powerpoint_ch07 teaching numbers

7/30/2019 Powerpoint_ch07 Teaching Numbers

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Teaching Numbers

Focus Questions:1. How does childrens number sense

develop?

2. How can technology help children

develop number sense?

3. What characteristics are associated with

the different counting stages?

4. How can teachers use questions topromote childrens thinking about

numbers?

Discuss what you already know and what you want to learn more about.


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Number Sense

A good intuition about numbers and their

relationships. It develops gradually as a

result of exploring numbers, visualizingthem in a variety of contexts, and relating

them in ways that are not limited by

traditional algorithms (Howden, 1989).


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Number Sense

Number Sense includes:

An understanding of number concepts and

operations on these numbers. The development of useful strategies for

handling numbers and operations.

The facility to compute accurately andefficiently, to detect errors, and to recognizeresults as reasonable.


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Number Sense

The ability and inclination to use this

understanding in flexible ways to make

mathematical judgments.

An expectation that numbers are useful and

that work with numbers is meaningful and

makes sense.

Brainstorm examples for each bullet item


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The meanings for the number five

suggested by young children


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Excerpts of Expectations from

theNumber and OperationsStandardGrades Pre-K-2

Principles and Standards for School

Mathematics

National Council of Teachers of

Mathematics

2000


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Understand numbers, ways of representing

numbers, relationships among numbers, and

number systems

Count with understanding and recognize how

many in sets of objects

Develop understanding of the relative position andmagnitude of whole numbers and of ordinal and

cardinal numbers and their connections.

Connect number words and numerals to the

quantities they represent, using various physical

models and representations

Review the Snapshot of a Lesson. Discuss the counting and early numberconcepts displayed.


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Prenumber Concepts are those that do not

rely on numbers but provide a foundation for

later number concepts and skills.

Prenumber Concepts

Classification

Patterns

Comparisons

Early Number Development Conservation

Group Recognition

[Brainstorm activities and materials that may be used to develop the five concepts]


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Prenumber Concepts

Classification

Patterns

Comparisons

Early Number Development

Conservation

Group Recognition

[Complete In the Classroom 7-1 and 7-2.

Refer to Figure 7-5. Discuss the different levels of involvement andunderstanding experienced in a whole class demonstration versus a small group,

hands on setting.


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Prenumber Concepts

Classification

- size, colour, shape,

Patterns

- copying a pattern

- finding the next one

- extending a pattern- create their own patterns

Comparisons



hands on setting.


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Early Number Development

Conservation

Group Recognition - subitizing



hands on setting.


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Conservation of Number

Groups of 5 counters are arranged in the

following patterns


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Student A

T: Are there more red, blue, or yellow counters? S: More blue.

T: How do you know?

S: I can tell by looking.

T: How many of each?

S: One, two, three, four, five... five red. One,

two, three, four, five...five blue. One, two,three, four, five...five yellow.

T: Five of each?

S: Yes.

T: Do you still think there are more blue?

S: Yes, I can just see there's more blue.


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Student B

T: Are there more red, blue, or yellow counters?

S: They're the same.

T: How do you know?

S: I counted them.

T: How many of each? S: One, two, three, four, five...Five red. Five

blue. Five yellow.

T: Five of each?

S: Yes.

Determine the children's conservation of number


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Group RecognitonSubitizing

Rectangular

Linear

Circular Scrambled


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Counting

Counting Principles

One-to-One Rule

Stable Order Rule

Order Irrelevance Rule

Cardinality Rule


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Counting

Counting Stages

Rote Counting

- involves only the ability to recite the number

names in sequence

Rational Counting

- requires the child to make a one-to one-correspondence between each number

name and one-and-only-one object.


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Counting Stages Rote Counting


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Counting Stages

Rational Counting


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Counting

Counting Strategies

Counting On

Counting Back

Skip Counting


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In the following slides, analyze the

children's use of the counting principles.

