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65 Cards in this Set
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 Back
___________ are based on a onemorethan or countbyones approach to quantity.

PreBaseTen 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 placevalue 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 ninetynine.


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 baseten blocks or drawings.

invented strategy


___________ is a rule or procedure for solving a problem.

algorithm


Using base10 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 lefthanded. 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 reteaching 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.

frontend


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.
