This document summarizes a presentation about developing number sense in students. It discusses clothesline math, an instructional tool using an open number line to build understanding of numbers and their relationships. It also defines number sense as a flexibility and automaticity with numbers, and the ability to choose strategies and judge answers. The presentation advocates for instructional routines to focus learning on mathematical practices and make lessons accessible for all. Attendees then planned clothesline math activities considering number choices, strategies, and questioning.

1. The Master Number Sense Maker
BCAMT Fall Conference • October 2019
ILSEHTOLC
N E M A T H

2. Welcome!
K-12 Numeracy Helping Teacher
email: hunter_c@surreyschools.ca
twitter: @ChrisHunter36
blog: reflectionsinthewhy.wordpress.com
Grade 5/6 Teacher
email: sabell_a@surreyschools.ca
twitter: @sabell_alex
hris unter
SA lex abell
C H

3. Place…
8 -8-3 0 102
… then Space!

4. What is Clothesline Math?
• a tool
• open & dynamic number line
• requires students establish
benchmarks and a scale
• helps students build
understanding of cardinality,
a sense of magnitude, and
proportional reasoning
-1 0-x x
2x
10 20
50
1
1
2
1
3
1
4
0
1
Chris Shore
Clothesline
The Master Number Sense Maker

5. • a routine
• intended for classroom
discourse
What is Clothesline Math?
-1 0-x x
2x
10 20
50
1
1
2
1
3
1
4
0
1
Chris Shore
Clothesline
The Master Number Sense Maker

6. 10 20
50
Clothesline
The Master Number Sense Maker

7. Think of a student you would
describe as having number sense.
What understandings and skills
does this student have?
What is Number Sense?

8. • a sense of what numbers mean
• an ability to look at the world in terms of
quantity and numbers
• an ability to make comparisons among
quantities
• flexibility, automaticity, and fluidity with
numbers
• an ability to perform mental math
• flexibility with problems
• automatic use of math information
• an ability to determine reasonableness of an
answer
• an ability to decide upon a strategy based on
the numbers in a problem
Number Sense
Understandings & Skills
pp. 9-10

9. • a sense of what numbers mean
• an ability to look at the world in terms of
quantity and numbers
• an ability to make comparisons among
quantities
• flexibility, automaticity, and fluidity with
numbers
• an ability to perform mental math
• flexibility with problems
• automatic use of math information
• an ability to determine reasonableness of an
answer
• an ability to decide upon a strategy based on
the numbers in a problem
Number Sense
Understandings & Skills
pp. 9-10
How does your list compare?
Any a-ha’s?
Which did you call upon in the
opening activity?

10. 1
2
1
3
1
4
0 1
Fractions

11. 1
2
1
3
1
4
0 1
Fractions
What misconceptions might students have?
How might you respond?

14. Place…

15. Place…

16. … and Space

17. 1
2
1
3
1
4
0 1
Fractions

18. 1
2
1
3
1
4
0 1
Fractions

19. 0 2
2
8
4
5
7
6
Fractions 2
1
3
4
Which is closer to 1?
or ?
7
6
4
5

20. Instructional Routines
HEINEMANN
Portsmouth, NH
for Reasoning
Routines
Fostering the
Mathematical
Practices in
All Students
Grace Kelemanik • Amy Lucenta • Susan Janssen Creighton
FOREWORD BY Magdalene Lampert
For more information about this Heinemann resource, visit http://heinemann.com/products/E07815.aspx
How?
“Instructional routines are specific
and repeatable designs for learning
that support both the teacher and
students in the classroom.”

21. "The predictable structure lets students pay less
attention to [‘What is it that I’m supposed to be
doing?,’ ‘What question will I be asked next?,’ or
‘How will things work today in the lesson?’] and more
attention to the way in which they and their
classmates are thinking about a particular math task.
For you as the teacher, the routines keep the flow of
the mathematics instruction deliberately predictable
so that, as you gain familiarity with them, you can
better attend to the most unpredictable elements of
your mathematics instruction: how your students are
making sense of the mathematics.” pp. 19-20

22. • a greater focus on learning
• building crucial mathematical
thinking habits
• access for a wide range of
learners
Why Use Instructional Routines?
HEINEMANN
Portsmouth, NH
for Reasoning
Routines
Fostering the
Mathematical
Practices in
All Students
Grace Kelemanik • Amy Lucenta • Susan Janssen Creighton
FOREWORD BY Magdalene Lampert
For more information about this Heinemann resource, visit http://heinemann.com/products/E07815.aspx

23. Curricular Competency
Connections
pp. 9-10

24. pp. 9-10

25. • Video

26. pp. 9-10
Which Curricular
Competencies did
you observe?

27. 400 500
?
Mystery Number

28. ? ?
12
Mystery Number 2

29. Andrew Stadel • @mr_stadel

30. oz
$
12.510
4 ?
Frozen Yogurt Problem

31. Resources
estimation180.coclotheslinemath.com

32. Resources
estimation180.com/clotheslinenemath.com kristenac

33. Resources
othesline kristenacosta.com/clotheslines

34. Resources
reflectionsinthewhy.wordpress.com/bcamt2019

36. Planning
Your Turn…
• What numbers will you
choose?
• What strategies do you
anticipate?
• What questions will you
ask?

37. Thank-you!
K-12 Numeracy Helping Teacher
email: hunter_c@surreyschools.ca
twitter: @ChrisHunter36
blog: reflectionsinthewhy.wordpress.com
Grade 5/6 Teacher
email: sabell_a@surreyschools.ca
twitter: @sabell_alex
hris unter
SA lex abell
C H