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25 Cards in this Set
- Front
- Back
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How is mathematical knowledge constructed? Give an analogy to help describe constructivism.
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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 |
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Mathematial knowledge constructed-
MET = SAE |
Materials- Sense
Effort- Active learners Tools- Existing knowledge |
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Describe the four features of a mathematical community of learners
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1. Ideas should be shared
2. Ideas should be respected 3. Math makes sense 4. It is okay to make mistakes! |
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Addition-
If A has a elements and B has b elements, then c is _____ |
AUB
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What is the formula for addition?
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a+b=c
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Label the formula
____ + ____ = ____ |
addend + addend = sum
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Subtraction
a-b=c if and only if _____ |
c+b=a
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a-b=c
What is c called? |
difference
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Label
____ x ____ = ____ |
factor x factor = product
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Division
a / b = q if and only if ____ |
q x b = a
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Label
____ / ____ = ____ |
dividend / divisor = quotient
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Identify the property
2(3+4) = (2x3)+(2x4) |
associative
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Identify the property
6+0=6 |
identity
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Identify the property
(2x3) x 8 = 2 x (3x8) |
distributive
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Identify the property
5x1=5 |
identity
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Identify the property
2+5=5+2 |
commutative
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Define basic facts
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For addition and multiplication, both addends or factors are less than 10. Subtraction and division correspond with addition and multiplication
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Define mastery
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means that the child can give a quick response (within 3 seconds) without resorting to non-efficient means, such as counting
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Define strategy
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This is the method or mental path of how to arrive at the answer
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What are the three steps to developing mastery of basic facts?
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1. memorizing facts
2. explicit strategy instruction 3. guided intervention |
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Describe the six characteristics of bases using base 10
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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 |
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What are the three types of fraction models?
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area= pizza
length= ruler sets= cupcakes |
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Give two meanings of top number and bottom number.
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Top number-
1. count 2. multiplier Bottom number- 1. name 2. divisor |
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Desribe the difference between invented and traditional strategies
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invented- more flexible, number originated, left to right
traditional- more rigid, digit oriented, right to left |
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What are the 4 guidelines for developing computation with fractions?
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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 |
