1. Common Core Mathematics Implementation III
Kindergarten
September 2013

2. Opening Activity: Got Dots
Unit 2 (Pages 15-77)
Dot Cards from (WHITE)
Unit 3 ( Pages 11-14)
Dot Cards from (GREEN)
Primary Standards Addressed:
K.CC.3 – Write number names from Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
K.CC.5 – Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.

3. Opening Activity: Got Dots
These tasks contain numerous activities where students engage in subitizing activities.
Subitizing introduces basic ideas of cardinality – “how many”, ideas of “more” or “less”, ideas of parts and wholes and their relationships, beginning arithmetic, and, in general, ideas of quantity.
Many of the tasks included throughout this unit involving subitizing and dot cards should be continued throughout the year.
Unit 1 Pages 14-15

4. Opening Activity: Got Dots
Count ‘Em
Place card face down in a deck
Turn one card over face up
The first player to say the quantity of dots on the cards keeps that card.
Partner must count the dots on the card to verify. No assuming. (SMP 6, 7)

5. Opening Activity: Got Dots
Who has More/Less/Same?
Two players turn over 1 card at the same time.
The first player to identify which card has more/less/same keeps the 2 cards. (SMP 3)
Before and After?
Cards are placed in a pile, face down. One player turns over the top card and the other player must state the number that comes after that number, the number that come before.
If the student can correctly identify all 3 numbers they keep the card, if not it is placed at the bottom of the draw pile. (SMP 1, 3, 6, 8)

6. Opening Activity: Got Dots
Line ‘Em Up
Give a student a set of cards and have them line the cards up in a specific order. (least to greatest- forward counting sequence, greatest to least-backward counting sequence) (SMP 1, 3, 6, 7)
Just explain this one and don’t do it.

7. Opening Activity: Got Dots
Counting to Anchors (Using the Green Cards)
Cards are placed in a pile face down. One player turns over the top card and states whether the number is closer to 10 to 20. The student must justify their reasoning. (Example: I have 16 and I know that 16 is closer to 20 because 15 is half-way to 20 and 16 is more than 15).
Then, starting at the number card the student must count aloud to the nearest anchor. If the student is correct in their counting sequence they collect the number card.
Students can use a 0-99 chart as an intervention to assist with the forward and backward counting sequence. (SMP 1, 3, 5, 6, 8)
10 to 20 number line… 10 15 20

8. Number Sense Trajectory – Putting it All Together
Read through this resource and highlight key ideas
Where do the Got Dots activities that we did fall? Why?
What are the implications of this chart for you and your students?

9. Trimester 1 Focus Standards
K.CC.3 – Write number names from Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
K.CC.5 – Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.
K.G.1 – Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside in front of, behind and next to.

10. Objectives Teachers will….
Engage in strategies and tasks to implement Common Core State Standards in Mathematics with all students, including English Learners this school year.
Understand Depth of Knowledge (DOK) and be able to distinguish between DOK levels for the math tasks.
Build a network of peer support and collaboration with grade alike teachers.
Review and engage in unit math tasks.

11. Agenda Opening Activity Why CCSSM? Depth of Knowledge and Rigor
Number Talk
Problem Solving
Units 1-3 Learning Stations
Planning Time

12. The CCSS Requires Three Shifts in Mathematics
Focus: Focus strongly where the standards focus
Coherence: Think across grades, and link to major topics within grades
Rigor: In major topics pursue conceptual understanding, procedural skill and fluency, and application with equal intensity.
Slide 7-15: 15 minutes

13. Why Common Core State Standards in Mathematics?
David Coleman speaking on focus in the Common Core State Standards. This video, produced by Engage NY, can be seen in its entirety at
Start at beginning and stop at 4:21

14. The CCSS Requires Three Shifts in Mathematics
Focus: Focus strongly where the standards focus
Coherence: Think across grades, and link to major topics within grades
Rigor: In major topics pursue conceptual understanding, procedural skill and fluency, and application with equal intensity.
Slide 7-15: 15 minutes 14

