Getting to the Core - sausd.us · Instructional Activities: ... angle classification (right,...

Getting to the Core

Geometry Fourth Grade

1

Fourth Grade Geometry

Table of Contents

Unit Overview 3 Van Hiele Theory of Geometric Thought 8 Preparing the Learner A – Collaboration and Pre-Assessment 9 Lesson 1 – Open Sort 16 Lesson 2 – Parallel and Perpendicular 23 Lesson 3 - Angles 34 Lesson 4 - Precision with Vocabulary 39 Lesson 5 - The Greedy Triangle 44 Lesson 6 - Shape Deconstruction 49 Lesson 7 – Map Project 55 Special Education Appendix 69

2

Sant

a A

na U

nifie

d Sc

hool

Dis

tric

t Com

mon

Cor

e U

nit P

lann

er-M

athe

mat

ics

Uni

t Titl

e:

Geo

met

ry

Gra

de

Leve

l/Cou

rse:

4th

Gra

de

Tim

e Fr

ame:

9 d

ays

Big

Idea

(E

ndur

ing

Und

erst

andi

ngs)

:

Obj

ects

can

be d

escr

ibed

, cla

ssifi

ed a

nd a

naly

zed

base

d on

thei

r att

ribut

es.

Esse

ntia

l Q

uest

ions

: •

How

can

par

alle

l and

per

pend

icul

ar li

nes

be id

entif

ied?

•H

ow c

an y

ou u

se o

nly

a rig

ht a

ngle

to c

lass

ify a

ll an

gles

?•

Wha

t geo

met

ric c

ompo

nent

s m

ake

up fi

gure

s?•

Wha

t pro

perti

es d

o ge

omet

ric o

bjec

ts h

ave

in c

omm

on?

Inst

ruct

iona

l Act

iviti

es:

Act

iviti

es/T

asks

Uni

ts h

ave

man

y ty

pes o

f les

sons

that

hav

e di

ffere

nt p

urpo

ses

Prep

arin

g th

e Le

arne

r A

CON

CEPT

LE

SSO

N 1

CON

CEPT

LE

SSO

N 2

CON

CEPT

LE

SSO

N 3

GET

TING

PR

ECIS

E LE

SSO

N 4

GET

TING

G

ENER

AL

LESS

ON

5 &

6

FORM

ATIV

E AS

SESS

MEN

T LE

SSO

N 7

ROBU

ST A

ND

DIFF

EREI

ATIO

N LE

SSO

NS

are

avai

labl

e to

cha

lleng

e th

e ac

cele

rate

d le

arne

r and

dee

pen

thei

r con

cept

ual u

nder

stan

ding

.

Each

less

on h

as re

sour

ces

in th

e ap

pend

ix fo

r stu

dent

s tha

t re

quire

add

ition

al s

uppo

rt.

SUM

MAT

IVE

ASSE

SSM

ENT

LESS

ON

7 Po

st

Asse

ssm

ent

Purp

ose:

Eng

age

stud

ents

, sp

ark

curio

sity,

“hoo

k” a

nd

nece

ssita

te

Sequ

ence

of p

robl

ems,

act

iviti

es, p

urpo

se to

de

velo

p sp

ecifi

c con

cept

s, de

signe

d to

sc

affo

ld, o

utco

me

is a

delic

ate

(frag

ile)

unde

rsta

ndin

g

Purp

ose:

att

end

to p

reci

sion,

pin

dow

n de

finiti

ons,

conv

entio

ns, s

ymbo

lism

Purp

ose:

use

conc

epts

cr

oss c

onte

xts,

gene

raliz

e vi

a va

riabl

es

and

para

met

ers a

nd

diffe

rent

type

s of

num

bers

, ope

ratio

ns,

func

tions

, str

uctu

res

Diffe

rent

stud

ents

wor

k on

diff

eren

t thi

ngs,

goal

s of b

oth

mov

ing

from

a fr

agile

to ro

bust

un

ders

tand

ing

via

a va

riety

of p

robl

ems

3

Desig

ning

for O

ppor

tuni

ties

for S

tand

ards

for M

athe

mat

ical

Pra

ctic

e ha

ppen

at t

he U

nit L

evel

Fr

om: B

ill M

cCal

lum

, Ph.

D., U

nive

rsity

of A

rizon

a

21st C

entu

ry

Skill

s:

Lear

ning

and

Inno

vatio

n:

Crit

ical

Thi

nkin

g &

Pro

blem

Sol

ving

C

omm

unic

atio

n &

Col

labo

ratio

n C

reat

ivity

& In

nova

tion

Info

rmat

ion,

Med

ia a

nd T

echn

olog

y:

Onl

ine

Tool

s S

oftw

are

Har

dwar

e

Esse

ntia

l A

cade

mic

La

ngua

ge:

Tier

II:

•C

lari

ficat

ion

•C

olla

bora

tion

•N

orm

s•

Arg

umen

t•

Para

llel

•Pe

rpen

dicu

lar

•A

ngle

•A

cute

ang

le•

Obt

use

angl

e•

Rig

ht a

ngle

•Pr

esen

ce•

Abs

ence

•V

ertic

es•

Equi

late

ral

•Is

osce

les

•Sc

alen

e

Tier

III:

•

Pigg

ybac

k•

Com

pass

Ros

e

Wha

t pre

-ass

essm

ent w

ill b

e gi

ven?

G

eom

etry

Pre

-Ass

essm

ent

How

will

pre

-ass

essm

ent g

uide

inst

ruct

ion?

Th

e G

eom

etry

pre

-ass

essm

ent w

ill in

form

the

teac

her w

ith th

e da

ta

need

ed th

at w

ill s

how

wha

t st

uden

ts a

lread

y kn

ow, w

hat t

hey

don’

t 4

know

, and

wha

t pos

sibl

e m

iscon

cept

ions

ther

e m

ight

be.

Stan

dard

s A

sses

smen

t of S

tand

ards

(inc

lude

form

ativ

e an

d su

mm

ativ

e)

Com

mon

Cor

e Le

arni

ng S

tand

ards

Tau

ght a

nd A

sses

sed

(incl

ude

one

or m

ore

stand

ards

for o

ne o

r mor

e of

the

area

s bel

ow. P

leas

e wr

ite o

ut th

e co

mpl

ete

text

for t

he st

anda

rd(s

) you

incl

ude.

)

Wha

t ass

essm

ent(

s) w

ill b

e ut

ilize

d fo

r th

is

unit?

(inc

lude

the

type

s of b

oth

form

ativ

e as

sess

men

ts (F

) tha

t will

be

used

thro

ugho

ut

the

unit

to in

form

you

r ins

truct

ion

and

the

sum

mat

ive

asse

ssm

ents

(S)

that

will

de

mon

strat

e stu

dent

mas

tery

of t

he st

anda

rds.)

Wha

t doe

s the

as

sess

men

t tel

l us?

Com

mon

Cor

e M

athe

mat

ics C

onte

nt S

tand

ard(

s):

4.G

.1 D

raw

poi

nts,

lines

, lin

e se

gmen

ts, r

ays,

angl

es (r

ight

, acu

te,

obtu

se),

and

perp

endi

cula

r an

d pa

ralle

l lin

es. I

dent

ify th

ese

in tw

o-di

men

sion

al fi

gure

s.

4.G

.2 C

lass

ify tw

o-di

men

siona

l fig

ures

bas

ed o

n th

e pr

esen

ce o

rab

senc

e of

par

alle

l or

perp

endi

cula

r lin

es, o

r th

e pr

esen

ce o

r ab

senc

e of

an

gles

of a

spec

ified

size

. Rec

ogni

ze r

ight

tria

ngle

s as a

cat

egor

y, a

nd

iden

tify

righ

t ang

les.

(Tw

o di

men

sion

al s

hape

s sho

uld

incl

ude

spec

ial

tria

ngle

s, e.

g., e

quila

tera

l, iso

scel

es, s

cale

ne, a

nd sp

ecia

l qua

drila

tera

ls,

e.g.

, rho

mbu

s, sq

uare

, rec

tang

le, p

aral

lelo

gram

, tra

pezo

id.)

F: C

olla

bora

tion

thro

ugho

ut th

e un

it of

stud

y.

F: P

ictu

re S

ort A

ctiv

ity

F: S

hape

Han

dout

Act

iviti

es

F: N

ote

Taki

ng G

uide

F:

Stu

dent

Mat

h Jo

urna

l

S: G

eom

etry

Ter

m B

ook

S:

Cul

min

atin

g To

wn

Act

ivity

S:

Pre

-Ass

essm

ent

S: P

ost A

sses

smen

t

Ong

oing

evi

denc

e of

stud

ents

’ un

ders

tand

ing

of

conc

epts

pre

sent

ed.

