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)