Geometry At a Glance Approximate Beginning Date Test … · ... 1.2 M: graph paper L: Plot points...

Geometry Curriculum Guide

Geometry – At a Glance

Approximate Beginning Date – Test Date Chapters to Cover and 9 Weeks calendar dates

1st 9 Weeks August 19th – October 16th

August 19th – September 3rd Ch 1: Essentials of Geometry

September 4th – September 21st Ch 2: Reasoning and Proof

September 21st – October 1st Ch 3: Parallel and Perpendicular Lines

October 2nd – October 20th (2 pays in to 2nd 9 weeks) Ch 4: Congruent Triangles

2nd 9 Weeks October 19th – December 4th

October 21st – November 4th Ch 5: Relationships within Triangles

November 5th – November 13th Ch 6: Similarity

November 16th – December 4th Ch 7: Right Triangles and Trigonometry

December 7th, begin review for Fall Exam, Semester ends on December 18th

3rd 9 Weeks January 1st – March 11th

January 5th – January 25th Ch 8: Quadrilaterals

January 26th – February 24th Ch 9: Properties of Transformations

February 25th – March 10th Ch 10: Properties of Circles

March 11th – Pi Day

4th 9 Weeks March 21st – Mary 31st

The beginning of the 4th 9 weeks will be used as time to complete concepts if we get behind in the other 9 weeks.

March 21st – April 8th Ch 11: Measuring Length and Area

April 11th – April 29th Ch 12: Surface Area and Volume of Solids

After chapter 12, use the remainder of the year for review for the final, SAT practice, and activities.

In Geometry, students will develop reasoning and problem solving skills as they study topics such as congruence and similarity, and

apply properties of lines, triangles, quadrilaterals, and circles. Students will also develop problem solving skills by using length, perimeter,


area, circumference, surface area, and volume to solve real-world problems.

Included in the following information are the key concepts students will learn throughout this course and the resources, materials, and

activities that will enhance this learning experience. The concepts for this course also include information that students will be tested over on

standardized tests, such as the SAT and the ITBS. Also included is an assessment stem for both low, medium, and high level questions. To

show complete mastery, a student would be able to answer all three levels of questioning.

Ongoing

Concepts Unit and Standard Key Understanding Resources, Materials,

and Activities

Assessment Stem

N-Q 1: Use units as a way to

understand problems and to guide

the solution of multi-step problems;

choose and interpret units

consistently in formulas; choose

and interpret the scale and the

origin in graphs and data displays.

-use units to aid in

solving word problems

and in creating and

reading graphs/data

displays

-convert units when

appropriate

R: Geometry textbook L: using units in solutions when

conversions are not necessary

M/H: use conversions in order to

determine a solution and understand

when units are squared (area) or

cubed (volume)

N-Q 2: Define appropriate

quantities for the purpose of

descriptive modeling.

-solve various real-

world word problems

R: Geometry textbook L/M/H: be able to solve many kinds

of word problems at various levels

N-Q 3: Choose a level of accuracy

appropriate to limitations on

measurement when reporting

quantities.

-determine the accuracy

and unit necessary

when answering word

problems

R: Geometry textbook L/M/H: understand the importance of

units and rounding in solutions

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)

-solve various real-

world word problems

R: Geometry textbook L/M/H: be able to solve many kinds

of word problems at various levels

G-MG 3: Apply geometric methods

to solve design problems (ex:

designing an object or structure to

satisfy physical constraints or

minimize cost; working with

typographic grid systems based on

ratios).

-apply the properties of

geometric figures to

solve word problems

R: Geometry textbook L: applying basic geometric figures

(lines, points)

M: apply 2d polygons

H: apply 3d figures


1st 9

Weeks Unit 1: Essentials of Geometry Key Understanding Resources, Materials,

and Activities

Assessment Stem

Wed, Aug

19

1st day of school: class structure and

calculator check out

M: class structure page,

calculator check out sheet

Wed, Aug

19

G-CO 1: Know precise definitions

of angle, circle, perpendicular line,

parallel line, and line segment,

based on the undefined notions of

point, line, distance along a line,

and distance around a circular arc.

-how/why geometry

was developed

-historical figures: the

Greeks, Euclid

-define point, line, and

plane (undefined terms)

-identify and name

figures: points, lines,

planes, segments, rays,

opposite rays

-identify intersections

-sketch intersections

R: Internet sources:

enotes.com, about.com

R: Geometry textbook

chapter 1.1, Painless

Geometry,

www.classzone.com

PowerPoint

A: identify points, lines,

planes and their

intersections in the

classroom

L: Name the points, lines, planes, etc.

given the figure.

M: Given the figure, is there more

than one way to name the lines,

planes, etc.?

H: Tell if the following situation is

possible, if so, make a sketch: Three

planes intersect in one line.

Thurs,

Aug 20







-use graphing to

represent points, lines,

etc., “algebra review”

from pg. 7

-understand measurable

versus non-measurable

figures

-”postulates”:

postulates vs. theorems,

Ruler Postulate,

Segment Addition

Postulate

-”congruent”

-introduce String Art

project


chapter 1.1, 1.2

M: graph paper

L: Plot points to create a segment.

M: Plot points to create a segment.

Find the length and midpoint of the

segment. Explain why a segment is

measurable, but a line or ray is non-

measurable.

H: Plot points to create a line or ray.

Extend the line or ray so that it

maintains proper slope.