Dia

gnos

tic

info

rmat

ion

for

inte

rven

tion

or

acce

lera

tion.

Stud

ent

com

preh

ensio

n of

un

it co

ncep

ts a

nd

the

Big

Idea

: O

bjec

ts c

an b

e de

scri

bed,

cl

assi

fied

and

anal

yzed

bas

ed o

n th

eir

attr

ibut

es.

Opp

ortu

nitie

s for

list

enin

g, sp

eaki

ng, r

eadi

ng, w

ritin

g, a

nd

thin

king

(Cite

Lite

racy

Sta

ndar

ds (a

s app

licab

le):

L

isten

ing

and

Spea

king

: Eng

age

effe

ctiv

ely

in a

rang

e of

col

labo

rativ

e di

scus

sion

s (on

e-on

-one

, in

grou

ps, a

nd te

ache

r-le

d) w

ith d

iver

se p

artn

ers o

n gr

ade

4 to

pics

and

text

s, bu

ildin

g on

oth

ers’

idea

s and

exp

ress

ing

thei

r ow

n cl

early

. 4.

1.a

Com

e to

dis

cuss

ions

pre

pare

d, h

avin

g re

ad o

r stu

died

requ

ired

mat

eria

l; ex

plic

itly

draw

on

that

pre

para

tion

and

othe

r inf

orm

atio

n kn

own

abou

t the

topi

c to

ex

plor

e id

eas u

nder

dis

cuss

ions

. 4.

2. b

Fol

low

agr

eed-

upon

rule

s for

dis

cuss

ions

and

car

ry o

ut a

ssig

ned

role

s.

Teac

her e

valu

atio

n of

stud

ent s

peak

ing

and

liste

ning

: F:

Ask

and

ans

wer

que

stio

ns in

pai

rs a

nd

colla

bora

tive

grou

ps d

urin

g an

d af

ter l

esso

ns.

F: W

ork

colla

bora

tivel

y us

ing

Col

labo

rativ

e C

onve

rsat

ion

sent

ence

fram

es to

cre

ate

clas

sroo

m n

orm

s fo

r the

uni

t of s

tudy

.

Whe

n ta

lkin

g ab

out

mat

hem

atic

s in

pa

irs a

nd

colla

bora

tive

grou

ps, d

o st

uden

ts

follo

w

prot

ocol

/rule

s/

5

4.2.

c Po

se a

nd re

spon

d to

spec

ific

ques

tions

to c

larif

y or

follo

w u

p on

info

rmat

ion,

an

d m

ake

com

men

ts th

at c

ontri

bute

to th

e di

scus

sion

and

link

to th

e rem

ark

of

othe

rs.

4.1.

d Re

view

the

key

idea

s exp

ress

ed a

nd e

xpla

in th

eir o

wn

idea

s and

un

ders

tand

ing

in li

ght o

f the

disc

ussio

n.

rout

ines

for

colla

bora

tive

disc

ussio

ns?

Stan

dard

s of

Mat

hem

atic

al

Prac

tice:

(Che

ck a

ll th

at a

pply

) 1.

Mak

e se

nse

of p

robl

ems a

nd p

erse

vere

in so

lvin

gth

em. 2.R

easo

n ab

stra

ctly

and

qua

ntita

tivel

y.3.

Con

stru

ct v

iabl

e ar

gum

ents

and

crit

ique

the

reas

onin

gof

oth

ers.

4.M

odel

with

mat

hem

atic

s.5.

Use

app

ropr

iate

tool

s stra

tegi

cally

.6.

Atte

nd to

pre

cisio

n.7.

Look

for a

nd m

ake

use

of st

ruct

ure.

8.Lo

ok fo

r and

exp

ress

regu

larit

y in

repe

ated

reas

onin

g.

Opp

ortu

nitie

s for

Obs

erva

ble

Dat

a (H

ow w

ill st

uden

ts de

mon

strat

e th

ese

Mat

hem

atic

al P

ract

ices

?)

•C

olla

bora

tive

disc

ussio

ns in

tegr

ated

in a

llle

sson

s.•

Con

stru

ctin

g re

ason

able

and

fact

bas

ed e

vide

nce

to d

efen

d th

eir

mat

hem

atic

al r

easo

ning

and

conc

lusi

ons.

•C

ulm

inat

ing

Act

ivity

•C

ompl

etio

n of

Geo

met

ry F

lip B

ook

•C

ompl

etio

n of

2-d

imen

sion

al fi

gure

s

Res

ourc

es/

Mat

eria

ls:

Text

(s) T

itles

: H

M G

rade

4 T

extb

ook,

Sax

on M

ath

Seri

es

Mat

hem

atic

al T

ools:

R

uler

s, ci

rcle

s (1/

4th o

f a c

utou

t for

eac

h st

uden

t)

Med

ia/T

echn

olog

y: D

iscov

ery

Scie

nce

Geo

met

ry V

ideo

s, Y

ou T

ube,

ST

Mat

h- G

eom

etry

Supp

lem

enta

ry M

ater

ials:

Tap

e, g

lue,

mar

shm

allo

ws,

coffe

e st

irre

rs, c

onst

ruct

ion

pape

r

Inte

rdis

cipl

inar

y C

onne

ctio

ns:

Cite

seve

ral i

nter

disc

iplin

ary

or c

ross

-con

tent

con

nect

ions

mad

e in

this

uni

t of s

tudy

(i.e

. lite

ratu

re, s

cien

ce, s

ocia

l st

udie

s, ar

t, et

c.)

•Li

tera

ture

(The

Gre

edy

Tria

ngle

)-Y

ou T

ube

vide

o•

Art

– G

eom

etry

Per

form

ance

Tas

k

6

http://illustrativemathematics.org/standards/practice











Diff

eren

tiate

d In

stru

ctio

n:

Bas

ed o

n de

sired

stud

ent o

utco

mes

, wha

t ins

truc

tiona

l va

riat

ion

will

be

used

to a

ddre

ss th

e ne

eds o

f Eng

lish

Lear

ners

by

lang

uage

pro

ficie

ncy

leve

l?

•Se

nten

ce fr

ames

are

pro

vide

d in

var

ying

deg

rees

of d

iffic

ulty

to fa

cilit

ate

acad

emic

lang

uage

and

conv

ersa

tions

.•

Use

of v

isual

org

aniz

ers t

o as

sist p

roce

ssin

gm

athe

mat

ical

idea

s.•

Scaf

f old

ing

by te

ache

r as

nec

essa

ry to

supp

ort

the

Engl

ish L

earn

er.

•Ex

plic

itly

teac

h ke

y ac

adem

ic v

ocab

ular

y.•

Use

of m

anip

ulat

es to

faci

litat

e co

ncep

tual

unde

rsta

ndin

g.

Bas

ed o

n de

sired

stud

ent o

utco

mes

, wha

t ins

truc

tiona

l va

riat

ion

will

be

used

to a

ddre

ss th

e ne

eds o

f stu

dent

s w

ith sp

ecia

l nee

ds, i

nclu

ding

gift

ed a

nd ta

lent

ed?

Spec

ial N

eeds

- •

Incl

usio

n of

App

endi

x to

pro

vide

add

ition

alre

sour

ces t

o he

lp p

repa

re st

uden

ts. *

•O

ppor

tuni

ties f

or v

erba

l reh

ears

al o

f con

cept

s.•

Use

of v

isual

org

aniz

ers.

•Ex

plic

itly

teac

h ke

y ac

adem

ic v

ocab

ular

y.

Acc

eler

ated

Lea

rner

s-

•C

once

pts o

f eac

h da

y’s l

esso

ns h

ave

been

exte

nded

to in

clud

e a

high

er le

vel o

f dep

th o

f co

mpl

exity

. •

Acc

eler

ated

stud

ents

can

cre

ate

thei

r ow

nre

pres

enta

tions

as a

n ex

tens

ion

to d

eepe

n th

eir

unde

rsta

ndin

g of

the

mat

hem

atic

al c

once

pts.

7


4th Grade Unit- Theory

The 4th grade Geometry Unit was based on research that explains how students develop their understanding of geometric concepts. In order to ensure students success in geometry and to develop their ability to think and reason in a geometric context, The van Hiele Model of the Development of Geometric Thought was utilized. The van Hiele model is a sequential model that has a five-level hierarchy of geometric thinking. In this unit we will be addressing the first three levels.