Focus on what the children know ratherthan what they do not know.


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Counting Principles: Student A

T: Here are some blocks in a row. Startwith this one on the end and count them.

S: One, two, three, four, five, SIX. Thereare six blocks.

T: What if you start at the other end of therow and count them?

S: One, two, three, four, five, SIX. Thereare six.


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Counting Principles: Student B

T: Here are some red blocks in a row. Start

with this one on the end and count them.

S: (Touches each of the 5 blocks) One, two,three, five, six. Six red blocks

T: Now count these blue blocks.

S: (Touches each of the 4 blocks) One, two,

three, five. Five blue blocks.


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Counting Principles: Student C

T: Here are some blocks in a row. Start

with the one on this end and count them.

S: One, two, three, four, five, six. There aresix.

T: What if you start at the other end of the

row and count them?

S: I already counted them! There are six!


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Counting Principles: Student D

T: Here are some red blocks (4) in a row.

Start with this one on the end and count

them. S: (Points to each but says two numbers

with each point) One, two, three, four, five,

six, seven, eight. Eight red blocks.


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Construct a Pattern

The color spinner will be used to select the colorsto be used in constructing the pattern.

Using the colors chosen, make a pattern that

repeats atleast twice in the time allotted.

When the time is up, compare patterns with others.Did you come up with a unique pattern idea?


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Construct a Pattern

Try another pattern with new colors ordifferent types of manipulatives.

Why should students have an opportunity toparticipate in patterning activities?

Do you have other suggestions forpatterning activities?


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Try out In the Classroom 7-3, Numbers on aCalendar. Then Make up additional problems andshare them with the class.

Use calculators to complete In the Classroom 7-4and 7-5. Discuss other calculator counting activitiesthat could be done with children.

Complete In the Classroom 7-6 and 7-7. Then usethe calculator and crayons to shade some of the100's charts. Look for patterns that emerge.

Use the five- and ten-frames


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Relationships Among Numbers

Spatial Relationships

One and Two More, One and Two Less

Number Benchmarks

Part-part-whole Relationships


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Spatial Relationships

Children can learn to recognize sets of objects in patterned

arrangements and tell how many without counting. Prior to

counting, children are aware of small numbers of things: one

nose, two hands, three wheels on a tricycle.


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One and Two More, One and Two Less

The two-more-than and two-less than relationships

involve more than just the ability to count on two or

count back two. Children should know that 7, for

example, is 1 more than 6 and also 2 less than 9.


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Number Benchmarks

1. Benchmarks or anchors give students a referencepoint. Since 10 plays such a large role in ournumeration system and because two fives make up10, it is very useful to develop relationships for the

numbers 1 to 10 to the important anchors of 5 and10. (e.g. 8 is 5 and 3 more or two away from 10)


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Part-part-whole Relationships

To conceptualize a number as being

made up of two or more parts.


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Writing numerals: samples

Samples taken from kindergarten

children during the third month of

school. The children were asked tobegin with one and write their numbers

to ten. The samples are intended to

show the wide range of writing skillsencountered within one class of

students.


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Chad: Third Month of Kindergarten


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Cody: Third Month of Kindergarten


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Steven: Third Month of

Kindergarten


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Elizabeth: Third Month of

Kindergarten


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Andrea: Third Month of

Kindergarten


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Jason: Third

Month of

Kindergarten

Joshua: Fifth Month of Second


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Joshua: Fifth Month of Second

Grade


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Writing Numerals

Start with very clear, very strong models.

Focus on one number at a time.

Provide maximum guidance at first.

Be accepting of initial efforts.

Gently reduce the amount of guidance.

Reward correct performance.

Review previously-learned material at regular

intervals.


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Frame for Development of Number

Emergent: pre-number reasoning

Early: counting all

Developing: counting on

Expanding: early grouping

Established: later grouping


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powerpoint_ch07 teaching numbers

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