Four Types of
Addition Facts That
Develop All Others
or better yet……
Building a Solid Foundation
in Number Sense
!
Lynn Rule [email protected]
!
You can download this presentation at www.mathrack.com
!
“If you have built your castles in
the air, your work need not be lost:
that is where they should be. Now
put the foundations under them.”
--David Thoreau
In this session:
1. What is Number Sense?
2. What are Number Relationships?
3. What are the Four Fact Strategies?
4. What is Fluency?
Learning is a messy business; constructing
understanding is hard work …
We can’t simply tell children about numbers and think that they
will ‘know’ them. Children will not develop numeracy development
by merely circling answers and writing in workbooks.
They have
to construct these understandings and build these relationships
in their minds, through experiences over time and through
discussing with others the relationships they encounter.
What Does Number Sense Mean to You?
!
• Making sense of numerical situations, and use what is known to figure out
what is unknown
!
• Understanding number meanings, knowing relationships between numbers,
knowing the size of numbers, and knowing the effects of operations on
numbers
!
• Construct an understanding of number and build relationships, through
experiences over time and through discussion
!
• Develop solid relationships with smaller numbers and use them as tools for
understanding larger numbers
!
• Number sense is never complete—It is a lifelong process that is promoted
through many and varied experiences with using and applying numbers
Do You Have A Good Understanding of What It Means
for a Child to Have Number Sense?
To have good number sense…
!
Children must understand the following basic concepts:
• Classification
• Patterning
• Subitizing
• Counting and Cardinality
• Number Relationships
• Decomposing and Composing Numbers
• Landmark Numbers
• Strategies for Computation
The Teacher’s Role in Developing Number Sense
• Encourage children to make sense of situations
!
• Invest time in the early years to allow children to
develop solid number understandings
!
• Meaningful Discussions/ Math
•
•
•
•
•
•
Number Talk
How did you get your answer? Can you prove it?
Can you explain it another way?
Did anyone think about it differently?
What is the most efficient strategy?
I agree or disagree because…
So you’re saying _________
So Where Do We Begin?
Daily Numeracy Routine
Math Routine
• Read Aloud Connected to Math Standard
• Numeral Identification (100’s Chart)
• Build the number using various math models
• One/ Two more and One/ Two less
• Ten more and Ten less
• How many more to get to the next friendly number
• Counting Circle
• Telling Time
Book Review
Context for Learning
Strong Arithmetic Knowledge
• Mathematics is not memorizing the basic facts and mastering the
algorithms for the four operations
!
• By contrast children need to develop strong integrated
mathematical knowledge
!
• Students need to know a lot about numbers
!
• Students need to solve many kinds of number problems
!
• Learning about numbers happens together with calculating and
organizing numbers
Let’s think about 48?
• What is 1 less than 48?
• What is 10 more than 48?
• How far back to 40?
• How many more to get to 50?
• Where is 48 positioned on a number line?
• What is half of 48?
Four Fact Strategies
Keep these in mind as we learn about
relationships….
• Plus Zero
• Ten Plus Something
• Doubles
• Make 10
Focus on Relationships
•
When we focus on relationships, it
helps give children flexibility when
dealing with their basic facts and
extending their knowledge to a new
task. When we build a child’s number
sense it promotes thinking instead of
just computing.
Number Relationships
• Spatial Patterns: Recognizing how many without
counting by seeing a visual pattern
• One/Two More or Less: Knowing which numbers are
one/two more and which are one/two less
• Landmarks of 5 and 10: How any number relates to 5
and 10
• Part Part Whole: Ability to conceptualize a number
as being made up of 2 or more parts
Activities to Develop Early Number
Concepts and Number Sense
Spatial Relationships
Subitizing
• The ability to identify the number in a collection or group
without counting
• Collections that number between 1 and 5
• Saves time in counting and is often more accurate
• De-emphasizes a counting by ones strategy
• Assists in simple addition and subtraction • Emphasis on automatic recognition of the number of items in a
collection
Spatial Relationships—Counting Recognizing how many without counting by seeing a visual pattern
• Activities that utilize concrete math tools
(MathRack, ten frames, dice patterns)
– Roll the Dice
– Three Dice Roll
– Write an Equation
– Dot Plate Flash
– Five Frame- also parts of 5
(Counting Spots)
– Spinner - also fact strategies
(Counting Spots)
– Playing Cards (Counting Spots)
– Sponge Ten/Five Frames
– Dominoes
(Counting Spots)
•
“In the United States, the manipulatives most
commonly used with young children are single
objects that can be counted-Unifix cubes, bottle
caps, chips, or buttons, while these
manipulatives have great benefits in the very
early stages of counting and modeling problems,
they do little to support the development of
the important strategies needed for
automaticity.” (Fosnot)
How many dots are there?
How many dots are there?
How to use a MathRack?
• The MathRack has a built-in structure the
encourages children to use their knowledge about
numbers instead of counting one to one.
Mastering the MathRack
To Build Mathematical Minds
How to use the MathRack
Start position-all beads to the right.
How to use the MathRack
Read this side
One/Two More and Less
• Allows students to be flexible thinkers and aides in
mental computation
!
• 9 + 5 = 10 + 5 - 1
• 59 + 25 = 60 + 25 - 1
29
How many beads? How do you know?
