1. Counting that Counts!

2. Count the objects in the jar on your table 3 ways.
Counting Jar
Count the objects in the jar on your table 3 ways.
Record 3 ways to represent the number of objects you counted on your counting jar sheet..
As participants walk in have them follow the directions on the board/projector.
Count the objects in the jar on your table 3 ways.
On the tri-fold paper at your table write/draw the 3 ways you represented that number.

3. How did you represent the number you counted?
Counting Jar
How did you represent the number you counted?
What are the ways you counted?
Were there any counting ways that were more efficient than others?
How are these ways connected to the way primary students learn to count?
As participants complete the counting activity ask them: What are the ways you counted? (2’s, 5’s, touching)
Were there any counting ways that were more efficient than others?
How are these ways connected to the way primary students learn to count?
Poster ways participants counted as they discuss them aloud.

4. Why is “counting” important?
Children’s understanding of a number is rooted in counting.
(Maclellan, 2001)
Ask: Why is counting important?
Counting is the foundation for understanding our number system and for the most part is the majority of the math done in primary grade.
While counting may seem simple, it actually complex and involves connections of a number of skills and concepts.
Children’s understanding of a number is rooted in counting.

5. What skills does our ACOS say students should acquire by the end of kindergarten?

6. What does cardinality mean?
When you count a group of objects, the last number you say tells how many there are in all.
Students who do not yet have cardinality recount the objects when asked, “How many?”
When you count a group of objects, the last number you say tells how many there are in all.
Students who do not yet have cardinality recount the objects when asked, “How many?”

7. Attendance: Count Around the Class
Count around the circle to determine the total number of students present.
Pause several times during the count to ask students how many people have counted so far.
Count around the circle to determine the total number of students present.
Pause several times during the count to ask students how many people have counted so far.
This activity helps students see that the number they say represents the number of students who have counted so far and that the last number represents the total number of students in class.
What are some other was we can differentiate this counting activity? (Possible answers: backwards, start counting at different numbers)

8. How do students need to count? Rote Counting
Students need to know the number names and their sequences-both forward and backward.
Ask: How do students need to count?
Students need to use numbers in meaningful ways to build understanding of quantity and number relationships.
Students need to know the number names and their sequences-both forward and backward.
Students practice counting from any number.
What are some ways you implement rote counting in your classroom?

9. Students should practice counting from any number.
23, 24, 25,26, 27…
Sequence of numbers forward AND BACKWARDS
30, 31, 32, 33, 34…

10. Skip Counting by 2s, 5s, 10s, 100s Starting at 0 5, 10, 15, 20…
Forward and backward
90, 80, 70, 60…
Children should be able to count forward/backward starting from zero and any number.

11. One to One Correspondence
One number stands for one object that is being counted
Keeping Track
Students develop strategies for organizing and keeping track as they count.
A student must know that one number stands for one object that is being counted. When young children first begin to count, they do not connect the numbers they are counting to objects they are counting. Children learn about one to one correspondence through repeated opportunities to count sets of objects and watch others as they count. It develops over time with students first counting small groups of objects and eventually larger groups.
Why do students need to “Keep Track?”

12. Hierarchical Inclusion
Numbers build by exactly one each time— smaller numbers are part of bigger numbers.
Children who have constructed the idea of hierarchical inclusion know that if you have six rocks and you take one away, there are five, or if you add a rock, there are seven.
It’s the idea of one more and one less.
Hierarchical Inclusion is numbers build by exactly one each time—smaller numbers are part of bigger numbers.
Children who have constructed the idea of hierarchical inclusion know that if you have six rocks and you take one away, there are five, or if you add a rock, there are seven. It’s the idea of one more and one less.

13. Conservation The number of objects is the same regardless
of their arrangement or the order in which
they were counted.
Conservation is another concept that students should develop as they learn to count. What is conservation? Conservation is the concept that a number of objects is the same regardless of their arrangement or the order in which they were counted.
Conservation of an object involves understanding that three is always three, whether it is three objects together or three objects apart.

14. Connecting Numbers to Quantities
Connect counting to cardinality
Understand that the last number name tell the number of objects counted
Connecting Numbers to Quantities involve connecting counting to cardinality.
It is understand that the last number named tells the number of objects counted.

15. Counting by Groups Counting a set of objects by equal groups
Make a set of a given number
Counts a set forward and backward
Students should also count by groups through counting sets of objects by equal groups, make a set of a given number, and count the set forward and backward.

16. Subitizing
Subitizing is the ability to immediately recognize the quantity of a small number of objects without counting.
Subitizing is the ability to immediately recognize the quantity of a small number of objects without counting. Research has shown subitizing to be foundational to basic arithmetic and other math skills. Many children who struggle with basic math also have trouble subitizing.

17. How many do you see?
Ask: How many did you see? How did you see it? How did you know it was six?
Quick Images can help students to develop understanding of quantity. Being able to conceptualize a number in a variety of ways will help students to use numbers flexibly, which is an important facet of number sense.
The teacher briefly shows an image of a quantity of a dot image for a brief amount of time, which encourages the children to subitize.
Students are asked to identify the quantity they saw and to describe the image.
This routine provides the opportunity for students to practice thinking efficiently about quantities.
Perceptual vs. Conceptual

18. How many do you see?

19. Counting On Cup
1.Work with a partner. Player 1: Turn over the top number card and put that number of counters in the cup.
2.Player 2: Roll the die and place that many counters next to the cup.
3.Together decide how many counters in all and fill in the record sheet.
4.Repeat until all the number cards have been used.

20. Counting Classroom Routines
The Counting Jar
Counting Around the Class
Dot Images
Counting Games
How could you differentiate these routines within your classroom?
Since children begin to learn these patterns by repetitive counting they are closely connected to their understanding of the particular number concept. Quantities up to 10 can be known and named without the routine of counting. This can help children in counting on (from a known patterned set) or learning combinations of numbers (seeing a pattern of two known smaller patterns).Young children should begin by learning the patterns of dots up to 6. Students should also associate the dot patterns to numbers, numerals, finger patterns, bead strings, etc. You can then extend this to patterns up to 10 when they are ready.Subitizing is a fundamental skill in the development of number sense, supporting the development of conservation, compensation, unitizing, counting on, composing and decomposing of numbers.

21. Video Evidence Watch the following video.
Reflect on your learning and how you will apply this in your classroom.
Think about these questions as you watch the video:
How do the students keep track or organize as they count?
How do the students determine the total?
Which students have you noted need intervention? Why?
We are to watch a video of students participating in counting activities in a classroom. Imagine you are the teacher in this classroom and your habit is to walk around with a clipboard and make anecdotal notes.
Think about these questions as you watch the video:
How do the students keep track or organize as they count?
How do the students determine the total?
Which students have you noted need intervention? Why?
Which students have you noted NEED INTERVENTION? WHY?
Hulbert June 2011

23. Reflection Questions
How did the students keep track or organize as they count?
How do the students determine the total?
Which students have you noted need intervention? Why?
Hulbert June 2011

24. Formative Assessment
1) What is formative assessment? 2) How can we formatively assess students’ mathematical progress?
Ask: What is formative assessment? How can we formatively assess students’ mathematical progress? (wait for responses)
Your students will have many opportunities to count and use numbers.

25. Observing Students as They Count
Counting Orally
Counting Quantities
Organizing a Count
Counting by Writing Numbers
You can learn a great deal by observing student as they talk, count aloud, count objects, and write numerals.

26. Share the following checklist with participants to utilize as documentation of ongoing progress (formative assessment).