Subitizing - Rossford Exempted Village Schools

Report
Hands On
Intervention Activities
for the Early Years (PreK – 2)
OCTM 2011
Diane Burtchin, District Mathematics Coach
Rossford Exempted Village School District
[email protected]
and
Catherine Schulte, Math Consultant
Clermont County ESC
[email protected]
Why Number Sense?
Students with strong Number Sense are:
• Good at mental calculation and estimation
• Fluid and flexible with numbers, the sense of
what numbers mean
• Able to look at the world and make
comparisons
• Not dependent upon Algorithms
If Number Sense is weak, students struggle
with these skills
Developmental Mathematics
Assessment (DMA)
Ohio Educators
• Dr. Mark Carter, Karen Boreman, and Dr. Debra Rucker
www.developmentalmathgroup.com
DMA
• Individually administered assessment
• Diagnostic (but can also be used as a screener in pK
and K)
• Preschool – Grade 2
Interventions
Number Concepts Activity Book
Early Number Concepts:
Preschool
• Matching: finding similar attribute(s) between
two or more objects.
• Sorting/Classification: arranging objects in a set
by agreed upon attribute(s)
• Comparing: observing similarities or differences
• Ordering: using the same rule to arrange objects
• Subitizing: instantly recognizing a small number
of objects without counting
Matching
• What activities do you provide in your classroom that
address the concept of matching?
• Let’s consider the Stuart Murphy book - A Pair of Socks
(read and follow up with activity)
• Other Activities:
– Memory, Candy Land, Uno Moo, Go Fish, Pop the Pig!
Match It! Who Am I?, Uno, Twister
– Mamas and Babies Cards or Figures
– Animal Pairs Cards
– Lids and bowls, paint card samples
– Making outfits
– Regular deck of cards
– DMA kit manipulatives
– Ellison Machine cut outs
Classification (Sorting)
•
•
•
•
Another Stuart Murphy book: 3 Little Firefighters
Sorting Cards Activity
Sorting Plastic Animals
Sorting a Variety of Objects (paper clips, colored
chips, colored animals, DMA manipulatives,
candy, etc.)
• Try asking students to sort by color
• Then try to sort a different way
Comparing
• Activity Ideas:
• Pig, Pigger, Piggest by Rick Walton
• Using piles of anything (DMA
manipulatives, coins, paper clips,
etc) have the students decide on
the following: greatest/least;
smallest/biggest or largest, etc.
(emphasis on vocabulary)
• Try three piles as well with the
following: big/bigger/biggest;
short/shorter/shortest; long,
longer, longest, etc.
• Set of 3 Nesting Dolls for the
same activity
Ordering
• Activities:
– Ordering of objects:
tupperware, measuring
cups and/or spoons,
nesting cups, F.P. colored
rings, measuring worms,
bear counters, plastic
animals, DMA
manipulatives, pom
poms, etc.
– Can order by size, length,
height
What is Subitizing?
• What is subitizing?
• Is “instantly seeing how many”
Clements, 1999
• “Is a fundamental skill in the development of
students’ understanding of number” Baroody, 1987
• Many researchers agree that counting focuses
on the unit and measurement focuses on the
whole. Subitizing focuses on BOTH.
Two Types of Subitizing
• Perceptual
– Recognizing a number without using any other
mathematical processes
• Children “see 3” without using any learned mathematical
knowledge
• Conceptual
– Advanced organizational plan for mathematics
• Children who see an 8 domino and “just know” the total
number
• They are seeing each side of the domino as composed of
four individual dots and as “one four”, so the 8 would be two
groups of 4 which is “one eight”
Subitizing
• Activities:
– Read 10 Black Dots by
Donald Crews
– Paper Plates Activity
– Index cards activity
– Finger, quantity, symbol
matching
– Dice and dominoes
– Ready, Set, Count! game
– 5 and 10 Frames
Advanced Number Concepts:
Kindergarten through Grade 2
• Word - Students need to know the number words appropriate
for their age level. They need to use the words in the appropriate
sequence, both counting forward and counting back.
