Learner Workbook
SMART NotebookTM Math Tools
Trainer Information
Name
Phone
Introduction to SMART Notebook Math Tools ......................................................... 1 Welcome .................................................................................................................................................. 2 SMART Notebook Math Tools Training .................................................................................................... 3 SMART Notebook Math Tools Training Course Map ............................................................................... 4 Teaching Math in the Classroom .............................................................................................................. 5 SMART Notebook Math Tools Features .................................................................................................. 7 What’s New in SMART Notebook Math Tools .......................................................................................... 8
Measurement Tools .................................................................................................... 9 Using the Measurement Tools ............................................................................................................... 10 Measuring Lengths and Angles .............................................................................................................. 11 Drawing Geometric Shapes ................................................................................................................... 14 Lesson Activity ....................................................................................................................................... 18
Advanced Shapes ..................................................................................................... 19 Creating Advanced Shapes and Using Manipulation Tools ................................................................... 20 Shape Division ....................................................................................................................................... 22 Irregular Polygons .................................................................................................................................. 23 Regular Polygons Tool ........................................................................................................................... 24 Lesson Activity ....................................................................................................................................... 25
Equations .................................................................................................................. 27 Handwriting Recognition for Mathematical Symbols .............................................................................. 28 Solving Equations ................................................................................................................................... 30 Equation Editor ....................................................................................................................................... 32 Lesson Activity ....................................................................................................................................... 35
Graphing .................................................................................................................... 37 Generating Graphs ................................................................................................................................. 38 Manipulating Graphs .............................................................................................................................. 39 Dynamic Graphing .................................................................................................................................. 42 Texas Instruments Emulators ................................................................................................................. 45 Lesson Activity ....................................................................................................................................... 46
Additional Information ............................................................................................. 47 Writing Equations ................................................................................................................................... 48 Writing Trigonometric Equations ............................................................................................................ 48 Writing Logarithmic Equations ................................................................................................................ 48 Solving Multiple Line Equations ............................................................................................................. 48 Dual Page Display and Pin Page ........................................................................................................... 48 Transparent Background ........................................................................................................................ 49 SMART Notebook Gallery ...................................................................................................................... 49 SMART Website ..................................................................................................................................... 49
Appendices ............................................................................................................... 51 Appendix A: Manipulating the SMART Notebook Measurement Tools .................................................. 53 Appendix B: Drop-down Menu Options for SMART Notebook Math Tools ............................................ 55 Appendix C: Math Symbols and Functions Supported by SMART Notebook Math Tools ..................... 57 Appendix D: Equation Editor for SMART Notebook Math Tools ............................................................ 59
Š 2010 SMART Technologies ULC. All rights reserved. SMART Notebook, SMART Board, SMART Exchange, smarttech and the SMART logo are trademarks or registered trademarks of SMART Technologies ULC in the U.S. and/or other countries. Texas Instruments,TI-nspire and TI-SmartView are trademarks of Texas Instruments. All other third-party company names and products are for identification purposes only and may be trademarks of their respective owners. Printed in Canada 03/2010.
SMART Notebook Math Tools Learner Workbook
Introduction to SMART Notebook Math Tools Course Outline Welcome to SMART Notebook™ Math Tools training. This workbook is intended to help you succeed with the training and keep as a reference guide. In this book you will learn how to enhance your math teaching skills and create activities with the special math options available in SMART Notebook Math Tools.
1
Introduction
Welcome Welcome to this SMART training event. We are excited that you are joining us today for SMART Notebook Math Tools training, and we look forward to helping you maximize your use of SMART Notebook Math Tools. We encourage you to ask questions and share your comments with the training specialist throughout the session.
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SMART Notebook Math Tools Learner Workbook
SMART Notebook Math Tools Training SMART recognizes the needs of teachers to use new and innovative teaching methods in their classes. Using SMART Notebook Math Tools collaborative learning software you can create and manipulate geometric shapes and objects designed to teach math concepts. Explore relationships with graphs and perform multiple tasks in the same workspace as your class notes which, in the past, required several different applications.
Target Audience Any middle or secondary school math teacher who authors and teaches math content. This course is designed for previous SMART Notebook users.