The van Hiele Levels of Geometric Thought Summary

(From Elementary and Middle School Mathematics, Teaching Developmentally, by John Van de Walle, Karen Karp, and Jennifer Bay-Williiams. Pearson Education, Inc., Boston (2010).)

Level 0: Visualization- Students know vocabulary, can identify shapes by its appearance, and can begin to classify shapes by similarities and differences.

Level 1: Analysis- Students begin to recognize parts of shapes, and as they look at them they make generalizations to understand the properties of shapes. Students refine their understanding of symmetry, angle classification (right, obtuse, acute), parallel and perpendicular.

Level 2: Informal Deduction- Students begin to understand the relationship between properties. For example, “If all four angles are right angles, then the shape must be a rectangle. If it is a square, then all angles are right angles. If it is a square, then it must be a rectangle.” If-then reasoning is established to lead to logical arguments of properties.

Level 3: Deduction-Students begin to develop definitions, theorems, corollaries, and postulates to establish geometric truths. Students are able to make conclusions based on abstract statements about geometric properties.

Level 4: Rigor- “The objects of thought at level 4 are deductive, axiomatic systems of geometry.” (Generally the level of college geometry courses)

The levels are sequential, hierarchical, and not age dependent. Our goal is to guide students through the progression of these levels.

8


Big Idea: Objects can be described, classified and analyzed based on their attributes.

Mathematical Standards:

Major emphasis standard : 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two dimensional figures.

4.G.2 Supporting Standard: Classify two-dimensional figures based on the presence or absence ofparallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category and identify right triangles.

Essential Questions:

How can parallel and perpendicular lines be identified?

How can you use a right angle to classify all angles?

What geometric components make up figures?

What properties do geometric shapes have in common?

9

L

esso

n: P

rep

A

Less

on 1

Le

sson

2

Less

on 3

Act

ivities

*

Pre

-Ass

essm

ent

* “S

ierp

insk

i Tri

angl

e”

*Col

labo

rati

ve

Con

vers

atio

n

*Com

pare

and

Con

tras

t a

tria

ngle

wit

h a

rect

angl

e *G

eom

etri

c fi

gure

sor

t *

Pres

enta

tion

of

sort

*C

reat

e a

Geom

etry

wor

d

bank

*Per

pend

icul

ar P

ictu

re

Sort

*P

aral

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Preparing the Learner A

SAUSD Common Core Lesson Planner Math Teacher:

Unit: Geometry Lesson: Prep A

Grade Level/Course: 4

Duration: 60 minutes Date:

Common Core and Content Standards

Listening and Speaking: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and texts, building on others’ ideas and expressing their own clearly. 4.1.a Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussions. 4.2. b Follow agreed-upon rules for discussions and carry out assigned roles. 4.2.c Pose and respond to specific questions to clarify or follow up on information, and make comments that contribute to the discussion and link to the remark of others. 4.1.d Review the key ideas expressed and explain their own ideas and understanding in light of the discussion.

Materials/ Resources/ Lesson Preparation

• Pre-Assessment• Post Big Idea and Essential Questions• Post Content and Language Objectives daily• Sierpinski Triangle handout – 1 per student• Collaborative Conversation Sentence Frames – 1 per group• Chart paper for Collaborative Talk Norms• Math Journal

Objectives

Content: Students will participate in two collaborative conversations, compare and contrast a small group discussion with a whole group discussion, and create classroom collaboration norms.

Language: Students will discuss “Sierpinski Triangle” to compose classroom collaboration norms.

Depth of Knowledge Level

Level 1: Recall Level 2: Skill/Concept Level 3: Strategic Thinking Level 4: Extended Thinking

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Common Core Instructional Shifts in Mathematics

Focus on the Standards

Coherence within and across grade levels

Rigor (Balance of conceptual understanding, procedural skill & fluency, and application of skills)

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UNDERSTANDING WORDS WORTH KNOWING

Clarification Collaboration Norms Argument

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Expand Evidence

Interrupting Respect

Pre-teaching Considerations

Student desks should be arranged in collaborative groups of four for the entire unit. Student should be able to work successfully in collaborative groups.

Lesson Delivery

Instructional Methods

Check method(s) used in the lesson:

Modeling Guided Practice Collaboration

Independent Practice Guided Inquiry Reflection

Lesson Opening

Prior Knowledge, Context, and Motivation: The purpose of this lesson is to practice how to work together in collaborative groups. Students will have a collaborative discussion which may include argument.

Body of the Lesson: Activities/ Questioning/ Tasks/ Strategies/ Technology/ Engagement

Lesson Overview

Teacher Directions • Pass out pre-assessment and explain to the students that the

purpose of the test is to see what they already know. Theyshould not worry if they don’t know the answers, just do thebest they can. The same test will be given at the end of the unitto measure growth.

• Introduce Content and Language Objectives.• Discuss ways to have a respectful discussion. Explain that in a

discussion it is ok to agree and disagree, but that it must bedone in a respectful way. To facilitate this we will be usingsentence frames. Pass out the sentence frames for collaborativeconversation and review them.

• Pass out “Sierpinski Triangle” to each student. Ask eachstudent to count how many triangles are in the picture. Givestudents 5 minutes to count the triangles on their own, and thenask them to discuss their answers with their collaborativegroup. Students should be able to give an answer and justify orexplain how they got it. If the students have different answers,(which is expected), have them use the sentence frames todebate the answer.

Differentiated Instruction:

English Learners: Collaborative sentence frames are provided on Collaborative Conversations handout.

Students Who Need Additional Support:

See Appendix

Accelerated Learners:

Allow students to create their own shape-like version of the Sierpinski Triangle. This activity can be extended over two days.

11



• To continue practicing collaborative conversations, have thestudents pair up with a second collaborative group to againdebate their answers. After approximately 10 minutes, open adiscussion with the whole class comparing/contrasting their twodiscussions. What issues came up when working in a largergroup as opposed to a smaller group? How did the grouphandle disagreement? What norms need to be established forcollaborative talk? Work with the students to create a list of 4-6 norms

o Suggested norms§ We listen to one another.§ We share our own ideas and explain them.§ We respect one another’s ideas, even if they are

different.§ We respectfully disagree and try to see the

other view.§ We let others finish explaining their ideas

without interrupting.§ We take turns and share time.

• Explain that throughout the unit the class will be using thenorms in their collaborative groups and have them copy thenorms into their math journal.

• Review Content and Language Objectives.• Homework – In student math journals, students write a

paragraph describing a successful collaborative group. (Whatwould you see? What would you hear?)

Lesson Reflection Teacher Reflection Evidenced by Student Learning/ Outcomes

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Directions: Answer each question. Some questions may have more than one correct answer.

1. Which of these is a line segment?

A B C

2. Which lines below are parallel?

A B C

3. Which polygon has two sets ofparallel lines?

A B C

4. How many acute angles are inthis polygon?

A 5

B 4

C 3

D 2

5. Draw an obtuse angle:

6. Which shapes have an obtuseangle?

A B

C D

7. Draw a shape with at least oneright angle. Label the parts of theshape.

8. Which of these shapes have NOright angles?A right triangle B rectangle C acute triangle

9. Which shapes have TWO sets ofparallel lines? A triangle B rectangle C trapezoid D parallelogram

10. Alex is teaching Nicolas abouttriangles. He says the triangle below is an acute triangle. Is he right or wrong? Explain how you know?

Pre-Assessment

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Collaborative Conversation Sentence Frames

What to say when you want clarification…

• Will you explain that again?

• I have a question about what you saidabout _____________.

• Do you mean that __________?

• Could you expand a little bit on what yousaid about _____________?

• Could you give an example of what youmean by ______________?

What to say when you want to build on another’s idea…

• You made a good point when you said_________.

• My idea is related to _______’s idea. Ithink _________.

• I see what you’re saying. I agreebecause ______________.

• My idea builds on _______’s idea. I think_________.

• I’d like to piggyback on that idea. I think__________.

What to say when you disagree…

• I see what you’re saying, but I think that___________.

• Another way to look at it is ________.

• I do agree with what you said about____________, but I think _________.

• I see it another way. Based on ________,I think _________.

• Another possibility might be _______.

• I have a different answer. I wrote down

What to say when you want to cite evidence from the text…

• On page____, paragraph _______, theauthor says ___________.

• When I read _______ on page _______, Ithought that _________.

• I think the text supports my thinking onpage _______, paragraph ______, by stating that ________.

• Another example of ______ is on page_____, paragraph, where the author states_____________.

