Goals for today
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Share “what works” with each other
Possibly learn some new things about K and 1st grade math
Get new resources and do some planning
Go inside other’s classrooms
Think about how to provide support as needed (“Daily 5”)
What about you?
• Introductions
3 sessions
1) Early number concepts (today)
2) Adding and subtracting to
solve problems (Mar. 13)
3) Describing shapes, measuring
length, telling time (Apr. 21)
Big Ideas about K-1 Math
1) What children learn in K and 1st grade is a foundation
for all other mathematics.
2) Early number concepts lead to addition and subtraction
fluency.
3) Common Core is a clear outline of learning
expectations.
4) Great resources are available for early numeracy
activities.
5) Diagnostic assessments can help students who are
behind their classmates.
Framework
• Counting – More/Less – Number Relationships
• Add/Subtract Situations – Strategies – Fluency
• Tens and Ones – Place Value – Multi-digit Operations
Resources
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Van de Walle and Lovin
Kathy Richardson
Grayson Wheatley
Elementary Math Resources wiki
Georgia and New York lesson plans
Classroom Visits
• Teaching Channel
• Number Talks
• Eventually your own classrooms??
Sharing and Planning
• Always share
• Keep track of “What I Want to Try”
• Make and take – Daily 5 – Math Work Stations
In a first grade class…
• Three children successfully solved addition and subtraction
tasks for two digit numbers.
• Fourteen of the twenty-one children used their fingers to
count all or count on as they solved such problems as
6 + 3 = ___ and 8 + 9 = ___.
• Three of the children needed cubes to solve such problems
and counted all the cubes.
• One child had difficulty counting more than seven cubes
accurately.
Your kindergarten class?
• Say the number sequence to 20? higher?
• Tell which group of objects has more? which has less? or
whether they are equal?
• Count a group of objects up to 10? to 20?
• Show a set of counters to represent a number?
• Recognize dot card groupings and say the number
represented, without counting.
Look at the math on the diagnostic
assessment – what percent have
accomplished each task?
Your 1st grade class
• Start counting at a number other than 1 and continue the
sequence?
• Count objects up to 20 in a group and write the numeral?
• Answer "How many more are needed to make 5 (or 10)?"
perhaps using 5- or 10-frame cards.
• Answer simple adding or subtracting problems like "Corey
has 4 markers. Her sister gives her 3 more markers. Now
how many markers does Corey have?" What strategies do
they use?
Common Core Standards
• Take a few minutes to look over the CCSS for K and 1.
• Put a check next to those standards that your students learn
well.
• Put a 0 next to those standards that are introduced but not
always learned to mastery.
• Put an X next to those standards that you currently don’t
address in a meaningful way.
It’s important to know the standards inside-out because they
guide your planning and teaching.
K-1 Number Concepts
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More, less, equal
Counting objects, “counting on”
Number relationships
Addition and subtraction problems using strategies
based on number relationships
• Place value (two digits)
Counting & number relationships
are the basis for
Problem solving
which leads to
Fluency with whole numbers
The End Goal
More, less, and same
• Entering kindergarten children can most always pick the set
that is more.
• Although the concept of less is logically equivalent to more,
the word “less” is often more difficult for children than
“more.”
• Whenever you ask “Which is more,” also ask “Which is less.”
Elementary Math Resources
Activities 1 & 2
Counting
• Counting tells how many things are in a set. When counting a
set of objects, the last word in the counting sequence names
the quantity for that set.
• Children will learn how to count before they understand that
the last count word indicates the amount of the set.
(the cardinality principle)
• Resources:
Let’s Count: Learning Numbers in Meaningful Ways (T.C.)
Illuminations Let’s Count to 10
Activities 3 & 4
Counting on and back
• Frequent short practice drills are recommended for children
who have difficulty with this.
• Number Talks Kindergarten video:
Counting Book
Activities 5, 6 & 7
Counting on and back
• Frequent short practice drills are recommended for children
who have difficulty with this.
• Number Talks Kindergarten video:
Counting Book
Activities 5, 6 & 7
• Developing Number Concepts: Kathy Richardson (golden)
• Read the section on counting, pp. 2-11
• What difficulties have you found?
What works for you?
What new activities might you try?
• Partner pair/choose one/table talk
Number relationships
• Numbers are related to each other through a variety of
number relationships. The number 7, for example, is
• more than 4, less than 9,
• composed of 3 and 4 as well as 2 and 5,
• is three away from 10,
• and can be quickly recognized in several patterned
arrangements of dots.
• Number relationships for 7 further extend to an
understanding of 17, 57 and 370. Starting at 17, how many
more are needed to make 20?
Simon Says
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Simon says, Show six fingers.
Janice, tell us about the way you showed six fingers.
Peter, yours is different. Tell us about yours.
Does anyone have a different way to show six fingers?
• Simon says, Show nine fingers.
Number relationships 1-10
Activities 8, 9 & 10
See the diagnostic assessment
for a few dot patterns
Subitizing
See the Dot-card
packet
Quick Images
Number Talks
Number relationships 1-10
Activities 11, 12 & 13
Frogs on a Log
Number relationships 1-10
Activities 14, 15 & 16
Five and ten frame cards
• The frame for seven provides a visual model of seven as two
more than five and three less than ten.
• Working with this model supports the eventual connection to
5 + 2 = 7 and 10 – 3 = 7.
• Video
• How to Teach a Child Math – Part 1
• How to Teach a Child Math - Part 2
• Packet
Number relationships 1-10
Activities 17 – 22
Graphics are from Van de Walle & Lovin,
Teaching Student-Centered Mathematics: Grades K-3
Be Patient!
