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Counting that Counts!

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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  1. Counting that Counts!

  2. 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..

  3. 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?

  4. Why is “counting” important? Children’s understanding of a number is rooted in counting. (Maclellan, 2001)

  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?”

  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.

  8. How do students need to count?Rote Counting • Students need to know the number names and their sequences-both forward and backward.

  9. Students should practice counting from any number. 23, 24, 25,26, 27… 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…

  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.

  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.

  13. Conservation The number of objects is the same regardless of their arrangement or the order in which they were counted.

  14. Connecting Numbers to Quantities • Connect counting to cardinality • Understand that the last number name tell 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

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

  17. How many do you see?

  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?

  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? Hulbert June 2011

  22. 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

  23. Formative Assessment 1) What is formative assessment? 2) How can we formatively assess students’ mathematical progress?

  24. Observing Students as They Count • Counting Orally • Counting Quantities • Organizing a Count • Counting by Writing Numbers

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