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Sierpinski Triangle

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Lesson 1


Unit: Geometry Lesson: 1

Grade Level/Course:

4



4 G 1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.G.2Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.


• Post Big Idea and Essential Questions• Post Content and Language Objectives daily• Geometric Figure Handout• construction paper – 1 piece per group• scissors• glue• homework handout• Chart paper for Word Bank• Collaborative Conversation Sentence Frames

Objectives

Content: Students will identify the properties of various geometric objects.

Language: Students will explain their rationale for sorting shapes and be able to justify their reasoning.
















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Lesson 1

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Student desks should be arranged in collaborative groups of four for the entire unit. Student should be able to work successfully in collaborative groups. Review posted norms.

Students should be familiar with creating a Double Bubble Thinking Map (Compare and Contrast). Students should have background about triangles and rectangles.

Lesson Delivery





Lesson Opening

Prior Knowledge, Context, and Motivation: Students will be familiar with classifying shapes based on their properties.


Lesson Overview

Math Warm-up Display the triangle and rectangle and ask the students to compare and contrast them using a Double Bubble map in their math journal. Possible student answers shown below.


English Learners:

We sorted our shapes by ________ because ______.


See Appendix

Accelerated Learners: Have the students resort the shapes in another way and explain their reasoning.

17


Lesson 1

Teacher Directions • Introduce Big Idea and Essential Questions. Once you have

introduced them please display them throughout the entire unit.• Introduce daily Content and Language Objective• Review Collaborative Conservation Frames• Pass out one piece of construction paper, geometric figure

handout, glue, and scissors.• Tell the students that they will be sorting their geometric figures

into groups after they have cut them out. Each group will decidehow to sort the figures based on a common geometric property(their choice).

• Remind students to follow group norms.• Tell students that they will be presenting their completed sort to

the class, and the class will guess how the shapes were sorted.• Give students 5-10 minutes to discuss, sort cards, and glue them

on the construction paper.• Collaborative groups will write the property they used to sort the

figures on the top of the construction paper so that it can befolded and hidden from view.

• All groups should present one of their groupings. Eachcollaborative group will guess how the shapes were sorted andwrite the group answer on a student whiteboard or piece of paper.When all groups have attempted to guess, the presenting groupwill explain how they sorted.

• As groups are presenting the teacher will create add the followingterms to the word bank of geometric terms as they are generatedby the students: line segment, point, ray, line, angle.

• After all groups have presented, the students should answer theessential question “What properties do geometric figures have incommon?” in their math journals.

Closure Review Content and Language Objectives

Homework • Lesson 1 homework handout


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Lesson 1

Shapes for Prior Knowledge Activity- Lesson 1

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Lesson 1

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Lesson 1

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Lesson 1

Lesson 1 Homework

Name:

Color the lines yellow.

Color the line segments blue.

Color the rays orange.

Color the lines green.

Color the points red.

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Lesson 2


Unit: Lesson: 2

Grade Level/Course:

4



4 G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.G.2Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.


• Review Big Idea and Essential Questions• Post Content and Language Objectives daily• Collaborative Conversation Sentence Frames• glue for each group• parallel T-chart handout• parallel picture sort handout• perpendicular T-chart handout• perpendicular picture sort handout• math journals• highlighters• Lesson 2 homework• 2 Video segments (2 minutes each)

o Show Parallel Video Clip http://app.discoveryeducation.com/player/?assetGuid=0d80ed2b-2c86-4aab-a4aa-062d612f09eb&fromMyDe=0&isPrinterFriendly=0&provider=&isLessonFromHealth=0&productcode=US&isAssigned=false&includeHeader=YES&homeworkGuid=

o Perpendicular Video Clip http://app.discoveryeducation.com/player/?assetGuid=0d80ed2b-2c86-4aab-a4aa-062d612f09eb&fromMyDe=0&isPrinterFriendly=0&provider=&isLessonFromHealth=0&productcode=US&isAssigned=false&includeHeader=YES&homeworkGuid=

Objectives

Content: Students will sort figures by their lines (parallel, perpendicular, and intersecting)

Language: Students will define parallel and perpendicular lines.












23

http://app.discoveryeducation.com/player/?assetGuid=0d80ed2b-2c86-4aab-a4aa-062d612f09eb&fromMyDe=0&isPrinterFriendly=0&provider=&isLessonFromHealth=0&productcode=US&isAssigned=false&includeHeader=YES&homeworkGuid









Lesson 2





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Lesson Delivery





Lesson Opening

Prior Knowledge, Context, and Motivation: Students should have background knowledge of parallel and perpendicular lines.


Lesson Overview

Review lesson 1 homework

Teacher Directions

• Introduce Big Idea and Essential Questions. Once you haveintroduced them please display them throughout the entire unit.As you proceed through the lessons you may want to add studentsor class generated answers to the questions.

• Introduce daily Content and Language Objective• Review Collaborative Conservation Frames

Activity 1 • Show Parallel Video Clip (2 minutes)

http://app.discoveryeducation.com/player/?assetGuid=0d80ed2b-2c86-4aab-a4aa-062d612f09eb&fromMyDe=0&isPrinterFriendly=0&provider=&isLessonFromHealth=0&productcode=US&isAssigned=false&includeHeader=YES&homeworkGuid=

• Pass out Parallel Picture sort handout and Parallel T-chart. Incollaborative groups, have the students cut out pictures and thentake turns choosing a picture card and placing it on the T-chart.They should explain to the group where they are placing the cardand why. Continue until all pictures have been sorted. During


English Learners:

This picture shows _____ lines because_________. This picture doesn’t show _____ lines because ______.

Students Who Need Additional Support: See Appendix

24







Lesson 2

the sort, the teacher will monitor the groups and ask questions about where the cards were placed. Students should be able to justify the placement of each picture card. Once cards are correctly placed, students may glue them to the chart.

• To check the sort, complete a whole class sort of the cards.Project the T-chart on the board, have students come up andchoose a shape, place it on the chart, and explain why. Studentswho disagree with the placement could then raise their hand andexplain why the picture card should be moved.

• Add parallel lines to your word bank.Activity 2

• Show Perpendicular Video Clip (2 minutes)http://app.discoveryeducation.com/player/?assetGuid=0d80ed2b-2c86-4aab-a4aa-062d612f09eb&fromMyDe=0&isPrinterFriendly=0&provider=&isLessonFromHealth=0&productcode=US&isAssigned=false&includeHeader=YES&homeworkGuid=

• Pass out Perpendicular Picture sort and Perpendicular T-chart. Incollaborative groups, have the students cut out pictures and thentake turns choosing a picture card and placing it on the T-chart.They should explain to the group where they are placing the cardand why. Continue until all pictures have been sorted. Duringthe sort, the teacher will monitor the groups and ask questionsabout where the cards were placed. Students should be able tojustify the placement of each picture card. Once cards arecorrectly placed, students may glue them to the chart.

• To check the sort, complete a whole class sort of the cards.Project the T-chart on the board, have students come up andchoose a shape, place it on the chart, and explain why. Studentswho disagree with the placement could then raise their hand andexplain why the picture card should be moved.

• Add perpendicular to the word bank.Closure

• Review Content and Language Objectives• Review Essential Question “How can parallel and perpendicular

lines be identified?” Have students write the essential questionand their answer in their math journal. If time, allow a fewstudents to share their answers.

Homework: • Handout – Students will look for parallel and perpendicular lines

in their home/neighborhood. They will draw a sketch of whatthey find.


Students can work individually on their picture sort for parallel and perpendicular lines. They will present to independently to the class. Students can extend the homework by creating their own True/False statements.

25







Lesson 2


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Lesson 2

Parallel T-Chart

Parallel Lines No Parallel Lines

27


Lesson 2

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Lesson 2

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Lesson 2

Perpendicular T-Chart

Perpendicular Lines No Perpendicular Lines

30


Lesson 2

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Lesson 2

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Lesson 2

Recording Sheet

What parallel and perpendicular lines do you see in or around your home or neighborhood? Sketch and label your results below.

33


Lesson 3


Unit: Lesson: 3






• Review Big Idea and Essential Questions• Post Content and Language Objectives daily• Collaborative Conversation Sentence Frames• ST Math• Shapes Handout – 1 per student• Construction paper• crayons• Circle cutout- 1 per group of 4 students (each student will use a ¼ piece)

Objectives

Content: Students will understand that a right

angle is 90 degrees, an obtuse angle is bigger than a right angle, and an acute angle is smaller than a right angle

Language: Students will be able to describe right, acute and obtuse angles.











8. Look for and express regularity in repeated reasoning.Common Core Instructional Shifts in Mathematics




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Angle Acute angle Obtuse angle Right angle

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Lesson 3

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Lesson Delivery





Lesson Opening

Prior Knowledge, Context, and Motivation:

Students should be familiar with terms and meanings of right angles, obtuse angles, and acute angles.