15. Webb’s Depth of Knowledge Levels (DOK)

16. Depth of Knowledge (DOK)
Norman Webb’s research
Complexity of cognitive processes
Not the verb alone to assign DOK level
Ways in which students interact with content
The DOK should reflect the complexity of cognitive processes demanded by the task outlined by the objective, rather than the difficulty. Ultimately the DOK level describes the kind of thinking required by a task not whether or not the task is “difficult”.
Based on Norman Webb’s research University of Wisconsin Center
It’s a scale of cognitive demand (thinking) to align standards with assessments
Smarter Balanced assessments will elicit evidence from students that is used to support claims about the extent to which students have the ability to integrate knowledge and skills across multiple assessments targets and are ready to meet challenges of college and careers.
Karin K. Hess, Ed.D 16

17. Dr. Karin Hess National Center for the Improvement of Educational Assessment
Dr. Karen Hess
National Center for the Improvement of Educational Assessment
Teachers will take notes using the note organizer handout

18. Recall of information (fact, definition, term, or property)
DOK Level 1 Recall
Recall of information (fact, definition, term, or property)
Use of a procedure
Apply an algorithm or formula
There is a correct answer
Adapted from Webb’s DOK and NAEP Levels of Complexity in Mathematics
Marge Perit and Karin Hess
And Karin Hess video 18

19. DOK 1 Kinder Task Listen and Do! Unit 1 Page 35
Other examples include one-to-one counting with no justification.

20. DOK Level 2 Skills and Concepts
Involves more than one step
Demonstrating conceptual understanding through models and explanations
Comparing and classifying information
Estimating
Interpreting data from a simple graph
Responses require students to make some decisions 20

21. DOK 2 Kinder Task Touch It, Count It, Chart It! Unit 1 Page 51
Number of Corners
Number of Faces
Draw on face of the solid shape
Everyday object
Cylinder
Cone
DOK 2 because multi-step, relate to real life, comparing the shapes,

22. DOK Level 3 (Extended Thinking)
Involves reasoning, planning and using evidence to solve a problem or algorithm.
Make and test conjectures
Interpret information from a complex graph
Solve complex problems
Explain concepts
Use concepts to solve non-routine problems
Provide mathematical justifications when more than one response or approach is possible

23. DOK 3 Kinder Task Grouping Shapes Cards Pages 56-67
Categorize the shapes and explain your reasoning to a peer and compare two shapes and justify reasoning.

24. DOK Level 4 Extended Thinking
Requires complex reasoning, planning and thinking generally over extended period of time (but not time spent only on repetitive tasks)
Students may be asked to relate to other content areas or to real-world applications in new situations
Work is typically published 24

25. DOK 4 Kinder Task Pattern Block Pictures Pages 68 - 72
2-3 Day Task
Students create a total of 5 pictures by combining pattern block shapes
Students count the number of each shape they used to create their pictures and record it
Students cut out and paste at least one of their pictures on construction paper to make a final product.
Students create questions about their picture(s). Such as which shape do I have more of?
Students share their picture with a small group and combine more pictures and count the number of shapes and make a graph representing the data.
Students share their pictures, tally marks and questions with the class.

26. Which DOK Level is this task at and why?
DOK levels handout

27. Opening Activity: Got Dots
Count ‘Em
Place card face down in a deck
Turn one card over face up
The first player to say the quantity of dots on the cards keeps that card.
Partner must count the dots on the card to verify. No assuming. (SMP 6, 7)
DOK 1

28. Opening Activity: Got Dots
Who has More/Less/Same?
Two players turn over 1 card at the same time.
The first player to identify which card has more/less/same keeps the 2 cards. (SMP 3)
Before and After?
Cards are placed in a pile, face down. One player turns over the top card and the other player must state the number that comes after that number, the number that come before.
If the student can correctly identify all 3 numbers they keep the card, if not it is placed at the bottom of the draw pile. (SMP 1, 3, 6, 8)
DOK 2

