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94 Cards in this Set
- Front
- Back
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what are the five strategies for computational estimation |
front-end strategy, clustering, rounding, compatible number, special number |
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focuses on the left most or highest place value digit and using zeros in all other positions |
front end strategy |
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used when a set of numbers is close to each other in value |
clustering strategy |
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looking for numbers that are close to special values that are easy to work with |
special number strategy |
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enhance an understanding of numeration, number properties and operations, and promote problem solving and flexible thinking |
mental computation |
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what is an algorithm |
step by step procedure for producing an answer |
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what are the four ways remainders in division problems can be viewed |
part of answer, remainder, round up , ignore the remainder based on context of problem |
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when do you use the term number |
when referring to a value |
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why do we teach place value today |
children see how number systems works and develop flexibility in using place value concepts |
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what is all whole number a and b in multiplication communitative property |
AXB= BXA |
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what is all whole number A and B in communtative property of addition |
A+B=B+A |
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what is the long multiplication algorithm based on |
distributive property of multiplication over addition |
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what is the identity element of multiplication |
1 |
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what is the identity element of addition |
0 |
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why is it important to interpret numbers in non standard ways like 6 tens times 4 |
understand the magnitude by which number grow when we multiply them |
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when you are first introducing long division algroithms, what should you start with |
stories so that division come out with no remainders and doesn't make sense to break apart into smaller sets |
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what are the properties of multiplication |
distributive property of multiplication over addition, associative property of addition, associative property of multiplication, identify property of addition/multiplication |
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what is the first way of illustrating basic facts of multiplication |
rectangular arrays |
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what shouldn't you use key words in word problems |
detrimental |
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when is a number sentence meaningless |
when has more than one answer proven |
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what is the most concrete model of fractions |
region model |
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what are two different systems for naming the same numbers |
fractions and decimals |
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what are the two uses of fractions |
describe part of wholes and describe ratios |
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what are the types under the part of whole interpretation |
regions and set |
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what is a region model |
continuous model |
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what is a set model |
discrete model |
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represent a relationship between two quantities |
ratios |
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what are the types of ratios |
part to part and part to whole |
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what order should teachers ask children to model fractions |
concretely, pictorially, symbolically |
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what is a discrete unit |
a set of distinct objects |
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what are continuous units |
continuous quantities like region |
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what are a list of models that help children interpret fractions |
unifix cubes, cuisenaire rods, fraction bars and fraction circles |
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any number that can be located on a number line "Girl, you so fake you not even on the number line" --Heather |
real number |
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are non-terminating and non-repeating. They have no other subsets, but it is an infinite set. |
irrational numbers |
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what are examples of rational numbers |
all whole numbers all mixed numbers all decimals that terminate and repeat fractions percentages negative integers |
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are dense and infinite set in three directions: positive, negative, and in between numbers.
all numbers that can be expressed in the form of a/b where a and b are integers and b is not zero |
rational numbers |
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are whole numbers and their additive inverses |
integers |
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what are all integers |
rational numbers |
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what is an additive inverse |
the numbers when added to another number gives the sum of zero |
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what directions is integers an infinite set |
positive and negative |
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all natural numbers plus zero; numbers that I use to identify cardinality |
whole numbers |
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numbers use to tell how many |
cardnality |
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what direction is whole numbers an infinite set |
positive by one number: 0 |
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what direction in counting or natural numbers an infinite set |
positive |
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numbers that I use to identify the cardinality of a set and numbers that I use when begin counting |
counting or natural numbers |
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name the same number 2/3 names the same number as 4/6 |
equivalent fractions |
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how do you know two fractions are equivalent |
they take up the same amount of space |
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what are fractions called with a numerator of one |
unit fractions |
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what is an equivalent fraction rule |
if I have a fraction and multiply the numerator and the denominator by the same number I will have an equivalent fraction |
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what is the relationship between whole number division and fraction notation |
when you have a # of objects that need to be equally shared between a # of sets that isn't a multiple of the # of objects the answers will not result in whole number but instead written in fraction notation
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what are two misunderstandings about multiplication and division |