Lesson Overview Teacher Directions

Review homework

• Review Big Idea and Essential Questions.• Review daily Content and Language Objective• Review Collaborative Conservation Frames

Math Warm-Up Math Talk: In teacher mode of ST Math, project on smart board or screen.

• Content>Test Drive Games>4th grade >OptionalObjectives>Lines and Angles> Parallel or Perpendicular

Choose students or groups to come to the computer/smart board, and identify the correct lines. They should also justify their answer. Be sure to complete the 3rd level where the students have to visualize where the lines will meet.

Activity 1: • Have students work in collaborative groups of four for this

activity.• Pass out Shapes Handout and a circle cutout to each group of

four.• Teacher will ask the students how their piece of the circle relates

to measuring angles. Let students discuss for 1-2 minutes thenshare out to the whole class.

• If necessary tell students:o a right angle is 90°o an obtuse angle is greater than 90°


English Learners:

This angle is a(n) __________ angle because _________.

These lines are ______ because ___________.

These lines are not ______ because _________.

A _________ measures _________ degrees.


See Appendix

Accelerated Learners: Students can walk around school to find examples of acute, right, and obtuse angles. If technology resources are available, students can take pictures

35


Lesson 3

o an acute angle is smaller than 90°• Add new terms to your word bank: angle, acute, obtuse, right• Students will each take ¼ of the circle cutout to use as a guide to

a right angle. Pass out the handout “Shapes”. Students willdetermine if the angles are right by placing their piece of thecircle cutout on each angle of all shapes. Teacher may need toshow examples and ask the students what angle it is and whatmakes it that type of angle.

o Color right angles redo Color acute angles blue (The angle is smaller than a right

angle.)o Color obtuse angles yellow (The angle is bigger than a

right angle.)Activity 2:

• Teacher will begin a collaborative discussion using the followingquestions:

o If you put all of the cutout pieces back together, whatshape is formed? ( Students should put the circle backtogether)

o How many right angles are in the entire shape?o What is the sum of all four of your right angles when put

together? (You may need to remind them of the 90°measurement)

o Where in real life do we talk about the 360°?

Closure: As a class, review the answers to Shapes handout. Have students write and answer Essential Question in their math notebook. “How can you use a right angle to classify all angles?”

Review Content and Language Objectives

Pass out homework – Angles Homework handout

of their angles, otherwise they may sketch their results.


36


Lesson 3

Shapes Name____________________________

Directions: If the angle is a right angle, color it red.

If the angle is an acute angle, color it blue.

If the angle is an obtuse angle, color it yellow. 37


Lesson 3

Name;_______________________________________ Date:_____________ Homework

Angles Homework Classify the angles as acute, obtuse, or right. Explain your reasoning.

1. 2.

_________________________ ___________________________

_________________________ ___________________________

3. 4.

_________________________ ___________________________

_________________________ ___________________________

5. 6.

_________________________ ___________________________

_________________________ ___________________________

Circle True or False for the following statements.

An obtuse angle is smaller than a right angle. True False An acute angle is smaller than a right angle. True False An obtuse angle has only 1 line and 1 point. True False A right angle can be measured with the corner of a _____

38


Lesson 4

Unit: Lesson: 4

Grade Level/Course:

4



4 G 1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.


• Post today’s Content and Language Objectives• Collaborative Conversation Sentence Frames• Post sentence frames• 1 piece of construction paper per student• tape or glue• math journals• scissors• Homework handout• ST Math

Technology: video 1 http://app.discoveryeducation.com/player/?assetGuid=da3df462-05df-4949-98e7-dc4430035cbb&fromMyDe=0&isPrinterFriendly=0&provider=&isLessonFromHealth=0&productcode=US&isAssigned=false&includeHeader=YES&homeworkGuid=

Objectives

Content:

Students will be able to identify the basic geometric figures.

Language:

Students will be able to explain the definitions of basic geometric terms.
















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KEY WORDS ESSENTIAL TO UNDERSTANDING WORDS WORTH KNOWING

39

http://app.discoveryeducation.com/player/?assetGuid=da3df462-05df-4949-98e7-dc4430035cbb&fromMyDe=0&isPrinterFriendly=0&provider=&isLessonFromHealth=0&productcode=US&isAssigned=false&includeHeader=YES&homeworkGuid




Lesson 4

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Line, line segment, ray, point, end point, angle, perpendicular, parallel, acute, obtuse, right



Lesson Delivery





Lesson Opening

Prior Knowledge, Context, and Motivation: Students should be familiar with basic geometric terms and definitions.


Lesson Overview

• Review Big Idea and Essential Questions. • Review daily Content and Language Objective • Review Collaborative Conservation Frames

Teacher Directions Math Warm-up: Math Talk: In order to reinforce the standards taught in lesson 2, in teacher mode of ST Math, project

• Content>Test Drive Games>4th grade >Optional Objectives>Lines and Angles> Which Angle> Level 1

Choose students or groups to come to the computer/smart board, and identify the correct lines. They should also justify their answer. Be sure to complete the 1st level where the students can match the shape with its name. Activity 1

• Review Big Idea and Essential Questions. Once you have introduced them please display them throughout the entire unit.

• Introduce daily Content and Language Objective • Play the 2 minute video to review the Geometric Terms.

http://app.discoveryeducation.com/player/?assetGuid=da3df462-05df-4949-98e7-dc4430035cbb&fromMyDe=0&isPrinterFriendly=0&provider=&isLessonFromHealth=0&productcode=US&isAssigned=false&includeHeader=YES&homeworkGuid=

Activity 2 • Students will work with a partner for this activity. • Review class word bank. • Pass out a piece of construction paper, scissors, and glue to

each student. • Instruct the students in how to create their foldable and

label the front with the Geometric math terms. (see picture)

Step 1


English Learners: Sentence Frames: A ________ is a _______ because ____________. Students Who Need Additional Support: See Appendix Accelerated Learners: Students can find real life models of the vocabulary terms in the classroom. Results can be recorded in their math journal and shared with the class.

40







Lesson 4

• Tell students that with their partner, they must discuss the termsand then match the correct definition to the correct geometricterm. Once the teacher has checked their results, the studentswill glue to correct definition under the corresponding term.They can then draw a picture on the open flap.

• Teacher should be moving around the room to monitor thestudents’ collaborative conversations and foldables.

• If time permits, students can share their foldables with theclass.

Review Big Idea and Essential Questions

Pass out homework page and explain

.


41


Lesson 4

A continuous straight

path that goes on without

end in opposite

directions.

An exact location in

space represented by a

dot.

Part of line with two

endpoints.

Part of a line that starts

at an endpoint and goes

on forever in one

direction.

An angle that measures

90°.


greater than 90°.


less than 90°.

Two rays that share a

common endpoint.

Lines that intersect to

form right angles.

Lines that are the same

distance apart at all points

and do not intersect.

42


Lesson 4

Name:______________________ Date:___________________

Homework

Directions: Use the figure above to answer the following questions.

1. Color the acute angles red. How many acute angles are in the figure? ___________

2. Color all the right angles blue. How many right angles are in the figure? ______________

3. Color the obtuse angles yellow. How many obtuse angles are in the figure? __________

4. How many parallel lines are in the figure? _____________

5. How many perpendicular lines are in the figure? _________

6. How many triangles do you see? ______________

43


Lesson 5


Unit: Lesson: 5

Grade Level/Course:

4





• Post Big Idea and Essential Questions• Post Content and Language Objectives daily• Collaborative Conversation Sentence Frames• Greedy Triangle video• Note taking guide• Greedy Triangle homework handout

Objectives

Content: Students will learn that all shapes can change or be modified. Students will look for specific patterns.

Language: Students will explain how a shape can change when a side is added to a figure.
















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Presence Absence

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44


Lesson 5



Lesson Delivery





Lesson Opening

Prior Knowledge, Context, and Motivation: Students should have background knowledge of geometric two-dimensional shapes. Students should also realize that shapes can change. They should be able to see patterns from shape to shape.


Lesson Overview

Teacher Directions

Review homework


Activity

• Today the class will be doing a close read of a video. They willbe watching the video 2 times. The first time the students shouldjust focus and watch the video. The second time, they willcomplete a note taking guide. Begin today’s lesson of howshapes change and are made up of various geometric parts byplaying the video of The Greedy Triangle to introduce concepts.After the first viewing, have a brief discussion of the story.

o What shapes did you see?o What do you notice when a side is added to a shape?o What patterns did you find?

