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CCSS IP Math II Teacher Resource Pacing Guide

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Suggested Pacing GuideCCSS IP MATH II TEACHER RESOURCE

OverviewThe sub-lessons in Walch Integrated Math are designed to be covered over one, two, or three days, depending on the depth and complexity of the topic. The pacing guide that follows provides suggested pacing, but this should be viewed as a flexible guideline only. If students need an extra day to solidify understanding, a one-day lesson may be spread over two days, or a two-day lesson may be spread over three days. Conversely, if students grasp a concept more quickly than suggested by the pacing guide, it is fine to shorten the duration of the lesson and move on to the next topic.

Each sub-lesson features several components. The estimated time for each component is given in parentheses. Components include: a Warm-Up, Instruction (including an Introduction, Key Concepts, and Guided Practice), a Problem-Based Task, and Practice.

Please note: PowerPoint versions of each sub-lesson’s Warm-Up and Instruction are provided. Warm-Up PowerPoints include a video clip and the Warm-Up Debrief. Instructional PowerPoints feature the Introduction, Key Concepts, and selected Guided Practice Examples with links to corresponding GeoGebra applets. Estimated times reflect presentation of these PowerPoint versions and applets.

Guided Practice, Scaffolded Practice, and Practice

For each Guided Practice in the Teacher Resource (TRB), corresponding Scaffolded Practice worksheets are provided in the Student Workbook (SWB). Practice problems may be assigned from the SWB and/or the parallel Student Resource (SRB) worksheet for in-class work or homework assignments. The SRB worksheets are designed to closely resemble the format of the SWB worksheets, but are composed of different problems for additional practice.

Please note: When a sub-lesson is spread across more than one class period, the Guided Practice Examples will also be spread across the same number of class periods. Assign Practice problems that correspond to the Guided Practice Example(s) you select for each day, to ensure appropriate prior instruction.

Suggested Progression of One-, Two-, and Three-Day Sub-LessonsOne Day

• Warm-Up PowerPoint and Debrief (10 minutes)

• Introduction and Key Concepts (10 minutes)

• One or two Guided/Scaffolded Practice Examples, including PowerPoint applet presentation as appropriate (15 minutes)

• Problem-Based Task and discussion (15 minutes)

• Homework: Practice from the SWB or SRB



CCSS IP MATH II TEACHER RESOURCESuggested Pacing Guide

Two Days

Day 1



• Two or three Guided/Scaffolded Practice Examples, including PowerPoint applet presentation as appropriate (15 minutes)

• In-class practice: selected problems from the SWB Practice (10 minutes)

• Homework: selected problems from the SRB Practice

Day 2

• Review Practice problems (10 minutes)

• One or two remaining Guided/Scaffolded Practice Examples, including PowerPoint applet presentation as appropriate (10 minutes)


• In-class practice: the remainder of the SWB Practice (10 minutes)

• Homework: the remainder of the SRB Practice

Three Days

Day 1



• One or two Guided/Scaffolded Practice Examples, including PowerPoint applet presentation as appropriate (15 minutes)

• Homework: selected problems from the SRB Practice

Day 2


• Two or three remaining Guided/Scaffolded Practice Examples, including PowerPoint applet presentation as appropriate (15 minutes)


• Homework: the remainder of the SRB Practice




Day 3


• In-class practice: selected problems from the SWB Practice (35 minutes)

• Homework: the remainder of the SWB Practice

Assessments and Station Activities

Each lesson includes a Pre-Assessment and a Progress Assessment, and each unit concludes with a Unit Assessment. Units also feature sets of Station Activities to complement instruction.

Pre-Assessments are short, multiple-choice assessments with five problems, designed to evaluate prior knowledge of the upcoming lesson. These are brief and should not factor into a student’s grade. Pre-Assessments are often given on the same day as the preceding lesson’s Progress Assessment, to prepare for the upcoming lesson.

Progress Assessments include 10 multiple-choice problems and one extended-response problem. Progress Assessments may not take an entire class period. The additional time may be used to review before the assessment, or to begin the next lesson after the assessment.

Unit Assessments include 12 multiple-choice problems and three extended-response problems, and generally require a full class period.

Station Activities generally require a full class period for the students to rotate through each station and then to engage in a class discussion at the end.




Unit

1: E

xten

ding

the

Num

ber S

yste

m (1

5 Da

ys)

Uni

t Ove

rvie

w: T

his i

ntro

duct

ory

unit

cove

rs m

any

of th

e fo

unda

tiona

l ski

lls n

eede

d fo

r the

rest

of t

he c

ours

e. S

tude

nts l

earn

ab

out r

atio

nal e

xpon

ents

and

the

prop

ertie

s of r

atio

nal a

nd ir

ratio

nal n

umbe

rs. T

his i

s fol

low

ed b

y op

erat

ing

with

pol

ynom

ials

. Fi

nally

, stu

dent

s def

ine

an im

agin

ary

num

ber a

nd le

arn

to o

pera

te w

ith c

ompl

ex n

umbe

rs.

Less

on 1

: Wor

king

with

the

Num

ber S

yste

m

Stud

ents

are

intr

oduc

ed to

the

prop

ertie

s of e

xpon

ents

, inc

ludi

ng ra

tiona

l exp

onen

ts. T

hey

use

thes

e pr

oper

ties t

o re

wri

te a

nd

eval

uate

exp

ress

ions

that

con

tain

ratio

nal e

xpon

ents

. Nex

t, st

uden

ts le

arn

the

prop

ertie

s of r

atio

nal a

nd ir

ratio

nal n

umbe

rs.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

1

Day

2Le

sson

1 P

re-A

sses

smen

t 1.

1.1:

Def

inin

g, R

ewri

ting,

and

Eva

luat

ing

Ratio

nal E

xpon

ents

Pre-

Ass

essm

ent

TRB:

U1-

1 In

stru

ctio

n/Pr

acti

ce

TRB:

U1-

4–17

SR

B: U

1-3–

10

SWB:

7–1

4

N–R

N.1

N

–RN

.2

Day

31.

1.2:

Rat

iona

l and

Irra

tiona

l Num

bers

and

The

ir P

rope

rtie

sTR

B: U

1-18

–30

SRB:

U1-

11–1

7 SW

B: 1

7–24

N–R

N.2

N

–RN

.3

Day

4Le

sson

1 P

rogr

ess A

sses

smen

t Le

sson

2 P

re-A

sses

smen

tTR

B: U

1-31

–32

TRB:

U1-

33




Less

on 2

: Ope

ratin

g w

ith P

olyn

omia

ls

Stud

ents

lear

n ho

w to

add

, sub

trac

t, an

d m

ultip

ly p

olyn

omia

ls. T

hese

skill

s hel

p st

uden

ts si

mpl

ify e

xpre

ssio

ns, a

nd a

re

foun

datio

nal s

kills

that

are

use

d in

late

r uni

ts a

nd in

futu

re m

ath

cour

ses.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

51.

2.1:

Add

ing

and

Subt

ract

ing

Poly

nom

ials

TRB:

U1-

35–4

7 SR

B: U

1-20

–26

SWB:

27–

34

A–A

PR.1

Day

61.

2.2:

Mul

tiply

ing

Poly

nom

ials

TRB:

U1-

48–6

1 SR

B: U

1-27

–33

SWB:

37–

43

A–A

PR.1

Day

7St

atio

n A

ctiv

ities

Set

2: O

pera

tions

with

Pol

ynom

ials

TRB:

U1-

121–

133

SWB:

81–

89A

–APR

.1

Day

8Le

sson

2 P

rogr

ess A

sses

smen

t Le

sson

3 P

re-A

sses

smen

tTR

B: U

1-62

–63

TRB:

U1-

64




Less

on 3

: Ope

ratin

g w

ith C

ompl

ex N

umbe

rs

Stud

ents

are

intr

oduc

ed to

the

imag

inar

y un

it i a

nd to

the

conc

ept o

f a c

ompl

ex n

umbe

r. Th

en, s

tude

nts l

earn

to a

dd, s

ubtr

act,

and

mul

tiply

com

plex

num

bers

. Stu

dent

s exp

lore

how

the

imag

inar

y un

it en

able

s the

m to

solv

e pr

oble

ms t

hat t

hey

wou

ld n

ot

othe

rwis

e be

abl

e to

solv

e.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

9

Day

10

1.3.

1: D

efin

ing

Com

plex

Num

bers

, i, a

nd i2

TRB:

U1-

67–7

8 SR

B: U

1-36

–41

SWB:

47–

53

N–C

N.1

Day

11

1.3.

2: A

ddin

g an

d Su

btra

ctin

g Co

mpl

ex N

umbe

rsTR

B: U

1-79

–91

SRB:

U1-

42–4

8 SW

B: 5

7–63

N–C

N.2

Day

12

1.3.

