Transcript Counting and Number Relationships - ESD123-Math

K-8 Mathematics Standards
Content Training
Counting and Number Relationships
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Valerie Adams, Math Coach, Intervention
Specialist, Virgie Robinson Elementary School,
Pasco School District
 [email protected]
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Develop understanding of counting and
number relationship standards for your grade
band.
Develop understanding of development of
counting number concepts.
Learn a variety of strategies for developing
counting and number relationships with
students.
Experience counting and number activities
related to standards.
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Allow ourselves and others to be seen as
learners.
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Monitor own airtime and sidebar conversations.
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Allow for opportunities for equitable sharing.
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Presume positive intentions.
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Be respectful when giving and receiving
opinions, ideas and approaches.
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For all students to learn significant
mathematics, content should be
taught and assessed in meaningful
situations.
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Conceptual Understanding
◦ Making sense of mathematics
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Procedural Proficiency
◦ Skills, facts, and procedures
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Mathematical Processes
◦ Using mathematics to reason and think
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At each grade level:
◦ 3-4 Core Content areas
◦ Additional Key Content
◦ Core Processes (reasoning, problem solving, communication)
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For each of these:
◦ Overview paragraph
◦ Performance Expectation
◦ Comments/Examples
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Use either your Standards Document or Strands
Document to find all K-8 references to counting and
number relationships
Go back and carefully read the Performance
Expectations and Explanatory Comments and Examples
for your grade level.
Note the expectations for the grade level above and
below yours.
What should your students already know?
What do you need to teach this year?
What do they need to know for next year?
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Often called instant recognition
Knowing how many in a collection without counting
Develops before counting and supports counting
Children often do not benefit from counting
experiences before they can subitize small numbers
Can be undermined by counting
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What does it mean to say someone can count?
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To say the names of the numbers in order.
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To count a collection of objects one by one and tell
how many.
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Each of the two meanings has their own set of
concepts and skills.
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The two concepts must come together for students
to understand quantity.
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Each object must be counted only once as the numbers
are said.
The numbers must be said once and always in the
conventional order.
The objects can be touched in any order and the
starting point and order in which the objects are
counted doesn’t affect how many there are.
The arrangement of the objects doesn’t affect how
many there are.
The last number said tells ‘how many’ in the whole
collection, it does not describe the last object touched.
(FSiM)
K.1.E
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“Get me 8 blocks”
Requires students to:
K.1.E
 Remember the number word.
 Count the number of objects.
 Monitor for the requested number while they
count.
If a child’s working memory is taken up with
the counting sequence this task is quite
difficult.
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While visiting another civilization we learned
their way of counting.
We can use the digits 0, 1, 2, 3, 4 only.
When we have one more than 4, that number is
called Zirkle and it moves to a new “place”.
The counting sequence looks like:
1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30
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K.1.A-G
1.1.A-C
1.1.E
2.1.A-G
We say the numbers like this:
One
Two
Three
Four
Zirkle
Zirkle one
Zirkle two
Zirkle three
Zirkle four
Two zirkle
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K.1.A-G
1.1.A-C
1.1.E
2.1.A-G
Write the numbers from 1 to 200 and
circle any patterns you see.
Create a number line from 0-43.
Count the objects in the bag and write how many.
Show 33 cubes.
Find three more and three less than 23 on the number
line.
Start at 43 and count backwards.
Discuss in your group:
What did you need to keep in mind while doing the
tasks? Which tasks were the most difficult for you?
What patterns did you see?
30 minutes
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K.1.A
K.1.D
1.1.A
1.1.E
2.1.A
2.1.E
Students need to:
 memorize 1, 2, 3, ….9, 10, 11, 12, 13.
 hear the 4-9 in 14, 15, 16, 17, 18, 19.
 predict and name the decades 10, 20, 30…
 repeat 1-9 in each decade 21,22,23,24…
 predict and name the hundreds 100, 200, 300.
 repeat the decade and 1-9 sequences in each of the
hundreds 234, 235, 236…
 predict and name the thousands.
 repeat the hundreds, decades and 1-9 sequences within
each of the thousands.
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say the places in order from left to right.
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Saying the counting sequence to a rhythm or actions helps us
remember the sequence.
The rhythm should be close to the speed of heart beats.
Using the same rhythm and actions to skip count helps
children explore the relationships between numbers, 2, 12,
22, 32…
Exploring the patterns in numbers helps us see relationships
among numbers and helps us understand the number
system.
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1.1.A
2.1.A
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Daniel’s counting by 2’s
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The quantity remains the same no matter
how you count it.
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Counting by a given number from any start point
START with 3 and JUMP 5. Go up to about 130
Record each landing number. 3, 8, 13…
Change the START and see what happens.
Keep the START at 3 and change the jump. What
happens?
What patterns do you see?
K.1.A
1.1.A
2.1.A
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Both use 0-9 pattern and ones, tens, hundreds,
K.1.B
thousands…
1.1.C
Some differences:
1.1.E
 -teen, -ty for ten
2.1.E
 11, 12,… no tens or ones marked
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thirteen and fifteen, different pronunciation
than three and five, ones first then “teen”
 We explicitly say the value of the numbers in hundreds,
thousands… one thousand, four hundred twenty-three.
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The value of the numeral is implied by the
position
1000400203
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First
Second
Third
1.1.D
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Thinking about the Big Ideas, Strategies and
Models from tonight, record in your Journal:
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Something new I learned
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Something I want to try
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Something I am still wondering about
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 First
Steps in Mathematics: Number
 Elementary and Middle School
Mathematics, John A. Van de Walle
 Developing Mathematical Ideas(DMI),
Building a System of Tens, Schifter,
Bastable, Russell
 Math Their Way, Mary Baratta-Lorton
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