Thinking in Collection I do not intend my powerpoints to be used as the lesson. I intend the ppt to guide your thinking about how you might develop a line

Thinking in Collection

I do not intend my powerpoints to be used as the lesson.I intend the ppt to guide your thinking about how you might

develop a line of inquiry with the image.

My goal is to practice manipulating numbers in your head with ease. If fingers come out to count, the task is not accomplishing its purpose. I want students interacting and explaining the ways they can track the numbers. Read and see.

Number Sense is built on a firm foundation of confidence with small quantity.

2014 Slides courtesy of Thinking 101 [email protected] All rights reserved.

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Thinking in Collection

At the end of the ppt you will find just the penguins followed by a blank slide if you want to use the image with your students.



What Do We Know about Practice?

If you want to remember and apply any facts, math or not, you need to practice under conditions that allow your brain to do its job. The human brain is continually inundated with information. It sorts, classifies, compares in order to make sense of that information. Association is how the brain “remembers”. It links things together in networks. The more senses involved when experiencing the information to be remembered, the better. The more vibrant, colourful and emotionally satisfying the experience the better.

Organizing in small collection makes it easier to “know” how many without stopping to count each one. Take a look...




As you read through keep in mind I am thinking like a teacher... How can I keep my students engaged in the visual long enough to actually experience some practice.

The quantities are small and easily manageable by the brain.

I want students to “play” through sets of numbers, manipulating them different ways to constantly come up with the same answer. The total is not in question and never the focus... The pathways to play in your head and not lose any numbers is more important to me.




I show the image that follows for 3 to 5 seconds... I do not scare the students with warning them it will be fast I just say take a quick look, then count to myself a slow 1000 2000 3000 4000 and move to the blank slide





Think to yourself or talk softly to a partner... How were the penguins arranged? Were they in groups? In rows?

Look again and carefully think about the arrangement

Penguins

2014 Slides courtesy of Thinking 101 [email protected] All rights reserved


Did you see sets of 2 and sets of 3?Can you “see” the sets in your mind without looking at the

picture again?

Use x or tics ✓ to represent penguins and draw the arrangement on your page.

(Responses may vary.)

I drew this: IS IT THE SAME AS THE PENGUINS?

✓✓ ✓✓✓✓ ✓✓✓✓✓ ✓✓✓

Penguins




✓✓ ✓✓✓✓ ✓✓✓✓✓ ✓✓✓

I SEE:

4

5

5


Did anyone thinkvertically to keep track


2,4,6 3,6,8

Can you show how I kept track this time?


I thought 3 and 3 make 6, then count by twos.


How many ways can you string these together mentally to add?

3,6,8,10,12,14 Can you follow my eye? Where did I start? Where did I finish? Come trace my pathway.


2 + 3 = 5 5 + 5 = 10 12 ,14Can you follow my eye? Where did I start? Where did I finish? Come trace my pathway.


2 + 1 = 3, 2 + 1 = 3 Now 3,6,9,12 and 2 is 14Can you follow my eye? Where did I start? Where did I finish? Come trace my pathway.


That should take less than 10 minutes. If you want to continue into more practice consider this:Use sets of 2 and 3 tics to build a collection of ? And play with a partner finding paths to count it.

(Do not focus on drawing penguins, represent the idea of a count with tics or x’s)

What number would be appropriate for your students. We do not want them to have to work hard to count. 16? 18? Be sure it works with twos and threes.




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Thinking in Collection I do not intend my powerpoints to be used as the lesson. I intend the ppt to guide your thinking about how you might develop a line