3: M

ultip

lyin

g Co

mpl

ex N

umbe

rsTR

B: U

1-92

–103

SR

B: U

1-49

–54

SWB:

67–

73

N–C

N.2

Day

13

Stat

ion

Act

iviti

es S

et 1

: Ope

ratio

ns w

ith C

ompl

ex N

umbe

rsTR

B: U

1-11

3–12

0 SW

B: 7

7–80

N–C

N.1

N

–CN

.2

N–C

N.3

Day

14

Less

on 3

Pro

gres

s Ass

essm

ent

TRB:

U1-

104–

105

U

nit A

sses

smen

tD

ay 1

5U

nit A

sses

smen

tTR

B: U

1-10

6–10

8




Unit

2: Q

uadr

atic

Fun

ctio

ns a

nd M

odel

ing

(29

Days

)U

nit O

verv

iew

: Stu

dent

s beg

in b

y ex

plor

ing

and

inte

rpre

ting

the

grap

hs o

f qua

drat

ic fu

nctio

ns. N

ext,

they

lear

n ho

w to

bu

ild q

uadr

atic

func

tions

from

a c

onte

xt a

nd h

ow to

car

ry o

ut o

pera

tions

with

func

tions

. Thi

s giv

es w

ay to

the

expl

orat

ion

of

othe

r typ

es o

f fun

ctio

ns, i

nclu

ding

squa

re ro

ot, c

ube

root

, abs

olut

e va

lue,

step

, and

pie

cew

ise

func

tions

. The

uni

t pro

gres

ses t

o an

alyz

ing

expo

nent

ial f

unct

ions

and

com

pari

ng li

near

, qua

drat

ic, a

nd e

xpon

entia

l mod

els g

iven

in d

iffer

ent f

orm

s. Th

e un

it en

ds w

ith tr

ansf

orm

ing

func

tions

and

find

ing

the

inve

rse

of fu

nctio

ns.

Less

on 1

: Ana

lyzi

ng Q

uadr

atic

Fun

ctio

ns

Stud

ents

lear

n w

hat a

qua

drat

ic fu

nctio

n is

and

how

to g

raph

one

. The

y le

arn

how

to fi

nd th

e ve

rtex

and

the

inte

rcep

ts o

f the

gr

aph

of a

qua

drat

ic fu

nctio

n, a

nd th

ey d

isco

ver t

he v

ario

us fo

rms o

f a q

uadr

atic

func

tion

and

how

eac

h fo

rm h

elps

iden

tify

key

feat

ures

of t

he g

raph

. Thi

s les

son

lays

the

foun

datio

n fo

r the

mor

e in

-dep

th e

xam

inat

ion

of q

uadr

atic

func

tions

in th

e

next

less

on.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

1

Day

2Le

sson

1 P

re-A

sses

smen

t 2.

1.1:

Gra

phin

g Q

uadr

atic

Fun

ctio

nsPr

e-A

sses

smen

t TR

B: U

2-1

Inst

ruct

ion/

Prac

tice

TR

B: U

2-4–

27

SRB:

U2-

4–20

SW

B: 7

–13

F–IF

.7a★

Day

32.

1.2:

Inte

rpre

ting

Var

ious

For

ms o

f Qua

drat

ic F

unct

ions

TRB:

U2-

28–4

9 SR

B: U

2-21

–34

SWB:

17–

24

F–IF

.7a★

F–

IF.8

a

Day

4Le

sson

1 P

rogr

ess A

sses

smen

t Le

sson

2 P

re-A

sses

smen

tTR

B: U

2-50

–51

TRB:

U2-

52




Less

on 2

: Int

erpr

etin

g Qu

adra

tic F

unct

ions

This

less

on d

elve

s dee

per i

nto

the

anal

ysis

of q

uadr

atic

func

tions

, giv

ing

stud

ents

an

oppo

rtun

ity to

use

equ

atio

ns, g

raph

s, ta

bles

, and

ver

bal d

escr

iptio

ns to

iden

tify

and

appl

y th

e ke

y fe

atur

es o

f the

func

tion’

s gra

ph. S

tude

nts a

lso

lear

n ho

w to

iden

tify

the

dom

ain

and

rang

e of

a q

uadr

atic

func

tion

and

how

to c

alcu

late

the

aver

age

rate

of c

hang

e. T

he sk

ills l

earn

ed in

this

less

on

prep

are

stud

ents

to a

pply

this

kno

wle

dge

to re

al c

onte

xts i

n th

e ne

xt le

sson

.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

5

Day

62.

2.1:

Inte

rpre

ting

Key

Fea

ture

s of Q

uadr

atic

Fun

ctio

nsTR

B: U

2-56

–77

SRB:

U2-

38–5

2 SW

B: 2

7–34

F–IF

.4★

Day

72.

2.2:

Iden

tifyi

ng th

e D

omai

n of

a Q

uadr

atic

Fun

ctio

nTR

B: U

2-78

–91

SRB:

U2-

53–6

0 SW

B: 3

7–45

F–IF

.5★

Day

8St

atio

n A

ctiv

ities

Set

1: G

raph

ing

Qua

drat

ic E

quat

ions

TRB:

U2-

403–

416

SWB:

161

–168

F–IF

.7a★

Day

92.

2.3:

Iden

tifyi

ng th

e A

vera

ge R

ate

of C

hang

eTR

B: U

2-92

–106

SR

B: U

2-61

–68

SWB:

49–

56

F–IF

.6★

Day

10

Less

on 2

Pro

gres

s Ass

essm

ent

Less

on 3

Pre

-Ass

essm

ent

TRB:

U2-

107–

110

TRB:

U2-

111




Less

on 3

: Bui

ldin

g Fu

nctio

ns

This

less

on p

rovi

des s

tude

nts w

ith th

e op

port

unity

to a

pply

thei

r kno

wle

dge

of q

uadr

atic

func

tions

to re

al-w

orld

con

text

s. By

m

odel

ing

scen

ario

s with

qua

drat

ic e

quat

ions

and

gra

phs,

stud

ents

dis

cove

r the

use

fuln

ess o

f bei

ng a

ble

to id

entif

y ke

y fe

atur

es

such

as t

he m

axim

um, m

inim

um, a

nd in

terc

epts

to so

lve

prob

lem

s.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

11

Day

12

2.3.

1: B

uild

ing

Func

tions

from

Con

text

TRB:

U2-

114–

133

SRB:

U2-

71–8

2 SW

B: 5

9–66

F–BF

.1a★

Day

13

2.3.

2: O

pera

ting

on F

unct

ions

TRB:

U2-

134–

148

SRB:

U2-

83–9

0 SW

B: 6

9–76

F–BF

.1b★

Day

14

Less

on 3

Pro

gres

s Ass

essm

ent

Less

on 4

Pre

-Ass

essm

ent

TRB:

U2-

149–

150

TRB:

U2-

151–

152




Less

on 4

: Gra

phin

g Ot

her F

unct

ions

Stud

ents

are

intr

oduc

ed to

seve

ral n

ew ty

pes o

f fun

ctio

ns th

at th

ey p

roba

bly

have

not

seen

bef

ore.

The

y ex

plor

e th

e gr

aphs

of

squa

re ro

ot fu

nctio

ns, c

ube

root

func

tions

, abs

olut

e va

lue

func

tions

, ste

p fu

nctio

ns, a

nd p

iece

wis

e fu

nctio

ns. T

he m

ater

ial

in th

is le

sson

allo

ws s

tude

nts t

o m

ove

beyo

nd th

e th

ree

type

s of f

unct

ions

they

hav

e al

read

y st

udie

d (li

near

, exp

onen

tial,

and

quad

ratic

) to

see

that

ther

e ar

e m

any

mor

e ty

pes o

f fun

ctio

ns.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

15

Day

16

2.4.

1: S

quar

e Ro

ot a

nd C

ube

Root

Fun

ctio

nsTR

B: U

2-15

6–18

9 SR

B: U

2-94

–116

SW

B: 7

9–86

F–IF

.7b★

Day

17

2.4.

2: A

bsol

ute

Val

ue a

nd S

tep

Func

tions

TRB:

U2-

190–

219

SRB:

U2-

117–

137

SWB:

89–

96

F–IF

.7b★

Day

18

2.4.

3: P

iece

wis

e Fu

nctio

nsTR

B: U

2-22

0–24

4 SR

B: U

2-13

8–15

2 SW

B: 9

9–10

6

F–IF

.7b★

Day

19

Less

on 4

Pro

gres

s Ass

essm

ent

Less

on 5

Pre

-Ass

essm

ent

TRB:

U2-

245–

248

TRB:

U2-

249–

251




Less

on 5

: Ana

lyzi

ng F

unct

ions

This

less

on b

egin

s with

an

in-d

epth

look

at e

xpon

entia

l fun

ctio

ns. T

hen,

stud

ents

lear

n to

com

pare

line

ar, q

uadr

atic

, and

ex

pone

ntia

l fun

ctio

ns th

at a

re p

rese

nted

in v

ario

us fo

rms—

tabl

es, e

quat

ions

, gra

phs,

and

wor

ds. T

his a

llow

s stu

dent

s to

see

the

sim

ilari

ties a

nd d

iffer

ence

s bet

wee

n th

ese

diffe

rent

cat

egor

ies o

f fun

ctio

ns, a

nd p

repa

res t

hem

for t

he m

ore

in-d

epth

stud

y of

fu

nctio

ns th

at th

ey w

ill e

ncou

nter

in fu

ture

mat

h co

urse

s.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

20

Day

21

2.5.

