Building Number Sense and Computational Fluency

Kid’s Hope Math Workshop 1/14/08 Mike Klavon Ottawa Area ISD [email protected]

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

2 1

Make Ten Addition

3 2

Make Ten Subtraction

12

-2 -3

Make Ten Subtraction

11

-1 -2

Subtract by Counting Up

11 8 = ____

Think: 8 + ___ = 11 How many more makes 10?

2 1

Subtract by Counting Up

12 7 = ____

Think: 7 + __ = 12 How many more makes 10?

3 2

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 [email protected]