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25 Cards in this Set

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How is mathematical knowledge constructed? Give an analogy to help describe constructivism.
It is constructed with materials, effort and tools.

Sense helps with materials
Active learners helps to acheive effort
Existing knowledge falls under tools.

Analogy- Before we start to build, we must know how to construct a house. We also need good workers who do not slack off as well as good building supplies
Mathematial knowledge constructed-

MET = SAE
Materials- Sense
Effort- Active learners
Tools- Existing knowledge
Describe the four features of a mathematical community of learners
1. Ideas should be shared
2. Ideas should be respected
3. Math makes sense
4. It is okay to make mistakes!
Addition-

If A has a elements and B has b elements, then c is _____
AUB
What is the formula for addition?
a+b=c
Label the formula
____ + ____ = ____
addend + addend = sum
Subtraction
a-b=c if and only if _____
c+b=a
a-b=c

What is c called?
difference
Label

____ x ____ = ____
factor x factor = product
Division
a / b = q if and only if ____
q x b = a
Label

____ / ____ = ____
dividend / divisor = quotient
Identify the property
2(3+4) = (2x3)+(2x4)
associative
Identify the property
6+0=6
identity
Identify the property
(2x3) x 8 = 2 x (3x8)
distributive
Identify the property
5x1=5
identity
Identify the property
2+5=5+2
commutative
Define basic facts
For addition and multiplication, both addends or factors are less than 10. Subtraction and division correspond with addition and multiplication
Define mastery
means that the child can give a quick response (within 3 seconds) without resorting to non-efficient means, such as counting
Define strategy
This is the method or mental path of how to arrive at the answer
What are the three steps to developing mastery of basic facts?
1. memorizing facts
2. explicit strategy instruction
3. guided intervention
Describe the six characteristics of bases using base 10
1. there are 10 numbers that are used when using base ten- 0,1,2,3,4,5,6,7,8 and 9
2. If you count by 5s, you get two columns- the 5s column and the last column
3. The numbers under 2 are all even numbers (every alternating number in the rows are even)
4. In a column, the first number (tens digit) "counts" or goes up by ones
5. you can count by tens by going down the right-hand column
6. In a row, one number "counts" (the ones digit goes 1,2,3...); or the second number (tens digit) stays the same
7. There are base 1- blocks that help us visualize the base ten system
What are the three types of fraction models?
area= pizza
length= ruler
sets= cupcakes
Give two meanings of top number and bottom number.
Top number-
1. count
2. multiplier

Bottom number-
1. name
2. divisor
Desribe the difference between invented and traditional strategies
invented- more flexible, number originated, left to right

traditional- more rigid, digit oriented, right to left
What are the 4 guidelines for developing computation with fractions?
1. Begin with simple contextual tasks
2. Connect meaning of fraction computation with whole number computatoin
3. Let estimation and informal methods play a big role in the development of strategies
4. Explore each of the operations using models