1: A

naly

zing

Exp

onen

tial F

unct

ions

TRB:

U2-

255–

268

SRB:

U2-

156–

162

SWB:

109

–116

F–IF

.8b

Day

22

2.5.

2: C

ompa

ring

Pro

pert

ies o

f Fun

ctio

ns G

iven

in

Diff

eren

t For

ms

TRB:

U2-

269–

287

SRB:

U2-

163–

174

SWB:

119

–126

F–IF

.9

F–LE

.3★

Day

23

Less

on 5

Pro

gres

s Ass

essm

ent

Less

on 6

Pre

-Ass

essm

ent

TRB:

U2-

288–

291

TRB:

U2-

292–

293




Less

on 6

: Tra

nsfo

rmin

g Fu

nctio

ns

Stud

ents

lear

n ho

w to

var

y th

e sh

ape

and

posi

tion

of a

func

tion

by m

ultip

lyin

g by

a n

umbe

r or a

ddin

g a

cons

tant

to v

ario

us

part

s of t

he fu

nctio

n. T

hese

ope

ratio

ns a

re c

alle

d tr

ansf

orm

atio

ns. T

he st

udy

of tr

ansf

orm

atio

ns h

elps

stud

ents

see

the

conn

ectio

n be

twee

n th

e al

gebr

aic

equa

tion

for a

func

tion

and

the

grap

hica

l rep

rese

ntat

ion

of th

e fu

nctio

n.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

24

2.6.

1: R

epla

cing

f(x)

with

f(x)

+ k

and

f(x +

k)TR

B: U

2-29

6–31

5 SR

B: U

2-17

7–18

8 SW

B: 1

29–1

36

F–BF

.3

Day

25

2.6.

2: R

epla

cing

f(x)

with

k •

f(x) a

nd f(

k • x)

TRB:

U2-

316–

339

SRB:

U2-

189–

203

SWB:

139

–147

F–BF

.3

Day

26

Less

on 6

Pro

gres

s Ass

essm

ent

Less

on 7

Pre

-Ass

essm

ent

TRB:

U2-

340–

344

TRB:

U2-

345

Less

on 7

: Fin

ding

Inve

rse

Func

tions

Stud

ents

are

intr

oduc

ed to

the

conc

ept o

f an

inve

rse

and

how

to d

eter

min

e th

e eq

uatio

n fo

r the

inve

rse

of a

giv

en fu

nctio

n.

Stud

ents

als

o le

arn

how

to u

se in

vers

e fu

nctio

ns to

solv

e re

al-w

orld

pro

blem

s.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

27

2.7.

1: F

indi

ng In

vers

e Fu

nctio

nsTR

B: U

2-34

8–36

3 SR

B: U

2-20

6–21

4 SW

B: 1

51–1

58

F–BF

.4a

Day

28

Less

on 7

Pro

gres

s Ass

essm

ent

TRB:

U2-

364–

365

U

nit A

sses

smen

tD

ay 2

9U

nit A

sses

smen

tTR

B: U

2-36

6–36

9




Unit

3: E

xpre

ssio

ns a

nd E

quat

ions

(38

Days

)U

nit O

verv

iew

: Stu

dent

s ree

xam

ine

the

basi

c st

ruct

ures

of e

xpre

ssio

ns, b

ut th

is ti

me

thes

e st

ruct

ures

are

app

lied

to q

uadr

atic

ex

pres

sion

s. Th

en, s

tude

nts l

earn

to so

lve

quad

ratic

equ

atio

ns u

sing

var

ious

met

hods

. Nex

t, st

uden

ts c

reat

e qu

adra

tic e

quat

ions

in

var

ious

form

s and

lear

n ho

w to

rear

rang

e fo

rmul

as to

solv

e fo

r a v

aria

ble

that

is b

eing

squa

red.

The

uni

t bui

lds o

n pr

evio

us

units

by

intr

oduc

ing

the

Fund

amen

tal T

heor

em o

f Alg

ebra

and

show

ing

stud

ents

how

com

plex

num

bers

are

solu

tions

to so

me

quad

ratic

equ

atio

ns. A

t thi

s poi

nt, s

tude

nts a

re in

trod

uced

to ra

tiona

l fun

ctio

ns. A

gain

, stu

dent

s lea

rn to

wri

te e

xpon

entia

lly

stru

ctur

ed e

xpre

ssio

ns in

equ

ival

ent f

orm

s. Th

e un

it en

ds b

y re

turn

ing

to a

fam

iliar

topi

c—so

lvin

g sy

stem

s of e

quat

ions

—bu

t no

w c

ompl

ex so

lutio

ns c

an b

e de

term

ined

.

Less

on 1

: Int

erpr

etin

g St

ruct

ure

in E

xpre

ssio

ns

Stud

ents

beg

in b

y re

view

ing

alge

brai

c vo

cabu

lary

, suc

h as

term

, fac

tor,

and

coeff

icien

t. N

ext,

they

ana

lyze

alg

ebra

ic e

xpre

ssio

ns to

se

e ho

w e

ach

term

of a

n ex

pres

sion

affe

cts t

he v

alue

of t

he e

xpre

ssio

n. U

nder

stan

ding

how

all

the

part

s of a

lgeb

raic

exp

ress

ions

an

d eq

uatio

ns w

ork

toge

ther

will

mak

e th

e pr

oces

s of c

reat

ing

equa

tions

eas

ier w

hen

enco

unte

red

in L

esso

n 3.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

1Le

sson

1 P

re-A

sses

smen

t 3.

1.1:

Iden

tifyi

ng T

erm

s, F

acto

rs, a

nd C

oeffi

cien

tsPr

e-A

sses

smen

t TR

B: U

3-1

Inst

ruct

ion/

Prac

tice

TR

B: U

3-4–

16

SRB:

U3-

3–10

SW

B: 7

–14

A–S

SE.1

a★

Day

2

Day

33.

1.2:

Inte

rpre

ting

Com

plic

ated

Exp

ress

ions

TRB:

U3-

17–2

9 SR

B: U

3-11

–17

SWB:

17–

24

A–S

SE.1

b★

Day

4Le

sson

1 P

rogr

ess A

sses

smen

t Le

sson

2 P

re-A

sses

smen

tTR

B: U

3-30

–31

TRB:

U3-

32




Less

on 2

: Cre

atin

g an

d So

lvin

g Qu

adra

tic E

quat

ions

in O

ne V

aria

ble

Stud

ents

lear

n to

cre

ate

quad

ratic

equ

atio

ns b

ased

on

real

-wor

ld sc

enar

ios,

and

to so

lve

quad

ratic

equ

atio

ns b

y ta

king

the

squa

re ro

ot o

f bot

h si

des.

Then

, stu

dent

s lea

rn h

ow to

fact

or q

uadr

atic

equ

atio

ns a

nd u

se th

e fa

ctor

ed fo

rm to

solv

e eq

uatio

ns.

The

less

on in

clud

es fa

ctor

ing

by g

roup

ing

and

com

plet

ing

the

squa

re. N

ext,

stud

ents

lear

n ho

w to

app

ly th

e qu

adra

tic fo

rmul

a to

solv

e eq

uatio

ns, a

nd fi

nally

they

solv

e qu

adra

tic in

equa

litie

s.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

53.

2.1:

Tak

ing

the

Squa

re R

oot o

f Bot

h Si

des

TRB:

U3-

36–4

6 SR

B: U

3-21

–25

SWB:

27–

33

A–C

ED.1

★

A–R

EI.4

b

Day

6

Day

73.

2.2:

Fac

tori

ngTR

B: U

3-47

–62

SRB:

U3-

26–3

4 SW

B: 3

7–43

A–S

SE.2

A

–CED

.1★

A

–REI

.4b

Day

8St

atio

n A

ctiv

ities

Set

1: F

acto

ring

TRB:

U3-

451–

458

SWB:

205

–208

A–S

SE.3

a★

Day

93.

2.3:

Com

plet

ing

the

Squa

reTR

B: U

3-63

–75

SRB:

U3-

35–4

0 SW

B: 4

7–53

A–S

SE.2

A

–CED

.1★

A

–REI

.4a

A–R

EI.4

bD

ay 1

03.

2.4:

App

lyin

g th

e Q

uadr

atic

For

mul

aTR

B: U

3-76

–89

SRB:

U3-

41–4

8 SW

B: 5

7–63

A–C

ED.1

★

A–R

EI.4

a A

–REI

.4b

Day

11

Day

12

3.2.