• For the second viewing of the video, give students the note takingguide. As the video plays, you may want to pause it to allow thestudents time to fill in their charts. After the video, the studentswill work in their collaborative groups to complete the chart. Theinformation for heptagon – decagon is inferred, but not clearlystated. However the students should be able to fill in the chartusing the pattern. When everyone has finished, go over the notetaking guide and correct any misconceptions. You may want tohave students share their sample drawing on the documentcamera.

• Review daily Content and Language Objectives.

Homework • The Greedy Triangle Homework handout. The students will look

at shapes and identify number of sides, number of angles, and


English Learners:

I saw _____ and _____.

The _____ changed when _______.

I saw a ___________ pattern.

This pattern changed when ________.


See Appendix


Ask students their ideas about why a shape with many sides and many angles (a dodecagon) would roll more than a shape with fewer sides and angles (a triangle).

45


Lesson 5

presence/absence of parallel and perpendicular lines.


46


Lesson 5

Name

right acute obtuse

The Greedy Triangle Notetaking Guide

number of anglesShape Name

number of sides Sample Drawing

47


Lesson 5

The Greedy Triangle Homework

Name

Directions: Look at each shape, count the number of sides, the number of each type of angle, and if there are parallel or perpendicular sides. Trace parallel sides red. Trace perpendicular lines in blue.

number of number of angles Lines Shape Sample

sides right acute obtuse Parallel Perpendicular

4 0 2 2 yes no

48


Lesson 6


Unit: Lesson: 6






• Post Big Idea and Essential Questions• Post Content and Language Objectives daily• Collaborative Conversation Sentence Frames• Stir sticks per student:

o 5- whole stir stickso 5- 2 ½ inch stir stickso 5 – 3 ½” inch stir sticks

• Mini Marshmallows – 20 per student• baggies• math journals

Objectives

Content: Students will be able to recognize the geometric components that make up shapes.

Language: Students will be able to name the geometric components of different shapes and describe the shape using an “if____, then ____ “statement.
















49


Lesson 6

Aca

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Vertices Equilateral Isosceles Scalene

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You may want to cover desks with a paper towel or piece of paper. Figures need to be constructed and left on a flat surface or they may fall apart.

Lesson Delivery





Lesson Opening

Prior Knowledge, Context, and Motivation: Students should be able to recognize and name the geometric components in isolation.


Lesson Overview

Teacher Directions


Review homework

Math Warm-up – “Pick Up Sticks Game” • Review homework• Pass out stir sticks• First students will drop the smaller 2 ½ inch stir sticks onto their

desk and look for different angles and lines. In their math journalthey will record their results.

Sample


English Learners:

I saw _______ and _____ when _________ was removed.

The marshmallow represents _________.

The sticks represent __________.

If __________, then_________.


50


Lesson 6

*If necessary, teacher may have to model this game.• Repeat with other sizes of stir sticks and then with all sizes

together.• Discuss as a class:

o What differences did you notice when using the shortersticks vs. all the sticks together?

o Did you notice any patterns?

Activity 1 • Pass out 20 marshmallows to each student.• Ask the students what they think the sticks represent and what do

the marshmallows represent? (Sticks – lines, rays, line segments.Marshmallows – points)

• Ask each student to make a shape using 3 sticks and 3marshmallows. Open up a discussion of the parts of the triangle.Introduce “if…then… If our shape has three lines and threeangles, then it is a triangle. (It consists of three line segments,three points, and three angles).

• In the students’ math journal, sketch the triangle and label thecomponents. (line segments, points, and angles)

• Remove one line segment and have pairs discuss the partsmaking up the figure. It now has two line segments and threepoints. It has one angle.

• Draw and name the type of angle in the math journal.• Remove the two points at the open end. Now describe the shape.

It has two rays, one angle, and one point.Activity 2

• Ask each student to make a new shape. They should use 4 sticksand 4 marshmallows. Open up a discussion of the parts of thequadrilateral. (It consists of four line segments, four points, andfour angles.) If it has four line segments and four angles, then itis a quadrilateral.

• In the students’ math journal, sketch the shape and label thecomponents. (line segments, points, and angles)

• Remove two line segments and three points from the shape.Again discuss the parts making up the figure. It now has tworays and one point. It has one angle.

• Draw and name the type of angle in the math journal.Activity 3

• Have the students create at least two new shapes and record the

See Appendix


Pair students together and have them create five new shapes by combining resources.

51


Lesson 6

shape in their journal. Then have them label the geometric components that make up the shape. Have them write an if ______, then _______ statement to go with each of their shapes.

Closure • Review Content and Language Objectives

• In math journals, have the students write and answer the essentialquestion

• What geometric components make up figures?

Homework • Hand out


52


Lesson 6

Name CCSS 4th Grade Lesson 6 Homework

Directions: Decide if each statement is true or false. Justify your answer with a complete sentence. Draw a picture of each underlined word.

1. A line has two end points. T F Your Drawing

2. A line segment has one endpoint and

extends without end in one direction. T F

3. A point represents a location in space. T F

4. Parallel lines will always intersect and

meet to form right angles. T F

53


Lesson 6

5. Perpendicular lines are lines that are always

the same distance apart and will never meet. T F Your Drawing

6. An angle is formed by two rays with a

common endpoint. T F

7. A ray is a closed figure made up of three

or more line segments. T F

8. Perpendicular lines form an obtuse angle. T F

54


Lesson 7


Unit: Geometry Lesson: 7 Performance Task

Grade Level/Course:

4





• Post Big Idea and Essential Questions• Post Content and Language Objectives daily• Collaborative Conversation Sentence Frames• 12” x 18” piece of white construction paper per student.• Geometry Map Project instruction handout• rulers• pencil• colored pencils or crayons

Objectives

Content: Students will recall and use geometric components and figures in order to complete a map project.

Language: Students will write two sets of directions for their map.
















55


Lesson 7

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Compass Rose

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Student desks should be arranged in collaborative groups of four for the entire unit. Students should be able to work successfully in collaborative groups. Review posted norms.

Lesson Delivery





Lesson Opening

Prior Knowledge, Context, and Motivation: Students should know the basic geometric figures and components.


Lesson Overview

Review homework

Teacher Directions

• Pass out construction paper and rulers. Make sure the studentshave pencils, and crayons or colored pencils.

• Explain to the students that they will be drawing a town that mustcontain all of the components listed on the Geometric MapProject sheet.

• Remind students that a compass rose should be included on theirmap. Assist students if necessary.

• Once the maps are completed, students need to write two sets ofdirections from one location to another on the map. Students willshare their maps and directions with their collaborative group.

• If time permits, teacher may have students share with wholeclass.

Homework Have the students take the map home and give directions to a parent from one location to another.


English Learners:


See Appendix


Have students write four or more sets of directions.

56


Lesson 7


57


Lesson 7

Geometry Performance Task

Your task is to design a map that includes several different kinds of lines, angles, and triangles. Your map can be of a town, your neighborhood, or an imaginary place. It must however include the following:

• Two sets of streets that are parallel.• Two sets of streets that are perpendicular.• One street that intersects another street to form an obtuse angle.• One street that is a line segment.• One street that is a line.• One street that is a ray.• An ice cream parlor made of a four sided shape.• A pool that must include an acute angle.• A pizza place with more than five sides.• A flag pole on a point.• Your map must also include a compass rose.

Remember to label your map with street and business names.

Once your map is completed, you are to write out two sets of directions from one place to another. Each set of directions must have one of these terms: parallel, intersecting, or perpendicular. These directions should be able to get your teacher and classmates from one place to another without getting lost!

Be prepared to share your map with the class!

58


Lesson 7

Geometry Performance Task Rubric

2 sets of streets that are parallel (2 points) 2 sets of streets that are perpendicular (2 points) 1 street that intersects another street

to form an obtuse angle (1 point)

1 street that is a line segment (1 point) 1 street that is a line (1 point) One street that is a ray (1 point) An ice cream parlor made of a 4 sided shape (2 points)

A pool that must include an acute angle (2 points) A pizza place with more than 5 sides (2 points)

A flag pole on a point. (1 point) Compass Rose (1 point)

2 sets of directions to go from one place to another using the words parallel, intersecting, or perpendicular (4 points)

Geometry Performance Task Rubric

2 sets of streets that are parallel (2 points) 2 sets of streets that are perpendicular (2 points) 1 street that intersects another street

to form an obtuse angle (1 point)

1 street that is a line segment (1 point) 1 street that is a line (1 point) One street that is a ray (1 point) An ice cream parlor made of a 4 sided shape (2 points)

A pool that must include an acute angle (2 points) A pizza place with more than 5 sides (2 points)

A flag pole on a point. (1 point) Compass Rose (1 point)

2 sets of directions to go from one place to another using the words parallel, intersecting, or perpendicular (4 points)

TOTAL:________ /20

(18-20 points= 5; 15-17 points= 4; 12-14 points=3; 9-11 points=2; 0-8 points=1)

TOTAL:________ /20

(18-20 points= 5; 15-17 points= 4; 12-14 points=3; 9-11 points=2; 0-8 points=1)

59


Lesson 7

Directions: Answer each question. Some questions may have more than one correct answer.