One/Two More or Less: Counting On/Counting Back !
Knowing which numbers are one/two more and which are one/two less
Activities that enhance the forward and backward
number sequence – Hop the Line
– Before and After
– Counting On
– Plus One
– One More One Less
– More or Less
– Five frame spinner + - 1,2,3
Landmark Numbers
• Numbers important to assist mental computation,
addition and subtraction
!
• Facilitate more effective counting and operation
strategies
!
• Finger Patterns and Spatial Patterns
!
• Using counters with five frames, ten frames, and the
MathRack to facilitate spatial relationships
How many beads? How do you know?
Benchmarks of 5 and 10
• Help children see how numbers relate to 5 and 10
becomes useful as they start to compute with
numbers. ex. If you know that 7 is 5 + 2 or it is
three less than 10 you could solve:
7+8
•
•
5
•
2
5 + (2+8)
13 - 7
3
47 + 6
4
(13-3) - 4
•
!
34
Turn and Talk
What are all the possible ways
children will figure out how many?
Thinking Flexibly
• 7+7+1
8
+
8
1
•
• 5+5+5
10
+
5
•
• 8 + (2 + 5)
20
5
•
Using The Number Path
• Show 8 + 7 on your MathRack
• Model what you did on your Number Path
• Write down a number sentence that represents how
you determine the total number of beads shown
•
Show 9 + 8 on your MathRack
•
Model what you did on your Number Path
•
Write down a number sentence that represents how
you determine the total number of beads shown
© 2013, Mathematically Minded
Using the MathRack to Subtract
• Show 15 - 9 on your MathRack
• Write down a number sentence that
represents how you determine the total
number of beads left
• What relationship did you use?
• Model what you did on your Number Path?
How many beads? How do you know?
Landmarks of 5 and 10 How any number relates to 5 and 10
!
Activities to build 5 plus and 10 plus facts
– 5 plus Match
– 10 Plus Match
– 5 plus Bingo
– 10 plus Bingo
– Rolling Cube (Counting Spots)
– Greg Tang gregtangmath.com/
Part-Part-Whole
• The three prior relationships help build the
part-part-whole concept:
•
Children who can decompose numbers,
understand a number’s relationship to 5 and
10, and know one/two more and less will see
both 8 + 7 and 38 + 7 in the same way.
•
When we build a child’s number sense it
promotes thinking instead of just
computing.
Part - Part - Whole
Ability to conceptualize a number as being made up of 2 or more parts
Activities to build part part whole
relationships
• Three sectioned plates
• 2 Color Count
• Turn Arounds
• Seven Sentences
• Whole--What are my parts?
• How many more to make 5, 9, 10
• Part- Part Whole Cards
Number Sense Assessment
Numbers 0-20
by Christina Tondevold
www.therecoveringtraditionalist.com
• Spatial
• One/Two More and Less
• Benchmarks 5 and 10
• Part-Part-Whole
✴ Rationale, Assessment Checklist,
Administering the Assessment for each
relationship!
How We Learn Best
!
Memorize this eleven digit number:
25811141720
!
Now look for a connection (relationship) within
numbers
!
2 5 8 11 14 17 20
Four Fact Strategies
• Plus Zero
• Ten Plus Something
• Doubles
• Make 10
10 + something
Doubles
Make Ten
Finding the Fives
© 2013, Mathematically Minded
What is Fluency?
Fluent-Mathematically Proficient
•
Accuracy-ability to produce an
accurate answer
•
Efficiency-ability to choose an
appropriate, expedient strategy
•
Flexibility-ability to use number
relationships with ease in
computation-compose and decompose
numbers
Fluency and Flexibility
• Fluency - efficient and accurate
• Flexibility - multiple solution strategies
determined by the problem
• Fluency is the by-product of flexibility.
Assessing fluency by occasionally using
timed tests is acceptable. Using timed
tests as an instructional tool to build
fluency is ineffective, inefficient, and
damaging to student learning.
--Henry and Brown
In this session...
•
We learned that Number Sense is never complete—It is a lifelong
process that is promoted through many and varied experiences with
using and applying numbers.
• We learned the importance of Relationships--it helps give children
flexibility when dealing with their basic facts and extending their
knowledge to a new task. When we build a child’s number sense it
promotes thinking instead of just computing.
•
We learned the importance of using Fact Strategies in combination
with relationships leads to fact fluency through understanding...not
memorization
• We learned that to be Fluent with our facts we need to be
efficient, accurate, and think flexibly.
“If you have built your castles in
the air, your work need not be lost:
that is where they should be. Now
put the foundations under them.”
--David Thoreau
Resources
• www.mathrack.com
• www.therecoveringtradionalist.com/
• www.mathematicallyminded.com
• www.countingspots.com
• Contexts for Learning Mathematics by Catherine Fosnot
• How the Brain Learns Mathematics by David Sousa
• Last to Finish by Susan Allen and Jane Lindaman
• Mastering the MathRack by Christina Tondevold
• Number Talks by Sherry Parrish
• Teaching Student Centered Mathematics K-3 by John Van de Walle
Building a Solid Foundation
in Number Sense
!
Lynn Rule [email protected]
!
You can download this presentation at www.mathrack.com
!