29. Opening Activity: Got Dots
Line ‘Em Up
Give a student a set of cards and have them line the cards up in a specific order. (least to greatest- forward counting sequence, greatest to least-backward counting sequence) (SMP 1, 3, 6, 7)
DOK 1 or 2

30. Opening Activity: Got Dots
Counting to Anchors (Using the Green Cards)
Cards are placed in a pile face down. One player turns over the top card and states whether the number is closer to 10 to 20. The student must justify their reasoning. (Example: I have 16 and I know that 16 is closer to 20 because 15 is half-way to 20 and 16 is more than 15).
Then, starting at the number card the student must count aloud to the nearest anchor. If the student is correct in their counting sequence they collect the number card.
Students can use a 0-99 chart as an intervention to assist with the forward and backward counting sequence. (SMP 1, 3, 5, 6, 8)
DOK 3

31. Number Talk
As I show each card put your thumb up when you can tell me how many dots you see and how you see them.
Provide sentence frame to assist EL students:
I see _____dots because______________.
I know the answer is ____ because ________.
Number Talk
Slides 30 – 45
15 minutes

32. Video K.1 Ten-Frames and Dot Cards
What questions does the teacher pose to build understanding?
What strategies are the students using to build meaning of the numbers?
What examples of subitizing, conserving number, and one-to-one correspondence do you notice?
What opportunities are created for the students to begin building an understanding of ten?
10 frames with 5 and 7 (use 9 here) with green ten frame dots on ring
Dots two sets of 5 like two dice
Four dots plus one.

33. Number Talk with Rekenreks
Use Rekenrek and Counters at the same time
Make 4 and copy my way. “Can you make 4 a different way?”
So and showed this way, does anyone else have this way. Is and the same numbers?
Show me how to make 6. Teacher makes a way and has students guess her way.

34. Video K.1 Ten-Frames and Dot Cards
What instructional Strategies does the teacher us to engage the students in the mathematics?
How does the teacher use rekenreks as a tool to build fluency with small numbers?
What role does the game “Can You Guess My Way?” play in the number talk?
How does the rekenrek provide opportunities for differentiation within number talk?
10 frames with 5 and 7 (use 9 here) with green ten frame dots on ring
Dots two sets of 5 like two dice
Four dots plus one.

35. Children Who Enjoy Problem Solving
Get into groups of 3 and number yourselves as 1, 2, and 3.
#1: p
#2: p
#3: p
NCTM article

36. Children Who Enjoy Problem Solving
Read your assigned section from the article.
Share key ideas with your group
Be prepared to share out with the whole group.
NCTM article

37. Kindergarten Problem Solving
There are 5 penguins. 2 are swimming. How many are not swimming?
This is a sample problem in unit 3 Week 4.
The action of “not” is more challenging than “How many left?” for young children.
Solve the problem in as many ways as you can? What DOK level is this?
Pass out unit 3 problem solving

38. Five Practices for Orchestrating Productive Discussions
Anticipating student responses to challenging mathematical tasks;
Monitoring students’ work on and engagement with the tasks;
Selecting particular students to present their mathematical work;
Sequencing the student responses that will be displayed in a specific order and
Connecting different students’ responses and connecting the responses to key mathematical ideas
Smith, M.S., & Stein, M.K. (in press). Orchestrating Mathematical Discussions. National Council of Teachers of Mathematics.
Handout
How are the five practices beneficial for our ELS? 38 38

39. Reflecting and Sharing
With a partner, discuss this question:
What Common Core Standards of Mathematical Practice did we use while we were engaging in solving the problem? Justify your thinking with evidence.
Teachers can find CCSSM Practice standard in the overview session of the binder.

