“…being good at mathematics involves many different ways of working…it involves asking questions, drawing pictures and graphs, rephrasing problems, justifying methods, and representing ideas in addition to calculating with procedures.”

-Jo Boaler, Professor of Mathematics Education, Stanford University

Working with Rich Mathematical Tasks

aski

ng q

uest

ions

draw

ing/

crea

ting

pict

ures

and

gra

phs

reph

rasi

ng p

robl

ems

just

ifyin

g m

etho

ds

repr

esen

ting

idea

s/co

ncep

ts/p

atte

rns

calc

ulat

ing

with

pro

cedu

res

Doe

s th

e ta

sk e

ntai

l…?

the

task

is in

quir

y ba

sed.

W

hy d

oes

this

wor

k? W

ould

doi

ng

____

_ he

lp a

ddre

ss _

____

? Wha

t w

ould

hap

pen

if I _

____

_?a

char

t/gr

aph/

visu

al is

cre

ated

in o

rder

to

com

mun

icat

e or

mak

e se

nse

of t

he

mat

hem

atic

s,

the

prob

lem

is

reco

ncep

tual

ized

in w

ay t

hat

faci

litat

es u

nder

stan

ding

the

need

to

appl

y m

athe

mat

ical

re

ason

ing

and

prov

ide

just

ifica

tion

is

embe

dded

with

in t

he t

ask

the

task

is m

ultid

imen

sion

al,

requ

irin

g flu

id r

epre

sent

atio

ns o

f the

m

athe

mat

ics

in d

iffer

ent

way

s(v

isual

ly, a

lgeb

raic

ally,

in w

ritin

g, or

gani

zed

in a

tabl

e, us

ing

colo

rs, e

tc.).

the

use

of s

kills

, co

mpu

tatio

ns, p

roce

dure

s, an

d al

gori

thm

s.

Ric

h m

athe

mat

ical

tas

ks

“…be

ing

good

at m

athe

mat

ics

invo

lves

man

y di

ffere

nt w

ays

of w

orki

ng…

it in

volv

es

aski

ng q

uest

ions

, dra

win

g pi

ctur

es a

nd g

raph

s, re

phra

sing

pro

blem

s, ju

stify

ing

met

hods

, and

repr

esen

ting

idea

s in

add

ition

to c

alcu

latin

g w

ith p

roce

dure

s.”

-Jo B

oale

r, Pr

ofes

sor

of M

athe

mat

ics

Educ

atio

n, S

tanf

ord

Uni

vers

ity

aski

ng q

uest

ions

draw

ing/

crea

ting

pict

ures

and

gra

phs

reph

rasi

ng p

robl

ems

just

ifyin

g m

etho

ds

repr

esen

ting

idea

s/co

ncep

ts/p

atte

rns

calc

ulat

ing

with

pro

cedu

res

Cre

ate

a pi

e ch

art t

hat r

eflec

ts y

our i

deal

bal

ance

bet

wee

n th

e si

x di

ffere

nt m

athe

mat

ical

com

pete

ncie

s in

dica

tive

of a

su

cces

sful

doe

r of

mat

hem

atic

s, a

ccor

ding

to B

oale

r.

.

.

Friday the 13th

This month there is no Friday the thirteenth, but this year there was one. Can you explain why every year must contain at least one Friday the thirteenth?

What’s the greatest number of Friday the thirteenths that can fall in one year?

Nrich Mathematicshttp://nrich.maths.org/610

Facilitator/Includer Resource Manager

Reporter Organizer

Remind your team to justify each mathematical statement

Search for connections among the different statements.

“How do you know that for sure?”

“How does that relate to…?”

Your group needs to organize your group’s results.

Your results need to be well organized, and use color, arrows, and/or other math tools to communicate your mathematics, reasons, and connections.

“How do we want to show that idea?”

Make sure your group reads all the way through the task before you begin. “Does everyone get what to do?”

Keep your group together. Make sure everyone’s ideas are heard.

“Did anyone see it a different way?”

“Are we ready to move on?”

Get and manage materials/resources for your team.

Make sure all questions are team questions; everyone has been tapped as a resource before you call the teacher.

Be prepared to join the teacher for a huddle and debrief your group.

Group Roles

Boaler, J. (2015). From Tracking to Growth Mindset Grouping. In Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching (First edition). San Francisco, CA: Jossey-Bass.

Teacher Roles

• assign competence to all students • raise ‘status’ of students who think

they may be of lower status in a group

• teach students to be responsible for each other’s learning

• establish group norms of respect, listening, and collaboration

• encourage students to build off of each other’s ideas

• teach broad, open, multidimensional mathematics

• math is so much more than executing procedures!

• ensure students are in mixed-ability groupings

Boaler, J. (2015). From Tracking to Growth Mindset Grouping. In Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching (First edition). San Francisco, CA: Jossey-Bass.

www.youcubed.org

Going beyond…

Can you find more than one way to make each number with four 4s?

Can you go beyond 20?

Can you use four 4s to find negative integers?

www.youcubed.org

Course Two – 2005

MARS Tasks — High School Course 2 www.scoe.org/mars Page 3

MARS tasks available at https://www.scoe.org/

Designing Rich Mathematical Tasks

• Can you open the task to encourage multiple methods, representations, and pathways?

• Can you make it inquiry based?

• Can you present the task before teaching the method?

• Can you make it visual?

• Can you make it “Low Floor” and “High Ceiling”?

• Can you add requirement for students to convince, reason, and justify?

Boaler, J. (2015). Rich Mathematical Tasks. In Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching (First edition). San Francisco, CA: Jossey-Bass.