Your favorite number…

Today’s Objectives

• Identify how the processes of connections and representation improve student understanding, retention, and achievement

• Identify ways to incorporate connections and representations into math class

Developing Understanding through Connections

John SanGiovanni

Elementary Mathematics Office

What is 12?

• Think of as many different ways to show 12 that you can.

• We will come together as a group in a few minutes to share our ideas.

How many different ways can we show 12?

Students naturally connect ideas they already have to

construct a new idea.

Van de Walle, J. (2007). Elementary and Middle School Mathematics: Teaching Developmentally (6th ed). Boston, MA: Pearson

Students naturally connect ideas they already have to

construct a new idea.

The more ideas used and the more connections made, the better we understand.

Van de Walle, J. (2007). Elementary and Middle School Mathematics: Teaching Developmentally (6th ed). Boston, MA: Pearson

Think-Pair-Share

• What things do we do in reading to build understanding and/or comprehension?

The Frayer Model

Definition (in own words) Facts/Characteristics

Examples Non-ExamplesPolygon

Definition (in own words) Facts/Characteristics

Examples Non-ExamplesPolygon

A simple closed, plane figure made up of three or more line segments.

Definition (in own words) Facts/Characteristics

Examples Non-ExamplesPolygon

A simple closed, plane figure made up of three or more line segments.

• Closed• Simple• 2-dimensional• 3 or more line   segments

Definition (in own words) Facts/Characteristics

Examples Non-ExamplesPolygon

A simple closed, plane figure made up of three or more line segments.

• Closed• Simple• 2-dimensional• 3 or more line   segments

Definition (in own words) Facts/Characteristics

Examples Non-ExamplesPolygon

A simple closed, plane figure made up of three or more line segments.

• Closed• Simple• 2-dimensional• 3 or more line   segments

Concept Circles

Concept Circles and Variations

Concept:

Types of angles

sphere pyramid

cone prism

Concept:

3 dimensional figures

Concept:

Prime Numbers

5

11

29

7

2

13

17

? obtuse

right

parallel

acute

Variation: What could the “ ?” be? Variation: Which does not belong?

Webbing

Take a moment with a partner to come up with as many supporting details about the topic as you can.

Multiplication

What details were we able to come up with?

Were we able tobeat HCPSS 3rd graders?

Using numbers, how many ways can you express 50?

Funny Numbers

Funny Numbers

Funny Numbers

Do you agree or disagree?

7/13 is close to 1/2.

6/37 is close to 0.

17/24 is close to 1.

Organized Tables can be used for highlighted characteristics of numbers or concepts.

Ideas can be added as units progress.

Consider these fractions.1/4 2/3 5/8 2/5

Draw a picture.

Are they close to 0, 1/2, or 1.

What do they mean?

What are they equivalent to?

On a number line

Representing Numbers,

1st Grade

Organizer’s to help develop problem solving…

There are 3 tennis balls in a can. The tennis team has 13 cans. How many tennis balls does the team have?

KNOW WANT SOLVE

What do I KNOW about the problem?

What do I WANT to find out? How will I SOLVE the problem?

Annie put 3 strawberries on her plate. She put 6 grapes on her plate. How many pieces of fruit did she have?

A primary example…

Whole

Part Part

3 strawberries 6 grapes

Pieces of Fruit

2 165 5 490 78 0.37

• Choose 2 numbers.• Think about how those numbers

might describe John.

What are 6 numbers that describe you?

• Write down 6 numbers that describe you on your square.

• Choose one of those numbers to write largely on the back of the square.

Creating a number quilt

• Students identify numbers that describe them (2, 165, 5, 490, 78, 0.37)

Creating a number quilt

• Students identify numbers that describe them (2, 165, 5, 490, 78, 0.37)

• Students write the numbers with descriptions/illustrations on small rectangles of construction paper (different colors)

2 165

Creating a number quilt• Students write the numbers with

descriptions/illustrations on small rectangles of construction paper (different colors)

• Students glue their quilt pieces on to a large piece of construction paper

2 165

490 78

5

0.37

Adapting a number quilt

• The number quilt can then be used to describe different ideas about a unit or topic.

NumeratorEquivalent fractions

Of a wholeMixed

numbers

Of a set

Denominator

An example of a number quilt…

3 - topics/units I will be teaching

2 - organizers I would like to use

1 - way I will use an organizer with one of the topics

The Vocabulary Cube• Important vocabulary

words are written on 5 faces of a cube.

• The terms are described in writing with pictures and examples.

• The 6th face shows the topic or unit with the five words “webbed” around it.

Fractions

numerator

equivalent

improper

Mixed-number

Adapting the Vocabulary Cube

• Identify the main ideas of a topic or lesson

• Illustrate how topic applies to the real-world or other content area

• Describe different problem solving strategies

• In place of “number of the day”

Fractions

numerator

equivalent

improper

Mixed-number

An example…