a grant funded by the usdoe and awarded by the fldoe mathematics and science partnership initiative....
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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
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.
Review…
How would we graph a line without technology?
y= x x y
How about with technology?
y = xy= 2xy= 3xy= - 2xy= x
y = mx+ b
Slope y = mx+ b
Positive slope Negative
slope
y = x + 2y = x + 5y = x - 4y = x +
y = mx+ b
y-intercepty = mx+ b
Positive intercept Negative intercept
y = - 3x + 8
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
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)
Students must be taught how to use the models or tools used as part of instruction
Online Geoboard
Let a 5 x 5 grid represent the whole (or “1”)
8
1
2
1
8
1
2
1
8
4
8
18
5
Addition of Fractions
Try these:
8
5
4
1
8
1
8
3
16
3
8
5
Let a 5 x 5 grid represent the whole (or “1”)
4
3
8
7
4
3
8
7
8
7
8
6
8
1
Subtraction of Fractions
Try these:
4
1
4
3
8
2
16
11
2
1
16
13
Area ◦ Pattern blocks, Geo-board, Geo-dot paper,
rectangular region
Set◦ Discrete items (marbles, dots, etc)
Length◦ Number Line, Cuisenaire Rod,
2
1
6
5
1 + 2/6
Using Pattern Blocks (Area Model)(let yellow hexagon represent 1)
2
1
6
5
Using a Set Model
SET: 12 units
6
21ANSWER
2
1
6
5
6
8
Length Model
or6
21
Let a 5 x 5 grid represent the whole (or “1”)
Interpretation: “three-fourths of one-half”
2
1
4
3
2
1
4
3
2
1
4
3of
8
3of the whole
Multiplication of Fractions
Try these:
4
1
2
14
3
2
12
1
8
18
1
2
1
divided by
Answer -- 6
4
3
8
1
4
3
8
1Interpretation:
How many are in ?
Try these
2
1
4
3
2
1
8
7
4
1
8
7
2
1
8
6
Transversal
7 6
8 5
3 1 2
4
Vertical Angles
Parallel Lines and Angles
7 6
8 5
3 1 2
4
Corresponding Angles
Parallel Lines and Angles
Alternate Interior Angles
7
6
8 5
3 1 2
4
Alternate Exterior Angles
Parallel Lines and Angles
7
6
8 5
3 1 103 2
4
What are the measures of all the other angles?
Parallel Lines and Angles
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?
Visual Representation of Mathematical Ideas
Example: National Library of Virtual Manipulatives
http://nlvm.usu.edu
Modeling Multiplication/Division of Fraction (Grade 6: Big Idea 1)
NCTM Illuminations http://illuminations.nctm.org/
Illustrating Volume & Surface Area (Grade 7 Big Idea 1)
Using the Graphing Calculator Texas Instruments
◦ Activity Exchange Center
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
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/
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
Test Generating Software
Every textbook publisher offers one
Others commercially available as well
Generate multiple versions of same test easily
Online access to mathematics resources
Tutoring (e.g., Dr. Math)
Mathematics Dictionaries with examples
FCAT Explorer
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
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?
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
Teacher productivity Producing Mathematically accurate representations Keeping and recording class information
Student Support Example: Ask Dr. Math Textbook Websites
Teaching and Learning
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
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
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
It will be launched during 2008-09 school year.
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.
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