EDE 4123 test 1
write an example for combinations
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write an example for equal groups
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write an example for multiplicative comparison
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write an example for part-part-whole
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addition/multiplication associative property
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addition/multiplication identity property
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distributive property
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write an example for compare
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write an example for join addition and subtraction
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write an example for measurement
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write an example for partition
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write an example for product of measures
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write an example for separate addition and subtraction
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write an example of a contextual story problem which demonstrates the properties of addition/multiplication communitive property
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identify 5 equivalent representations of 473
-3 hundreds, 17 tens, 3 ones -1 hundred, 27 tens, 3 ones -1 hundred, 37 tens, 3 ones -2 hundreds, 20 tens, 73 ones -3 hundreds, 15 tens, 23 ones
list the dos for teaching basic facts
-ask students to self monitor -focus on self improvement -drill in short time segments -work on facts over time -involve families -make drill enjoyable -use technology -emphasize importance of self monitor
what are the necessary behaviors associated with counting?
-producing the standard list of counting words in order -connecting the sequence in a one-to-one manner with the items in the set being counted -assigning each item counted one and only one counting word
explain why key words should not be taught
-sends wrong messages about doing mathematics. key words encourages children to ignore meaning and structure of a problem -they are misleading. word/phrase suggests an operation that is incorrect -many problems dont contain them. with out them students are left without a strategy -don't work with two step problems
list the dots of teaching basic facts
-use lengthy time tests -use public comparison of mastery -proceed through facts in order of 0-9 -work on all facts at once -move to memorization too soon -use facts as a barrier to good math -use fact mastery as a prerequisite for calculator use
list the digits in the order in which students should learn to write them
1,4,7,2,5,3,6,9,0,8
how does the number of the day routine and the models for multi-digit numbers activity promote place value understanding
students see 1 more, 1 less, 10 more, 10 less students see how place value changes as the numbers change in ones and ten places
list the three ways of counting set objects
unitary-by ones base 10- counting by groups of tens and ones equivalent-counting with the non-standard base 10 groupings
explain how ten frames should be used for addition
with the ten frame with ten squares and how the square gets a dot. the dots represent numbers and it helps students recognize numbers using their anchor numbers 5 and 10
what is a referent?
measure of things in the real world
explain how a place value mat should be used in teaching addition and subtraction of multi-digit numbers
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list skills/concepts that are taught through shapes of numbers activity and the Mickey Mouse ticket to class activity
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explain the similarities and differences among models of equivalent representations
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how should multiplication be introduced to students? how should multiplication by 1 be introduced to students?
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list 3 stages of counting
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list examples of three kinds of basic 10 models
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what is number sense?
a good intuition about numbers and their relationships. develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating then in ways that are not limited by traditional algorithms
join
action (addition and subtraction)
separate
action (addition and subtraction)
what is computational estimation
actual computation, involves some mental computation with at least 2 estimated quantities, computational estimates-not a guess, specific algorithms that produce approx. results rather than exact
what is computational fluency
addition and subtraction strategies that build on decomposing and composing numbers in flexible ways that contribute to students overall number sense
what are the names of the various parts of addition, subtraction, multiplication, and division number sentences
addition: addend + addend= sum subtraction: minuend-subtrahend=difference multiplication: multiplicand x multiplier= product division: dividend/divisor=quotient
explain what a base-10 representation is and what equivalent representation is
base 10- uses max number of 100s, 10s, and 1s equivalent representation: anything but base 10
explain each of the three developmental phases towards computational fluency in terms of student behaviors (direct modeling, invented strategies, traditional algorithms)
directed modeling: use of base 10 models along with counting directly represent the meaning of an operation of story problem invented strategy- any strategy other than the traditional algorithms that does not involve using physical materials or drawings but does include written recordings and mental methods when appropriate traditional: making sense of a procedure as a process
what are the 4 story problem structures for multiplication
equal groups, multiplicative comparison, product of measures, and combinations
explain the strategies for computational estimation
front-end: compute with front digits rounding: round each factor and then compute compatible numbers: particularly with division, adjust numbers so a whole number answer results
what is the role of a referent?
give meaning to a name
how does the place value concepts evident in the 1-100 chart
highlight patterns-skip counting by 2,5,10 count and recognize 2-digit numbers moving left-right or right-left takes away or adds one unit moving up or down takes or adds one long
explain the three differences b/n invented strategies and traditional algorithms
invented strategies are: number oriented rather than digit oriented left-handed rather than right-handed range of flexible options rather than one right way
explain why ten frames should be used for addition
it is used so students can relate other numbers to 10. this helps build computation skills
what are the 4 story problem structures for addition and subtraction?
join, separate, part-part-whole, compare
describe what the teacher does when employing each of the three approaches to teaching basic facts (memorization, explicit strategy instruction, and guided intervention)
memorization- using a drill strategy- doesn't work explicit strategy- teachers support student thinking rather than giving students something new to remember. students get to choose strategies guided intervention- focuses on open ended strategies. teacher may not explain a strategy but carefully sets up tasks when students notice number relationships
describe activities we did in class to promote place value development
models for multi-digit numbers: showing how numbers change based on movement around 100 chart number of the day- 1 less, 1 more, 10 more, 10 less
compare
no action (addition and subtraction)
part-part-whole
no action (addition and subtraction)
what is mental math
occurs mentally and involves performing computations answer must be exact- do not use paper and pencil for computation
what are the two story problem structures for division?
partiton, measurement
explain what a basic fact is
refers to those relationships in which two parts are less than 10 EX: 3=2=5