• Quantity - Students should learn to demonstrate an
understanding of quantity through appropriate object counting.
• Symbol - All school-aged students need to know how to identify
and write age level appropriate numeral symbols.
• Relationships:
–
–
–
–
–
1 or 2 more
1 or 2 less
Visual patterns
Comparisons
Part/part/ whole & place and value
Developing Early Number Concepts
Word
Relationships
Quantity
Symbol
Word Activities
Counting
• Counting books – forward/back
• Counting Activities
• Counting Centers
• Number lines, 0-99 chart, 1-30 chart, etc
• Number before/after
Quantity Activities
Object Counting
•
•
•
•
•
•
Number Concept Dot Activities
Counting with Other Objects
Counting Different Arrangements
Different Starting Points
Hand Me
Board games such as Chutes & Ladders, Hi Ho Cherry O,
The Ladybug Game, Five Little Monkeys and so forth
• Be sure to emphasize the concept of cardinality!
– A student has cardinality if he/she can tell you how many are in
a set without recounting the entire set.
– You check on this by asking after each counting activity “How
many are in this set?”
Symbol Activities
Identifying/Writing
• Identifying Symbols
– Match game
– Cover/Uncover
• Writing Numerals
– Tracing, sandpaper, clay, pipe cleaners
– Guess My Number
– Telephone Game
Relationships
•
•
•
•
•
One and two more
One and two less
Visual patterns
Comparisons
Part-Part-Whole,
Place and Value
•
•
•
•
•
•
Dot Patterns
Dominoes
5 frames
10 frames
Part-whole mats
Slide cards
Center Time!
• On each table there is a tub with a number of
activities for the related topic.
• This is not a comprehensive list!
• As you review the activities, you are
encouraged to record your thinking on the
sheet provided. (Wow-Wonder-Steal)
• We will pass the tubs so that each table can
review as many as possible in the time
remaining.
Questions/Comments
• What is your thinking?
• What questions can we answer for you?
Diane Burtchin
[email protected]
Catherine Schulte
[email protected]
Example of Questions on the DMA
Match each question from the DMA to one of
the Early Number Concepts:
Sort these into piles. How did you sort them?
Find a strip that matches this one.
Find one that is longer than this one.
I am going to flash my fingers. Show me with your fingers what
you saw me do.
Put these in order from shortest to longest.
Example of Interventions
Which skill is this intervention going to address?
Play “I Spy” games with the child using ‘smaller than’, ‘larger
than’, or ‘heavier than’ or ‘lighter than’
http://www.scholastic.com/ispy/
Example of Questions on the DMA
Match each question from the DMA to one of
the Advanced Number Concepts:
Count back from 5.
Count the Unit Dots. Point to each dot as you count.
Write the number 6.
Tell me the numerals I show you.
This is 2. What is one more?
This is 5. What is one less than five?
I have made 5 using 4 red and 1 blue. Make 5 another way using
both colors.
Example of Interventions
Which skill is this intervention going to address?
Use counting nursery rhymes.
Model how to tag and move objects into a counted set.
Provide tracing activities (in flour, sand, shaving cream) for
reinforcement of numerals 0-9
Model and support how to recognize the quantity without
counting
What Have We Learned in Our District
Through the DMA’s?
• Completed over 200 DMA’s in REVS
• All Kindergarteners are now screened with the
DMA in our district
• Some trends:
– Issues with cardinality at lower levels
– More/less showed weaknesses (sometimes due to
language)
– Two biggest areas of concern: Subitizing and
Part/Part/Whole
Matching
• Understanding of 1-to-1 correspondence
• Basis for our number system
• Prerequisite skill for conservation
– Different – easier for students to establish
– Same – harder for students to determine
• Move to items that have the same amount
• Include remainders or extras as students will
encounter in the next grade levels
Classification (Sorting)
• Looking at characteristics of different
items and finding characteristics that
are the same
• Start with one attribute (usually color)
• When looking at two or more attributes,
looking at collections
Comparing
Relationship of
More
Less
Same
 These relationships are basic to the concept of
number
 Remember that these children are not yet
counting so the comparisons need to be obvious
Seriation (Ordering)
• Foundational to our number system
• Putting items in order is prerequisite to
putting numbers in order
• Why?
