powerpoint_no. 2 numeration_place value

7/30/2019 Powerpoint_No. 2 Numeration_Place Value

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NUMERATION: PLACE VALUE


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Place value representation of numbers

Grouping or trading

Models of place value

Developing place value

Regrouping and renaming


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Excerpts of Expectations from theNumber and Operations Standard

Grades Pre-K-8

Principles and Standards for School

Mathematics National Council ofTeachers of Mathematics

2000


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Understand numbers, ways of representing

numbers, relationships among numbers, and

number systemsGrades Pre-K-2 Use multiple models to develop initial understandings of place

value and the base-ten number system.

Develop a sense of whole numbers and represent and use them inflexible ways, including relating, composing, and decomposingnumbers.

Connect number words and numerals to the quantities theyrepresent, using various physical models and representations.

Grades 3-5 Understand the place-value structure of the base-ten number

system and be able to represent and compare whole numbers anddecimals.

Recognize equivalent representations for the same number andgenerate them by decomposing and composing numbers.


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Stages of Conceptual Development

for Whole Numbers

Pre Numbers

Early Numbers Introduction to Place Value

Reinforcement of Place Value

Extension of Place Value


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Representation

Material

Language Symbols

NUMBER


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Naming numbers

5- Frame 10 - Frame


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Naming larger numbers Bundling sticks

Base 10 blocks


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Place Value Models(for base ten)1. Proportional-The material for 10 is ten times

the size of 1; 100 is ten times the size of 10.

Ex. base ten blocks, bean sticks, bundledsticksTens Ones

2 3


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Place Value Models(for base ten) Non-proportional-The material does not

maintain any size relationships.Ex. money,

abacus, color tiles or chips

Tens Ones


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Place Value ModelsConcrete Physical Models =>

Semi-concrete

Organizational Models

Tens Ones Symbolic

2 5 Representational

Models

25


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Sequence of developingnumbers and place value

Refer Curriculum Specification KBSR


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Two-digit numbers Establish a system of place value

tens ones

Number names

one ten and six ones

orsixteen

tens ones

1 6


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Sequence to develop the 2-digit

numbers1. Multiples of ten; material & language

2.

22 to 29 in tens and ones3. Teen numbers 11 - 19

4. Compare numbers: by ones, by tens

5. Sequence number: before, after, ordinalnames

6. Counting on, counting back


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3-digit numbers: consolidate place

value and establish renaming1. 10 tens make 1 hundred; hundreds,

tens and ones

2. Recording 3-digit numbers:

297, then 459, 615, then508, 400

3. Highlight number of tens: 321, 3084. Compare, order and sequence

5. Counting on, counting back


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Larger numbers: extending place

value

thousand hundred ten one


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Larger numbers: extending place

value

1. Abacus

2. Number expander


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Interviewer, "Circle in your drawing what the six means.

Circle what this part (points to one) means."

Abbie: Fifth Month of Second Grade


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Interviewer, "I'm going to say a number and I want you

to write it... thirteen...sixty-seven...one hundred

twenty...three hundred twenty-four... four hundred

eight...three thousand, five hundred twenty-three.Abbie: Fifth Month of Second Grade


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Interviewer, "Circle in your drawing what the 4 means.

Circle what this part (points to one) means."

Clay: Fifth Month of Fourth Grade


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to write it... fifty-six...three hundred forty-eight...four

hundred five...two thousand, seven hundred thirty

one...thirty-five thousand, forty-eight.Clay: Fifth Month of Fourth Grade


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Interviewer, "Circle in your drawing what the 4 means.

Circle in your drawing what this part (points to one)

means."

Elsa: Fifth Month of Fourth Grade


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to write it... three hundred forty-eight...four hundred

five... two thousand, seven hundred thirty-one...thirty-five

thousand, forty-eight."Elsa: Fifth Month of Fourth Grade


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Rounding Numbers Round down, round up, round off

Round to the nearest tens, hundreds,

thousands, ten thousands,

Rules for rounding


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Example:

(i) Round 428 to the nearest ten

1. How many tens does the number have? 42

2. Which tens could the number round to? 42 tens or 43tens

3. Which one is nearer? 43 tens

428 rounds to 43 tens, or 430.

(ii) Round 428 to the nearest hundred

powerpoint_no. 2 numeration_place value

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