Fri, Aug Project shows the tangible String Art Project: A: String Art Project

http://www.classzone.com/


21 relationship between points, lines,

and planes and how they are used to

construct 3d shapes and objects

choose patterns and

string, begin project in

class, project due on

Monday Aug 24

M: back boards, nails,

string, patterns,

Mon, Aug

24

This section defines bisectors in

order to:

G-CO 9: Prove theorems about

lines and angles. Theorems include:

vertical angles are congruent; when

a transversal crosses parallel lines,

alternate interior angles are

congruent and corresponding angles

are congruent; points on a

perpendicular bisector of a line

segment are exactly those

equidistant from the segment's

endpoints.

-define: midpoint,

bisector

-understand there is

only one midpoint, but

many kinds of bisectors

-finding segment

lengths using bisectors

-Midpoint Formula

-Distance Formula


chapter 1.3

L: Use the formula to find the

midpoint of a segment given the

endpoints./ Measure the length of a

segment.

M:Given one endpoint and the

midpoint, find the other endpoint./

Use the Segment Addition Postulate

to find the length of a segment.

H: Use the midpoint formula and the

segment addition postulate to

determine lengths of several collinear

segments using variables and

algebraic equations.

Tues,

Aug 25







-parts of an angle

-naming angles

-measuring angles,

using a protractor

-classifying angles

-red square to mark

right angles

-Angle Addition

Postulate

-angle bisectors,

congruent angles


chapter 1.4

M: protractors

L: Given the angle measure, state

whether the angle is acute, right, or

obtuse.

M: Use the protractor to measure the

angle, state whether the angle is acute,

right or obtuse, and correctly name

the angle.

H: Use the angle addition postulate to

find angle measures using algebraic

equations.

Wed, Aug

26

G-CO 12: Make formal geometric

constructions with a variety of tools

and methods (compass and

straightedge, string, reflective

devices, paper folding, dynamic

-construct segments and

angles

R: Geometry textbook pg.

33-34

M: protractor, compass

L/M/H: use a compass and ruler to

copy and bisect segments and angles


geometric software, etc.). Copying

a segment; copying an angle;

bisecting a segment; bisecting an

angle; constructing perpendicular

lines, including the perpendicular

bisector of a line segment; and

constructing a line parallel to a

given line through a point not on

the line.

Thurs,

Aug 27

This section defines types of angles

in order to:











endpoints.

-identify and apply

types of angles:

complementary,

supplementary,

adjacent, vertical, and

linear pair

-interpreting from a

diagram, what you can

and cannot conclude


chapter 1.5

L: identify types of angles

M: For all types of angles, when given

one measure find the measure of

another

H: use equations to find angle

measures

Fri, Aug

28

This section classifies polygons in

order to:





cylinder)

-define polygon, parts

of a polygon

-convex vs concave

polygons

-classify polygons

-define equilateral,

equiangular, and regular

-find side lengths in

regular polygons

Geometry textbook

chapter 1.6

L: classify polygons

M: identify convex vs concave

H: use equations to find side lengths

Mon, Aug

31

G-GPE 7: Use coordinates to

compute perimeters of polygons

and areas of triangles and

-find perimeter,

circumference, and area

of squares, rectangles,

Geometry textbook

chapter 1.7

L: find area and perimeter of all

polygons when given measurements

M: find appropriate lengths to find


rectangles, e.g., using the distance

formula

triangles, and circles;

this does NOT include

composite polygons

-solving multi-step

problems

-finding unknown

lengths, solving for a

variable in a formula

area and perimeter of all polygons

H: use distance formula to find area

and perimeter

Review on Tues, Sept 1 and Wed,

Sept 2

Test on Thurs, Sept 3

1st 9

Weeks Unit 2: Reasoning and Proof Key Understanding Resources, Materials,

and Activities

Assessment Stem

Fri, Sept

4

Inductive reasoning will prepare

students for proofs, such as those

given in G-CO 6, 7, and 8.

-define inductive

reasoning

-visual patterns

-number patterns

-Fibonacci Sequence

-make and test

conjectures

-finding

counterexamples


chapter 2.1

L: Given the description of a pattern

write/sketch the next figure or

number.

M: Describe the pattern and

write/sketch the next figure or

number.

H: Make and test a conjecture relating

to a group of numbers, and explain

your results. Ex: Make and test a

conjecture about the product of any

two odd numbers.

Tues,

Sept 8

-Fibonacci Sequence:

its history and

importance, and how it

applies in nature

R: United Streaming

video: Patterns,

Symmetry and Beauty

L: Given the description of the

Fibonacci Sequence, give the next

number. List examples of where it

appears in nature.

M: Describe the pattern of the

Fibonacci Sequence and give the next

number. Retell the history of its

creation and where it appears in

nature.


H: Explain the creation of the

Fibonacci Sequence from the view of

Fibonacci during the period. How did

affect their understanding of the

world? Apply this idea to

Theology/Creation.

Wed,

Sept 9







-analyze conditional

statements and identify

the hypothesis and

conclusion

-negation of statements

-write the converse,

inverse, and

contrapositive

-”good” definitions,

perpendicular lines

-biconditional

statements


chapter 2.2

L: Identify the hypothesis and

conclusion in a conditional statement.

M: Rewrite a conditional statement in

if-then form. Determine if the

conditional statement and its negation

are true of false. Write the converse,

inverse, and contrapositive of the

conditional statement.

H: Using a conditional statement and

its converse, determine if a definition

is a 'good' definition.

Thurs,

Sept 10

Deductive reasoning will prepare

students for proofs, such as those


-define deductive

reasoning

-Law of Detachment

-Law of Syllogism

-identify whether

inductive or deductive

reasoning is used

-reasoning from a graph


chapter 2.3

L: Make a valid conclusion given a

situation. Ex: Mary goes to the

movies every Friday and Saturday.

Today is Friday. What is the

conclusion?

M: Given true statements, write a new

conditional statement.

H: Understand the difference between

inductive and deductive reasoning.

Use inductive and deductive

reasoning to show a conjecture is true.