– So students put items in an order so the items
are counted once and only once
• Seriation
– Ordering objects by size, length, or height
– Making decisions
So How Do We Help Students Develop
The Ability To Subitize?
• Start young children out with activities related
to perceptual subitizing to build initial ideas of
cardinality (fingers, rhythms, spatial-auditory)
• Move into more complex ideas that contain
part/part/whole (like dominoes and colored
dots)
• Be certain to vary the patterns (multiple
representations of numbers)
• Paper Plate Activity
Factors Influencing Subitizing
• The spatial arrangement influences the level of
difficulty
• Younger children (ages 2-4)- able to do linear
arrangements easier than others
• Older children (age 5 and up)- exposure for the
types of arrangements should progress from
rectangular to linear to circular to scrambled
• Therefore, we should start exposing them to multiple
representations early to build this ability to subitize
Preventing the Gaps
• Activities for Pre-K & K to provide
intentional instruction
• Focus: Number
Concepts
Object Counting
•
•
•
•
•
•
Number Concept Dot Activities
Counting with Other Objects
Counting Different Arrangements
Different Starting Points
Hand Me
Board games such as Chutes & Ladders, Hi Ho Cherry O,
The Ladybug Game, Five Little Monkeys and so forth
• Be sure to emphasize the concept of cardinality!
– A student has cardinality if he/she can tell you how many are in
a set without recounting the entire set.
– You check on this by asking after each counting activity “How
many are in this set?”
Writing Symbols-Symbol Motor Plan
Down
Over
Part Way Round
Diagonal
Circle
All digits can be made with one
or a combination of these 5 strokes!
Symbol Motor Plan Activities
• Guess My Number (p.43)
• Formation using sand, play dough,
shaving cream, etc.
Symbol to Quantity
• Cover – Up
– Roll die/dice and cover the number/s that appear
– First person to “cover – up” is the winner
• Uncover
– Cover all numbers, roll the dice, uncover the
numbers
– First person to “uncover” is the winner
Subitizing Order
First:
Use your subitizing plates
with the typical dot
arrangements of
numbers 1 to 5
Subitizing Order
Then:
Add different arrangements to the activity!
Subitizing – Conceptual
Remember –
Different arrangements lead to different
decompositions of that number
Number Bonds - Relationships
Move towards number bonds using numbers up to 5.
5
3
2
5
1
?
Subitizing Order
• Finally:
Introduce to 5-Frames
Relationships – Visual Patterns
5-Frames
• Subitizing – brain can only “see” 6; after 6 the
brain moves to part-part-whole
• Need your 5-frame mat and counters
• Show us a 3 on your 5-frame
• What did you do?
• Why?
• How far from 5 is 3?
• How many more counters would be needed to
make 5?
Relationships – Visual Patterns
10-Frames
• Pre-K and K:
– Research says that place value does not occur
during Pre-K, K and 1st grade
– Rather the focus is on “10 and some more”
– Place value begins in the 20’s
Relationships - Comparisons
•
•
•
•
Pg. 67
Compare Greater or Fewer
Make the Same
Make Fewer
Relationships – Part-Part-Whole
Pg. 79
• Two Parts Behind My Back
Combining Word, Quantity and Symbol
• Always make your number lines interactive –
adding on, removing symbols, etc. (Number
line with the word, symbol, and quantity)
• Brainstorm other ideas for connecting these
ideas and record them on the sheet provided.
Each group will add to the list.
Aha’s!
• What was a big aha for you?
• What did you really like?
• What is still a stumbling block?

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