5: S

olvi

ng Q

uadr

atic

Ineq

ualit

ies

TRB:

U3-

90–1

04

SRB:

U3-

49–5

6 SW

B: 6

7–73

A–S

SE.2

A

–CED

.1★

A

–REI

.4b

Day

13

Less

on 2

Pro

gres

s Ass

essm

ent

Less

on 3

Pre

-Ass

essm

ent

TRB:

U3-

105–

106

TRB:

U3-

107




Less

on 3

: Cre

atin

g Qu

adra

tic E

quat

ions

in T

wo

or M

ore

Varia

bles

Stud

ents

solid

ify p

revi

ousl

y le

arne

d sk

ills b

y ap

plyi

ng th

em to

pro

blem

solv

ing.

Stu

dent

s cre

ate

and

grap

h qu

adra

tic e

quat

ions

, bo

th w

ith a

nd w

ithou

t a re

al-w

orld

con

text

, and

pra

ctic

e us

ing

stan

dard

form

, fac

tore

d fo

rm, a

nd v

erte

x fo

rm. S

tude

nts a

lso

lear

n ho

w to

rear

rang

e fo

rmul

as in

whi

ch th

e va

riab

le th

at is

bei

ng so

lved

for i

s squ

ared

.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

14

Day

15

3.3.

1: C

reat

ing

and

Gra

phin

g Eq

uatio

ns U

sing

Sta

ndar

d Fo

rmTR

B: U

3-11

1–13

8 SR

B: U

3-60

–81

SWB:

77–

84

A–S

SE.3

a★

A–C

ED.2

★

Day

16

3.3.

2: C

reat

ing

and

Gra

phin

g Eq

uatio

ns U

sing

the

x-in

terc

epts

TRB:

U3-

139–

155

SRB:

U3-

82–9

1 SW

B: 8

7–94

A–S

SE.3

a★

A–C

ED.2

★

Day

17

3.3.

3: C

reat

ing

and

Gra

phin

g Eq

uatio

ns U

sing

Ver

tex

Form

TRB:

U3-

156–

169

SRB:

U3-

92–9

9 SW

B: 9

7–10

3

A–S

SE.3

b★

A–C

ED.2

★

Day

18

Stat

ion

Act

iviti

es S

et 3

: Qua

drat

ic T

rans

form

atio

ns in

V

erte

x Fo

rmTR

B: U

3-46

8–48

5 SW

B: 2

13–2

20A

–SSE

.3b★

F–

IF.7

a★

F–IF

.8a

F–BF

.3

Day

19

3.3.

4: R

earr

angi

ng F

orm

ulas

TRB:

U3-

170–

183

SRB:

U3-

100–

107

SWB:

107

–113

A–C

ED.4

★

Day

20

Less

on 3

Pro

gres

s Ass

essm

ent

Less

on 4

Pre

-Ass

essm

ent

TRB:

U3-

184–

186

TRB:

U3-

187




Less

on 4

: Fun

dam

enta

l The

orem

of A

lgeb

ra

Stud

ents

gai

n m

ore

prac

tice

with

pol

ynom

ial i

dent

ities

by

expl

orin

g th

ose

that

con

tain

com

plex

num

bers

. Nex

t, st

uden

ts le

arn

one

of th

e m

ost u

sefu

l alg

ebra

ic th

eore

ms,

the

Fund

amen

tal T

heor

em o

f Alg

ebra

, whi

ch te

lls th

e nu

mbe

r of s

olut

ions

, bot

h

eal a

nd c

ompl

ex, t

hat a

pol

ynom

ial c

an h

ave.

Stu

dent

s app

ly th

is th

eore

m w

hen

solv

ing

quad

ratic

equ

atio

ns th

at h

ave

co

mpl

ex so

lutio

ns.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

21

Day

22

3.4.

1: E

xten

ding

Pol

ynom

ial I

dent

ities

to In

clud

e

Com

plex

Num

bers

TRB:

U3-

190–

211

SRB:

U3-

110–

124

SWB:

117

–124

N–C

N.8

(+)

Day

23

3.4.

2: S

olvi

ng Q

uadr

atic

Equ

atio

ns w

ith C

ompl

ex S

olut

ions

TRB:

U3-

212–

237

SRB:

U3-

125–

143

SWB:

127

–134

N–C

N.7

N

–CN

.9 (+

)

Day

24

Stat

ion

Act

iviti

es S

et 2

: Sol

ving

Qua

drat

ics

TRB:

U3-

459–

467

SWB:

209

–212

N–C

N.7

A

–SSE

.3a★

A

–REI

.4b

Day

25

Less

on 4

Pro

gres

s Ass

essm

ent

Less

on 5

Pre

-Ass

essm

ent

TRB:

U3-

238–

239

TRB:

U3-

240–

242




Less

on 5

: Rat

iona

l Equ

atio

ns

Stud

ents

furt

her d

evel

op th

eir p

robl

em-s

olvi

ng sk

ills b

y le

arni

ng h

ow to

cre

ate

and

solv

e ra

tiona

l equ

atio

ns fr

om c

onte

xt. N

ext,

they

lear

n ho

w to

gra

ph ra

tiona

l fun

ctio

ns a

nd u

se th

ese

grap

hs to

solv

e re

al-w

orld

pro

blem

s.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

26

Day

27

3.5.

1: C

reat

ing

Ratio

nal E

quat

ions

TRB:

U3-

247–

268

SRB:

U3-

148–

162

SWB:

137

–144

A–C

ED.1

★

Day

28

3.5.

2: G

raph

ing

Ratio

nal E

quat

ions

TRB:

U3-

269–

301

SRB:

U3-

163–

187

SWB:

147

–156

A–C

ED.2

★

Day

29

3.5.

3: C

reat

ing

Ratio

nal I

nequ

aliti

esTR

B: U

3-30

2–34

1 SR

B: U

3-18

8–22

0 SW

B: 1

59–1

67

A–C

ED.1

★

Day

30

Less

on 5

Pro

gres

s Ass

essm

ent

Less

on 6

Pre

-Ass

essm

ent

TRB:

U3-

342–

346

TRB:

U3-

347–

348

Less

on 6

: Writ

ing

Expo

nent

ial E

xpre

ssio

ns in

Equ

ival

ent F

orm

s

Stud

ents

exp

lore

the

usef

ulne

ss o

f rew

ritin

g ex

pone

ntia

l exp

ress

ions

in e

quiv

alen

t for

ms i

n or

der t

o so

lve

real

-wor

ld p

robl

ems

invo

lvin

g ex

pone

ntia

l gro

wth

and

dec

ay.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

31

Day

32

3.6.

1: W

ritin

g Ex

pone

ntia

l Exp

ress

ions

in E

quiv

alen

t For

ms

TRB:

U3-

351–

374

SRB:

U3-

224–

241

SWB:

171

–178

A–S

SE.3

c★

Day

33

Less

on 6

Pro

gres

s Ass

essm

ent

Less

on 7

Pre

-Ass

essm

ent

TRB:

U3-

375–

377

TRB:

U3-

378–

379




Less

on 7

: Sol

ving

Sys

tem

s of

Equ

atio

ns

Stud

ents

bui

ld o

n th

eir p

rior

kno

wle

dge

of sy

stem

s of l

inea

r equ

atio

ns fr

om p

revi

ous c

ours

es b

y ex

tend

ing

the

conc

ept t

o in

clud

e qu

adra

tic e

quat

ions

. Stu

dent

s lea

rn to

solv

e sy

stem

s mad

e up

of a

line

ar a

nd a

qua

drat

ic e

quat

ion

by g

raph

ing,

and

th

en b

y us

ing

alge

brai

c m

etho

ds. T

he q

uadr

atic

equ

atio

ns in

volv

ed a

re fo

r bot

h pa

rabo

las a

nd c

ircl

es.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

34

3.7.

1: S

olvi

ng S

yste

ms G

raph

ical

lyTR

B: U

3-38

2–40

1 SR

B: U

3-24

4–25

7 SW

B: 1

81–1

89

A–R

EI.7

Day

35

Day

36

3.7.

2: S

olvi

ng S

yste

ms A

lgeb

raic

ally

TRB:

U3-

402–

420

SRB:

U3-

258–

269

SWB:

193

–201

A–R

EI.7

Day

37

Less

on 7

Pro

gres

s Ass

essm

ent

TRB:

U3-

421–

426

U

nit A

sses

smen

tD

ay 3

8U

nit A

sses

smen

tTR

B: U

3-42

7–43

0




Unit

4: A

pplic

atio

ns o

f Pro

babi

lity

(21

Days

)U

nit O

verv

iew

: Stu

dent

s beg

in b

y de

finin

g ev

ents

, app

lyin

g th

e A

dditi

on R

ule,

and

lear

ning

abo

ut in

depe

nden

ce. T

hen,

they

pr

ogre

ss to

war

d co

nditi

onal

pro

babi

litie

s and

the

Mul

tiplic

atio

n Ru

le. T

his b

uild

s int

o us

ing

com

bina

tori

cs to

cou

nt a

nd

calc

ulat

e pr

obab

ilitie

s. F

inal

ly, s

tude

nts l

earn

to m

ake

and

anal

yze

deci

sion

s bas

ed o

n pr

obab

ility

.