A B C


A B C


A B C


A 5

B 4

C 3

D 2


6. Which shapes have an obtuseangle?

A B

C D

7. Which of these polygons has onlyright angles?

A triangle B rectangle C square

8. Which of these polygons has NOright angles?A right triangle B rectangle C acute triangle

9. Which shapes have TWO sets ofparallel lines? A triangle B rectangle C trapezoid D parallelogram

10. Alex is teaching Nicolas abouttriangles. He says the triangle below is an acute triangle. Is he right or wrong? Explain how you know?

Post-Assessment

60


Lesson 7

61


Answer Keys

Post-Assessment


A B C


A B C


A B C


A 5

B 4

C 3

D 2


6. Which shapes have obtuseangles?

A B

C D

7. Which of these polygons has onlyright angles?

A triangle B rectangle C square

8. Which of these polygons has NOright angles?A right triangle B rectangle C acute triangle

9. Which shapes have TWO sets ofparallel lines?A triangle B rectangle C trapezoid D parallelogram

10. Alex is teaching Nicolas abouttriangles. He says the trianglebelow is an acute triangle. Is heright or wrong? Explain how youknow?

The triangle is a right triangle because it has a right angle.

62


Answer Keys

Sierpinski Triangle Answer Key

Total of 44 Triangles

63


Answer Keys

Name

Answer Key

Directions: Decide if each statement is true or false. Justify your answer with a complete sentence. Draw a picture of each underlined word.

1. A line has two endpoints. T F Your Drawing

A line does not have two endpoints. A line is

drawn between two points and continues without end

in both directions.

2. A line segment has one endpoint and extendswithout end in one direction.

T F

A line segment has 2 endpoints and does not go on

without end in in any direction.

3. A point represents a location in space. T F

4. Parallel lines will always intersect and meet toform right angles.

T F Parallel lines are lines that will never intersect

and are always the same distance apart. 64


Answer Keys

5. Perpendicular lines are lines that are always

the same distance apart and will never meet. T F Your Drawing

Perpendicular lines are lines that intersect and meet to

form right angles.

6. An angle is formed by two rays with a

common endpoint. T F

7. A ray is a closed figure made up of three

or more line segments. T F

8. Perpendicular lines form an obtuse angle. T F Perpendicular lines form right or 90° angles.

65


Answer Keys

66


Answer Keys

Name:______________________ Date:___________________

Homework

Directions: Use the figure above to answer the following questions.

1. Color the acute angles red. How many acute angles are in the figure? ___45________

2. Color all the right angles blue. How many right angles are in the figure? _____0________

3. Color the obtuse angles yellow. How many obtuse angles are in the figure? ____25______

4. How many parallel lines are in the figure? _____10________

5. How many perpendicular lines are in the figure? ____0_____

6. How many triangles do you see? _____25+_________

67


Answer Keys

Name

right acute obtuse

Triangle 3 0 3 0Answers may vary depending on how students draw the shape.

Quadrilateral 4 4 0 0Answers may vary depending on how students draw the shape.

Pentagon 5 2 0 3Answers may vary depending on how students draw the shape.

Hexagon 6 0 0 6Answers may vary depending on how students draw the shape.

Heptagon 7 0 0 7Answers may vary depending on how students draw the shape.

Octagon 8 0 0 8Answers may vary depending on how students draw the shape.

Nonagon 9 0 0 9Answers may vary depending on how students draw the shape.

Decagon 10 0 0 10Answers may vary depending on how students draw the shape.

The Greedy Triangle Notetaking Guide

number of anglesShape Name

number of sides Sample Drawing

68

Getting to the Core

Special Education

Appendix

69

Su

per

ior

Sta

nd

ard

sS

up

port

ive

Sch

ool

Cli

mate

Su

cces

sfu

l S

tud

ents

Sp

ecia

l E

du

cati

on

Dev

elop

men

t of

Ap

pen

dic

es

The

San

ta A

na

Un

ifie

d S

cho

ol D

istr

ict,

in t

he

fou

nd

ati

on

th

at

ALL

st

ud

ents

will

be

colle

ge

an

d c

are

er r

ead

y, is

cre

ati

ng

a c

om

pila

tio

n o

f re

sou

rces

incl

ud

ing

sca

ffo

lds,

str

ate

gie

s, a

cco

mm

od

ati

on

s, a

nd

m

od

ific

ati

on

s. T

hes

e su

pp

ort

s w

ill e

nsu

re t

ha

t st

ud

ents

wit

h

dis

ab

iliti

es, a

ma

jori

ty o

f w

ho

m a

re E

ng

lish

lea

rner

s, w

ill h

ave

th

e a

cces

s a

nd

su

pp

ort

nec

essa

ry t

o b

e co

lleg

e a

nd

ca

reer

rea

dy.

CC

SS A

pp

licat

ion

to

Stu

den

ts w

ith

Dis

abili

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sSt

ud

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wit

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isab

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tud

ents

elig

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un

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e In

div

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als

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isab

iliti

es A

ct (

IDEA

) m

ust

be

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to

exc

el w

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in t

he

gen

eral

cu

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ulu

m a

nd

be

pre

par

ed f

or

succ

ess

in t

hei

r p

ost

sch

oo

l liv

es,

incl

ud

ing

colle

ge a

nd

/or

care

ers.

In o

rder

fo

r st

ud

ents

to

mee

t h

igh

aca

dem

ic s

tan

dar

ds

and

to

fu

lly d

emo

nst

rate

th

eir

con

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tual

an

d p

roce

du

ral k

no

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dge

an

d s

kills

in m

ath

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atic

s, r

ead

ing,

wri

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g, s

pea

kin

g,

and

list

enin

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ngl

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lan

guag

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ts),

th

eir

inst

ruct

ion

mu

st in

corp

ora

te s

up

po

rts

and

ac

com

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s.-O

ran

ge C

ou

nty

De

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f Ed

uca

tio

n, 2

01

2

70

Lesson Preparing the Learner A

Teacher Talk

This lesson is designed to helping the teacher understand where students are with

collaborative conversations. The teacher will know if students require additional

instruction in positive collaborative conversation

Additional visuals for student use (to clarify, to disagree, to add on, and to cite

evidence) are provided

71

To Clarify

Will you explain that again?

I have a question about what you said about _____________.

Could you give an example of what you mean by ______________?

To Build On

You made a good point when you said _________.

I see what you’re saying. I agree because ______________.

My idea builds on _______’s idea. I think _________.

To Disagree

Another way to look at it is ________.

I do agree with what you said about ____________, but I think _________.

I have a different answer. I wrote down that _______________.

To Cite Evidence

When I read _______ on page _______, I thought that _________.

I think the text supports my thinking on page _______, paragraph ______, by stating that ________.

Another example of ______ is on page _____, paragraph, where the author states_____________.

72

To Build On

You made a good point when you said _________.

I see what you’re saying. I agree because ______________.

My idea builds on _______’s idea. I think _________.

73

To Clarify

Will you explain that again?

I have a question about what you said about _____________.

Could you give an example of what you mean by ______________?

74

To Disagree

Another way to look at it is ________.

I do agree with what you said about ____________, but I think _________.

I have a different answer. I wrote down that _______________.

75

Evidence

When I read _______ on page _______, I thought that _________.

I think the text supports my thinking on page _______, paragraph ______, by stating that ________.

Another example of ______ is on page _____, paragraph, where the author states_____________.

76

Lesson 1

Teacher Talk

Students will be sorting shapes and justifying their answers. Your students may benefit from some to

the accommodations and modifications below:

Based on your students' fine motor skills, you may want to precut the "geometric

shapes handout" and place them in a baggie, before you handout the materials.

Instead of having the students do the "T-Chart and sort”, you may want to create a tree

map with your students and sort the figures using the "common geometric property."

For the homework, it suggested that you complete this homework together (whole

group), before passing it out for the students to do at home independently.

OR

Start the homework with your students (doing questions that might be more difficult)

and then have them complete the rest of the homework assignment independently at

home.

77

Lesson 2

Teacher Talk

Students will be sorting figures by their lines. Students will have to know the definitions

of parallel and perpendicular lines.

