EDE 4123 Test #1
Why we should use ten frames
1.So that students can relate other numbers to ten 2.They help build computation skills
NCTM standards of Number Sense
1.Well understood number meanings 2.multiple relationships among numbers 3. recognition of the relative magnitude of numbers (Hurricane Katrina) 4. Knowledge of the effect of operations on numbers 5. Referents to measure of things in the real world
Computational Estimation
Involves some mental computation with at lest two estimated quantities It is not a guess
Cardinality
Meaning that is attached to counting
How to develop place value
Two meanings of tens: 10 individual units, 1 log Three meaning of hundred: 100 individual units, 10 logs, 1 flat
Model of Place Value
proportional groupable proportional pregroupable non-proportional
Nonproportional
teddy bear counters, money
combination
the two numbers in a multiplicative problem represent different types of things; the answer will be a new thing (shirt shorts combined form outfit)
Direct modeling
the use of manipulatives or drawings along with counting to directly represent the meaning of an operation or story problem
Compare problem structure
there is no action
Proportional groupable
unifix cubes/multilink
Factors of Counting
1. Numeral writing and recognition 2. counting on and counting back 3. relationships of more/less/same
Zero (Multiplication)
0 sets of anything is 0 or any number of sets of size 0 is still 0
Problem structure for Multiplication
1. Equal Groups 2. Multiplicative Comparison 3. Combinations 4. Product of measure
Why should be use invented strategies over traditional algorithms?
1. Invented strategies are number oriented rather than digit oriented (245 is seen as 2 hundreds, 4 tens, 5 ones) 2. Invented strategies are left handed rather than right handed. 3. Invented strategies are flexible rather than rigid. This strategy is based on the numbers. If you are flexible, stop and look at the quantities first. Provide student with think time.
Addition and Subtraction Problem Structures
1. Join 2. Separate 3. Part Part Whole 4. Compare
Traditional Algorithms for Addition and Subtraction
1. Require an understanding of regrouping 2. begin with base 10 materials on place value mat 3. always have students model and record so the written procedure becomes apparent 4. For addition both numbers will be modeled on the place value mat, then pushed together 5. For subtraction only the top number will be modeled then the second number will be removed, leaving two parts the answer and what remains of the whole
Benefits of Student Invented Strategies
1. Students make fewer errors 2. Less re-teaching is required 3. Students develop number sense 4. Invented strategies are the basis for mental computation and estimation 5. Flexible methods are often faster than the traditional algorithms 6. Algorithm invention is itself significantly important process of "doing math"
Development of Counting Skills
1. producing the standard list of counting words in order 2. Connecting the sequence in a one to one manner with the items in the set being counted. The items must get one and only one count.
Ways in which remainders can be handled
1. the remainder can be discarded leaning a smaller whole number answer 2. The remainder can force the answer to the next highest whole number 3. The answer is rounded to the nearest whole number for the approximate result
Why Key words should not be used
1.Encourages students to ignore the meaning and structure of the problem 2. Often Misleading 3.Many do not have key words 4.They do not work with 2 step problems
part part whole problem structure
2 types of 1 thing
Commutative (Multiplication)
4 groups of 2 and 2 groups of 4 result in the 2 same number of items.
Algorithm
A role or procedure for solving a problem
Subtitizing
Ability to "just see it"
Invented Strategy
Any strategy other than the traditional algorithm does not involve physical materials such as base ten blocks or drawings (ex. true/false)
Mental Math vs. Computational Estimation
Both occur mental but mental math is exact computation is estimation
Properties of Addition
Commutative Associative Zero/Identity
Development phase of computational fluency
Direct modeling invented strategy algorithm
Activity of Number Sense
Fill in the Blanks Activity: Students will be provided with a paragraph of missing numerical words that are placed in the word box. Students must reason through the words to decide which numerical word fix the correct placement.
Number Sense
Howden "A good intuition about numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.
Identity (multiplication)
Multiplying by 1 does not change the identity of the number
Commutative
Pair contextual problems that have the same addends
Problem Structure for division
Partition Measurement
Activity example of Counting
Shapes of Numbers: the student will have to group the shapes into a group that has specific qualities
How we should use ten frames
Should be used as practice for students to build mental computation skills and number sense.
Estimation Strategies
Specific algorithms that produce approximate results rather than exact results. Front end method Rounding method Using compatible numbers
Measurement
The size of each group is known, but not the number of groups
Equivalent represetnations
When you can represent a number in as many ways as possible except the base 10 representation
Distributive (multiplication)
a(b+c) a times b plus a times c; add first and then multiply or multiply each and then add.
Associative
adding three addends in several different orders
Zero/Identity
adding zero to a number does not change its identity
Equal groups
answer is the same type of thing as one of the numbers in the problem
multiplicative comparison
answer is the same types of thing as one of the number in the problem, but two quantities are being compared
Proportional pregroupable
base 10 blocks (already stuck together)
Ways of counting sets
by ones by groups and ones by tens and ones
Properties of Multiplication
commutative associative zero identity distributive
Associative (Multiplication)
multiplying 3 factors in any order results int eh same product
Join problem structure
must have an action
separate problem structure
must have an action
Partition (Division)
number of groups is know, but not the size of each group
Rounding Method
should only be taught on a number line
Compatible numbers
something you would not get through rounding or front end
Front end method
start at the front (27+38=20+30); (20+30=50); (50+20=70)