1. First Grade PARTNERS for Mathematics Learning Module 3 Partners 1

2. Pizza Toppings First grade students surveyed the faculty of their2
Pizza Toppings
First grade students surveyed the faculty of their
school to find out their favorite kinds of pizza.
They found that 20 liked pepperoni, 23 liked
sausage and 17 liked mushrooms. Of these faculty
members, 2 were vegetarian and only ate
mushrooms, 6 liked sausage and mushrooms
together and 5 liked pepperoni and sausage
combined. Eight liked all three toppings on their
pizza. How many faculty members responded to
the survey?
Partners
for Mathematics Learning

3. 3
Pizza Toppings

4. 4
Pizza Toppings

5. Sorting and Classifying5
Sorting and Classifying
 How do you use sorting and
classifying in your daily life?
 Why are sorting and classifying skills
important for children?
Partners
for Mathematics Learning

6. Sorting and Classifying6
Sorting and Classifying
In the everyday world, these concepts…
 begin in infancy
 are used daily
 help people organize and understand their
surroundings
Partners
for Mathematics Learning

7. Sorting and Classifying7
Sorting and Classifying
In the mathematical sense, these concepts…
 help children learn to think analytically
 help children express their thoughts more
clearly
 encourage growth of clear, logical thinking
 Attributes describe properties or relationships
of objects
 Recognizing attributes allows students to sort
and classify
Partners
for Mathematics Learning

8. What can teachers do?  Provide sorting/classifying activities8
What can teachers do?
 Provide sorting/classifying activities
involving all learning styles
 Children should hear classification explained
and discussed
 Children should see classifications emerge
 Children should sort and classify concrete
materials
 Children should be able to explain their
thinking
Partners
for Mathematics Learning

9.  Provide a variety of materials for sorting 9
What can teachers do?
 Provide a variety of materials for sorting
 Allow time for free exploration and self
selection of materials
 Engage students in important conversations
 “Tell me about the materials you chose”
 “What kinds of groups did you make?”
 “How did you get that idea?”
 “What other kinds of groups can you make?”
Partners
for Mathematics Learning

10. Making Hoops  Cut the centers out of two paper plates,10
Making Hoops
 Cut the centers out of two paper plates,
leaving the rim approximately 3/4” wide
 Stack the plates
 Use a brad to attach them
 Use the plates stacked
for single rule
 Spread the plates
for two rules
Partners
for Mathematics Learning

11. Sorting and Classifying11
Sorting and Classifying
 Sorting Stuff (unstructured)
 Guess My Rule (1 rule, unstructured)
not the
rule
Partners
for Mathematics Learning

12. Sorting and Classifying12
Sorting and Classifying
 Guess My Rule (2 rules, unstructured)
Partners
for Mathematics Learning

13. Literature Connection13
Literature Connection
Just Like Me
by Barbara J. Neasi
Partners
for Mathematics Learning

14. 14
Just Like Me
Partners
for Mathematics Learning

15. 15
Just Like Me
Partners
for Mathematics Learning

16. Sorting and Classifying16
Sorting and Classifying
 Difference Train
Partners
for Mathematics Learning

17. Sorting and Classifying17
Sorting and Classifying
 Difference Mat
Partners
for Mathematics Learning

18. Developing Understanding of Pattern18
Developing Understanding of Pattern
 Recognize underlying order and
predictability in patterns
 Exposure to patterns throughout school day
 Create simple patterns
 Concrete materials vs printed pages
 Pattern unit or core: shortest string of
elements which repeat
Partners
for Mathematics Learning

19. Developing Understanding of Pattern19
Developing Understanding of Pattern
 Recognize patterns made with different
materials as actually the same pattern
 Translate patterns from one form to
another
 Generalize patterns by describing them
with letters
clap snap snap clap snap snap A B B A B B
Partners
for Mathematics Learning

20. Repeating Patterns  Rhythmic clap, clap, snap  Color  Shape20
Repeating Patterns
 Rhythmic
clap, clap, snap
 Color
 Shape
Partners
for Mathematics Learning

21. Repeating Patterns  Design  Position  Fill  Size Partners 21
for Mathematics Learning

22. Translating Patterns  What did you have to think22
Translating Patterns 
Act out a rhythmic pattern
Verbalize the pattern as you do it
Show that same pattern with snap cubes
Show the pattern with other materials
What did you have to think
about for each of these
tasks ?
Partners
for Mathematics Learning