Less

on 1

: Eve

nts

This

intr

oduc

tory

less

on d

efin

es p

roba

bilit

y an

d pr

ovid

es st

uden

ts w

ith th

e op

port

unity

to le

arn

the

man

y vo

cabu

lary

wor

ds

asso

ciat

ed w

ith p

roba

bilit

y, in

clud

ing

the

conc

epts

of e

xper

imen

ts, o

utco

mes

, sam

ple

spac

es, e

vent

s, an

d se

t not

atio

n. T

hen,

st

uden

ts le

arn

how

to so

lve

prob

abili

ty p

robl

ems w

ith th

e A

dditi

on R

ule.

Fin

ally

, stu

dent

s lea

rn th

e di

ffere

nce

betw

een

inde

pend

ent a

nd d

epen

dent

eve

nts.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

1

Day

2Le

sson

1 P

re-A

sses

smen

t 4.

1.1:

Des

crib

ing

Even

tsPr

e-A

sses

smen

t TR

B: U

4-1–

2 In

stru

ctio

n/Pr

acti

ce

TRB:

U4-

6–32

SR

B: U

4-4–

23

SWB:

7–1

7

S–CP

.1★

Day

34.

1.2:

The

Add

ition

Rul

eTR

B: U

4-33

–47

SRB:

U4-

24–3

3 SW

B: 2

1–28

S–CP

.7★

Day

44.

1.3:

Und

erst

andi

ng In

depe

nden

t Eve

nts

TRB:

U4-

48–6

8 SR

B: U

4-34

–46

SWB:

31–

41

S–CP

.2★

Day

5Le

sson

1 P

rogr

ess A

sses

smen

t Le

sson

2 P

re-A

sses

smen

tTR

B: U

4-69

–73

TRB:

U4-

74–7

5




Less

on 2

: Con

ditio

nal P

roba

bilit

y

Stud

ents

lear

n w

hat c

ondi

tiona

l pro

babi

lity

is, a

nd h

ow to

solv

e pr

oble

ms i

n w

hich

con

ditio

nal p

roba

bilit

y ex

ists

. The

n, th

e co

ncep

t is e

xpan

ded

to u

sing

two-

way

freq

uenc

y ta

bles

to o

rgan

ize

info

rmat

ion

and

solv

e pr

oble

ms.

Last

ly, s

tude

nts l

earn

how

to

solv

e co

nditi

onal

pro

babi

lity

prob

lem

s usi

ng th

e M

ultip

licat

ion

Rule

.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

6

Day

74.

2.1:

Intr

oduc

ing

Cond

ition

al P

roba

bilit

yTR

B: U

4-79

–102

SR

B: U

4-50

–68

SWB:

45–

52

S–CP

.3★

S–

CP.5

★

S–CP

.6★

Day

8

Day

94.

2.2:

Usi

ng T

wo-

Way

Fre

quen

cy T

able

sTR

B: U

4-10

3–12

5 SR

B: U

4-69

–84

SWB:

55–

65

S–CP

.4★

S–

CP.5

★

S–CP

.6★

Day

10

4.2.

3: T

he M

ultip

licat

ion

Rule

TRB:

U4-

126–

147

SRB:

U4-

85–9

8 SW

B: 6

9–76

S–CP

.8★

(+)

Day

11

Stat

ion

Act

iviti

es S

et 1

: Pro

babi

lity

TRB:

U4-

257–

271

SWB:

121

–129

S–CP

.1★

S–CP

.2★

S–CP

.3★

Day

12

Less

on 2

Pro

gres

s Ass

essm

ent

Less

on 3

Pre

-Ass

essm

ent

TRB:

U4-

148–

151

TRB:

U4-

152




Less

on 3

: Com

bina

toric

s

Stud

ents

are

intr

oduc

ed to

com

bina

tions

and

per

mut

atio

ns a

nd h

ow to

cal

cula

te b

oth.

The

y us

e th

ese

pow

erfu

l con

cept

s to

solv

e a

vari

ety

of p

robl

ems.

The

n, st

uden

ts c

ombi

ne th

e pr

obab

ility

skill

s dev

elop

ed e

arlie

r in

this

uni

t with

com

bina

tori

cs to

so

lve

mor

e re

al-w

orld

pro

blem

s.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

13

Day

14

4.3.

1: C

ombi

natio

ns a

nd P

erm

utat

ions

TRB:

U4-

155–

174

SRB:

U4-

101–

112

SWB:

79–

86

S–CP

.9★

(+)

Day

15

4.3.

2: P

roba

bilit

y w

ith C

ombi

nato

rics

TRB:

U4-

175–

190

SRB:

U4-

113–

119

SWB:

89–

96

S–CP

.9★

(+)

Day

16

Less

on 3

Pro

gres

s Ass

essm

ent

Less

on 4

Pre

-Ass

essm

ent

TRB:

U4-

191–

193

TRB:

U4-

194–

195

Less

on 4

: Mak

ing

and

Anal

yzin

g De

cisi

ons

Stud

ents

app

ly sk

ills g

aine

d fr

om p

revi

ous l

esso

ns in

this

uni

t to

deci

de w

heth

er a

situ

atio

n is

fair

by

anal

yzin

g th

e pr

obab

ilitie

s of

the

poss

ible

out

com

es. T

hen,

they

ana

lyze

the

prob

abili

ties a

ssoc

iate

d w

ith v

ario

us si

tuat

ions

in o

rder

to m

ake

deci

sion

s, ca

lcul

ate

estim

ates

, and

det

erm

ine

whi

ch c

hoic

e is

mos

t lik

ely

to re

sult

in th

e de

sire

d ou

tcom

e.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

17

Day

18

4.4.

1: M

akin

g D

ecis

ions

TRB:

U4-

198–

217

SRB:

U4-

122–

133

SWB:

99–

106

S–M

D.6

★ (+

)

Day

19

4.4.

2: A

naly

zing

Dec

isio

nsTR

B: U

4-21

8–23

7 SR

B: U

4-13

4–14

7 SW

B: 1

09–1

17

S–M

D.7

★ (+

)

Day

20

Less

on 4

Pro

gres

s Ass

essm

ent

TRB:

U4-

238–

242

U

nit A

sses

smen

tD

ay 2

1U

nit A

sses

smen

tTR

B: U

4-24

3–24

8




Unit

5: S

imila

rity,

Rig

ht T

riang

le T

rigon

omet

ry, a

nd P

roof

(46

Days

)U

nit O

verv

iew

: Stu

dent

s beg

in b

y le

arni

ng a

bout

mid

poin

ts a

nd o

ther

poi

nts o

f int

eres

t in

a lin

e se

gmen

t. Th

en, t

hey

wor

k w

ith d

ilatio

ns a

nd si

mila

rity

, whi

ch b

uild

s int

o le

arni

ng a

bout

and

pro

ving

the

vari

ous s

imila

rity

stat

emen

ts. N

ext,

stud

ents

le

arn

abou

t spe

cial

ang

les i

n in

ters

ectin

g lin

es a

nd a

bout

rela

tions

hips

am

ong

the

angl

es fo

rmed

by

a se

t of p

aral

lel l

ines

in

ters

ecte

d by

a tr

ansv

ersa

l. St

uden

ts th

en re

turn

to w

orki

ng w

ith tr

iang

les a

nd p

rovi

ng th

eore

ms a

bout

them

, inc

ludi

ng

the

Inte

rior

Ang

le S

um T

heor

em, a

s wel

l as t

heor

ems a

bout

isos

cele

s tri

angl

es, m

idse

gmen

ts, a

nd c

ente

rs o

f tri

angl

es.

Nex

t, st

uden

ts w

ill e

xplo

re p

roof

s inv

olvi

ng p

aral

lelo

gram

s and

oth

er q

uadr

ilate

rals

. The

uni

t end

s with

an

intr

oduc

tion

to

trig

onom

etri

c ra

tios a

nd so

lvin

g pr

oble

ms u

sing

thos

e ra

tios a

nd th

e Py

thag

orea

n Th

eore

m.

Less

on 1

: Lin

e Se

gmen

ts

Stud

ents

lear

n ho

w to

find

the

leng

th o

f a se

gmen

t in

the

coor

dina

te p

lane

by

usin

g th

e di

stan

ce fo

rmul

a, a

nd th

ey c

alcu

late

the

coor

dina

tes o

f the

mid

poin

ts o

f seg

men

ts. T

he d

ista

nce

and

mid

poin

t for

mul

as a

re th

en u

sed

to so

lve

prob

lem

s. Th

ese

form

ulas

ar

e us

ed fo

r sev

eral

pro

ofs l

ater

in th

e un

it.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

1Le

sson

1 P

re-A

sses

smen

t 5.

