your favorite number…. today’s objectives identify how the processes of connections and...
TRANSCRIPT
![Page 1: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/1.jpg)
Your favorite number…
![Page 2: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/2.jpg)
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
![Page 3: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/3.jpg)
Developing Understanding through Connections
John SanGiovanni
Elementary Mathematics Office
![Page 4: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/4.jpg)
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.
![Page 5: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/5.jpg)
How many different ways can we show 12?
![Page 6: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/6.jpg)
![Page 7: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/7.jpg)
![Page 8: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/8.jpg)
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
![Page 9: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/9.jpg)
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
![Page 10: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/10.jpg)
Think-Pair-Share
• What things do we do in reading to build understanding and/or comprehension?
![Page 11: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/11.jpg)
The Frayer Model
![Page 12: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/12.jpg)
Definition (in own words) Facts/Characteristics
Examples Non-ExamplesPolygon
![Page 13: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/13.jpg)
Definition (in own words) Facts/Characteristics
Examples Non-ExamplesPolygon
A simple closed, plane figure made up of three or more line segments.
![Page 14: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/14.jpg)
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
![Page 15: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/15.jpg)
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
![Page 16: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/16.jpg)
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
![Page 17: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/17.jpg)
![Page 18: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/18.jpg)
![Page 19: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/19.jpg)
![Page 20: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/20.jpg)
Concept Circles
![Page 21: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/21.jpg)
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?
![Page 22: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/22.jpg)
Webbing
Take a moment with a partner to come up with as many supporting details about the topic as you can.
![Page 23: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/23.jpg)
Multiplication
What details were we able to come up with?
Were we able tobeat HCPSS 3rd graders?
![Page 24: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/24.jpg)
![Page 25: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/25.jpg)
![Page 26: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/26.jpg)
![Page 27: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/27.jpg)
Using numbers, how many ways can you express 50?
![Page 28: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/28.jpg)
![Page 29: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/29.jpg)
![Page 30: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/30.jpg)
![Page 31: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/31.jpg)
![Page 32: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/32.jpg)
![Page 33: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/33.jpg)
Funny Numbers
![Page 34: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/34.jpg)
Funny Numbers
![Page 35: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/35.jpg)
Funny Numbers
![Page 36: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/36.jpg)
![Page 37: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/37.jpg)
Do you agree or disagree?
![Page 38: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/38.jpg)
7/13 is close to 1/2.
6/37 is close to 0.
17/24 is close to 1.
![Page 39: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/39.jpg)
![Page 40: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/40.jpg)
Organized Tables can be used for highlighted characteristics of numbers or concepts.
Ideas can be added as units progress.
![Page 41: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/41.jpg)
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
![Page 42: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/42.jpg)
![Page 43: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/43.jpg)
Representing Numbers,
1st Grade
![Page 44: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/44.jpg)
Organizer’s to help develop problem solving…
![Page 45: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/45.jpg)
There are 3 tennis balls in a can. The tennis team has 13 cans. How many tennis balls does the team have?
![Page 46: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/46.jpg)
KNOW WANT SOLVE
What do I KNOW about the problem?
What do I WANT to find out? How will I SOLVE the problem?
![Page 47: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/47.jpg)
![Page 48: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/48.jpg)
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…
![Page 49: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/49.jpg)
Whole
Part Part
3 strawberries 6 grapes
Pieces of Fruit
![Page 50: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/50.jpg)
2 165 5 490 78 0.37
• Choose 2 numbers.• Think about how those numbers
might describe John.
![Page 51: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/51.jpg)
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.
![Page 52: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/52.jpg)
Creating a number quilt
• Students identify numbers that describe them (2, 165, 5, 490, 78, 0.37)
![Page 53: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/53.jpg)
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
![Page 54: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/54.jpg)
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
![Page 55: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/55.jpg)
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
![Page 56: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/56.jpg)
![Page 57: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/57.jpg)
An example of a number quilt…
![Page 58: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/58.jpg)
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
![Page 59: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/59.jpg)
![Page 60: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/60.jpg)
![Page 61: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/61.jpg)
![Page 62: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/62.jpg)
![Page 63: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/63.jpg)
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
![Page 64: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/64.jpg)
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
![Page 65: Your favorite number…. Today’s Objectives Identify how the processes of connections and representation improve student understanding, retention, and achievement](https://reader035.vdocument.in/reader035/viewer/2022062408/56649e295503460f94b16f84/html5/thumbnails/65.jpg)
An example…