Fri, Sept

11

During class students will be able to interact with a variety of

logic puzzles including: Enigmathics, traditional logic

puzzles, Magnatiles, toothpick puzzles, 3d puzzles,

pentominoes

A: logic puzzles

Mon, Interpreting diagrams will prepare -review of Postulates 1- R: Geometry textbook L: Identify postulates from a diagram.


Sept 14 students for proofs, such as those


11

-identify postulates

from a diagram

-use information to

sketch a diagram

-what can and cannot be

assumed from a

diagram, interpreting 3d

diagrams

chapter 2.4 M: Use a diagram to determine if

statements are true or false.

H Use a diagram to write example

statements of postulates.

Tues,

Sept 15

A-REI 1: Explain each step in

solving a simple equation as

following from the equality of

numbers asserted at the previous

step, starting from the assumption

that the original equation has a

solution. Construct a viable

argument to justify a solution

method.

-algebraic properties of

equality, including

distributive properties

-apply the algebraic

properties to steps of

solving an equation

-Reflexive, Symmetric,

and Transitive

Properties

-writing two-column

proofs when solving

equations


chapter 2.5

L/M: Complete a two-column proof,

to prove an algebraic expression.

H: Complete a two-column proof,

using algebraic expressions in a

geometric figure. Ex: Algebraic

expressions for angle measures 7x+22

and 4x-8 and the sum of the angles is

124. Prove the value of x.

Wed,

Sept 16











endpoints.

-Reflexive, Symmetric,

and Transitive

properties applied to

segments and angles

-write two-column

proofs involving

segments and angles


chapter 2.6

L: Complete a fill-in-the blank two-

column proof.

M: Complete a matching two-column

proof.

H: Write a two-column proof.

Thurs,

Sept 17



-Right Angles

Congruence Theorem


chapter 2.7

L: Complete a fill-in-the blank two-

column proof.










endpoints.

-Congruent

Complements Theorem

-Congruent

Supplements Theorem

-Linear Pair Postulate

-Vertical Angles

Congruence Theorem

-use these theorems and

postulates to find angle

measures and prove

they are correct

M: Complete a matching two-column

proof.

H: Write a two-column proof.

Assign Ch 2 take home test on Fri,

Sept 18, test due on Mon, Sept 21

1st 9

Weeks Unit 3: Parallel and

Perpendicular Lines

Key Understanding Resources, Materials,

and Activities

Assessment Stem

Mon,

Sept 21







-identify parallel lines,

skew lines, and parallel

planes in 3d figures

-Parallel and

Perpendicular

Postulates

-angles formed by

transversals


chapter 3.1

L/M/H: Identify pairs of angles

formed by a transversal. Identify

parallel lines, skew lines, and parallel

planes in 3d figures

Tues,

Sept 22-

Wed,

Sept 23










-find angle measures

given parallel lines and

a transversal

-complete simple proofs

involving parallel lines

and transversals


chapter 3.2, 3.3

L: Find angle measures involving

parallel lines and transversals.

M/H: Complete proofs involving

parallel lines and transversals.



endpoints.

Thurs,

Sept 24

G-GPE 5: Prove the slope criteria

for parallel and perpendicular lines

and use them to solve geometric

problems (e.g., find the equation of

a line parallel or perpendicular to a

given line that passes through a

given point).

-what is slope?

-slope formula and

rise/run

-identify negative,

positive, zero, and

undefined slope

-find the slopes of lines

-slopes of parallel and

perpendicular lines

-draw a line

perpendicular to

another line


chapter 3.4

L: Identify lines as having positive

slope, negative slope, no slope, or

undefined slope.

M: Find the slope of a line given two

points or the line on a graph.

H: Given the slope and one

coordinate, find the missing

coordinate.

Fri, Sept

25

G-GPE 5: Prove the slope criteria

for parallel and perpendicular lines

and use them to solve geometric

problems (ex: find the equation of a

line parallel or perpendicular to a

given line that passes through a

given point).

A-CED 2: Create equations in two

or more variables to represent

relationships between quantities;

graph equations on coordinate axes

with labels and scales.

A-REI 10: Understand that the

graph of an equation in two

variables is the set of all its

solutions plotted in the coordinate

plane, often forming a curve (which

could be a line).

-slope-intercept form

-write equations of lines

from a graph, and for

parallel and

perpendicular lines

-standard form

-graphing lines in

standard form

-for 3.6, go over

theorems about

perpendicular lines

-do some of the 3.6

exercises together


chapter 3.5, 3.6

L: Write the equation of a line and

graph the line.

M: Show lines are parallel or

perpendicular by using slope.

H: Graph two perpendicular lines.

Understand perpendicular lines can be

used to form a right triangle.


Assign Review on Mon, Sept 28

Go over review on Tues, Sept 29

Test on Wed, Sept 30

Thurs,

Oct 1

G-CO 12: Make formal geometric

constructions with a variety of tools

and methods (compass and

straightedge, string, reflective

devices, paper folding, dynamic

geometric software, etc.). Copying

a segment; copying an angle;

bisecting a segment; bisecting an

angle; constructing perpendicular

lines, including the perpendicular

bisector of a line segment; and

constructing a line parallel to a

given line through a point not on

the line.

-construct parallel lines

-Plato and his

contributions to

constructions


chapter 3 (pg. 152)

M: ruler, compass

R: internet source:

http://en.wikipedia.org/wi

ki/History_of_geometry#

Plato

L/M/H: use a compass and ruler to

create parallel lines

1st 9

Weeks Unit 4: Congruent Triangles Key Understanding Resources, Materials,

and Activities

Assessment Stem

Fri, Oct 2 G-CO 10: Prove theorems about

triangles. Theorems include:

measures of interior angles of a

triangle sum to 180 degrees; base

angles of isosceles triangles are

congruent; the segment joining

midpoints of two sides of a triangle

is parallel to the third side and half

the length; the medians of a triangle

meet at a point.