1.1:

Mid

poin

ts a

nd O

ther

Poi

nts o

n Li

ne S

egm

ents

Pre-

Ass

essm

ent

TRB:

U5-

1 In

stru

ctio

n/Pr

acti

ce

TRB:

U5-

3–25

SR

B: U

5-2–

16

SWB:

7–1

4

G–G

PE.6

Day

2Le

sson

1 P

rogr

ess A

sses

smen

tTR

B: U

5-26

–27




Less

on 2

: Inv

estig

atin

g Pr

oper

ties

of D

ilatio

ns

Stud

ents

exp

lore

the

prop

ertie

s of d

ilatio

ns, t

he d

iffer

ence

bet

wee

n ri

gid

and

non-

rigi

d m

otio

ns, a

nd th

e m

eani

ng o

f a sc

ale

fact

or. T

hese

skill

s are

firs

t exp

lore

d in

isol

atio

n an

d th

en th

roug

h th

e co

ntex

t of a

pplic

atio

ns.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

3

Day

4Le

sson

2 P

re-A

sses

smen

t 5.

2.1:

Inve

stig

atin

g Pr

oper

ties o

f Par

alle

lism

and

the

Cent

erPr

e-A

sses

smen

t TR

B: U

5-28

–30

Inst

ruct

ion/

Prac

tice

TR

B: U

5-34

–56

SRB:

U5-

20–3

4 SW

B: 1

7–27

G–S

RT.1

a

Day

55.

2.2:

Inve

stig

atin

g Sc

ale

Fact

ors

TRB:

U5-

57–7

1 SR

B: U

5-35

–40

SWB:

31–

37

G–S

RT.1

b

Day

6Le

sson

2 P

rogr

ess A

sses

smen

t Le

sson

3 P

re-A

sses

smen

tTR

B: U

5-72

–76

TRB:

U5-

77–7

9




Less

on 3

: Def

inin

g an

d Ap

plyi

ng S

imila

rity

Stud

ents

stud

y th

e pr

oper

ties o

f sim

ilari

ty, a

nd th

ey e

xplo

re th

e A

ngle

-Ang

le S

imila

rity

Sta

tem

ent a

s a w

ay to

pro

ve th

at tw

o tr

iang

les a

re si

mila

r. Th

e le

sson

focu

ses o

n si

mila

r tri

angl

es, w

hile

the

Stat

ion

Act

iviti

es se

t ext

ends

the

conc

ept t

o ot

her f

igur

es.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

7

Day

85.

3.1:

Def

inin

g Si

mila

rity

TRB:

U5-

82–1

04

SRB:

U5-

43–5

7 SW

B: 4

1–53

G–S

RT.2

Day

95.

3.2:

App

lyin

g Si

mila

rity

Usi

ng th

e A

ngle

-Ang

le (A

A) C

rite

rion

TRB:

U5-

105–

120

SRB:

U5-

58–6

8 SW

B: 5

7–66

G–S

RT.3

Day

10

Stat

ion

Act

iviti

es S

et 1

: Sim

ilari

ty a

nd S

cale

Fac

tor

TRB:

U5-

661–

673

SWB:

303

–310

G–S

RT.1

b G

–SRT

.2D

ay 1

1Le

sson

3 P

rogr

ess A

sses

smen

t Le

sson

4 P

re-A

sses

smen

tTR

B: U

5-12

1–12

7 TR

B: U

5-12

8–12

9




Less

on 4

: Pro

ving

Sim

ilarit

y

Stud

ents

ext

end

thei

r kno

wle

dge

of tr

iang

le si

mila

rity

stat

emen

ts to

incl

ude

Side

-Ang

le-S

ide

(SA

S) a

nd S

ide-

Side

-Sid

e (S

SS).

Not

e th

at th

ese

stat

emen

ts, w

hich

rely

on

the

ratio

s of t

he si

des a

nd n

ot th

e le

ngth

s of t

he si

des,

shou

ld n

ot b

e co

nfus

ed w

ith

the

SAS

and

SSS

met

hods

of p

rovi

ng c

ongr

uenc

e. T

hese

sim

ilari

ty st

atem

ents

are

then

use

d to

pro

ve th

e Py

thag

orea

n Th

eore

m.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

12

Day

13

5.4.

1: P

rovi

ng T

rian

gle

Sim

ilari

ty U

sing

Sid

e-A

ngle

-Sid

e (S

AS)

an

d Si

de-S

ide-

Side

(SSS

) Sim

ilari

tyTR

B: U

5-13

2–14

8 SR

B: U

5-72

–82

SWB:

69–

77

G–S

RT.4

Day

14

5.4.

2: W

orki

ng w

ith R

atio

Seg

men

tsTR

B: U

5-14

9–16

9 SR

B: U

5-83

–95

SWB:

81–

92

G–S

RT.4

Day

15

5.4.

3: P

rovi

ng th

e Py

thag

orea

n Th

eore

m U

sing

Sim

ilari

tyTR

B: U

5-17

0–19

0 SR

B: U

5-96

–109

SW

B: 9

5–10

5

G–S

RT.4

Day

16

5.4.

4: S

olvi

ng P

robl

ems U

sing

Sim

ilari

ty a

nd C

ongr

uenc

eTR

B: U

5-19

1–21

3 SR

B: U

5-11

0–12

4 SW

B: 1

09–1

21

G–S

RT.5

Day

17

Less

on 4

Pro

gres

s Ass

essm

ent

Less

on 5

Pre

-Ass

essm

ent

TRB:

U5-

214–

219

TRB:

U5-

220–

222




Less

on 5

: Pro

ving

The

orem

s Ab

out L

ines

and

Ang

les

This

less

on c

ontin

ues t

he e

xplo

ratio

n of

pro

ofs.

Stud

ents

dis

cove

r a p

roof

for t

he V

ertic

al A

ngle

s The

orem

, as w

ell a

s pro

ofs o

f th

eore

ms c

once

rnin

g th

e an

gles

that

are

form

ed w

hen

para

llel l

ines

are

cut

by

a tr

ansv

ersa

l.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

18

Day

19

5.5.

1: P

rovi

ng th

e V

ertic

al A

ngle

s The

orem

TRB:

U5-

226–

255

SRB:

U5-

128–

148

SWB:

125

–136

G–C

O.9

Day

20

Day

21

5.5.

2: P

rovi

ng T

heor

ems A

bout

Ang

les i

n Pa

ralle

l Lin

es C

ut b

y a

Tran

sver

sal

TRB:

U5-

256–

282

SRB:

U5-

149–

169

SWB:

139

–149

G–C

O.9

Day

22

Stat

ion

Act

iviti

es S

et 2

: Par

alle

l Lin

es a

nd T

rans

vers

als

TRB:

U5-

674–

685

SWB:

311

–317

G–C

O.9

Day

23

Less

on 5

Pro

gres

s Ass

essm

ent

Less

on 6

Pre

-Ass

essm

ent

TRB:

U5-

283–

290

TRB:

U5-

291–

293




Less

on 6

: Pro

ving

The

orem

s Ab

out T

riang

les

Stud

ents

exp

lore

d pr

oofs

invo

lvin

g si

mila

rity

of t

rian

gles

in p

revi

ous l

esso

ns in

this

uni

t. In

this

less

on, t

hey

retu

rn to

tria

ngle

s to

dis

cove

r sev

eral

mor

e pr

oofs

of s

ome

of th

e pr

oper

ties o

f tri

angl

es.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

24

Day

25

5.6.

1: P

rovi

ng th

e In

teri

or A

ngle

Sum

The

orem

TRB:

U5-

297–

319

SRB:

U5-

173–

189

SWB:

153

–163

G–C

O.1

0

Day

26

5.6.

2: P

rovi

ng T

heor

ems A

bout

Isos

cele

s Tri

angl

esTR

B: U

5-32

0–34

3 SR

B: U

5-19

0–20

6 SW

B: 1

67–1

76

G–C

O.1

0

Day

27

5.6.

3: P

rovi

ng th

e M

idse

gmen

t of a

Tri

angl

eTR

B: U

5-34

4–37

4 SR

B: U

5-20

7–23

1 SW

B: 1

79–1

92

G–C

O.1

0

Day

28

Day

29

5.6.