40. Trimester 1 Focus Standards
K.CC.3 – Write number names from Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
K.CC.5 – Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.
K.G.1 – Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside in front of, behind and next to.

41. Units 1- 3 Learning Stations
Use the learning station reflection guidelines as you attend each station

42. Learning Station Where’s Abe?
Materials:
1 penny and 25 counters
2 Where’s Abe? Playing Boards
Directions:
Each player is given a playing board. Player 1 has the penny and places it in any square on the board and does not identify the square to player 2.
Player 1 must ensure that his board remains out of sight from player 2. (Use an open folder)
Player 2 asks questions to find out where player 2 has hidden Abe.

43. Learning Station Where’s Abe?
Directions, continued
Example question might be, “Is Abe above the pink square?”
With each question player 1 can only respond with “Yes” or “No”. This forces player 2 to be more specific in their questioning.
The only question that player 2 CANNOT ask is if Abe is in the same row/column as a shape.
Once player 2 finds Abe the roles are switched.

44. Learning Station More or Less
Materials
Game Board (Numbers 0-8 or 2-11)
Recording Sheet
Red/Yellow counters
6 sided Die
More/less Spinner
Grouping
Students play in pairs

45. Learning Station More or Less
Objective
Be the first to get three in a row
Directions
Each player takes turns rolling the die and spinning the spinner.
One your turn, you may choose to cover up a number that represents the dice and spinner, then record your thinking on the recording sheet

46. Learning Station Numbers-Pictures-Words
Materials
Number, picture, word cards (Take out one of the 3 to play memory)
Objective:
Match the most pairs of cards
Grouping:
Play in groups of 2 or 3
Directions:
Played like concentration or memory by matching the numeral, phrase and/or picture
Modification:
Have students match the cards first

47. Learning Station The Counting Cup
Materials:
Cups with different amount counters inside and labeled with a letter
Recording sheet
Objective:
Count and record objects in a cup
Grouping:
Partners

48. Learning Station The Counting Cup
Directions:
Model for students by pouring out the contents of on of the labeled cups.
Have students make estimates as to how many are in the cup and explain their strategy for making that estimate
Then have students count the counters as they lie, without moving them. The counters may be touched but not moved or reorganized.
Once they are counted a first time, they may then re-organize them into a ten frame or an array and count them again.

49. Learning Station The Cardinal Cup
Grouping:
Playing mat
Numbered cards
20 objects for the cup and 20 counters to keep score
Cup
Dice or spinner
Grouping
Whole group and/or partners

50. Learning Station The Cardinal Cup – Part I
Directions (Counting Forward)
Place number cards face down in a pile.
Player 1 turns over the top card and places that many cubes in the cup and counts out loud as each cube is placed into the cup.
Once player 1 is finished counting, player 2 removes the contents from the cup by placing the counting on the counting mat.
If the first player was correct in counting out the cubes they receive 1 chip to be placed on their ten-frame.

51. Learning Station The Cardinal Cup – Part II
Directions (Count forward and/or backward)
Place number cards face down in a pile.
Player 1 turns over the top card and places that many cubes in the cup and counts out loud as each cube is placed into the cup.
Once player 1 has finished placing all the counters into the cup, they turn over the next card from the pile and add/remove cubes to/from the cup to match the second card.
As player 1 adds/removes cubes from the cup they must count out loud forward or backward in sequence, with the starting number being the quantity in the cup.

52. Planning Time Continue reviewing upcoming tasks with your peers.
Time to access Haiku in the TPC
Begin planning for the 3 focus standards and the lesson study for those standards
Explore a formative assessments for units 1 and 2. Unit 1 is on Pages 56 – 67 and unit 2 is in a handout

53. Reflecting and Sharing
Cause Outcome
Event
If we ____, _____, and _____, then we are successfully implementing CCSSM. As a result, our students will be _____, _____, and _____.
We are
successfully implementing
CCSSM