Some students may benefit from the individual circle maps that help to define the

different lines.

The teacher may use the following supports:

circle maps of each type of line

78

Acu

te

Par

alle

lLi

ne

s

Bo

th li

ne

s m

easu

re

exac

tly

18

0°

Lin

es

that

ar

e in

th

e sa

me

pla

ne

an

d

do

no

t in

ters

ect

The

sam

e d

ista

nce

ap

art

at a

ll p

oin

ts

Mat

h B

oo

k

Life

Ex

per

ien

ces

Rai

lro

ad

trac

ks

80

Acu

te

Pe

rpe

nd

icu

lar

Lin

es

Co

nta

ins

4

angl

es t

hat

m

easu

re

exac

tly

90

°

Lin

es

that

in

ters

ect

to

fo

rm

righ

t an

gles

Cre

ates

4

pe

rfec

t co

rner

s

Mat

h B

oo

k

Life

Ex

per

ien

ces

An

in

ters

ect

ion

o

r 4

way

st

op

on

a

hig

hw

ay

81

Lesson 3

Teacher Talk

Students will be learning about the different angles: right, obtuse, acute. They will be

able to describe the properties of the angles.

Students may benefit from the following supports:

circle maps of each type of angle

sort organizer to provide guidance for students who might need it

- Some students may benefit from “I do, we do, you do” when sorting the

angles. It is important to choose an angle from each of the 4 categories on the sort

to ensure student understanding of angle properties.

82

Will

mat

ch a

n in

dex

car

d c

orn

er p

erf

ectl

yA

cute

Acu

te

An

gle

An

an

gle

wit

h a

m

easu

re le

ss t

han

th

at o

f a

righ

t an

gle

or

90

°

Smal

ler

than

a

righ

t an

gle

Wh

en a

do

or

is p

arti

ally

o

pen

it

crea

tes

an

acu

te a

ngl

e

Mat

h B

oo

k

Life

Ex

per

ien

ces

Will

be

co

vere

d b

y an

ind

ex c

ard

Un

it

man

ipu

lati

ve

83

Will

mat

ch a

n in

dex

car

d c

orn

er p

erf

ectl

yA

cute

Ob

tuse

An

gle

An

an

gle

wit

h a

m

easu

re g

reat

er

than

th

at o

f a

righ

t an

gle

or

90

°an

d

less

th

an s

trai

ght

line

or

18

0°

Larg

er

than

a

righ

t an

gle

Wh

en

a d

oo

r is

pu

shed

all

the

way

op

en

it

cre

ates

an

o

btu

se a

ngl

e

Mat

h B

oo

k

Life

Ex

per

ien

ces

Will

sti

ck o

ut

bey

on

d a

n in

dex

ca

rd

Un

it

man

ipu

lati

ve

84

Acu

teR

igh

t A

ngl

e

An

an

gle

that

m

easu

res

exac

tly

90

°

Mak

es t

he

shap

e o

f an

“L”

or

and

in

vert

ed

“L”

Cre

ates

a

pe

rfec

t co

rner

Mat

h B

oo

k

Life

Ex

per

ien

ces

Will

mat

ch a

n

ind

ex c

ard

co

rner

p

erf

ectl

y

Un

it

man

ipu

lati

ve

85

Sort Organizer

Right Angle Shape

Acute Angle Shape

Obtuse Angle Shape

More than 1 Geometric Property

86

Lesson 4

Teacher Talk

Students will define basic geometric terms. The lesson includes effective strategies and

materials that benefit all students. These supports are in form of video, peer

collaboration, and the use of visual resources. Please rotate around groups to ensure

that students receive immediate corrective feedback and additional support, as needed.

87

Lesson 5

Teacher Talk

Students will learn that shapes can change or be modified. Some students may benefit

from the following accommodations or modifications to the lesson:

Students will have the opportunity to have an unencumbered watch of The

Greedy Triangle video. Do not pause, stop, or interject during this first

unencumbered watch.

During the second watch teachers may want to implement an “I do, we do, you

do” note taking process with the Note-taking Guide as a whole group or in a

small group format.

88

Lesson 6

Teacher Talk

Students will be asked to identify what makes up geometric shapes, along with creating different types

of geometric shapes. Your students may benefit from the following accommodations and modifications:

Before playing the "Pick Up Sticks Game" your students may benefit practicing finding

angles in a small or whole group format. You may practice using the "Premade Pick Up

Sticks Pictorial".

Pass one page and some crayons to each group. Allow them to

use the crayons to color the different angles or lines they see.

Then have them record their answers in their journal.

For activities 1-3, your students may benefit from a visual for each triangle that they are

creating to support their task completion.

89

Equ

ilate

ral T

rian

gle

All 3

sid

es

are

Equal

90

Iso

scel

es T

rian

gle

On

ly 2

sid

es a

re

Equal

91

Scal

ene

Tria

ngl

e

No

sid

es a

re Equal

92

Lesson 6 HomeworkName the type of angle below (right, obtuse, & acute):

Name _____________________

Name the type of lines (perpendicular, or parallel) below:

Look at the triangle and answer the questions below:

How many sides are equal? How many sides are equal? How many sides are equal?

93

Ho

w m

any

acu

te a

ngl

es, r

igh

t an

gles

, p

aral

lel l

ines

, an

d p

erp

end

icu

lar

lines

d

oes

yo

ur

gro

up

see

?

94

Lesson 7

Teacher Talk

Students are asked to individually create a map that has all the lines, angles and geometric shapes that

have been learned throughout the unit. Your students may benefit from the following accommodations

and modifications:

Depending on your students’ levels, rather than having the students create a map, you

have the option to modify their test by giving them a Premade Map and then have them

answer questions where they have to label the angles, lines, and geometric shapes.

Before you give your students the Premade Map and questions, as a whole group, use

the “Practice Map” to find the following:

parallel, perpendicular, and intersecting lines

line segments, lines, and rays

acute, obtuse, and right angles.

95

Map

Ass

essm

ent

Dis

ney

Way

Katella AveBall Road

Tram

5 Freeway

Mic

key,

Min

i Mo

use

, Go

ofy

, an

d

Do

nal

d D

uck

Par

kin

g Lo

t

Dai

sy’s

Dip

-n-D

ots

Ice

Cre

am

Plu

to’s

P

izza

P

alac

e

Park Way

96

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____

____

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____

____

____

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at a

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at a

re p

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at a

re t

wo

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eet

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at a

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r? _

___

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at in

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at is

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ape

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___

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____

____

____

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at is

th

e n

ame

of

nam

e o

f th

e s

hap

e w

ith

acu

te a

ngl

es?

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____

____

____

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at is

th

e n

ame

of

the

piz

za p

lace

th

at h

as m

ore

th

an 5

sid

es?

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____

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____

____

____

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at d

ire

ctio

ns

do

es

the

co

mp

ass

rose

hav

e o

n t

he

map

? __

____

____

____

____

____

____

97

Lin

e

Segm

en

t

Ray

Lin

e

Par

alle

l Lin

es

Acu

te A

ngl

e

Ob

tuse

An

gle

Pe

rpe

nd

icu

lar

Lin

es

99

Gro

up

Me

mb

er

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es

____

____

____

____

____

____

____

____

____

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at a

re t

wo

str

eet

s th

at a

re p

aral

lel?

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____

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at a

re t

wo

str

eet

s th

at a

re p

erp

en

dic

ula

r? _

___

____

____

__

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e o

ne

str

eet

th

at in

ters

ect

s an

oth

er s

tre

et t

o f

orm

an

ob

tuse

an

gle

. __

____

____

____

____

____

____

__

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e o

ne

str

eet

th

at is

a li

ne

se

gme

nt.

__

____

____

____

___

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e o

ne

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eet

th

at is

a li

ne

.___

____

____

____

____

____

__

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e o

ne

str

eet

th

at is

a r

ay. _

___

____

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____

____

____

_

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at is

th

e n

ame

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the

fo

ur

sid

ed

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ape

ice

cre

am p

arlo

r? _

___

____

____

____

____

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__

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at is

th

e n

ame

of

nam

e o

f th

e s

hap

e w

ith

acu

te a

ngl

es?

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____

____

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____

____

____

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at is

th

e n

ame

of

the

piz

za p

lace

th

at h

as m

ore

th

an 5

sid

es?

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____

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at d

ire

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hav

e o

n t

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map

? __

____

____

____

____

____

____

100

Getting to the Core - sausd.us · Instructional Activities: ... angle classification (right,...

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Transcript of Getting to the Core - sausd.us · Instructional Activities: ... angle classification (right,...