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A heirachical learning trajectory that is ongoing

Magnitude

Ability to say the

counting sequence

"1,2,3,4....

One to One

Correspondence

1 2 3 4

The last number you

say when counting objects

tells how many there are

"There are 3"

Hierachical

Inclusion

Part/Whole

Relationships

6=

Compensation

-1+1

Unitizing

19 and 1

18 and 2

17 and 3

Visual

Routines

Quick

Images

Rekenrek

Ten

Frames

Counting

Routines

Count

Around

the Circle

5,10,15,20

38,43,48,53

Choral

Counting

Start &

Stop

Counting

Chorally, individually,

or counting around the circle-

Count by 10's

starting from 26

and stopping at 176

or for fractions-

start at 4 1/2 and

count by halves stopping at 14

It can be as simple or complicated

as the group needs it to be

Organic

Number

Line

Playing with

Quantities

Ten Wand

Ways to

Make a

Number

Today's

Number

Mental

Math

12+12

10 2 +10 2

Calendar & Data

Routines

Calendar

Collecting

Data over a

long period of

time

Counting

the days

in school

Assess

Teach

Conceptual

(cc) photo by twicepix on Flickr

Subitizing

Magnitude

20=

Counting

Perceptual

One to One

Hierarchical

inlcusion

Cardinality

Part/whole

Subitizing

Compensation

See small amounts

as a whole-perceptual

Subitize two or more

small amounts as

one quantity-conceptual

Unitizing

Tell which set is

bigger w/o counting

(cc) photo by tudor on Flickr

Daily Math

5+1=6

Counting

Ability to adjust and

work with quantities

in a more flexible way

4+2=6

Number Sense?

What steps are all along the way?

one number for one object

Consider parts

of a number

&

Cardinality

Numbers build by exactly on each time

smaller numbers are part of bigger numbers

"1 2 3"

=5

+

=7

0 2

2,4,6,8,10

13,15,17,19,21

3,6,9,12

141,144,147,150

110,100,90,80

Playing with relationships

When is___big?

When is___small?

Make___using 3 addends

Divide___in half

Flexibility

Ways to make

100

50+50 40+60

90+10 81+19

80+20 20+80

50

49+1

48+2

47+3

46+4

470

400+70+0

diagnostic

formative

(cc) photo by theaucitron on Flickr

summative

Target

Instruction

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