-classify triangles by

angles and sides

-interior and exterior

angles of triangles

-finding angle measures

-corollary to the

triangle sum theorem


chapter 4.1

L: What is the sum of the angles of a

triangle?

M: When given two angle measures

of a triangle, find the measure of the

third angle.

H: Given algebraic equations for

angle measures in a triangle, find the

measure of each angle.

Mon, Oct

5

G-SRT 5: Use congruence and

similarity criteria for triangles to

solve problems and to prove

relationships in geometric figures.

-what are congruent

figures?

-writing a congruence

statement


chapter 4.2

L: Determine if triangles are

congruent when given all

measurements.

M/H: Determine if triangles are


-identify corresponding

parts

-third angle theorem

-congruent parts of

congruent triangles

-CPCTC

congruent when not given all

measurements

Tues, Oct

6

This activity will lead to proving

congruence by SSS.





-investigate triangles

and quadrilaterals to

determine how much

information is needed

to show figures are

congruent. Do the

Explore 1 and 2

together, Draw

Conclusions with a

partner.


233

A: Investigate Congruent

Figures using SSS

M: straws

L/M/H: Determine how much

information is needed to tell whether

two figures are congruent.

Wed, Oct

7





-SSS postulate

-determine if triangles

are congruent by SSS

-using the distance

formula for SSS

-write congruence

statements

-stability of a triangle

-watch short video over

triangles and bridges

-assign spaghetti bridge

project


chapter 4.3

R: short video over

triangles and bridges

A: Spaghetti Bridge

M: spaghetti, glue,

project instructions

L: Determine if figures are stable.

Determine if triangles are congruent

by SSS

M: Write congruence statements for

congruent triangles.

H: Use the distance formula to show

triangles are congruent.

Thurs,

Oct 8





-included angles

-SAS postulate

-define leg and

hypotenuse in right


chapter 4.4

L: Identify the included angle.

M: Determine if triangles are

congruent by SAS or HL.

H: Complete proofs involving SAS or


triangles

-HL theorem


are congruent by SAS

or HL

HL.

Fri, Oct 9 G-SRT 5: Use congruence and




-ASA postulate and

AAS theorem

-define paragraph and

flow proofs (don't

necessarily do any, but

make sure they know

there are other kinds of

proofs)

-review of triangle

congruence postulates

and theorems, pg. 252


are congruent by SSS,

SAS, HL, ASA, or AAS


chapter 4.5

L: Determine how triangles are

congruent.

M: Use distance formula, slope

formula, and angle measurements to

show triangles congruent. (Pg. 253

#21)

H: Complete proofs involving triangle

congruence.

This section can be skipped. If it is

not skipped, apply G-SRT 5.

This section is a review

of the previous sections.

If the previous sections

are covered well, this

section can be skipped.


chapter 4.6

Mon, Oct

12




triangle sum to 180; base angles of

isosceles triangles are congruent;

the segment joining midpoints of

two sides of a triangle is parallel to

the third side and half the length;

the medians of a triangle meet at a

point.

-parts of an isosceles

triangle

-base angles theorem

and its converse

-corollary to the base

angles theorem and its

converse

-applying side lengths

and angle measures to

isosceles and equilateral

4.7 L: Find angle measures and side

lengths; no equations.

M/H: Find angle measures and side

lengths using equations.


triangles

Test over 4.1-4.7:

Assign review on Tues, Oct 13

Go over review on Wed, Oct 14

Test on Thurs, Oct 15 (2nd 9 weeks grade)

Fri, Oct

16

G-CO 2: Represent transformations

in the plane using, e.g.,

transparencies and geometry

software; describe transformations

as functions that take points in the

plane as inputs and give other

points as outputs. Compare

transformations that preserve

distance and angle to those that do

not (e.g., translation versus

horizontal stretch)

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.

G-CO 6: Use geometric

descriptions of rigid motions to

-transformations, image

vs pre-image

-congruence

transformations

-translate figures

-reflect figures over x

and y axis

-identify rotations


chapter 4.8

L: identify the type of transformation

M: use rules to perform

transformations

H: when given a transformation,

write a rule


transform figures and to predict the

effect of a given rigid motion on a

given figure; given two figures, use

the definition of congruence in

terms of rigid motions to decide if

they are congruent.

G-CO 7: Use the definition of

congruence in terms of rigid

motions to show that two triangles

are congruent if and only if

corresponding pairs of sides and

corresponding pairs of angles are

congruent.

G-CO 8: Explain how the criteria

for triangle congruence (ASA, SAS,

and SSS) follow from the definition

of congruence in terms of rigid

motions

Mon, Oct

19

Go over 4.8 hw, for quiz tomorrow

Break Spaghetti Bridges

test grade for 2nd 9 weeks

Tues, Oct

20

Quiz over 4.8

Finish breaking any bridges

2nd 9

Weeks Unit 5: Relationships within

Triangles


and Activities

Assessment Stem




triangle sum to 180 degrees; base

angles of isosceles triangles are

congruent; the segment joining

-define midsegment

-Midsegment theorem

-placing figures in a

coordinate plane

-variable coordinates


chapter 5.1

L: Define midsegment.

M: Find the length of the midsegment

of a triangle.

H: Find the midsegment of a triangle

on a coordinate grid.


midpoints of two sides of a triangle

is parallel to the third side and half

the length; the medians of a triangle

meet at a point.











endpoints.

