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Transcript of A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative....
![Page 1: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/1.jpg)
A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSEPartnership to Rejuvenate and Optimize Mathematics and Science Education
![Page 2: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/2.jpg)
A math educator once asked his daughter, who was in Algebra 1, if she knew what slope was. She said yes. He asked her what it was. She replied that it is the m in y = mx + b. When asked to elaborate, she could only go back to equations and rules. She got an A in algebra from her teacher.
MA.6.A.3.2 Write, solve, and graph one- and two- step linear equations and inequalities.
![Page 3: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/3.jpg)
Review…
How would we graph a line without technology?
y= x x y
How about with technology?
![Page 4: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/4.jpg)
y = xy= 2xy= 3xy= - 2xy= x
y = mx+ b
![Page 5: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/5.jpg)
Slope y = mx+ b
Positive slope Negative
slope
![Page 6: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/6.jpg)
y = x + 2y = x + 5y = x - 4y = x +
y = mx+ b
![Page 7: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/7.jpg)
y-intercepty = mx+ b
Positive intercept Negative intercept
![Page 8: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/8.jpg)
y = - 3x + 8
![Page 9: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/9.jpg)
Grade 6: Big Idea : Develop an understanding of and fluency with multiplication of division of fractions and decimals
Benchmark: MA.6.A.1.1 – Explain and justify procedures for multiplying and dividing fractions and decimals.
Power Point Presentations
![Page 10: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/10.jpg)
Students should have addressed the following in prior grades:◦ Grade 3 Big Idea 2 -- Develop an understanding of
fractions and fraction equivalence Explored the meaning of fractions
Grade 4 Big Idea 2 -- Develop an understanding of decimals, including the connection between fractions and decimals
Includes using various models to represent fractions.
Grade 5: Big Idea 2-- Developing an understanding and fluency with addition and subtraction of fractions
explored fractions using a variety of models (e.g., length, set, area)
![Page 11: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/11.jpg)
Students must be taught how to use the models or tools used as part of instruction
Online Geoboard
![Page 12: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/12.jpg)
Let a 5 x 5 grid represent the whole (or “1”)
8
1
2
1
![Page 13: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/13.jpg)
8
1
2
1
8
4
8
18
5
Addition of Fractions
![Page 14: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/14.jpg)
Try these:
8
5
4
1
8
1
8
3
16
3
8
5
![Page 15: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/15.jpg)
Let a 5 x 5 grid represent the whole (or “1”)
4
3
8
7
![Page 16: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/16.jpg)
4
3
8
7
8
7
8
6
8
1
Subtraction of Fractions
![Page 17: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/17.jpg)
Try these:
4
1
4
3
8
2
16
11
2
1
16
13
![Page 18: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/18.jpg)
Area ◦ Pattern blocks, Geo-board, Geo-dot paper,
rectangular region
Set◦ Discrete items (marbles, dots, etc)
Length◦ Number Line, Cuisenaire Rod,
![Page 19: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/19.jpg)
2
1
6
5
1 + 2/6
Using Pattern Blocks (Area Model)(let yellow hexagon represent 1)
![Page 20: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/20.jpg)
2
1
6
5
Using a Set Model
SET: 12 units
6
21ANSWER
![Page 21: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/21.jpg)
2
1
6
5
6
8
Length Model
or6
21
![Page 22: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/22.jpg)
Let a 5 x 5 grid represent the whole (or “1”)
Interpretation: “three-fourths of one-half”
2
1
4
3
![Page 23: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/23.jpg)
2
1
4
3
2
1
4
3of
8
3of the whole
Multiplication of Fractions
![Page 24: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/24.jpg)
Try these:
4
1
2
14
3
2
12
1
8
18
1
2
1
![Page 25: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/25.jpg)
divided by
Answer -- 6
4
3
8
1
4
3
8
1Interpretation:
How many are in ?
![Page 26: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/26.jpg)
Try these
2
1
4
3
2
1
8
7
4
1
8
7
2
1
8
6
![Page 27: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/27.jpg)
Transversal
7 6
8 5
3 1 2
4
Vertical Angles
Parallel Lines and Angles
![Page 28: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/28.jpg)
7 6
8 5
3 1 2
4
Corresponding Angles
Parallel Lines and Angles
![Page 29: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/29.jpg)
Alternate Interior Angles
7
6
8 5
3 1 2
4
Alternate Exterior Angles
Parallel Lines and Angles
![Page 30: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/30.jpg)
7
6
8 5
3 1 103 2
4
What are the measures of all the other angles?