23. Translating with Manipulatives23
Translating with Manipulatives
 Type of manipulative affects difficulty
 Use various types throughout year
 Snap cubes and color tiles are easiest
 Focus on attribute of color only
 Collections of objects are more difficult
 Include multiple attributes
 Require decision on focus attribute
Partners
for Mathematics Learning

24. 24
Pattern Match
Partners
for Mathematics Learning

25. Pattern Block Train Task25
Pattern Block Train Task
 Sam built a pattern with his pattern blocks
 What would the 16th block be if he kept
building the pattern?
 Show how you know with pictures, words,
or numbers
Partners
for Mathematics Learning

26. How Many Does She Need? Task26
How Many Does She Need? Task
 Mary wants to build a train with 18 blocks
 This is her pattern
 How many of each block does she need to
build the whole train?
 Show how you know with pictures, words
or numbers
Partners
for Mathematics Learning

27. What’s Right? Pattern Task27
What’s Right? Pattern Task
 Joshua was the 9th child in line when
his class lined up in the pattern sitting,
kneeling, standing, standing
 Joshua was standing
 Was he doing the right action?
 Show how you know
Partners
for Mathematics Learning

28. How Many? Pattern Task  Twenty children lined up across the front28
How Many? Pattern Task
 Twenty children lined up across the front
 They were in a pattern: sitting, sitting,
standing
 How many children would be sitting and
how many would be standing? Explain how
you know
 Tell how you know what the twelfth child is
doing?
Partners
for Mathematics Learning

29. Triplet Pattern Task  Triplets Ann, Jan and Fran always like to29
Triplet Pattern Task
 Triplets Ann, Jan and Fran always like to
do the exact same things
 If their first grade class lines up in an
arms up, arms down, arms out pattern,
where could each of them be in the line?
 Show how you know
Partners
for Mathematics Learning

30. Looking at Student Work30
Looking at Student Work
1. How Many Does She Need?
2. What’s Right?
3. How Many?
4. Triplets
What do you know about each student?
What questions would you ask each?
Partners
for Mathematics Learning

31. Patterns on Hundreds Charts31
Patterns on Hundreds Charts
Start at 23.
Count by 1 ʼ s to 31.
Start at 57.
Count to 48 by 1 ʼ s.
Partners
for Mathematics Learning

32. Patterns on Hundreds Charts32
Patterns on Hundreds Charts
Start at 8.
Count by 10 ʼ s to 98
Start at 94.
Count to 14 by 10 ʼ s
Partners
for Mathematics Learning

33. Models with the Hundred Chart33
Models with the Hundred Chart
 Build 23, 24 and 25 with models; locate
each number on the Hundred Chart
 Build all the numbers in the 41 row
What do you notice?
What happens at the end of the row?
Partners
for Mathematics Learning

34. Models with the Hundred Chart34
Models with the Hundred Chart
 Build 34, 44, 54 with models; locate each
on the hundreds chart
 Build all the numbers in the 7 column
What do you notice?
Partners
for Mathematics Learning

35. Missing Numbers Work with a partner and fill in the missing35
Missing Numbers
Work with a
partner and fill
in the missing
numbers in the
highlighted
spaces
How did you
decide which
numbers were
missing?
Partners
for Mathematics Learning

36. 36
Hundred Chart Rules
Partners
for Mathematics Learning

37. Hundred Chart Neighbors37
Hundred Chart Neighbors
What numbers belong in each box?
How do you know?
Partners
for Mathematics Learning

38. Hundreds Chart Challenge38
Hundreds Chart Challenge
Partners
for Mathematics Learning

39. Assessment Tasks  What numbers can you write that are39
Assessment Tasks
 What numbers can you write that are
below 100 and have a 5 in the tens place?
 What could the mystery number be if it is
between 10 and 100 with one 7 in it?
 Is there more than one possible answer?
 How do you know if you have them all?
Partners
for Mathematics Learning

40. Number Patterns  Skip Count by 2s  Start at 0 • Whisper/Shout40
Number Patterns
 Skip Count by 2s
 Start at 0
• Whisper/Shout
• Whisper & snap/ Shout & clap
 Start at 1
• Whisper/ Shout
• Whisper & arms down/ Shout & arms up
 Hundred Board Recording
Partners
for Mathematics Learning

