A grant funded by the USDOE and awarded by the FLDOE Mathematics and Science Partnership Initiative. Presentation developed by Florida PROMiSE Partnership 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 = x y= 2x y= 3x y= - 2x y= x y = mx+ b

Slope y = mx+ b Positive slope Negative slope

y = x + 2 y = x + 5 y = x - 4 y = x + y = mx+ b

y-intercept y = 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”)

Addition of Fractions

 Try these:

 Let a 5 x 5 grid represent the whole (or “1”)

Subtraction of Fractions

 Try these:

 Area ◦ Pattern blocks, Geo-board, Geo-dot paper, rectangular region  Set ◦ Discrete items (marbles, dots, etc)  Length ◦ Number Line, Cuisenaire Rod,

1 + 2/6 Using Pattern Blocks (Area Model) (let yellow hexagon represent 1)

Using a Set Model SET: 12 units

Length Model or

 Let a 5 x 5 grid represent the whole (or “1”) Interpretation: “three-fourths of one-half”

of the whole Multiplication of Fractions

 Try these:

divided by Answer -- 6 Interpretation: How many are in ?

Try these

Transversal Vertical Angles Parallel Lines and Angles

Corresponding Angles Parallel Lines and Angles

Alternate Interior Angles Alternate Exterior Angles Parallel Lines and Angles

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

Modeling Multiplication/Division of Fraction (Grade 6: Big Idea 1)

NCTM Illuminations 

Illustrating Volume & Surface Area (Grade 7 Big Idea 1)

Using the Graphing Calculator  Texas Instruments Texas Instruments ◦ Activity Exchange Center Activity Exchange Center

Other software tools  GeoGebra GeoGebra A freeware drawing pad  The Geometer’s Sketchpad & Cabri Geometry The Geometer’s SketchpadCabri Geometry Dynamic construction & demonstration tools  Tinkerplots 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 EE

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 CalculatorGraph 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 Glencoe  Holt, Rinehart, & Winston Holt, Rinehart, & Winston  McDougal Littell McDougal Littell  Prentice Hall 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 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.