Your favorite number…. Today’s Objectives Identify how the processes of connections and...
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Transcript of Your favorite number…. Today’s Objectives Identify how the processes of connections and...
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…