-perpendicular bisectors

-applying the

perpendicular bisector

theorem and its

converse

-define concurrent

-point of concurrency,

circumcenter

-locations of

circumcenters in

various types of

triangles


chapter 5.2

L: Find side lengths using

perpendicular bisectors; simple

equations.

M: Find side lengths using

perpendicular bisectors; complex

equations.

H: Use a ruler to find the circumcenter

of a triangle.

*there is no common core standard

to match this concept

-define angle bisector

-angle bisector theorem

and its converse

-applying the angle

bisector theorem


incenter


chapter 5.3

L: Finding angle measures with angle

bisectors.

M/H: Solving word problems.

*there is no specific common core

standard to match this concept, but

understanding altitudes helps when

finding the area of a triangle:





formula.

-define median


centroid

-applying the centroid

to triangles

-applying the centroid

to graphs and

coordinates

-altitudes of a triangle


orthocenter


chapter 5.4

L: Find measurements of centroids

and side lengths in triangles.

M: Find centroids using coordinates

of a triangle.

H: Differentiate between

perpendicular bisectors, angle

bisectors, medians, and altitudes when

given a figure.


-application to isosceles

triangles







-Triangle Inequality

theorem

- use inequalities in a

triangle (PSAT)

- understand how angle

measures relate to side

lengths (PSAT)

-hinge theorem, use

logic to determine how

changing one angle

effects another


chapter 5.5, 5.6

L: Understand that not all lengths will

form a triangle.

M/ H: Determine if given lengths will

form a triangle.

Find a comprehensive activity for

this chapter – no test

2nd 9

Weeks Unit 6: Similarity Key Understanding Resources, Materials,

and Activities

Assessment Stem

G-GPE 6: Find the point on a

directed line segment between two

given points that partitions the

segment in a given ratio.

-what are ratios? relate

to fractions

-simplify ratios with

like units and using

conversions

-write ratios to compare

lengths

-use ratios to find a

dimension

-extended ratios

-what is a proportion?

-solve proportions

-geometric mean, as a

specific type of

proportion


chapter 6.1

M: conversion list

L: Write and simplify a ratio. Solve a

proportion.

M: Use extended ratios to find angle

measures in a triangle. Solve a

proportion with algebraic equations as

factors using the distributive property

and the foil method.

H: Given the perimeter of a rectangle

and the length to width ratio, find the

length and width.


The concept of scale leads to

understanding similarity.




relationships in geometric figures

-properties of

proportions

-use the properties of

proportions to find side

lengths in figures

-what is scale and scale

drawings?

-scale drawings, maps


chapter 6.2

L: Find side lengths in figures.

M/H: Use scale and scale factors to

solve word problems.

Map Activity, Blueprint Activity





-define similar,

corresponding sides and

angles

-similarity statements

-scale factor

-finding side lengths in

similar figures

-perimeters in similar

figures

-corresponding lengths

in similar polygons


chapter 6.3

L: Determine if figures are similar.

M: Find lengths and perimeters in

similar figures.

H: Use scale factors to find other

lengths in figures.

Scale Activity

G-SRT 3: Use the properties of

similarity transformations to

establish the AA criterion for two

triangles to be similar.

-Angles and Similar

Triangles activity, pg.

381

-AA postulate

-apply the AA postulate

-indirect measurement


chapter 6.4

A: Angles and Similar

Triangles, pg. 381

M: protractors, rulers

L: Determine if triangles are similar

by AA.

M: Find side lengths in similar

triangles.

H: Determine triangle similarity with

coordinates.





-use the SSS and SAS

similarity theorems

-choosing a similarity

method, AA, SAS, or

SSS


chapter 6.5

L: Determine if triangles are similar

by SAS, SSS, or AA.

M/H: Find the scale factor and side

lengths in similar triangles.


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.

-Proportionality

Theorem and its

converse

-use the proportionality

theorem to find the

length of a segment


chapter 6.6

L/M/H: Find segment lengths using

the proportionality theorem.

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.

-define dilation, center

of dilation, and scale

factor of a dilation

-reduction vs.

enlargement

-draw dilations

-show that figures from

dilations are similar

-finding scale factor


chapter 6.7

L: Draw dilations.

M: Find the scale factor.

H: Determine side lengths of a

dilation.

Assign review on

Go over review on

Test on

*maybe do a project test for this

chapter instead


2nd 9

Weeks Unit 7: Right Triangles and

Trigonometry


and Activities

Assessment Stem

Understanding the Pythagorean

Theorem leads to:

G-SRT 8: Use trigonometric ratios

and the Pythagorean Theorem to

solve right triangles in applied

problems.

-apply Pythagorean

Theorem to find a

missing length

-understand the

Pythagorean Theorem

is derived from the

distance formula

-use Pythagorean

Theorem to find the

area of an isosceles

triangle

-use Pythagorean

Triples to find a

missing length

-history of Pythagoras


chapter 7.1

R: Internet info on

Pythagoras

L: Apply the Pythagorean Theorem to

find a missing length.

M: Find the area of an isosceles

triangle.

H: Use the distance formula and the

Pythagorean Theorem to prove/solve

a right triangle on a coordinate graph

-Pythagoras and his

contribution to

mathematics

R: United Streaming

video: Culture and Math,

Ancient Greeks

L: Name the person who contributed

to the Pythagorean Theorem.

M: Explain how the Pythagorean

Theorem would have been used

during the time of Pythagoras

H: Explain how mathematicians, like

Pythagoras, contributed to their

society and culture. How do you think

they were viewed by others?

*There is no common core standard

for this concept

-converse of the

Pythagorean Theorem

-verify right triangles

-classify triangles as

right, acute, or obtuse


chapter 7.2

L: Determine if triangles are right

triangles.

M: Determine if triangles are right,

acute, or obtuse.

