training number talks

1. Number Talks
USD305
Linda Ponton

3. Why Use Number Talks?
O Preparing students to be mathematically
proficient and compute correctly,
efficiently, and flexibly
O Efficiency refers to the ability to choose an
appropriate, practical strategy for a specific
computation problem.
O Flexibility means the ability to use number
relationships with ease in computation.

4. Key Components
O Classroom environment and community
O Classroom discussion
O The teacher’s role
O The role of mental math
O Purposeful computation problems

5. Classroom
O Build a cohesive classroom community
O Set procedure and expectations:
O Location
O Wait time
O Accept all answers
O Encourage student communication

6. Discussion
O Teacher writes problem on the board
(horizontally)
O Student signal (to chest)
O Teacher calls for answer (accept all
correct and incorrect)
O Students share their strategies and justify
their answer

7. Teacher’s Role
O Watch the 2nd Grade video clip
O Discuss with a partner
O What is the teacher’s role in the number
talk?
O What features of this video would you like
to see in your classroom?

8. Mental math
O Key component because it encourages
students to build on number relationships
to solve problems.
O Students are encouraged to rely on what
they know and understand about the
numbers and how they are interrelated.
O Develops efficient, flexible strategies with
accuracy
O Strengthen students’ understanding of
place value

9. Purposeful Computation
Problems
O Type of Problems
O Goal Setting

10. Let’s try one…
12 x 6

11. Number Talks
OI would like to defend…
OI would like to dispute…
OI agree with…
OI disagree with …
OI do not understand …
OHow did you decide to …

12. Conclusion
O Guide students to learn a new strategy
O Try another problem (same day or next)
and tell them to try “Susie’s” strategy.

13. Day 2
OWhat a Number Talk might look like
at your grade level.
OThe problems are designed to elicit
specific strategies that focus on
number relationships.
OThe problems are solved mentally.

14. Four Goals for K-2
Number Talks
Developing number sense
Developing fluency with small numbers
Subitizing
Making Tens

15.  Fluency Number Talks Using Dot Images
 Fluency Number Talks Using Rekenreks
 Fluency Number Talks Using Five and Ten
Frames
Kindergarten

16. K: dot images

17. K: 10 Frames 17

18. K: Rekenrek
http://www.mathlearningcenter.org/web-apps/number-rack/

19. 1st Grade
O Counting All/Counting On
O Doubles/Near Doubles
O Making Tens
O Landmark or Friendly Numbers
I recommend beginning with number dots or ten frames.

20. 9 and 1 make 10. Rewrite 56 as 55 + 1.
Add 1 to 9 to get 10 before adding 55.
56 + 9 = 55 + 10
= 65
55 1

21. 8 and 2 make 10. Rewrite 136 as 134+2.
Add 2 to 8 to get 10 before adding 134.

22. 1. Darren has 37 guppies and 9 swordtails. How
many fish does he have altogether?
2. Jane has 46 comic books. Her mother
buys her another 8 comic books. How many
comic books does she have now?

23. Addition Strategies

24. 2nd Grade
O Counting All/Counting On
O Doubles/Near Doubles
O Making Tens
O Landmark or Friendly Numbers
O Breaking Each Number into its Place
Value
O Compensation
O Adding Up in Chunks

25. 6 + 6
6 + 5
6 + 7
Doubles or Near Doubles

26. 9 + 9
9 + 8
9 + 10

27. 15 + 15
16 + 16
15 + 14
15 + 16

28. 6 + 8 + 4
4 + 9 + 6
6 + 4

29. 8 + 2
8 + 2 + 11
8 + 13
8 + 15
Landmark or
Friendly Numbers

30. 12 + 17
15 + 14
13 + 16
11 + 17
Place Value

31. 7 + 10
7 + 20
7 + 30
7 + 40

32. 5 + 5
4 + 6
6 + 6
5 + 7
compensation

33. 19 + 6
9 + 16
9 + 26
29 + 6

34. Subtraction

35. 3-5th Grades
O Making Tens
O Making Landmark/Friendly Numbers
O Doubles/Near-Doubles
O Breaking each number into place-value
O Adding up in chunks

36. 7+3
7+5+3
3+6+7

37. Landmark Friendly
Numbers
O19+2
O19+5
O19+8
O19+12
compensation

40. 36 + 22
12 + 37
13 + 14
24 + 32
Place Value

41. 3rd Grade

42. Subtraction Strategies

43. Models to Anchor Strategies

44. Real-Life Context
O Mr. Novack’s and Ms. Shelby’s third-grade
classrooms are raising money to buy
equipment for the school science lab. Mr.
Novack’s students have earned $119 and
Ms. Shelby’s class has raised $126. How
much money have the classes earned for
their project?

45. Real-Life Context
O Ms. Melvin’s and Mr. Tindle’s third-grade
classrooms are competing to raise money
for a school garden. Ms.Melvin’s class
has raised $151, and Mr. Tindle’s class
has raised $96. How much more money
does Mr. Tindle’s class need to earn to
catch up with Ms. Melvin’s students?

46. 4th Grade

47. Multiplication Using Arrays
Here is an array showing 6 x
4
This shows 6
rows with 4
counters in each
row
1
2
3
4
5
6
2 3 4
The 6 is listed first
because this tells
us how many
groups there are.
The 4 tells how
many are in each
group.
6 x 4 = 24

48. Partial Products – 1 by 3
639 = 600 + 30 + 9
x 5
3,19
5
+ 3000
45 5 x 9
150 5 x 30
5 x
600
639

49. Area Model – 1 by 3
5 x 639 = ?
5 150 45
30 9+x 600 +
5 x 639 = 3,195
3,000
150
+ 45
3,19
5
3,000

50. Partial Products – 2 by 2
45
x 53
2,385
15 3 x 5
120 3 x 40
250 50 x 5
+ 2,000 50 x 40

51. Area Model 2 by 2
2,250
+ 135
2,385
45 x 53 = ?
2,000 120
50 3+x
40
5 250 15
2,250 135
45 x 53 =
2,385

52. 36 x 5
18 x 10
9 x 20

53. 4 x 3 x 4
2 x 2 x 12
8 x 3 x 2
2 x 2 x 3 x 4
12 x 4

54. I have 12 counters.
How could I arrange them into equal rows?

55. What number sentences could you write to go with this
array?

56. Model

57. Partial Products

58. 100 (100 x
36=3600)
- 3,600
4,291
Subtract
100 (100 x 36=3600)- 3,600
7 219 R7
Subtract
691
10 (10 x 36=360)- 360
331
9 (9 x 36=324)- 324
36 7,891

59. We can also use an array to solve a division problem!
84 ÷ 4
80 4
4
4 x ? = 80 20 4 x ? = 41
20 + 1 = 21.
4 x 21 = 84
So 84 ÷ 4 = 21.

60. Resources

61. Fractions