribed angles, radii, and chords. Include
the relationship between central, inscribed, and circumscribed angles; inscribed
angles on a diameter are right angles; the radius of a circle is perpendicular to the
tangent where the radius intersects the circle.
G-GC.4 (+)
Construct a tangent line from a point outside a given circle to the circle.
G-GPE.1
Derive the equation of a circle of given center and radius using the Pythagorean
Theorem; complete the square to find the center and radius of a circle given by an
equation.
Methods of Differentiated Instructions
Revolution K-12, a student-driven online learning platform, is used to differentiate instruction for all
students in class and subject areas.
All students are held to the Common Core-aligned standards. Teacher performs formative assessments
through lessons to check student understanding, including cold-calling, student board work, and exit
tickets. Teacher circulates room to perform further formative assessments and to guide small groups and
individuals.
Lower-performing students are grouped heterogeneously with higher-performing students using
assessment data, interests, and work habits, to encourage student-to-student engagement and learning.
They are also provided guided notes and graphic organizers to build schemas.
English Language Learners are paired with students who are fluent in English, and given extra time.
Vocabulary is pronounced several times and accompanied by alternative words or phrases that are
simplified. Visual aids, including pictures, Smart boards, and manipulatives, help students make clear
connections to the text.
Students with Special Needs are grouped with helpers and given instructions or assessments with
simplified language or extra time. Color-coding on the Smart board help illustrate steps required to solve
a problem. Hands-on activities are provided to help construct student learning.
Gifted/Honor students are given challenge problems during lessons, homework, and summative
assessments, which earn extra credits. They are expected to complete the whole worksheet, and are
given challenge (e.g. open-ended) problems that develop higher-level thinking.
Geometry Unit 11 (Ch. 11+12)—Last unit
Class website (lesson handout and homework answers): http://PassGeometry.weebly.com
Please ask your parents or guardians not to schedule vacations before May 24.
Attend as much tutoring after school and Saturday Academies as possible, so you can
earn a Regents score you can be proud of.
Flash cards or similar study tool required by lesson 44.
To receive full credits, you must copy/summarize questions, copy diagrams, and show work.
5 full tutoring sessions = 10% on a test, or 3 HW passes
Lesson 41—How do we derive the formula for areas of parallelograms and triangles?
HW #41: Finish worksheets
Lesson 42—How do we find perimeters and area of geometric figures?
HW #42: Finish worksheets
Lesson 43—Perimeter and area of circles
HW #43: P750: 12, 13, 15, 16
P758: 13, 16
Lesson 44—How do we identify solids and the intersection of the plane and the solids?
Lesson 45—Aim: How do we find the surface areas of solids? (Section 11.5)
HW #45: P806 – 808: 3, 4, 6, 7, 12 – 14, 18, 20
Lesson 46—Aim: How do we calculate the volumes of solids? (2 days)
HW #46: Must copy these questions onto loose-leaf paper.
Solve the following in two different ways.
Using the formula d  ( y 2  y1 ) 2  ( x2  x1 ) 2
On graph paper. Construct right triangles.
2) The coordinates of point R are (–3,2) and
1) The coordinates of point R are (–3,2) and the the coordinates of point T are (4, 1). What is
coordinates of point T are (4, 1). What is the length
the length of RT ?
of RT ?
3) The endpoints of PQ are P(-3,1) and Q(4,25).
Find the length of PQ.
4) The endpoints of PQ are P(-3,1) and
Q(4,25). Find the length of PQ.
5) If the measures of the angles of a triangle are represented by 2x, 3x  15, and 7 x  15, the triangle is
(1) an isosceles triangle
(2) a right triangle
(3) an acute triangle (4)an equiangular triangle
6) Which diagram represents the figure with the greatest volume?
7) The volume of a cylinder is 12,566.4 cm3. The height of the cylinder is 8 cm. Find the radius of the
cylinder to the nearest tenth of a centimeter.
HW #47: P798 – 799: 3 – 5, 25 – 27
P823 – 824: 7 – 12, 21, 22
Lesson 48—Regents questions on solids (doubles as test review)
HW #48: Complete worksheets (and review for test)
Unit 11 (Ch. 11+12) Uniform Unit Test
Common Core Standards Addressed
G-SRT.9 (+) Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary
line from a vertex perpendicular to the opposite side.
G-GMD.1
Give an informal argument for the formulas for the circumference of a circle, area of a
circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s
principle, and informal limit arguments.
G-GMD.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
G-GMD.4
Identify the shapes of two-dimensional cross-sections of three-dimensional objects,
and identify three-dimensional objects generated by rotations of two-dimensional
objects.
G-MG.2
Apply concepts of density based on area and volume in modeling situations (e.g.,
persons per square mile, BTUs per cubic foot).
G-MG.3
Apply geometric methods to solve design problems (e.g., designing an object or
structure to satisfy physical constraints or minimize cost; working with typographic
grid systems based on ratios)._
Methods of Differentiated Instructions
Revolution K-12, a student-driven online learning platform, is used to differentiate instruction for all
students in class and subject areas.
All students are held to the Common Core-aligned standards. Teacher performs formative assessments
through lessons to check student understanding, including cold-calling, student board work, and exit
tickets. Teacher circulates room to perform further formative assessments and to guide small groups and
individuals.
Lower-performing students are grouped heterogeneously with higher-performing students using
assessment data, interests, and work habits, to encourage student-to-student engagement and learning.
They are also provided guided notes and graphic organizers to build schemas.
English Language Learners are paired with students who are fluent in English, and given extra time.
Vocabulary is pronounced several times and accompanied by alternative words or phrases that are
simplified. Visual aids, including pictures, Smart boards, and manipulatives, help students make clear
connections to the text.
Students with Special Needs are grouped with helpers and given instructions or assessments with
simplified language or extra time. Color-coding on the Smart board help illustrate steps required to solve
a problem. Hands-on activities are provided to help construct student learning.
Gifted/Honor students are given challenge problems during lessons, homework, and summative
assessments, which earn extra credits. They are expected to complete the whole worksheet, and are
given challenge (e.g. open-ended) problems that develop higher-level thinking.