H: Use coordinates for triangles to

classify using the distance formula.


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.

-identifying similar

triangles with the

altitude drawn

-using similarity and

proportions to find

lengths

-geometric mean

theorems


chapter 7.3

L: Write a ratio comparing lengths in

similar triangles.

M: Use proportions to find a missing

length or show triangles are similar.

Find the geometric mean given two

numbers.

H: Apply the geometric mean

theorems to triangles.

G-SRT 6: Understand that by

similarity, side ratios in right

triangles are properties of the angles

in the triangles, leading to

definitions of trigonometric ratios

for acute angles.

-apply the 45-45-90

triangle theorem

-working with square

roots

-apply the 30-60-90

triangle theorem


chapter 7.4, Painless

Geometry

L: Explain why some triangles are

called special right triangles.

M: Find a missing length in a special

right triangle.

H: Given a special right triangle on a

coordinate graph, be able to locate the

coordinate of a vertex.

This concept leads to:

G-SRT 8: Use trigonometric ratios



problems.

-define trigonometric

ratio

-write tangent ratios

-use tangent to find side

lengths

-combine tangent with

special right triangles


chapter 7.5

L: Write tangent ratios.

M: Find side lengths using tangent.

H: Use tangent to find the area of a

triangle.

G-SRT 7: Explain and use the

relationship between the sine and

cosine of complementary angles.

-define sine and cosine

ratios

-write sine and cosine

ratios

-use sine and cosine to

find side lengths

-angles of elevation and

depression

-combine sine and

cosine with special

right triangles


chapter 7.6

L: Write sine and cosine ratios.

M: Find side lengths using sine or

cosine.

H: Use sine and cosine to find

perimeter or area of a figure.

G-SRT 8: Use trigonometric ratios -using inverse R: Geometry textbook L: Write inverse ratios.




problems.

trigonometric ratios to

find angle measures

-solving right triangles

chapter 7.7 M/H: Solve right triangles.

Review on

Test on

Begin Semester Review on

go over review on

3rd 9

Weeks Unit 8: Quadrilaterals Key Understanding Resources, Materials,

and Activities

Assessment Stem






cylinder)

-use patterns to

determine the sum of

interior angles of a

polygon

A: Investigate Angle

Sums in Polygons, pg.

506

M: straightedge






cylinder)

-how to name polygons

-interior angles of

polygons

-interior angles of

quadrilaterals

-find the sum of interior

angles

-find the number of

sides of a polygon

-find an unknown angle

measure

-exterior angles

theorem


chapter 8.1

L: Find the sum of the interior angles

of a polygon.

M: Solve equations using the interior

and exterior angles of polygons.

H: Find the number of sides when

given the sum of the interior angles.


parallelograms. Theorems include:

opposite sides are congruent,

opposite angles are congruent, the

-define parallelogram

-properties of

parallelograms

-use the properties of


chapter 8.2, 8.3

M: quadrilateral

L/M/H: Use the properties of

parallelograms to find side lengths

and angle measures.


diagonals of a parallelogram bisect

each other, and conversely,

rectangles are parallelograms with

congruent diagonals.

parallelograms

-show that a

quadrilateral is a

parallelogram

properties chart

A: begin a Venn diagram

for quadrilaterals

G-GPE 4: Use coordinates to prove

simple geometric theorems

algebraically. For example, prove or

disprove that a figure defined by

four given points in the coordinate

plane is a rectangle; prove or

disprove that the point (1, √3) lies

on the circle centered at the origin

and containing the point (0, 2).

-properties of

rhombuses, rectangles,

and squares


chapter 8.4

M: quadrilateral

properties chart

A: Venn diagram

for quadrilaterals


rhombuses, rectangles, and squares to

find side lengths and angle measures.










-properties of

trapezoids and isosceles

trapezoids

-midsegments of

trapezoids

-properties of kites


chapter 8.5

M: quadrilateral

properties chart

A: Venn diagram

for quadrilaterals


trapezoids and kites to find side

lengths and angle measures.





cylinder)

-identify quadrilaterals

given various properties


chapter 8.6

M: quadrilateral

properties chart,

properties chart for

homework

A: Venn diagram

for quadrilaterals

L/M/H: Identify polygons based on

properties, such as angle measures

and side lengths given.

Assign review on

Go over review on


Test on

Create 3d drawings -create orthographic

and isometric drawings


550-551

M: graph paper, isometric

dot paper

3rd 9

Weeks Unit 9: Properties of

Transformations


and Activities

Assessment Stem

N-VM 1: Recognize vector

quantities as having both magnitude

and direction. Represent vector

quantities by directed line

segments, and use appropriate

symbols for vectors and their

magnitudes (e.g., v, |v|, ||v||, v).











horizontal stretch)






-review

transformations, image

vs. pre-image

-prime notation

-translate figures

-define isometry

(congruence

transformation)

-write a translation rule

-define vectors, and

parts of vectors,

component form

-identify vector

components

-use vectors to translate

figures


chapter 9.1

L: Translate a figure.

M: Write the rule for a translation.

H: Use translations and vectors to

solve word problems, and solve for

side lengths and angle measures.

















they are congruent.







congruent.

G-CO 8: Explain how the criteria

for triangle congruence (ASA, SAS,

and SSS) follow from the definition

of congruence in terms of rigid

motions

N-VM 6: Use matrices to represent

and manipulate data, e.g., to

represent payoffs or incidence

relationships in a network

-define matrix and

dimensions

-represent figures using

matrices


chapter 9.2


N-VM 8: Add, Subtract, and

multiply matrices of appropriate

dimensions

N-VM 12: Work with 2x2 matrices

as transformations of the plane, and

interpret the absolute value of the

determinant in terms of area.











horizontal stretch)













-adding and subtracting

matrices

-represent translations

using matrices

-multiplying matrices

(this will be applied to

reflections in the next

section)





they are congruent.







congruent.