4: P

rovi

ng C

ente

rs o

f Tri

angl

esTR

B: U

5-37

5–41

6 SR

B: U

5-23

2–26

1 SW

B: 1

95–2

05

G–C

O.1

0

Day

30

Less

on 6

Pro

gres

s Ass

essm

ent

Less

on 7

Pre

-Ass

essm

ent

TRB:

U5-

417–

422

TRB:

U5-

423




Less

on 7

: Pro

ving

The

orem

s Ab

out P

aral

lelo

gram

s

Man

y of

the

geom

etri

cal p

roof

s tha

t stu

dent

s hav

e se

en a

re b

roug

ht to

geth

er in

this

less

on, w

hich

exp

lore

s the

theo

rem

s for

pa

ralle

logr

ams a

nd o

ther

spec

ial q

uadr

ilate

rals

.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

31

Day

32

5.7.

1: P

rovi

ng P

rope

rtie

s of P

aral

lelo

gram

sTR

B: U

5-42

6–45

3 SR

B: U

5-26

4–28

3 SW

B: 2

09–2

19

G–C

O.1

1

Day

33

5.7.

2: P

rovi

ng P

rope

rtie

s of S

peci

al Q

uadr

ilate

rals

TRB:

U5-

454–

487

SRB:

U5-

284–

307

SWB:

223

–229

G–C

O.1

1

Day

34

Stat

ion

Act

iviti

es S

et 3

: Rho

mbi

, Squ

ares

, Kite

s, an

d Tr

apez

oids

TRB:

U5-

686–

696

SWB:

319

–325

G–C

O.1

1

Day

35

Less

on 7

Pro

gres

s Ass

essm

ent

Less

on 8

Pre

-Ass

essm

ent

TRB:

U5-

488–

490

TRB:

U5-

491–

492

Less

on 8

: Exp

lorin

g Tr

igon

omet

ric R

atio

s

Stud

ents

are

intr

oduc

ed to

trig

onom

etri

c ra

tios.

Stud

ents

lear

n ho

w to

cal

cula

te th

ese

ratio

s, an

d ex

plor

e si

ne a

nd c

osin

e as

co

mpl

emen

ts. T

his i

ntro

duct

ion

to tr

igon

omet

ry p

repa

res s

tude

nts f

or th

e ne

xt le

sson

, in

whi

ch tr

igon

omet

ric

ratio

s are

use

d to

so

lve

prob

lem

s, as

wel

l as f

or th

e m

uch

deep

er st

udy

of tr

igon

omet

ry in

late

r cou

rses

.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

36

Day

37

5.8.

1: D

efin

ing

Trig

onom

etri

c Ra

tios

TRB:

U5-

496–

523

SRB:

U5-

311–

329

SWB:

233

–243

G–S

RT.6

Day

38

5.8.

2: E

xplo

ring

Sin

e an

d Co

sine

As C

ompl

emen

tsTR

B: U

5-52

4–54

0 SR

B: U

5-33

0–33

9 SW

B: 2

47–2

55

G–S

RT.7

Day

39

Less

on 8

Pro

gres

s Ass

essm

ent

Less

on 9

Pre

-Ass

essm

ent

TRB:

U5-

541–

544

TRB:

U5-

545–

546




Less

on 9

: App

lyin

g Tr

igon

omet

ric R

atio

s

Stud

ents

use

the

trig

onom

etri

c ra

tios l

earn

ed in

the

prev

ious

less

on a

nd th

e Py

thag

orea

n Th

eore

m to

solv

e pr

oble

ms.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

40

5.9.

1: C

alcu

latin

g Si

ne, C

osin

e, a

nd T

ange

ntTR

B: U

5-55

0–57

3 SR

B: U

5-34

3–35

8 SW

B: 2

59–2

67

G–S

RT.8

★

Day

41

5.9.

2: C

alcu

latin

g Co

seca

nt, S

ecan

t, an

d Co

tang

ent

TRB:

U5-

574–

593

SRB:

U5-

359–

371

SWB:

271

–279

G–S

RT.8

★

Day

42

5.9.

3: P

robl

em S

olvi

ng w

ith th

e Py

thag

orea

n Th

eore

m

and

Trig

onom

etry

TRB:

U5-

594–

614

SRB:

U5-

372–

385

SWB:

283

–290

G–S

RT.8

★

Day

43

5.9.

4: P

rovi

ng th

e Py

thag

orea

n Id

entit

yTR

B: U

5-61

5–63

1 SR

B: U

5-38

6–39

5 SW

B: 2

93–3

00

F–TF

.8

Day

44

Stat

ion

Act

iviti

es S

et 4

: Sin

e, C

osin

e, a

nd T

ange

nt R

atio

s, an

d A

ngle

s of E

leva

tion

and

Dep

ress

ion

TRB:

U5-

697–

707

SWB:

327

–332

G–S

RT.6

G

–SRT

.7

G–S

RT.8

★

Day

45

Less

on 9

Pro

gres

s Ass

essm

ent

TRB:

U5-

632–

635

U

nit A

sses

smen

tD

ay 4

6U

nit A

sses

smen

tTR

B: U

5-63

6–64

2




Unit

6: C

ircle

s W

ith a

nd W

ithou

t Coo

rdin

ates

(30

Days

)U

nit O

verv

iew

: Stu

dent

s stu

dy th

e pr

oper

ties o

f cir

cles

, inc

ludi

ng c

entr

al a

nd in

scri

bed

angl

es, c

hord

s of a

cir

cle,

and

tang

ents

to

a c

ircl

e. T

hen,

they

bui

ld o

n th

is k

now

ledg

e to

exp

lore

pol

ygon

s cir

cum

scri

bed

by o

r ins

crib

ed in

a c

ircl

e. N

ext,

stud

ents

m

ove

on to

the

prop

ertie

s of t

ange

nt li

nes a

nd th

eir c

onst

ruct

ion.

Stu

dent

s are

intr

oduc

ed to

radi

ans,

and

they

use

radi

ans t

o fin

d th

e ar

ea o

f a se

ctor

and

the

circ

umfe

renc

e an

d ar

ea o

f a c

ircl

e. S

tude

nts b

uild

from

one

- and

two-

dim

ensi

onal

are

nas t

o a

thre

e-di

men

sion

al o

ne b

y ex

plor

ing

mor

e de

eply

the

volu

me

form

ulas

for c

ylin

ders

, pyr

amid

s, co

nes,

and

sphe

res.

The

links

be

twee

n al

gebr

a an

d ge

omet

ry a

re e

xplo

red

thro

ugh

deri

ving

the

equa

tions

for c

ircl

es a

nd p

arab

olas

. Fin

ally

, stu

dent

s use

co

ordi

nate

s to

prov

e ge

omet

ric

theo

rem

s abo

ut c

ircl

es a

nd p

arab

olas

.

Less

on 1

: Int

rodu

cing

Circ

les

This

less

on b

egin

s by

intr

oduc

ing

circ

les a

nd v

ocab

ular

y re

late

d to

cir

cles

, inc

ludi

ng c

entr

al a

nd in

scri

bed

angl

es. N

ext,

stud

ents

exp

lore

the

rela

tions

hip

betw

een

chor

ds a

nd th

e an

gles

and

arc

s the

y cr

eate

. The

n, st

uden

ts le

arn

the

defin

ition

s of a

ta

ngen

t lin

e an

d a

seca

nt li

ne, a

nd th

e pr

oper

ties a

ssoc

iate

d w

ith e

ach.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

1

Day

2Le

sson

1 P

re-A

sses

smen

t 6.

1.1:

Sim

ilar C

ircl

es a

nd C

entr

al a

nd In

scri

bed

Ang

les

Pre-

Ass

essm

ent

TRB:

U6-

1–2

Inst

ruct

ion/

Prac

tice

TR

B: U

6-5–

27

SRB:

U6-

4–21

SW

B: 7

–15

G–C

.1

G–C

.2

Day

36.

1.2:

Cho

rd C

entr

al A

ngle

s Con

ject

ure

TRB:

U6-

28–4

2 SR

B: U

6-22

–30

SWB:

19–

27

G–C

.2

Day

46.

1.3:

Pro

pert

ies o

f Tan

gent

s of a

Cir

cle

TRB:

U6-

43–6

2 SR

B: U

6-31

–42

SWB:

31–

42

G–C

.2

Day

5Le

sson

1 P

rogr

ess A

sses

smen

t Le

sson

2 P

re-A

sses

smen

tTR

B: U

6-63

–67

TRB:

U6-

68




Less

on 2

: Ins

crib

ed P

olyg

ons

and

Circ

umsc

ribed

Tria

ngle

s

Stud

ents

lear

n ho

w to

con

stru

ct a

cir

cle

that

is in

scri

bed

in a

tria

ngle

by

first

find

ing

the

poin

t of c

oncu

rren

cy o

f the

ang

le

bise

ctor

s (th

e in

cent

er).

Then

, stu

dent

s mov

e on

to th

e co

nstr

uctio

n of

cir

cum

scri

bed

circ

les,

whi

ch re

quir

es th

em to

firs

t fin

d th

e po

int o

f con

curr

ency

for t

he p

erpe

ndic

ular

bis

ecto

rs (t

he c

ircu

mce

nter

). Fi

nally

, stu

dent

s exp

lore

the

prop

ertie

s of

insc

ribe

d qu

adri

late

rals

.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

66.

