Building Number Sense and Computational Fluency

1. Building Number Sense and Computational Fluency Kid’s Hope Math Workshop 1/14/08 Mike Klavon Ottawa Area ISD mklavon@oaisd.org

2. 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)

3. 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

4. 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).

5. 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?”

7. 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)

8. 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

9. What does the research say?

10. 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

11. 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.

12. 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?”

13. 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.

14. 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”

15. 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”

16. 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.

17. 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.

18. Addition and Subtraction Strategies • Make 10 addition • Ten Frames • Race to 100 • Make 10 Subtraction • Ten Frames • Count-back • Count-up • Race from 100

19. Make Ten Addition 8 + 3 = ____ 11 2 1

20. Make Ten Addition 7 + 5 = ____ 12 3 2

21. Make Ten Subtraction 12  5 = ____ 7 -2 -3

22. Make Ten Subtraction 11  3 = ____ 8 -1 -2

23. Subtract by Counting Up 11  8 = ____ Think: 8 + ___ = 11 3 2 1 How many more makes 10?

24. Subtract by Counting Up 12  7 = ____ Think: 7 + __ = 12 5 3 2 How many more makes 10?

25. Basic Facts Workshop • Please scan the workshop ideas labeled “Introduce It!” and “Develop It”. • What thoughts or questions do you have on these strategies?

26. 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.

27. Thank You! Contact Information: Mike Klavon Ottawa Area Intermediate School District (616) – 738 – 8940 Ext. 4100 mklavon@oaisd.org