G-CO 3: Given a rectangle,

parallelogram, trapezoid, or regular

polygon, describe the rotations and

reflections that carry it onto itself.

















-define line or

reflection

-graph reflections in

horizontal and vertical

lines

-graph reflections in

y=x and -x

-reflection rules

-do a double reflection

example

-reflections with

matrices


chapter 9.3

L: Graph reflections in the x and y

axis.

M: Graph reflections in y=x and y=-x

H: Graph reflections using matrices.






they are congruent.







congruent.

N-VM 10: Understand that the zero

and identity matrices play a role in

matrix addition and multiplication

similar to the role of 0 and 1 in the

real numbers. The determinant of a

square matrix is nonzero if and only

if the matrix has a multiplicative

inverse.












-review definitions

rotation, center of

rotation, and angle of

rotation

-draw a rotation with a

protractor

-rules for rotations

-rotate a figure using

the rules

-rotation rules using

matrices


chapter 9.4

M: protractors

L: Rotate using the rules.

M/H: Rotate using a protractor.















they are congruent.







congruent.












-define composition of

transformations

-define glide reflection

-find the image of a

glide reflection

-perform various types

of composition of

transformations


chapter 9.5

L: Perform a composition of

transformations.

M/H: Describe, write a rule for, a

composition of transformations.










they are congruent.







congruent.

Work on Tessellation project on

Project due on

-use tessellations as a

way to perform a

composition of

transformations

R: Geometry textbook pg

616-618

M: instructions packet






-define line symmetry

and line of symmetry

-identify lines of

symmetry (ex: circles)

-define rotational

symmetry and center of

symmetry

-identify rotational

symmetry


chapter 9.6

L: Be able to identify line symmetry.

M/H: Be able to identify line and

rotational symmetry.

N-VM 7: Multiply matrices by

scalars to produce new matrices,

e.g., as when all of the payoffs in a

-review definition of

dilation, reduction, and

enlargement


chapter 9.7

L: Perform dilations

M: Determine the scale factor of

dilations.


game are doubled.

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.

-identify dilations

-draw dilations

-scalar multiplication

-apply scalar

multiplication to

dilations

H: Perform a composition of

transformations that includes

dilations.

Assign review on

Go over review on

Test on

3rd 9

Weeks Unit 10: Properties of Circles Key Understanding Resources, Materials,

and Activities

Assessment Stem







G-C 1: Prove that all circles are

similar.

G-C 2: Identify and describe

relationships among inscribed

angles, radii, and chords. Include

the relationship between central,

inscribed, and circumscribed

angles; inscribed angles on a

-define and identify

parts of a circle

-radius and diameter

relationship

-coplanar circles

-common tangents

-verify a tangent to a

circle

-find the radius of a

circle

-property of tangents

with a common external

point


chapter 10.1

M: circle notes

L: Identify parts of a circle.

M/H: Use equations to find lengths of

tangents.


diameter are right angles; the radius

of a circle is perpendicular to the

tangent where the radius intersects

the circle.










the circle.

-define central angle,

minor arc, major arc,

and semicircle

-naming arcs

-measures of arcs

-Arc Addition postulate

-congruent circles and

congruent arcs


chapter 10.2

L: Identify arcs as minor, major, or

semicircle.

M: Find measures of a few arcs in a

circle.

H: Find measures of many arcs in a

circle.










the circle.

-use congruent chords

to find arc measures

-bisecting arcs

-how to use

perpendicular bisectors

in circles

-using a diameter with a

chord

-chords equidistant

from the center of a

circle


chapter 10.3

L: Know which chords are congruent

in a circle.

M/H: Use equations to determine

lengths of chords.

G-CO 13: Construct an equilateral

triangle, a square, and a regular

hexagon inscribed in a circle.






-define inscribed angle

and intercepted arc

-use inscribed angles to

find angle and arc

measures

-define inscribed

polygon and

circumscribed circle

-inscribed quadrilaterals


chapter 10.4

L: Determine arc measures.

M: Determine angles measures of

inscribed polygons.

H: Construct inscribed polygons.






the circle.

G-C 3: Construct the inscribed and

circumscribed circles of a triangle,

and prove properties of angles for a

quadrilateral inscribed in a circle.










the circle.

-find angle and arc

measures with tangent

lines and chords

-find angle and arc

measures with angles

inside and outside

circles


chapter 10.5

L: Find arc measures with tangent

lines.

M: Find one angle measure using

inside or outside measurements.

H: Find several angle measures using

inside or outside measurements.










the circle.

-segments of the chord

theorem

-find lengths of

segments inside a circle

-segments of secants

theorem

-find lengths of

segments from secants

-segments of secants

and tangents theorem

-find lengths of chords

from secants and

tangents


chapter 10.6

L: Determine segment lengths given

basic numbers.

M: Determine segment lengths given

equations.

H: Determine segment lengths given

complicated equations and word

problems.

G-GPE 1: Derive the equation of a -standard form for the R: Geometry textbook L: Identify the center and radius 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 and equation.










equation of a circle,

comes from

Pythagorean Theorem

-write the equation of a

circle given the graph

-write the equation of a

circle given the center

and radius

-graph a circle given the

equation

-apply graphs of circles

to word problems

chapter 10.7 circle given the equation.

M: Graph a circle given the equation.

Write the equation given the graph.

H: Determine if certain points lie on a

circle.