multiplication means bigger and division means smaller |
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what is the rule to follow when adding fractions with the same denominator |
add the numerators and keep the denominators the same |
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when teaching operations with fractions what do you start with |
real world problems, lots of manipulative experiences, draw lots of pictures, |
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what interpretation do you use for multiplying fractions with whole numbers |
repeated addition interpretation of multiplication |
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what do you always want to use as a reference when learning how to multiply a fraction times a fraction |
the whole "1" fraction bar |
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during concept development what types of fractions do you leave the answer in the form of |
improper fractions not mixed fractions |
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what are two numbers called when there product is 1 |
recipercals |
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what does performing the operation with a reciprocal undo |
the operation |
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what questions do you ask when the divisor is larger than the dividend |
how much of the divisor is contained in the dividend |
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what question do you ask when the divisor is smaller than the dividend |
how many of the divisor is contained in the dividend |
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what is the difference between mental computation and estimation |
mental computation involves finding an exact answer with out paper and pencil and estimation is finding a approximate answer |
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what will children develop if they are encouraged to compute mentally |
develop their own strategies |
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what are the reasons for having and using algorithms |
1. power 2. reliability 3. accuracy 4. speed |
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prerequisites for paper and pencil computation |
1. know some basic facts 2. good understanding of place value system 3. understand some math properties of whole numbers like commutative and distributive |
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children record each partial sum individually before combining the partial sums to find the sum
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partial sum algrithm |
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what two interpretations of multiplication can help children understand the concept of multiplication when developing a multiplication algorithm |
equal groups and array interpretations |
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the number in each group |
divisor |
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the total number of sets |
dividend |
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the resulting number of groups |
quotient |
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with mental computation with division problems was is the best way to think of division |
inverse of multiplication |
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what are the prerequisite topics include for understanding fraction concepts |
comparing fractions, number sense about fractions, recognizing equivalence |
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what are strategies for learning fraction computation |
real world connections, manipulative materials and pictures |
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what is one reason for the difficulty many children have with fraction computation |
compute fraction symbols before developed understanding of fractions |
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what are four goals of instruction regarding fraction computation |
1. recognize situations involve operations of fractions 2. find the answer using models 3. need to estimate the answer 4. need to find the exact answer |
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what can multiplication can be interpreted as |
repeated addition |
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what can division be presented as |
repeated subtraction |
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what is probably the easiest multiplication situation for children to interpret with fractions |
fraction by a whole number |
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what are two types of division problems possible in fraction divsion |
partitive and measurement |
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which types of division problems with fractions are the easiest to be presented first |
fraction divisors and whole number dividends |
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result in fairly low level performance and a lack of understanding, particularly if concepts are taught procedurally |
place value approach |
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what are some key points for reading and writing decimals |
decimal point, decimal names, decimal notation |
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what are some concrete and semi concrete models to use for developing decimals number sense |
base ten blocks, decimal squares, graph paper grids, number line, and money |
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what do you want to use to introduce adding and subtracting decimals |
join and separate situations |
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what interpretation is the easiest for multiplication and division of decimals |
equal groups, and array for multiplication and measurement for division |
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what is a long division story problem |
you have 354 dollars to buy 2 gifts. You must spend the same amount on both gifts and spend all your money. How much will each gift cost? |
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what is a long multiplication story problem |
I have 2 boxes of crayons where each box has 12 crayons. How many crayons do I have? |
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what is a multiplication problem with a fraction times a whole number |
There were 3 flavors of cake at the bake sale. I bought 1/2 of each cake. How many cakes did I buy? |
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what is a multiplication problem with a fraction time a fraction written in improper form |
I have 1/2 of a apple. I gave each of my 2 friends 1/2 of my apple. How much of an apple does each friend get |
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what is a multiplication problem with a whole number times a mixed number |
a loaf of bread weighs 2 pounds. I have 3 1/2 loafs. How many pounds of bread do I have? |
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what is a multiplication problem with a mixed number times a mixed number |
a loaf of bread weights 3 1/2 pounds. I have 1 1/2 loaves. How many pounds of bread do I have? |
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what is a word problem using the area model of multiplication with fractions |
Mr. Smith owns 1/2 acre of land. He gave each of his 3 sons 1/3 of his land. How much of an acre did each son get? |
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what is a word division problem where ask how many |
It takes 1/4 yd. of a ribbon to make a bow. I have 1/2 yd. How many bows can I make? |
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what is a word division problem where ask how much |
It takes 1/2 yd of ribbon to make a bow. I have 1/4 yd. How much of the needed ribbon do I have? |
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Fractions |