2.1:

Con

stru

ctin

g In

scri

bed

Circ

les

TRB:

U6-

71–9

5 SR

B: U

6-45

–62

SWB:

45–

54

G–C

.3

Day

76.

2.2:

Con

stru

ctin

g Ci

rcum

scri

bed

Circ

les

TRB:

U6-

96–1

12

SRB:

U6-

63–7

3 SW

B: 5

7–65

G–C

.3

Day

86.

2.3:

Pro

ving

Pro

pert

ies o

f Ins

crib

ed Q

uadr

ilate

rals

TRB:

U6-

113–

127

SRB:

U6-

74–8

4 SW

B: 6

9–77

G–C

.3

Day

9St

atio

n A

ctiv

ities

Set

3: C

ircu

mce

nter

, Inc

ente

r, O

rtho

cent

er,

and

Cent

roid

TRB:

U6-

389–

402

SWB:

185

–192

G–C

O.1

2 G

–CO

.13

G–C

.3D

ay 1

0Le

sson

2 P

rogr

ess A

sses

smen

t Le

sson

3 P

re-A

sses

smen

tTR

B: U

6-12

8–13

1 TR

B: U

6-13

2–13

3




Less

on 3

: Con

stru

ctin

g Ta

ngen

t Lin

es

This

bri

ef le

sson

show

s how

to c

onst

ruct

a ta

ngen

t lin

e th

roug

h a

give

n po

int o

n a

circ

le, a

nd h

ow to

con

stru

ct a

tang

ent l

ine

thro

ugh

a po

int t

hat i

s not

on

the

circ

le.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

11

6.3.

1: C

onst

ruct

ing

Tang

ent L

ines

TRB:

U6-

136–

161

SRB:

U6-

87–1

05

SWB:

81–

90

G–C

.4 (+

)

Day

12

Less

on 3

Pro

gres

s Ass

essm

ent

TRB:

U6-

162–

165

Less

on 4

: Fin

ding

Arc

Len

gths

and

Are

as o

f Sec

tors

Stud

ents

con

tinue

thei

r stu

dy o

f cir

cles

by

lear

ning

how

to c

alcu

late

arc

leng

th b

ased

on

the

rela

tions

hip

betw

een

the

arc

leng

th,

the

radi

an m

easu

re o

f the

cen

tral

ang

le, a

nd th

e le

ngth

of t

he ra

dius

. The

n, st

uden

ts le

arn

how

to c

alcu

late

the

area

of a

sect

or,

agai

n us

ing

the

leng

th o

f the

radi

us a

nd th

e m

easu

re o

f the

cen

tral

ang

le in

radi

ans.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

13

Less

on 4

Pre

-Ass

essm

ent

6.4.

1: D

efin

ing

Radi

ans

Pre-

Ass

essm

ent

TRB:

U6-

166

Inst

ruct

ion/

Prac

tice

TR

B: U

6-16

9–18

1 SR

B: U

6-10

9–11

5 SW

B: 9

3–99

G–C

.5

Day

14

Day

15

6.4.

2: D

eriv

ing

the

Form

ula

for t

he A

rea

of a

Sec

tor

TRB:

U6-

182–

193

SRB:

U6-

116–

120

SWB:

103

–109

G–C

.5

Day

16

Stat

ion

Act

iviti

es S

et 1

: Cir

cum

fere

nce,

Ang

les,

Arc

s, Ch

ords

, and

In

scri

bed

Ang

les

TRB:

U6-

363–

376

SWB:

167

–176

G–C

.2

G–C

.5

Day

17

Less

on 4

Pro

gres

s Ass

essm

ent

Less

on 5

Pre

-Ass

essm

ent

TRB:

U6-

194–

195

TRB:

U6-

196




Less

on 5

: Exp

lain

ing

and

Appl

ying

Are

a an

d Vo

lum

e Fo

rmul

as

Stud

ents

hav

e se

en th

e fo

rmul

as fo

r cir

cum

fere

nce

and

area

of a

cir

cle

in p

revi

ous m

ath

cour

ses.

In th

is le

sson

, stu

dent

s pr

ove

why

thes

e fo

rmul

as w

ork,

and

they

als

o se

e a

proo

f of t

he ra

tio π

. The

n, st

uden

ts m

ove

on to

exp

lore

the

form

ulas

for

calc

ulat

ing

the

volu

mes

of c

ylin

ders

, pyr

amid

s, co

nes,

and

sphe

res.

Thro

ugh

the

stud

y of

vol

ume,

stud

ents

are

exp

osed

to

Cava

lieri

’s Pr

inci

ple.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

18

6.5.

1: C

ircu

mfe

renc

e an

d A

rea

of a

Cir

cle

TRB:

U6-

200–

221

SRB:

U6-

124–

138

SWB:

113

–120

G–G

MD

.1

Day

19

Day

20

6.5.

2: V

olum

es o

f Cyl

inde

rs, P

yram

ids,

Cone

s, an

d Sp

here

sTR

B: U

6-22

2–24

4 SR

B: U

6-13

9–15

3 SW

B: 1

23–1

30

G–G

MD

.1

G–G

MD

.3★

Day

21

Less

on 5

Pro

gres

s Ass

essm

ent

Less

on 6

Pre

-Ass

essm

ent

TRB:

U6-

245–

247

TRB:

U6-

248




Less

on 6

: Der

ivin

g Eq

uatio

ns

Stud

ents

dis

cove

r tw

o of

the

four

con

ic se

ctio

ns, t

he c

ircl

e an

d th

e pa

rabo

la. T

he st

udy

of th

e ci

rcle

con

tinue

s, th

is ti

me

com

bini

ng c

ircl

es w

ith a

lgeb

ra a

s stu

dent

s dis

cove

r the

alg

ebra

ic e

quat

ion

for a

cir

cle.

The

n, st

uden

ts le

arn

how

to c

reat

e eq

uatio

ns fo

r par

abol

as u

sing

the

geom

etri

c de

finiti

on o

f a p

arab

ola.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

22

Day

23

6.6.

1: D

eriv

ing

the

Equa

tion

of a

Cir

cle

TRB:

U6-

252–

277

SRB:

U6-

157–

174

SWB:

133

–139

G–G

PE.1

Day

24

Stat

ion

Act

iviti

es S

et 2

: Spe

cial

Seg

men

ts, A

ngle

Mea

sure

men

ts,

and

Equa

tions

of C

ircl

esTR

B: U

6-37

7–38

8 SW

B: 1

77–1

83G

–C.1

G

–C.2

G

–C.4

G

–C.5

G

–GPE

.1D

ay 2

56.

6.2:

Der

ivin

g th

e Eq

uatio

n of

a P

arab

ola

TRB:

U6-

278–

305

SRB:

U6-

175–

195

SWB:

143

–152

G–G

PE.2

Day

26

Less

on 6

Pro

gres

s Ass

essm

ent

Less

on 7

Pre

-Ass

essm

ent

TRB:

U6-

306–

308

TRB:

U6-

309




Less

on 7

: Usi

ng C

oord

inat

es to

Pro

ve G

eom

etric

The

orem

s Ab

out C

ircle

s an

d Pa

rabo

las

Stud

ents

furt

her e

xpan

d th

eir u

nder

stan

ding

of t

he c

onne

ctio

n be

twee

n ge

omet

ric

defin

ition

of c

ircl

es a

nd p

arab

olas

and

the

alge

brai

c eq

uatio

ns fo

r the

se sh

apes

. Stu

dent

s use

figu

res i

n th

e co

ordi

nate

pla

ne to

illu

stra

te a

nd p

rove

theo

rem

s abo

ut c

ircl

es

and

para

bola

s alg

ebra

ical

ly.

Day

Are

a of

stu

dy/c

onte

ntPa

ges

Stan

dard

(s)

Day

27

Day

28

6.7.

1: U

sing

Coo

rdin

ates

to P

rove

Geo

met

ric

Theo

rem

s Abo

ut

Circ

les a

nd P

arab

olas

TRB:

U6-

313–

339

SRB:

U6-

199–

217

SWB:

155

–163

G–G

PE.4

Day

29

Less

on 7

Pro

gres

s Ass

essm

ent

TRB:

U6-

340–

342

Uni

t Ass

essm

ent

Day

30

Uni

t Ass

essm

ent

TRB:

U6-

343–

349

End-

of-C

ours

e A

sses

smen

tD

ay 3

1En

d-of

-Cou

rse

Ass

essm

ent

Plea

se g

o to

wal

ch.c

om/u

pdat

es a

nd re

gist

er to

rece

ive

End-

of-C

ours

e A

sses

smen

ts a

nd o

ther

upd

ates

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ccss ip math ii teacher resource suggested …walch.com/pdf/ccss_math_ii_pacing_guide.pdfccss ip...

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