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114 Cards in this Set
- Front
- Back
When working with number sense, what should a teacher start with?
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measures of length, weight, and time
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What is a very difficult task for young children?
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estimating
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In early estimation, teacher need to help children with ____________.
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about
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When helping children with "about", you look at what things?
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-more or less than
-close to # or # -less than #, between #, or more than # -about ________? |
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Counting tells how many things are in a what?
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set
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When counting a set of objects, the last word in the counting sequence names what?
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the quantity for the set
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When counting a set of objects, the last word in the counting sequence names the quantity for the set. This is known as what?
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cardinality
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Numbers are related to each other through a variety of what?
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number relationships
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The number 7 is more than 4, two less than 9, composed of 3 and 4 as well as 2 and 5, is three away from 10, and can be quickly recognized in what?
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several patterned arrangements of dots
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______________ are intimately tied to the world around us.
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number concepts
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Application of ___________ to real settings marks the beginning of making sense of the world in a mathematical manner.
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number relationships
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Application of number relationships to real settings marks the beginning of ________ ____________ of the world in a mathematical manner
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making sense
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In Pre-K and Kindergarten most children can already identify _____ and those who cannot are considered at risk.
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more
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In ________ and ________ they have more exposure to “which is more”.
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Pre-k and Kindergarten
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Most children have difficulty with this.
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Less
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________ should be paired with the word more.
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Less
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Make a conscious effort to ask Which is _______?
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less
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Children should construct sets using ________ as well as make comparisons or choices between two given sets.
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counters
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In the progression of Number Development in Pre-K and K, students should do what two activities?
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Make sets of More/Less/Same
Find the same amount |
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When should Children have a fair understanding of counting?
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at midyear in kindergarten
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Meaningful counting activities begin in what?
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preschool
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_______ attached to counting is the key conceptual idea on which all other number concepts are developed.
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meaning
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Meaning attached to counting is the key ____________ idea on which all other number concepts are developed.
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conceptual
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Early counting involves at least 2 separate skills. One is that a child must be able to produce the standard list of what?
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counting words in order (one, two, three)
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Helping students read and write single digit numbers has nothing to do with __________.
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number concepts
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Having them match numbers to pictured sets versus tracing over the numbers is during what stage?
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numeral writing and recognition
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In the numeral writing and recognition, what activity should you have them do?
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find and press on the calculator
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In the numeral writing and recognition stage, you should have them ____________ numbers to pictured sets instead of tracing over the numbers.
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match
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What are the 4 stages in the progression of number development in Pre-K to K?
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Relationship of more, less than, the same
Early counting Numeral Writing and Recognition Counting on and Counting back |
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In counting on and counting back, students should work with difficult skills by doing what?
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having frequent short practice drills
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What stage should students do these activities?
Up and Back Counting Counting on with Counters Real Counting On |
counting on and counting back
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__________ is a “good intuition about numbers and their relationships.
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number sense
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____________ develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms”
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number sense
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The NCTM standards state that as students work with numbers, they gradually develop flexibility in thinking about numbers, which is a hallmark of __________.
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number sense
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The NCTM standards state that as students work with __________, they gradually develop flexibility in thinking about numbers, which is a hallmark of number sense.
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numbers
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Number sense develops as students understand ___________.
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the size of numbers
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Number sense develops as students develop multiple ways of thinking about and representing numbers, use numbers as referents, and develop _______ about the effects of operations on numbers.
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accurate perceptions
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Patterned sets, 1 and 2 more and 1 and 2 less, part-part-whole, and anchors of 5 and 10 are what?
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the 4 relationships that should be used to teach children about the numbers 1-10
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Patterned sets should be what?
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instantly recognized
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When using patterned sets, children can learn to recognize what?
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sets of objects in patterned arrangements and tell how many without counting (dice)
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Patterned sets activities encourage reflective thinking about the patterns so that the _____________ will be constructed.
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relationships
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Patterned sets can aid in _________ or learning combinations of numbers.
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counting on
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Dot plates and Dot Plate Flash are used with what?
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learned patterned sets
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What are the 4 relationships that should be used to teach children about the numbers 1-10?
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patterned sets
1 and 2 more and 1 and 2 less part-part-whole anchors of 5 and 10 |
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Early counting involves at least 2 separate skills. One is that a child must be able to produce the standard list of counting words in order (one, two, three…) The second is that a child must be able to connect this sequence in a __________ manner with the items in the set being counted. (each item must get one count)
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one-to-one
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There should be ___________ attached to counting.
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meaning
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Children will learn ______ to count before they understand that the last count word indicates the ________ of the set (cardinality)/
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how
amount |
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Children who understand that the last count word indicates the AMOUNT of the set have mastered what?
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The cardinality principle
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Just because children can count orally does not mean they have attached _______ to their counting.
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meaning
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Just because children can ______________ does not meant they have attached meaning to their counting.
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orally count
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What activity can students use in early counting?
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fill the chutes
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What are these activities used with?
Counters- Covered Parts Missing-Part Cards Connecting Cubes |
part-part-whole relationships
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Addition and subtraction are __________.
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connected
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Addition names the ________in terms of the parts.
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whole
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Subtraction names a ___________.
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missing part
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___________ involves counting groups of like size and determining how many are in all.
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multiplication
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___________ and division are related.
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multiplication
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__________ names a missing factor in terms of the known factor and the product.
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division
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__________ can be used to solve contextual problems for all operations and to figure out what operation is involved in a problem regardless of the size of the numbers.
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models
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_______ can be used to give meaning to number sentences.