• The principal tool that children will use as they construct these
relationships is the one number tool they possess: counting.
• Initially, then, you will notice a lot of counting, and you may
wonder if you are making progress.
• Have patience! Counting will become less and less necessary
as children construct these new relationships and begin to use
the more powerful ideas.
Activities 23 – 26
Good basis for assessing
Careful observation during number relationship station activities
will tell you a lot about where your children are with number
concepts.
Usually classroom work is sufficient for moving most students
along the learning progressions. But when informal observation
leads you to believe that a child needs additional support, direct
assessment is crucial.
Kathy Richardson Assessing Math Concepts
Assessing Math Concepts
Kathy Richardson’s Assessment Series
Concept 1: Counting Objects
Concept 2: Beginning Number Relationships
Concept 3: Comparing Numbers
Concept 4: Identifying and Combining Parts
Concept 5: Number Combinations
Concept 6: Decomposing Numbers to Ten
Concept 7: One Ten and Some More
Changing Numbers Assessment Kathy Richardson
• Show the numeral 6. What is this numeral?
Can you make a pile of 6?
• Show the numeral 10. What is this numeral?
Can you change this pile (of 6) so there are 10?
• Show the numeral 7. What is this numeral?
If you change this pile (of 10) so there are 7,
do you think you need to get some more or
take some away?
• Do you know how many you need to add/take away? Go
ahead and change the pile to 7.
• Show the numeral 9. What is this numeral? If you change
this pile (of 7) so there are 9, do you think you need to get
some more or take some away?
• Do you know how many you need to add/take away? Go
ahead and change the pile to 9.
• Going Back – to 5: If the child tried to change one number to
another but had difficulty, continue with the following
numbers: Show me 2. Change 2 to 5. Change 5 to 4.
• Going On – to 15: If the child was able to change the
numbers with ease, continue with the following: Change 9 to
13. Change 13 to 11. Change 11 to 15.
Popsicle Stick Math: Making 10
How could you use this in your class?
• Developing Number Concepts: Kathy Richardson (golden)
• Read the section on more and less, pp. 129-134
• Dig deeply into More/Less Activities
• Read the More/Less Trains
assessment (purple p. 3)
Number Relationships 10-20
• Very important for basic addition fact families.
• Kindergarten and early first grade children should be able to
see a set of six with a set of 10 and know that the total is 16 –
but they should not be asked to state that the 1 in 16
represents “one ten” or that the 6 represents “six ones.”
(what’s a one?)
Beyond Fingers: Place Value & the Numbers 11-19
Activities 27, 28 & 29
Double and near-doubles
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Double 3 is the bug double
Double 4 is the spider double
Double 5 is the hand double
Double 6 is the egg carton double
Double 7 is the two-week double
Double 8 is the crayon double
Double 9 is the 18-wheeler double
Numbers to 100: Intro
• The hundreds chart is an essential tool for every K-3
classroom!
Counting Collections to 100
Skip Counting with
Counting Collections
Notice the “Questions to
Consider”
Coming to Know Number
Real world number sense
• Estimation and measurement:
• Will it be more or less than 10 footprints long? Will the apple
weigh more or less than 20 wooden blocks? Are there more or
less than 15 unifix cubes in this long bar?
• Closer to ______ or to _______? 5 or 20 footprints, 10 or 30
blocks, 10 or 50 cubes?
• About _______? … how many footprints? how many blocks?
how many unifix cubes?
Activities 30 & 31
Make and Take Break
Is it reasonable?
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Could the teacher be 15 feet tall?
Could your living room be 15 feet wide?
Can a person jump 15 feet high?
Could three children stretch their arms 15 feet?
• Number sense is the bridge to mathematical proficiency at all
levels.
Counting & number relationships
are the basis for
Problem solving
which leads to
Fluency with whole numbers
Math Talks
…to develop basic number concepts
After the video, go around your table one at a time and describe
one thing you liked or noticed in the teaching episode.
Then open up the discussion to responses and further
discussion.
Benefits
Students have the opportunity to:
• Clarify their own thinking.
• Consider and test other strategies to see if they are
mathematically logical.
• Investigate and apply mathematical relationships.
• Build a repertoire of efficient strategies.
• Make decisions about choosing efficient strategies for
specific problems.
The teacher’s role
• Since the heart of number talks is classroom conversations, it
is appropriate for the teacher to move into the role of
facilitator.
“By changing my question
from ‘What answer did you
get?’ to ‘How did you solve
this problem?’ I was able to
understand how they were
making sense of
mathematics.”
Procedures and expectations
1. Select a designated location that allows you to maintain
close proximity to your students for informal observations
and interactions.
2. Provide appropriate wait time for the majority of the
students to access the problem.
3. Accept, respect, and consider all answers.
4. Encourage student communication throughout the number
talk.
Five small steps
1. Start with smaller problems to elicit thinking from multiple
perspectives
2. Be prepared to offer a strategy from a previous student.
3. It is all right to put a student’s strategy on the back burner
if you’re not following their thinking or can’t think of a good
question to help them untangle their reasoning.
4. As a rule, limit your number talks to 5 to 15 minutes.
5. Be patient with yourself and your students as you
incorporate number talks into your regular math time.
Instructional Resources
Our own wiki for sharing teaching ideas, resources, web links
http://elementary-math-resources.wiki.inghamisd.org/home
• Choose something from today’s session (or a couple things) to
try before the next session. Come back with examples of
students’ work from what you tried.
• Next session March 6, here.
• Focus on addition and subtraction.
Something to try…