Counting and Place Value

My rant is over - for now.  Now is the time that I need to start focusing in on what the kids need and what the teachers need to help them meet their needs.

After mulling this over for a few days, this would be the professional development I would give to the teachers the first week of school.

Objectives:
1. Understand the skills necessary to count.
2. Understand the relationship of each place in a place value chart.
3. Understand the importance of teaching using the sequence:

Concrete  - Representational - Abstract

Although they have heard this many times, I don't think they understand the importance - especially when it comes to counting and place value.

1.  If I have a lot of time, I would spend time teaching the "funny numbers" from Kathy Richardson.  This is teaching different names for the numbers 1 - 7.

1.seeze

2.nudge

3.jingle

4.drift

5.ramp

6. groan

7. quiver

The purpose is to get the teachers to be put in the place of the students.  They have to learn unfamiliar vocabulary and attach the numerical value to that vocabulary.  Teachers are asked to come up with statements such as "I have quiver and take away drift, so I have jingle left."

The teachers are then introduced to nonsense symbols related to words ~ This helps them feel the frustrations that the students may be feeling as they are trying to learn sequence, vocabulary, value, and symbols at the same time.

This is excellent, especially for kindergarten teachers who may take for granted that the children know the counting vocabulary and the numerical value of those words.

2.  (This is probably where I would start with the entire staff) Introduce counting in base 5 - done with a document camera.  Teachers would have a similar chart and around 30 counters/unifix cubes.  The finished chart would look like this:

1	2	3	4	10
11	12	13	14	20
21	22	23	24	30
31	32	33	34	40
41	42	43	44	100

Questions to ask:  In the number 32(5) , how would you determine the value of 32(5) in base 10? Can you prove it?

Anticipated Answers:
Teachers will show the 3 groups of 5 and the 2 ones to show 17. 
Some teachers may opt to count on the chart to 32.

Tie in to Teaching:  How did the chart and the manipulatives help you understand base 5 numbers?

2.  Now would be a good time to introduce the place value chart for base 5, asking the teachers to come up with the value of each place:

		25	5	1
			3	2

 Question to ask: What is the relationship between the value of the places?  Can you extend the chart?

At this point, you may be asking yourself, "Isn't this much ado about nothing?  What value is it to learn to count in base 5 or learn the place value of base 5?"

Too many times teachers say that this is easy and they can get through this quickly.  Then there are still fourth and fifth graders that are struggling with place value. 
This is like a professional basketball player telling a six-year-old that making a jump shot is easy.  Of course it is, if you are 7feet 5 inches tall.  It is not that easy when you are 3 feet 4 inches tall!

A 30 year old teacher has been working with place value for at least 22 years.  Of course it should be easy to the teacher!

The finale for this day would be to have the teachers count to 25 using the binary system, and then having them explain the place value of each digit in the binary system.

The exit question/card would be SO WHAT???  What have you learned while working in different bases that helped you?  What manipulatives were useful?  What will you do in your classroom while teaching counting and place value?