Parallel Lines and Angles
![Page 31: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/31.jpg)
What are advantages of using PowerPoint Presentations (PPP)?
What considerations must teachers make if they choose to use PPP?
How could PowerPoint help teachers and students manage make-up work?
![Page 32: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/32.jpg)
Visual Representation of Mathematical Ideas
Example: National Library of Virtual Manipulatives
http://nlvm.usu.edu
![Page 33: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/33.jpg)
Modeling Multiplication/Division of Fraction (Grade 6: Big Idea 1)
![Page 34: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/34.jpg)
NCTM Illuminations http://illuminations.nctm.org/
![Page 35: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/35.jpg)
Illustrating Volume & Surface Area (Grade 7 Big Idea 1)
![Page 36: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/36.jpg)
Using the Graphing Calculator Texas Instruments
◦ Activity Exchange Center
![Page 37: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/37.jpg)
Other software tools GeoGebra
• A freeware drawing pad
The Geometer’s Sketchpad & Cabri Geometry
• Dynamic construction & demonstration tools
Tinkerplots
• Software to help students learn about data
![Page 38: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/38.jpg)
Equation Editor (as part of Word or PPP)
Allows you to express mathematics accurately as part of presentation or worksheets
Without EE ¾ x 6/8 With EE8
6 x
4
3
http://www.dessci.cm/en/products/mathtype/
![Page 39: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/39.jpg)
WinPlot and TI-Screen Capture (as part of Word or PPP)
Allows you to express mathematical representation as part of presentations or worksheets
Screen Capture of TI Calculator
x
y
Graph created using WinPlot
![Page 40: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/40.jpg)
Test Generating Software
Every textbook publisher offers one
Others commercially available as well
Generate multiple versions of same test easily
![Page 41: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/41.jpg)
Online access to mathematics resources
Tutoring (e.g., Dr. Math)
Mathematics Dictionaries with examples
FCAT Explorer
![Page 42: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/42.jpg)
Textbook Websites Usually have practice tests and/or quizzes
Also have other resources tied directly to the text.
Florida’s adopted Grade 6 texts Glencoe
Holt, Rinehart, & Winston
McDougal Littell
Prentice Hall
![Page 43: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/43.jpg)
Is it important to use technology to teach mathematics? Why or why not?
What are appropriate uses of technology? Inappropriate uses?
What should you consider when deciding to use technology or not?
![Page 44: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/44.jpg)
Technology is an essential tool for learning mathematics in the 21st century, and all schools must ensure that all their students have access to technology. Effective teachers maximize the potential of technology to develop students’ understanding, stimulate their interest, and increase their proficiency in mathematics. When technology is used strategically, it can provide access to mathematics for all students.
Full position statement
![Page 45: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/45.jpg)
Teacher productivity Producing Mathematically accurate representations Keeping and recording class information
Student Support Example: Ask Dr. Math Textbook Websites
Teaching and Learning
![Page 46: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/46.jpg)
Allows the visualization of concepts difficult to show otherwise Allows the examination of multiple examples with ease Allows a focus on concepts rather than calculations Allows access to real-time data to make mathematics relevant to
students
◦ (e.g., use of real world examples such as orange production in Florida for analysis)
Allows student to make and test conjectures
◦ What happens when …
Promotes student independence in mathematical problem-solving Reinforces mathematics learning
![Page 47: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/47.jpg)
![Page 48: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/48.jpg)
The CPALMS will:
Increase access for all teachers to high quality information and resources aligned with the standards
Support the delivery of teacher professional development
Support teacher application of new content and pedagogical knowledge in the classroom
![Page 49: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/49.jpg)
The CPALMS will include the following:
Searchable database of standards and benchmarks
Levels of cognitive complexity for each benchmark
Mathematics and Science Course Descriptions
Course builder tool for districts
Electronic course approval system
Online PD on the use of course descriptions
![Page 50: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/50.jpg)
It will be launched during 2008-09 school year.
![Page 51: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/51.jpg)
We’ve only touched the surface of what’s available.
Don’t be afraid to learn from your student.
Just like any tool, technology only helps when used correctly/appropriately.
![Page 52: A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f135503460f94c2782f/html5/thumbnails/52.jpg)