41. Number Pattern Charts  Eyes All Around Us What do you see?41
Number Pattern Charts
 Eyes All Around Us
 Cut faces from magazines,
gluing them in rows from 1 to 5
faces
 Label each row with the total
number of eyes
 At the bottom write from 1 to
10 across and then 11 to 20
under it
 Circle the numerals that match
the number of eyes in each
row
What do you see?
Partners
for Mathematics Learning

42. Pumpkins, Eyes, and Teeth43
Pumpkins, Eyes, and Teeth 
Cut a large pumpkin
Draw two jack-o-lantern eyes
Draw three scary teeth
Add your pumpkin to the chart
Help label the counts
Partners
for Mathematics Learning

43. Number Pattern Charts  Triangle Sides
 Use toothpicks to build triangles in rows of 1 to 5
 Draw the triangles in rows on paper
 Write the number of toothpicks needed to make the
triangles at the end of each row
 Write the numerals from 1 to 15 at
the bottom of the paper
 Circle the numerals that match the
number of toothpicks in each row
What do you see?
Partners
for Mathematics Learning

44. Pumpkins, Eyes, and Teeth44
Pumpkins, Eyes, and Teeth
Partners
for Mathematics Learning

45. Pumpkins, Eyes, and Teeth45
Pumpkins, Eyes, and Teeth
Partners
for Mathematics Learning

46. Skip Counting Picture Patterns46
Skip Counting Picture Patterns
Partners
for Mathematics Learning

47. Ringo Rango Dinosaurs have knees. I can count by 3 ʼ s. 47
Ringo Rango, Tingo Tango
Dinosaurs have hives.
I can count by 5 ʼ s.
Dinosaurs have knees.
I can count by 3 ʼ s.
Ringo Rango
Ringo Rango, Tingo Tango
Dinosaurs have skins.
I can count by 10 ʼ s.
Dinosaurs have shoes.
I can count by 2 ʼ s.
Partners
for Mathematics Learning

48. Use of Variables 8+ = 14 5 + 4 = a + 0=a  As a specific unknown48
Use of Variables
 As a specific unknown 8+
= 14
5 + 4 =
 As a generalized pattern
a + b = b + a
a + 0=a
 As a varying quantity relationship
A=l x w
Partners
for Mathematics Learning

49. Variables as a Specific Unknown49
Variables as a Specific Unknown
 Children need to
 Think of variables as numbers that can be
operated on and manipulated like other
numbers
 Recognize “box” in an equation not as an
answer space but as a yet-to-be determined
number
 Write a number in the box to show what the
box represents
Partners
for Mathematics Learning

50. Variables as a Specific Unknown50
Variables as a Specific Unknown
 Amy has 8 pencils and Tom has 5
 Write a number sentence that tells how
many more pencils Amy has than Tom has
Partners
for Mathematics Learning

51. 8 - 5=  5+  =8 Variables as a Specific Unknown51
Variables as a Specific Unknown
 Amy has 8 pencils and Tom has 5
 Write a number sentence that tells how
many more pencils Amy has than Tom has
8 - 5= 
5+  =8
Partners
for Mathematics Learning

52. Variables as a Specific Unknown52
Variables as a Specific Unknown
 If Thomas had 7 marbles after he gave
away 5, write a number sentence that tells
how many marbles he had at the beginning
Partners
for Mathematics Learning

53. Variables as a Specific Unknown53
Variables as a Specific Unknown
 If Thomas had 7 marbles after he gave
away 5, write a number sentence that tells
how many marbles he had at the beginning
7 + 5 =
- 5 = 7
Partners
for Mathematics Learning

54. Variables as Pattern Generalizers54
Variables as Pattern Generalizers
 Commutative Property of Addition
a + b = b + a
The order of the addends
does not change the sum
Partners
for Mathematics Learning

55. C ommutative P roperty of A ddition55
C ommutative P roperty of A ddition
 Jack ate 3 red M&Ms and 5 yellow M&Ms
from his package
 Shonda ate 5 yellow M&Ms and 3 red
M&Ms from her package
 Who ate the most M&Ms?
 How can you prove it?
Partners
for Mathematics Learning

56. Commutative Property of Addition56
Commutative Property of Addition
• Jerry is on page 24 of his book
• He plans to read 16 more pages
tomorrow
• What page will he be on then?
• Malia cut out 16 hearts
• She cut out 24 more hearts today
• How many hearts does she have?
for Mathematics Learning

