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65 Cards in this Set

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___________ are based on a one-more-than or count-by-ones approach to quantity.
Pre-Base-Ten Concepts
Groupings with fewer than the maximum number of tens can be referred to as what?
equivalent representations
What does it mean by proportional models of place value?
groupable and pregrouped
Give an example of a groupable model of place value.
counters and cups, cubes, bundles of sticks
Give an example of pregrouped model.
Base ten blocks (rods, unit, flat), little ten frame cards
When developing place value concepts
you should teach counts as ones and tens and ones and discuss why the result is what?
the same
When developing _____________
you should teach counts as ones and tens and ones and discuss why the result is the same.
place value concepts
Models that clearly reflect the relationships of ones, tens, and hundreds are those for which the ten can actually be made or grouped from the singles is what kind of model?
groupable (cup of beans example)
In __________ models, children cannot actually take pieces apart or put them together.
pregrouped
_________ models can be used by students who no longer need to understand how ten unites makes "a ten" or by some students who need to return to place-value concepts.
nonproportional
Money is an example of a __________ model.
Nonproportional
__________ models do not show the model for a ten as physically ten times larger than the one.
nonproportional
What are the 3 ways of counting sets of objects?
1. Counting by ones (singles)
2. Counting by groups and singles
3. Counting by tens and ones
_________ are variations of the grouping activities.
equivalent representations of numbers
What is the first thing you should do in the suggested sequence for teaching oral and written names for numbers?
start with the names twenty, thirty, forty....ninety
What is the second thing you should do in the suggested sequence for teaching oral and written names for numbers?
Do all the names from twenty through ninety-nine.
What is the third thing you should do in the suggested sequence for teaching oral and written names for numbers?
emphasize the teens as exceptions - they are formed backwards. Do these last.
What can teachers use to assist with writing numbers?
place value mats
__________ is a flexible method of computing that varies with the numbers and the situation.
Invented strategy
__________________ involve taking apart and combining numbers in a wide variety of ways.
flexible methods of computation
Most of the partitions of numbers are based on place value or ________ numbers - number pairs that work easily together.
compatible
______________ require a good understanding of the operations and properties of the operations.
flexible methods of computation
___________ is having efficient, flexible and accurate methods for computing.
computational fluency
What are the three developmental phases towards computational fluency?
1. Direct Modeling
2. Invented Strategy
3. Algorithm
_________ is the use of manipulative or drawings along with counting to directly represent the meaning of an operation or story problem. You use physical materials.
direct modeling
_______________ is any strategy other than the traditional algorithm that does not involve using physical materials such as base-ten blocks or drawings.
invented strategy
___________ is a rule or procedure for solving a problem.
algorithm
Using base-10 blocks to represent the numbers in as many ways as you can is an example of what?
equivalent representation
_____________ involves alternative strategies for computing math that are easier and faster, and most of the time mental. They contribute to our overall number sense.
computational fluency
Discuss and explain the three differences between invented strategies and traditional algorithms.
See graphic organizer
Invented strategies vs. Traditional algorithms: Name the 1st difference and explain.
Invented strategies are number oriented. They look at the numbers to compute the problem. Traditional algorithms look at the digits. For example, in an invented strategy approach to 43 + 32, you might start with looking at 40 +30. In the traditional algorithm, you would start by looking at 3+2, then 4+3. It is thought that this unteaches place value.
Invented strategies vs. traditional algorithms: Name 2nd difference and explain.
Invented strategies are left-handed. They start with the largest part of the numbers, which are those represented by the left most numbers. Traditional algorithms begin with the digits on the right in a number.
Invented strategies vs. traditional algorithms: Name the 3rd difference and explain.
Invented strategies are flexible. The strategy can change with the numbers involved. Traditional algorithms are rigid, and there is one right way.
______________ are the basis for mental computation and estimation.
invented strategies
In _____________ students make fewer efforts.
invented strategies
With ______________ there is less re-teaching required.
invented strategies
In _______________ students develop number sense.
invented strategies
__________ are flexible methods that are often faster than the traditional algorithms.
invented strategies
In ________________ algorithm invention itself is a significantly important process of "doing mathematics".
invented strategies
____________ involves some computation. It is NOT a guess.
computational estimation
Partitioning, measuring off, repeated subtraction, and missing factors (think multiplication) are examples of what?
invented strategies
Avoid using the phrase "_______", and say it's one number being put into so many sets evenly instead.
goes into
The goal in using an area model is to get students to see that what?
ones x ones = ones
ones x tens = tens
tens x ones = tens
tens x tens = hundreds
What are the three strategies for computational estimation?
front end
rounding
compatible numbers
___________ methods focus on the leading or leftmost digits in numbers, ignoring the rest.
front-end
In __________ methods you substitute a “nice” number that is close so that some computation can be done more easily.
rounding
____________are something useful to look for when computing two or three numbers that can be grouped to make benchmark values. (10, 100, 500).
compatible numbers
In ________________, the answer must be exact, but they do not use paper and pencil for their calculations.
mental math
The _______________ helps children develop the idea of “a ten” as both a single entity and as a set of ten units. The children mentally construct the concept and impose it on the model.
place value mat
____________ is how students learn mathematics.
problem solving
What are the 5 content standards?
number and operations
algebra
geometry
measurement
data analysis and probability
What is Level 1 on the DOK chart?
Recall - Recall information such as facts, definition, term, or simple procedure, or applying a formula
Name the three things mathematics teachers should assess.
concepts and procedures
mathematical processes
dispositions
What is the content of the lesson taught THROUGH problem solving?
The 5 Math content strands
What is the content of the lesson taught ABOUT problem solving?
Problem solving strategies
What is Level 2 on the DOK chart?
Skill/Concept - Engagement of some mental processing beyond a habitual response.
What is Level 3 on the DOK chart?
Strategic Thinking - Requires reasoning, planning, using evidence, and higher level thinking.
What are the 5 content standards?
number and operations
algebra
geometry
measurement
data analysis and probability
What is Level 1 on the DOK chart?
Recall - Recall information such as facts, definition, term, or simple procedure, or applying a formula
Name the three things mathematics teachers should assess.
concepts and procedures
mathematical processes
dispositions
What is the content of the lesson taught THROUGH problem solving?
The 5 Math content strands
What is the content of the lesson taught ABOUT problem solving?
Problem solving strategies
What is Level 2 on the DOK chart?
Skill/Concept - Engagement of some mental processing beyond a habitual response.
What is Level 3 on the DOK chart?
Strategic Thinking - Requires reasoning, planning, using evidence, and higher level thinking.
What is Level 4 on the DOK chart?
Extended Thinking - Requires complex reasoning, planning, developing, and thinking most likely over an extended period of time.