Whole Numbers and Numerations Number Sense Algebra Building on What Children Already Know The Big Picture Development of Numbers and Numeration 5 Components 1. Developing number meanings

2. Exploring relationships with manipulatives

3. Understanding the relative magnitudes of numbers

4. Developing intuitions about the relative effect of operating on numbers

5. Developing referents for meaures of common objects and situations Standard states that all students should understand patterns, relations, and functions. Able to represent and analyze mathematical situations and structures by using algebraic symbols. Able to use mathematical models to represent and understand quantitative relationships. Be able to analyze change in various contexts. Prior learning to name and write numbers, children have already developed considerable number sense Teachers need to use this as a foundation for new learning about numbers Using this foundation will result in a smoother transition into new materials, that is does not appear new to the child Instead new material appears to be an

extension of what is already known: resulting

in better understanding, more likely to be remembered,

and easier to apply in varied settings. Children should understand the concept of the quantitative value before the written expression is introduced. Teachers should provide many examples of the number being introduced before introducing the written numeral.

Examples: Reinforce the number by

asking the student to show the number Once the children have fully developed the concept of twoness, they are ready to learn the symbolic notation for the number. 3 Goals Identify Name Write 6 Objectives When shown a quantity=say the number

When shown a quantity=write the number

When show a number=show the quantity

Shown a number= say the number

Given a number orally=show the quantity

Given a number orally=write the number 1-1 Correspondence:

ability to assign a number for each unit added during counting

Important to understand that something is being counted Teachers should physically count as well as verball count in order to demonstrate this concept One-Digit Numbers Two-Digit Numbers Three or More Digits Rounding Numbers Adapting the Lesson for a Diverse Group Concretely: Attaching a mental image to a number 3 objects vs. "3" Stay away from arranging objects horizontally "Full Development": when teaching numbers 1-9, make sure to have complete understanding of the previous number before moving to the next number. Connecting a new number to

previous knowledge will make

the new numbers meaningful to

children Activity 2 Activity 3 Concept of "0"

1. taught only after

several numbers. Activity 5 Activity 6 Activity 7 Activity 8 Children need to learn what the number "looks like" through mental images. Numbers greater than 10, need

an organized mental image of

recognizable quantity. 10-Frame

1. An effective way to

structure the mental image for numbers in the teens

2. Bundled sticks are another way to model two-digit numbers.

3. It is important for teachers to show how two digit numbers are a combination of tens and ones. Activity 9 Activity 10 Activity 11 Activity 12 Base-10 Blocks: small cubes, rods,

flats, large cubs How can base-10 blocks help teach numbers to young students? Connect to the students' knowledge of

two-digit numbers. Important for the students to see numbers visually represented before learning the names or writing the numerals. It is important for children to be able to read or say three-digit numbers Activity 15 Activity 18 Activity 19 Activity 20 Use visualization Activity 21 Activity 22 Activity 23 Standards The learning principle The number and operations standard The communication standard The connection standard The representation standard Pre-Number Quantitative Vocabulary One-to-One correspondence Each new topic needs to refer back to what the child already knows that can serve as the basis for building the new idea. Students need to make the connection that the language they use to describe natural activities in their lives and the language used to describe mathematical activities in the classroom are the same Activity 1 Children need to visualize and think of these numbers in terms of their basic units. Increase the amount of development Provide more visual information Add more kinesthetic activity Plan for more oral communication about mathematics from the children Plan for continual monitoring of learning

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# Whole Numbers and Numerations

Chapter 5

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