57. C ommutative P roperty of A ddition57
C ommutative P roperty of A ddition
True or False?
2 + 4 = =
3+3=3+3
9-2 =2-9
8+7=7+8
5+4=4+5 = =
Partners
for Mathematics Learning

58. Commutative Property of Addition58
Commutative Property of Addition
How would you add these?
4+7+6
8+6+6 10 12 7 10 17 20 17
Partners
for Mathematics Learning

59. Variables as Pattern Generalizers59
Variables as Pattern Generalizers
 Identity Property of Addition
a + 0 = a
Adding 0 to any number
does not change the number
Partners
for Mathematics Learning

60. Identity Property of Addition60
Identity Property of Addition
True or False?
2 + 0 = 20
3+0=3
0+9 =9
8+0=0+8
5 + 0 = 15
= 11
How many coins did William have when he
emptied his pockets and found 4 coins in his
left pocket and none in his right pocket?
Partners
for Mathematics Learning

61. Balance and Equality Which shape weighs the most? Explain Partners 61
for Mathematics Learning

62. Balance and Equality Which shape weighs the most?62
Balance and Equality
Which shape weighs the most?
Which shape weighs the least?
Explain
Partners
for Mathematics Learning

63. Balance Scales Variables63
Balance Scales Variables
Use a total of 20 tiles to balance the scale
What could be the value of each shape?
Partners
for Mathematics Learning

64. Balance Scales Variables64
Balance Scales Variables
Use a total of 20 tiles to balance the scale
What could be the value of each shape?
Partners
for Mathematics Learning

65. 8 + 2 = 1 + 8 + 1  Relate the scale to an equation65
Balance Scales Variables
 Relate the scale to an equation = = =
Partners
for Mathematics Learning

66. 66
Number Balances
 Relate the equations to a number balance = = =
Partners
for Mathematics Learning

67. Spill It and Number Balances67
Spill It and Number Balances
Partners
for Mathematics Learning

68. Find the Missing Values68
Find the Missing Values
Partners
for Mathematics Learning

69. Reflection and Application69
Reflection and Application
 Scan the new first grade math
standards and the big ideas
 What are two ideas from this
module that you will incorporate
in your classroom instruction as
you teach the new standards?
Partners
for Mathematics Learning

70. Renee Cunningham Kitty Rutherford Robin Barbour Mary H. Russell 70
DPI Mathematics Staff
Everly Broadway, Chief Consultant
Renee Cunningham Kitty Rutherford
Robin Barbour Mary H. Russell
Carmella Fair Johannah Maynor
Amy Smith
Partners for Mathematics Learning is a Mathematics-Science
Partnership Project funded by the NC Department of Public Instruction.
Permission is granted for the use of these materials in professional
development in North Carolina Partners school districts.
Partners
for Mathematics Learning

71. PML Dissemination Consultants
Susan Allman
Julia Cazin
Ruafika Cobb
Anna Corbett
Gail Cotton
Jeanette Cox
Leanne Daughtry
Lisa Davis
Ryan Dougherty
Shakila Faqih
Patricia Essick
Donna Godley
Cara Gordon
Tery Gunter
Barbara Hardy
Kathy Harris
Julie Kolb
Renee Matney
Tina McSwain
Marilyn Michue
Amanda Northrup
Kayonna Pitchford
Ron Powell
Susan Riddle
Judith Rucker
Shana Runge
Yolanda Sawyer
Penny Shockley
Pat Sickles
Nancy Teague
Michelle Tucker
Kaneka Turner
Bob Vorbroker
Jan Wessell
Daniel Wicks
Carol Williams
Stacy Wozny

72. 2009 Writers Jeane Joyner, Co-PI and Project Director Partners Staff
Kathy Harris
Rendy King
Tery Gunter
Judy Rucker
Penny Shockley
Nancy Teague
Jan Wessell
Stacy Wozny
Amanda Baucom
Julie Kolb
Partners Staff
Freda Ballard, Webmaster
Anita Bowman, Outside Evaluator
Ana Floyd, Reviewer
Meghan Griffith, Administrative Assistant
Tim Hendrix, Co-PI and Higher Ed
Ben Klein , Higher Education
Katie Mawhinney, Co-PI and Higher Ed
Wendy Rich, Reviewer
Catherine Stein, Higher Education
Please give appropriate credit to the Partners
for Mathematics Learning project when using the
materials.
Jeane Joyner, Co-PI and Project Director

73. First Grade PARTNERS for Mathematics Learning Module 3 Partners 73