1. STRONG START
Thursday, June 23, 2016
Morning

2. Agenda Game Protocol: Dice Tasks
Early Number Relationships: Subitizing
Break
Early Number Relationships: 1 More/1 Less
Lunch
Early Number Relationships: Anchors to 5 and 10
Rekenreks
Intro to Team Projects

3. Dice Tasks From Day 3 Debriefing

4. Game Protocol Mathematical Curiosities Foundational Math Concepts
Math Skill
Purposeful Questions for Skills
Equitable Engagement and Access
Best Use
15 min
Debrief Racing Bears with game protocol

5. Learning Targets

6. Learning Targets We are learning to …
Understand how early number concepts develop in Grades K-2.
Scaffold experiences for K-2 children that develop a solid understanding of number that will lead to basic fact fluency.
Connect early number concept development to CCSSM expectations.

7. Dot Patterns

8. Dot Pattern

9. Find the Same Amount Lay the cards out face up.
Pick one card in the collection.
Find another card with the same amount.
Tell how you know they are the same.
Take turns and continue finding pairs.

10. Debrief of Find the Same Amounts
Imagine you are watching your students play each game.
What would success tell you about their mathematical understanding with Find the Same Amounts?
What would struggles tell you about their mathematical understanding with Find the Same Amounts?

11. Through the Lens of the Math Content
As you reflect on the use of the dot patterns, what do they help young child understand about numbers in relationship to the CCSSM standards?
K.OA.3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = and 5 = 4 + 1).

12. Four Types of Number Relationships
Work with 3-5 year olds can focus on helping children construct these 4 relationships once early counting is starting to take root.
Review hand-out and summarize what each means.

13. 360° Connection Looking Backward
How does this idea relate to counting and cardinality?
Looking Forward
How does this idea relate to addition and subtraction?

14. Dot Pattern

15. Planning for Dot Pattern
Describe in words and number the different ways someone may "see" each of your three dot patterns.
Show how you will record each way.

16. YOUR TURN to practice (Groups of 2)
Subitizing Practice
YOUR TURN to practice (Groups of 2)
Teacher flashes a Dot Pattern Card to your group for 3-5 seconds
Teacher flashes the dot pattern another time for 3 seconds so student can make adjustments to their thinking
Teacher asks students to explain how they saw the dot pattern
Student explains how many dots they saw and how they saw them.
Record the matching expression
Teacher records student thinking on their white board.
Make connections between their different ways of seeing the number

17. Professional Reading and Reflection

18. Beyond Counting by Ones
Read “Beyond Counting By Ones: ‘Thinking in Groups’ as a Foundation for Number and Operation Sense” (Huinker, 2011). Write down how this reading clarified your understanding of subitizing and its importance for connecting counting with cardinality.

19. Focus Topics or Standards
Reflection/Summary
Summarize some key points and classroom ideas related to the topics or focus standards in this session.
Focus Topics or Standards
Summary of Key Points
Classroom
Ideas to Try

20. Thursday, June 23, 2016 Afternoon
STRONG START
Thursday, June 23, 2016
Afternoon

21. Learning Targets We are learning to …
Understand how early number concepts develop in Grades K-2.
Scaffold experiences for K-2 children that develop a solid understanding of number that will lead to basic fact fluency.
Connect early number concept development to CCSSM expectations.

22. 1 or 2 MORE/Less

23. Connections Now, what if I space this a little differently
Please memorize this eleven digit number​
Now, what if I space this a little differently
What pattern do you see?
Now, please memorize this eleven digit number.
When we learn facts, seeing relationships is critical!

24. Four Types of Number Relationships
Work with 3-5 year olds can focus on helping children construct these 4 relationships once early counting is starting to take root.
Review hand-out and summarize what each means.

25. More than counting..
Requires students to reflect on they way that numbers are related to each other. Let’s take 4 and 6 for example.
6 is two more than 4
4 is two less than 6
Counting on is a useful tool to construct these ideas.
We want students to understand where a number falls on the number line and its relationship to other numbers.

26. Make a 2 more set Grab a set of Dot Cards.
Your task is to construct a set of counters that is two more than the set shown on the card.
What connections can you make to solving addition and subtraction problems?

27. Hierarchical Inclusion
If I have 7 of something, I also have 6, 5, 4… What would it look like if a student understood this idea? How would it cause issues if a student did not understand this idea?

28. Ladybug book Show this on the Number Path.
What happens each time you turn a page?
Which ladybug is the "Number 1" bug?
When is that one there?

29. Assessing this Relationship
10 frames – call out numbers and have students show you that many counters
Intentionally start to call numbers that are 1 or 2 more and 1 or 2 less
Watch who clears their board and who is able to add on or take away just the needed amount

30. Four Types of Number Relationships
Work with 3-5 year olds can focus on helping children construct these 4 relationships once early counting is starting to take root.
Review hand-out and summarize what each means.

31. 360° Connection Looking Backward
How does this idea relate to counting and cardinality?
Looking Forward
How does this idea relate to addition and subtraction?

