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Building Number Sense and Computational Fluency
Kid’s Hope Math Workshop
1/14/08
Mike Klavon
Ottawa Area ISD
Who am I?
• 3+ Years as a K-12 Math Consultant (OAISD)• 12 Years HS Teaching Experience (Holland HS)• 3 Years K-5 Math Ed. Course (MSU)• Married with 4 children
– Gina (Secret!)– Jarod (8)– Aubrey (7)– Gianna (6)– Dominik (4)
Why are we here?
• To explore accessibility tools and strategies for building number sense and fluency in addition and subtraction:
– Tools• Dot Cards
• Five and Ten-Frames
– Strategies• Make ten addition• Make ten subtraction
– Count-back– Count-up
What is Number Sense?
Number sense refers to a child’s fluidity and flexibility with numbers, the sense of what numbers mean, and an ability to perform mental mathematics and to look at the world and make comparisons (Case, 1998; Gersten & Chard, 1999).
A world without Number Sense
• Ma and Pa Kettle– While viewing the video clip, please think
about the following question:
“Do some of your students see numbers like Ma and Pa Kettle?”
Why Teach Number Sense?
• Building number sense
– leads to automatic use of math information
– is a key ingredient in the ability to solve basic arithmetic computations.
(Gersten and Chard, 2001)
What is Computational Fluency?
• NCTM’s Principles and Standards for School Mathematics (2000)
– “Fluency refers to having efficient, accurate, and generalizable methods (algorithms) for computing that are based on well-understood properties and number relationships.”
NCTM, 2000, p. 144
What does the research say?
Number Sense Strategies
• Counting• Spatial Relationships• One More / Two More / One Less / Two less• Anchors to 5 and 10• Part-Part-Whole Relationships
Note: The following activities are borrowed from “Teaching Student-Centered Mathematics,
Grades K-3, by John A. Van de Walle, 2006
Learning Patterns Activity
• To introduce the patterns, provide each student with about 10 counters and a piece of construction paper as a mat. Hold up a dot plate for about 3 seconds.
– “Make the pattern you saw using the counters on the mat. How many dots did you see? How did you see them?
– Discuss the configuration of the patterns and how many dots. Do this with a few new patterns each day.
Dot Plate Flash
• Hold up a dot plate for only 1 to 3 seconds.
– “How many did you see? How did you see it?”
– Observe which patterns were easier/harder? How did students group the dots (do they always tend to use one number)?
– – Discuss “How many did you see? How did you see it?”
Make a Two-More-Than Set
• Provide students with about six dot cards. Their task is to construct a set of counters that is two more than the set shown on the card.
– Option(s): You can change the task to construct a set that is two less than the set shown on the card. (Do not use the one card for this activity.)
– Similarly, spread out eight to ten dot cards, and find another card for each that is two less than the card shown.
Five-Frame Flash Activity
• Flash five-frame cards to the class or group, and see how fast the children can tell how many dots are shown.
– Variations: Saying the number of spaces on the card instead
of the number of dots Saying one more than the number of dots (or two
more, and also less than) Saying the “five fact” – for example, “Three and
two make 5”
Ten-Frame Flash Activity
• Flash ten-frame cards to the class or group, and see how fast the children can tell how many dots are shown.
– Variations: Saying the number of spaces on the card instead
of the number of dots Saying one more than the number of dots (or two
more, and also less than) Saying the “ten fact” – for example, “Six and four
make ten”
Part-Part-Whole: I Wish I Had…
• Hold out a dot plate or ten frame showing 6 or less. Say, “I wish I had six.”
– The children respond with the part that is needed to make 6. Counting can be used to check.
– Options: The game can focus on a single whole, or the “I wish I had” number can change each time.
Anchors of 10
• Hold out a dot plate or ten frame showing 10 or less. Say, “How many more makes 10?”
– The children respond with the part that is needed to make 10. Counting can be used to check.
– Options: Students can record the number families for making ten.
Addition and Subtraction Strategies
• Make 10 addition– Ten Frames– Race to 100
• Make 10 Subtraction– Ten Frames
• Count-back• Count-up
– Race from 100
Make Ten Addition
8 + 3 = ____
2 1
11
Make Ten Addition
7 + 5 = ____
3 2
12
Make Ten Subtraction
12 5 = ____
-2 -3
7
Make Ten Subtraction
11 3 = ____
-1 -2
8
Subtract by Counting Up
11 8 = ____ Think: 8 + ___ = 11
2 1
3
How many more makes 10?
Subtract by Counting Up
12 7 = ____ Think: 7 + __ = 12
3 2
5
How many more makes 10?
Basic Facts Workshop
• Please scan the workshop ideas labeled “Introduce It!” and “Develop It”.
– What thoughts or questions do you have on these strategies?
Work Time
• Options:– Look through the resources to see other
activities that are available to support your students.
– Begin cutting dot cards, five and ten-frame cards and numeral cards to be used with your students.
Thank You!
Contact Information:
Mike Klavon
Ottawa Area Intermediate School District
(616) – 738 – 8940 Ext. 4100