Session Timing SMART Notebook Math Tools training is a half-day SMART course.
Learning Objectives After completing this course, you will be able to: • Understand and maximize the benefits of the software • Teach math concepts using SMART Notebook Math Tools • Integrate math applications into your lesson files
3
Introduction
SMART Notebook Math Tools Training Course Map
4
INTRODUCTION
10 minutes
MEASUREMENT TOOLS
45 minutes
ADVANCED SHAPES
35 minutes
EXPRESSIONS AND EQUATIONS
25 minutes
GRAPHING
40 minutes
REVIEW
20 minutes
ADDITIONAL RESOURCES
5 minutes
SMART Notebook Math Tools Learner Workbook
Teaching Math in the Classroom SMART Notebook Math Tools is a software solution for teaching different math concepts.
Extension What are some current challenges teachers face when creating and delivering math content for their students?
5
Introduction
Brainstorming – What do you currently use? 1 List all software applications you currently use for your Math lessons.
2 Which applications do you use to teach the following concepts: • Measurement
• Creating 2D geometric shapes
• Math symbols and diagrams
• Solving equations numerically and graphically
• Graphing
How do you integrate multiple applications into your lesson?
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SMART Notebook Math Tools Learner Workbook
SMART Notebook Math Tools Features
SMART Notebook Math Tools provides you with the same features as SMART Notebook software, so you can create and deliver engaging, interactive learning experiences to suit any grade, subject and learning style. Some of the features of SMART Notebook Math Tools are: • Advanced math shapes and shape manipulation • Equation handwriting recognition • Equation editor and equation solver • Graphing
7
Introduction
What’s New in SMART Notebook Math Tools SMART Notebook Math Tools includes a Secondary Toolbar that provides easy access to math-specific tools you can use in your lessons. . Equation Editor
TI Calculators Launch Button
Irregular Polygons
Regular Polygons
Measurement Tools
Graph Tables
Graphs
You can customize the Secondary Toolbar by dragging tools to and from the Customize Toolbar window.
In the above diagram, the circled tools (Measurement Tools and Regular Polygons) are now part of SMART Notebook software. The tools inside the rectangle are part of SMART Notebook Math Tools. You will also find there are added math options for existing tools only available in SMART Notebook Math Tools. NOTE: See Appendix B: Drop-down menu options for SMART Notebook Math Tools.
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SMART Notebook Math Tools Learner Workbook
SMART Notebook Math Tools: Measurement Tools Using the Measurement Tools In this section you will learn how to use the SMART Notebook Measurement Tools to enhance your math lessons.
9
Measurement Tools
Using the Measurement Tools SMART Notebook software enables you to add a ruler, protractor or compass to a SMART Notebook page and use it as a measurement, demonstration and drawing tool to enhance your math lessons. By default, the Measurement Tools button is on both the SMART Notebook toolbar and the Secondary Toolbar.
Extension How can you use these tools in your lessons? • Ruler
• Protractor
• Geodreieck protractor
• Compass
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SMART Notebook Math Tools Learner Workbook
Measuring Lengths and Angles
SMART Notebook Measurement Tools make it easy for teachers and students to measure the lengths and angles of objects in a .notebook file. The measurement tools allow you to perform more tasks than traditional math tools, which makes learning more interactive and engaging.
11
Measurement Tools
Measuring Distance To show lengths of objects, lines or distances between points in your .notebook file, use the ruler or the SMART Geodreieck protractor by ARISTO™. These tools have incremental markings for measuring, just like traditional measuring tools. You can move and resize these tools, enabling you to deliver more engaging and interactive lessons.
NOTE: The ruler has both metric and Imperial units. The Geodreieck protractor only has metric units.
Exercise 1: Scale Drawing Measurement Let’s say you want to use scale drawings to demonstrate the concepts of ratios and proportions. Here’s an exercise you can use with the ruler to demonstrate to your students. Open Exercise 1.notebook on the USB storage device you received to complete the following activity: 1 Measure the actual height of a student 2 Obtain or take a photograph of the student next to another unmeasured object 3 Insert the photograph in your .notebook file and use the notebook ruler to measure the images of the student and object 4 Use the ratio of the student’s actual height to the student’s image height, to determine the actual height of the object
NOTE: See Appendix A: Manipulating the Measurement Tools for more information on manipulating the Measurement Tools.