Assign review on

Go over review on

Test on

Pi Day on Fri, March 11

4th 9

Weeks Unit 11: Measuring Length

and Area


and Activities

Assessment Stem

Ch 11





formula

G-MG 2: Apply concepts of density

based on area and volume in

modeling situations (e.g., persons

per square mile, BTUs per cubic

-find areas of squares,

rectangles, triangles,

and parallelograms

-Postulate 26- area

Addition Postulate

-solve for unknown

measures, using a

formula


chapter 11.1

M: Area Notes sheet

L: Find areas of various polygons.

M/H: Find areas of composite figures.


foot)





formula

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)

-height of a trapezoid,

perpendicular height

-area of a trapezoid,

rhombus, kite


chapter 11.2

L: Find areas of various polygons.






-review ratios, review

ratios of perimeters in

similar figures

-ratio of areas of similar

figures

-find and apply ratios

for area


chapter 11.3

L: Identify the relationship between

ratio of sides, ratio of perimeters, and

ratio of areas.

M: Use ratios to find perimeters and

areas of similar figures.

H: Explain how the ratios of similar

figures relates to dilations.

G-C 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.

-review circumference

of a circle

-use the circumference

formula to find distance

traveled

-define arc length, show

how the formula relates

to circumference

-find arc lengths,

circumference, and

radii


chapter 11.4

L: Find the circumference of a circle.

M: Understand how arc length relates

to circumference and how area of a

sector relates to area of a circle.

H: Understand how circumference can

be used to find distance traveled.

G-C 5: Derive using similarity the

fact that the length of the arc

intercepted by an angle is

proportional to the radius, and

-review area of a circle

-define sector of a circle

-find areas of sectors


chapter 11.5

L: Find area of a circle and area of a

sector.

M: Find areas of composite figures.

H: Find areas of shaded regions, in


define the radian measure of the

angle as the constant of

proportionality; derive the formula

for the area of a sector.

which multiple areas must be found

and subtracted.





formula

-define center of the

polygon, radius of the

polygon, apothem of

the polygon, and central

angle of a regular

polygon

-find angle measures

-find perimeter and area

of a regular polygon


chapter 11.6

L: Find areas of regular polygons.



for this concept.

-define probability vs

geometric probability

-use lengths to find

probability

-use area to find

probability


chapter 11.7

A: Bean Toss, pg. 770

L: Define probability and understand

how it is used in the real-world.

M: Use lengths to find geometric

probability.

H: Use area to find geometric

probability.

Assign review on

Go over review on

Test on

4th 9

Weeks Unit 12: Surface Area and

Volume of Solids


and Activities

Assessment Stem

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

-define and identify

nets

-define polyhedron,

faces, edges, and

vertices

-identify and name

polyhedra

-Euler's Theorem

-convex vs concave


chapter 12.1


792

L: Determine if the solid is a

polyhedra or not polyhedra.

M: Name the solid. Name the cross-

section.

H: Sketch the given solid. Sketch

solids with cross-sections.


-Platonic solids

-describe the cross

section


for this concept.

-define prism, lateral

faces and lateral edges

-define surface area vs

lateral area

-how nets apply to

surface area

-right vs oblique prisms

-find surface area of

prisms

-define cylinder and

right cylinder

-find surface area of a

cylinder


chapter 12.2

L: Find surface area of solids.

M: Identify solids formed by nets.

H: Find surface areas of composite

figures.


for this concept.

-define pyramid, vertex,

and regular pyramid

-find lateral area and

surface area of a

pyramid

-define cone, vertex,

right cone, lateral

surface

-find lateral area and

surface area of a cone


chapter 12.3

L: Find surface area of solids.

M: Identify solids formed by nets.

H: Find surface areas of composite

figures.

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.

-define volume

-find volume of a cube

-Postulate 29, Volume

Addition Postulate

-find volume of a prism

and cylinder

-Cavalieri's Principle

-volume of an oblique


chapter 12.4

A: Pg. 825 #33 would be

a great activity

L: Find volume of solids.

M: Find volume of composite figures.

H: Understand and apply density to

problems.


G-GMD 2: Give an informal

argument using Cavalieri's principle

for the formulas for the volume of a

sphere and other solid figures

G-GMD 3: Use volume formulas

for cylinders, pyramids, cones, and

spheres to solve problems.

cylinder




-find volume of a

pyramid and cone

-apply trig to find

volume

-find volume of

composite solids


chapter 12.5

L: Find volume of solids.

M: Find volume of composite figures.

H: Understand and apply density to

problems.




-define sphere, center,

radius, chord, and

diameter

-find surface area of a

sphere

-great circles

-find volume of a

sphere


chapter 12.6

L: Find surface area and volume of

spheres.

M/H: Find surface area and volume of

composite figures.


for this concept

-define similar solids

-identify similar solids

-Similar Solids

Theorem

-use scale factor of

similar solids

-find the scale factor

-compare similar solids


chapter 12.7

L: Determine the scale factor when

comparing two solids.

M/H: Understand how changing

measurements will effect the surface

area and volume of solids.

Assign review on

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for this concept.

Activity if time allows

-draw isometric and

orthographic views of

various figures

R: Geometry textbook Pg.

551

M: isometric dot paper

L: compare and contrast orthographic

views and isometric views

M: Draw orthographic and isometric

views of figures.

H: Apply orthographic and isometric

views to finding perimeter, area, and

volume of figures.


for this concept

Activity is time allows

-understand the

concepts learned this

year relate to Euclidean

geometry

-discuss various forms

of non-Euclidean

geometry and its history

and arguments for and

against

M: video: Non-Euclidean

Geometry

L: Understand the concepts learned

are based on Euclid's findings.

M: Name some types of non-

Euclidean geometry and their main

ideas.

H: Explain the significance of Euclid's

findings during the time period and

how this would have affected others,

especially those who did not agree

with him.

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