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.