BullPack - ELM 555 Summer 2017 Elem Math Foundational Terms and Concepts Flashcards
Describe Conservation of Number
We can just call this “conservation”. Conservation means that a student has internalized the idea that dots or objects can be in different arrangements and still have the same value. With Subtilizing you can work on this by demonstrating the same value with several different formations and say: What! how could they be the same value - they Look Different!
What is the associative property and why is it so handy?
The associative property of addition states that a + (b + z) is equal to (a + b) + z. This property holds for addition and for multiplication. You can have numbers Associate differently (notice they did not MOVE) and still maintain their value. From this I know that 8 + (2 + 3) is equal to (8 + 2) + 3. By re-thinking through the components of my value I can see that the total is just 10 + 3. Hey, that’s 13!
What is the commutative property and why is it so important?
The commutative property of addition states that r + g = g + r In other words I can MOVE the parts of my addition expression without changing its value. This is also true for multiplication. This is handy because it helps me to understand conservation of number (hey! different but still equal!). I can build this idea while subtilizing because I can switch the order of cards and have a discussion about how students can know and explain that the value did not change even though the order did!!
Race To Ten Game, Circuit Game - What are some Learning Trajectories I can work on and Assess while playing the Race to Ten game?
You are on your own here. We will work on this in class a lot in Session 2 and 3. Check your notes.
Place Value Comparer versus Internalized Sense of the Number Line to 10
A place value comparer understands that 32 is larger than 28 because she understands the weighted nature of the number system. She sees that 3 tens has to be larger than 2 tens, no matter how many ones there are!
This same person, though, might not understand that 32 is closer to 28 than it is to 39. She might think that, because the numbers are both in the Thirties, that they are closer. Someone with an internalized sense of the number line to 100 understands that 32 and 28 are each 2 away from 30. So that is 4 total. 39, on the other hand is 7 away from 32 and is farther away.
