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Counting that Counts!. 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. Counting Jar How did you represent the number you counted? What are the ways you counted ?

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Counting that Counts!

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Counting that counts

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..


Counting that counts

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?


Counting that counts

Why is “counting” important?

Children’s understanding of a number is rooted in counting.

(Maclellan, 2001)



What does cardinality mean
What does cardinality mean? end of kindergarten?

  • 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?”


Attendance count around the class
Attendance: end of kindergarten? 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.


How do students need to count rote counting
How do students need to count? end of kindergarten? Rote Counting

  • Students need to know the number names and their sequences-both forward and backward.


Counting that counts

Students should practice counting from any number. end of kindergarten?

23, 24, 25,26, 27…

30, 31, 32, 33, 34…


Skip counting by 2s 5s 10s 100s
Skip Counting end of kindergarten? by 2s, 5s, 10s, 100s

  • Starting at 0 5, 10, 15, 20…

  • Forward and backward

    90, 80, 70, 60…


One to one correspondence
One to One Correspondence end of kindergarten?

  • One number stands for one object that is being counted

Keeping Track

  • Students develop strategies for organizing and keeping track as they count.


Hierarchical inclusion
Hierarchical Inclusion end of kindergarten?

  • 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.


Conservation
Conservation end of kindergarten?

The number of objects is the same regardless

of their arrangement or the order in which

they were counted.


Connecting numbers to quantities
Connecting Numbers to Quantities end of kindergarten?

  • Connect counting to cardinality

  • Understand that the last number name tell the number of objects counted


Counting by groups
Counting by Groups end of kindergarten?

  • Counting a set of objects by equal groups

  • Make a set of a given number

  • Counts a set forward and backward


Subitizing
Subitizing end of kindergarten?

  • Subitizing is the ability to immediately recognize the quantity of a small number of objects without counting.


How many do you see
How many do you see? end of kindergarten?


How many do you see1
How many do you see? end of kindergarten?


Counting on cup
Counting On Cup end of kindergarten?

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.


Counting classroom routines
Counting Classroom Routines end of kindergarten?

  • The Counting Jar

  • Counting Around the Class

  • Dot Images

  • Counting Games

  • How could you differentiate these routines within your classroom?


Video evidence
Video Evidence end of kindergarten?

  • 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?

Hulbert June 2011


Reflection questions
Reflection Questions end of kindergarten?

  • 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


Formative assessment
Formative Assessment end of kindergarten?

1) What is formative assessment?

2) How can we formatively assess students’ mathematical progress?


Observing students as they count
Observing Students as They Count end of kindergarten?

  • Counting Orally

  • Counting Quantities

  • Organizing a Count

  • Counting by Writing Numbers


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