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models
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Joining amount to initial (starting) amount is what kind of problem?
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join
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Amount removed from the initial amount is what kind of problem?
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separate
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Collection, a set of things we have is what kind of problem?
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part-part-whole
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Comparison of two quantities; which has more (how many more), which has less (how many less) is what kind of problem?
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compare
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Number and size of the groups are known (repeated addition) is what kind of problem?
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equal groups (multiplication)
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Based on one set being a multiple of the other is what kind of problem?
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multiplicative comparison
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____________ problems are where the size of the sets is unknown (fair-sharing).
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partition (division)
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In ____________ the number of sets is unknown but the size of the sets is known (repeated subtraction).
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measurement (division)
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The remainder is discarded
when the remainder can______ the answer to the next highest whole number. |
force
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The remainder is discarded when the answer is ______to the nearest whole number for an approximate result.
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rounded
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Key words are often _________.
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misleading
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Many times the key word or phrase in a problem suggests an operation that is ________.
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incorrect
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Many problems have no ________, except the overly simple problems found in primary textbooks.
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key words
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_________ strategy sends the wrong message about doing mathematics.
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key word
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The most important approach to solving any contextual problem is to __________ it and make sense of it.
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analyze
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The___________ approach encourages students to ignore the meaning and structure of the problem and look for an easy way out.
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key word
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Give an example of an addition Commutative Property.
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a+b = b+a
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Give an example of an addition Associative Property.
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a+b+c = c+b+a
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Give an example an addition Zero Property.
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a+0=a
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Give an example of a multiplication Associative Property.
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(a+b)+c=a+(b+c)
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Give an example of multiplication of Zero Property.
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a x 0 = 0
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Give an example of the Identify Property.
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a x 1= a
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Give an example of the Distributive Property.
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a(b+c)= ab+ac
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_________ provide the foundation for strategies that help students remember basic facts.
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number relationships
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____________ is the most powerful way to think of subtraction facts.
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"think addition" (6 + _____ = 13)
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Because mastery of the basic facts is a developmental process, students move through stages, starting with _________, then to more efficient reasoning strategies, and eventually to _________.
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counting
quick recall |
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What are the four steps to the basic fact strategies?
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1. introduce new strategy
2. let them practice new strategy 3. add new strategy to previously learned strategies 4. let them practice both strategies |
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What strategy do these belong with?
Two ways: Known fact (7+3=10) Derived fact (7+5=12) |
addition facts
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What strategy do these belong with?
One More than and Two More Than How Many Feet Are in the Bed (book) One More Than and Two More Than with Dice and Spinners |
addition facts
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What strategy do these belong with?
Facts With Zero What’s Alike? Zero Facts |
addition facts
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What strategy do these belong with?
Doubles Double Images Calculator Doubles |
addition facts
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What strategy do these belong to?
Near Double On the Double |
addition facts
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What strategy do these belong to?
Make a 10 Fact or Up Over 10 Move to Make 10 Make 10 on the Ten-Frame |
addition facts
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What strategy do these belong to?
10 Frame Facts or 10 Facts Doubles Plus Two or Two-Apart Facts Make-10 Extended Remaining Facts |
additinon facts
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What strategy do this belong to?
Think Addition |
subtraction facts
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What strategy do these belong to?
Using known addition facts to produce the unknown quantity or part (“What goes with this part to make the total?”) Apples in the Trees |
subtraction facts
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What strategy do these belong to?
Sums to 10 Facts with Zero One-less-than two-less-than Ten-Frame Facts |
subtraction facts
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What strategy do these belong to?
Down Over 10 Take from the 10 Apples in Two Trees Missing-Number Cards |
subtraction facts
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What strategy do these belong to?
Doubles Clock Facts |
multiplication facts
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What strategy do these belong to?
Five Facts: Array Zeros and Ones: Array |
multiplication facts
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What strategy do these belong to?
Nifty Nines: Array, Fingers, Patterns in the Nine Facts,(Numbers add up to be nine 2 x 9=18 [1+8=9]) |
multiplication facts
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What strategy do these go with?
Helping Facts – Using Known Facts to Derive Other Facts -Double and Double Again -Double and One More Set -Half Then Double -Add One More Set |
teaching multiplication facts
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Recognizing that more drill will not work and providing hope is something you should do for what?
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remediation
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These are strategies for what?
Inventory the known and unknown facts for each student in need Diagnose strengths and weaknesses Focus on reasoning strategies Build in success Provide engaging activities for drill |
remediation
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Which addition and subtraction problem is the only one that has action in it?
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join
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Which two addition and subtraction problems have no action?
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part-part-whole and compre
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"How many more" is part of what kind of problem?
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compare
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One and Two More, One and Two less involves more than just counting on two or counting back two, children should know what?
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that 7 is 1 more than 6 and also 2 less than 9
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Dot cards: Make a Two-More-Than Set
Deck of More-or-Less cards: more or Less Calculator (a Calculator Two-More-Than Machine) are activities for what? |
teaching children One and Two More, One and Two less
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Anchoring Numbers to 5 and 10
help children relate what? |
5 and 10 to other numbers
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In anchoring numbers to 5 and 10 the most important model is what?
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the 10 frame
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½ Ten Frame- Five-Frame Tell-About
Ten Frame- Crazy Mixed-Up Numbers and Ten-Frame Flash are activities for what? |
anchoring numbers to 5 and 10
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__________________ help conceptualize that a number is made up of two or more parts (most important relationship that can be developed)
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part-part-whole relationships
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In _____________ most activities focus on a single number for the entire activity.
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part-part-whole relationships
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