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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
ab=c if and only if _____ 
c+b=a

ab=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 nonefficient 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 righthand 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 