32. Benchmarks or Anchors to Five and Ten

33. Four Types of Number Relationships
Work with 3-5 year olds can focus on helping children construct these 4 relationships once early counting is starting to take root.
Review hand-out and summarize what each means.

34. Anchoring to the Numbers 5 & 10
“Anchoring to 5” is the ability to understand the relationship of numbers specifically to the number 5. “Anchoring to 10” is the ability to understand the relationship of numbers specifically to the number 10.

35. Five Frame Place ____ on your frame.
What can you tell me about the number?
How many more do you need to get to 5?
CCLM

36. Five Frame Place ____ on your frame.
What can you tell me about the number?
How many more do you need to get to 5?
CCLM

37. How many do you see? How many more do you need to get to 5?
What can you tell me about three?
How many more do you need to get to 5?

38. How many do you see? How do you see them?
How many more do you need to get to 5?

39. How many do you see? How do you see them?
How many more do you need to get to 5?

40. Your turn! Anchoring Quantities to 5
Materials number cards: 6, 7, 8, 9 and a 5 frame
Fill your 5 frame.
Turn over a card.
Add counters next to the five frame to show how many are on the number card.
Discuss how each number is anchored to 5.
Sentence frame: 8 is 3 more than 5; 5 is 3 less than 8
____ is _____ more than 5; 5 is ___ less than ____. 8

41. Making Connections to Operations
Teachers can write expressions like “2 + 3”and “4 + 1” to show the operation. “It is helpful for students to have experience just with the expression so they can conceptually chunk this part of the equation.”
(OA Progressions, p. 8)

42. How many do you see? How do you see them?
You were just anchoring quantities to 5!

43. Your turn! Anchoring Quantities to 5
Materials number cards: 6, 7, 8, 9 and a 5 frame
Fill your 5 frame.
Turn over a card.
Add counters next to the five frame to show how many are on the number card.
Discuss how each number is anchored to 5.
Sentence frame: 8 is 3 more than 5; 5 is 3 less than 8
____ is _____ more than 5; 5 is ___ less than ____. 8

44. Ten Frame

45. Extending Up to 10 How many dots do you see? How do you see them?
How many more to 10? How do you know?

46. Extending Up to 10 How many dots do you see? How do you see them?
How many more to 10? How do you know?

47. How many dots do see? How do you see them?
How many more to 10?
How do you know?
State the pair numbers that make ten.
How might we anchor these images back to 5?

48. Frames for Structuring Number Knowledge
Five Frame
K-3; K-4; K-5
Ten Frame
K-4; K-5; Grade 1
Two Critical Ideas:
Structure number knowledge with anchors to five and ten through the use of five and ten frames.
Provide experiences that encourage students to look for and regularly use relationships among numbers to solve problems.
Double Ten Frame
Showing 8 + 6
Grade 1; Grade 2
Huinker (2012) Structuring Number Knowledge with Anchors to Five and Ten p. 5

49. The use of ten frames provides a visual tool that supports students in the mathematical practice to “look for and make use of structure” (MP7). The structure is knowledge of ten. This includes developing part-whole understanding of ten through its decompositions and its relationships to other numbers. Huinker, 2012, p. 7

50. K.OA.3 & K.OA.4
K.OA.3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = and 5 = 4 + 1).
K.OA.4. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

51. What do you notice about the examples in K.OA.3?
What is the difference between these two standards?
What is a student thinking when they are working on each one?
What might they model? What might they sound like?
Write a word problem that would go with each standard

52. PRR
Huinker (20102): Structuring Number Knowledge with Anchors to Five and Ten
Pull out 2-3 quotes that show the mathematical benefits of using five and ten frames in PK-2 classrooms and comment on them.
Reflect on the power of visual representations in instruction that leads to fact fluency.

53. Rekenrek

54. What? Developed at the Freudenthal Institute in the Netherlands.
Widely used in other countries to help students reason about numbers, subitize, build fluency, and compute using number relationships.
Take a look at your rekenrek…
What do you notice about its structure?
Turn and share

55. Getting Acquainted Context is key -- story problem
Vocabulary – be consistent
Start position
Beads “in play” or “working”
Beads “out of play” or “at rest”
All beads are “in play”

56. Getting Started With Rekenreks
Show me!!
Rekenrek Flash!
Make and Match
With numeral cards
With five frames
With ten frames
With dot patterns

57. Four Types of Number Relationships
Work with 3-5 year olds can focus on helping children construct these 4 relationships once early counting is starting to take root.
Review hand-out and summarize what each means.

58. Focus Topics or Standards
Reflection/Summary
Summarize some key points and classroom ideas related to the topics or focus standards in this session.
Focus Topics or Standards
Summary of Key Points
Classroom
Ideas to Try

59. Team Projects

60. Team Project
Administrator Information & Individual Strong Start Implementation Goals The purpose of this project is to begin a conversation on ways to strengthen your school’s mathematics program based on Strong Start Math learning.