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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