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SMART Notebook Math Tools Learner Workbook
Measuring Angles You can use either the protractor or the Geodreieck protractor to demonstrate how to measure angles. You can move, resize and extend the protractor to complete a full circle (360ยบ). You can also insert measured angle drawings from the protractor to use in various activities, such as comparing or finding congruent angles.
NOTE: See Appendix A: Manipulating the Measurement Tools for more information on manipulating the Measurement Tools.
Exercise 2: The Sum of the Angles in a Triangle The protractor also allows you to insert a measured angle into your .notebook file. You can then manipulate this angle like any other SMART Notebook object. For instance, if you want to demonstrate that the sum of angles in a triangle is equal to 180ยบ, you can join the measured angles together to create a straight line.
Open Exercise 2.notebook on the USB storage device you received to complete the following activity: 1 Use the Shapes tool to create a triangle on a SMART Notebook page 2 Measure the interior angles with the protractor, and then add each angle to the page 3 Reposition the angles together to form a straight line 4 Add the angles together to show the sum of 180ยบ TIP: You can display the interior angles of the triangle by selecting Show/Hide Interior Angles from the object drop-down menu.
13
Measurement Tools
Drawing Geometric Shapes
With Measurement Tools, you can create math drawings quickly and easily that will enhance your lessons and reinforce mathematical concepts.
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SMART Notebook Math Tools Learner Workbook
Drawing Straight Lines There are situations that require you to draw straight lines or angles of specific lengths. Draw along the edges of the ruler and the Geodreieck protractor to create straight lines.
NOTE: See Appendix A: Manipulating the Measurement Tools for more information on manipulating the Measurement Tools.
Exercise 3: Drawing Measured Shapes The ruler is a great tool for demonstrating how to visualize concepts by drawing and measuring objects. Let’s say you want to demonstrate how to add vectors. You can determine the vector sum by performing a series of calculations using formulas. Physically drawing and measuring the vectors allows students to estimate the results and confirm their calculations. Open Exercise 3.notebook on the USB storage device you received to complete the following activity: 1 Use the ruler to measure and draw vectors a and
b as shown
2 Connect the vectors with line c 3 Use the ruler to measure the magnitude c and angle x of the resultant vector
NOTE: The resultant vector (which represents the vector sum) is drawn from the tail of the first vector to the head of the last vector.
15
Measurement Tools
Exercise 4: Intersecting and Parallel Lines SMART Notebook Math Tools includes a measurement tool called the Geodreieck protractor. The purpose of this tool is to provide a straight edge at a right angle, or another planar angle, to a baseline. Let’s say you want to demonstrate the relationship between intersecting and parallel lines with corresponding angles. Open Exercise 4.notebook on the USB storage device you received to complete the following activity:
1 Draw a horizontal line with the Geodreieck protractor 2 Move the protractor using the guide lines and draw another line parallel to the first 3 Rotate the Geodreieck protractor at a desired angle to the lines 4 Draw a line intersecting the parallel lines 5 Draw a line parallel to the intersecting line
Extension Both the ruler and the Geodreieck protractor have similar properties for measurement and drawing. Provide some examples when you would use each tool. • Ruler
• Geodreieck protractor
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SMART Notebook Math Tools Learner Workbook
Drawing Arcs and Circles You can use the protractor or compass to easily create arcs and circles to use in your lessons. Simply draw along the round edge of the protractor to create an arc. The compass functions just like a traditional compass, which makes instructional demonstrations easy for students to understand.
NOTE: See Appendix A: Manipulating the Measurement Tools for more information on manipulating the Measurement Tools.
Exercise 5: Drawing Circles with Known Diameters Using the measurement tools in SMART Notebook software enables you to create arcs and circles of specific dimensions. This allows you to demonstrate concepts such as finding the area of a circle. Open Exercise 5.notebook on the USB storage device you received to complete the following activity:
1 Use the ruler to draw a horizontal line that’s half the diameter (radius) of your desired circle 2 Draw a circle with the compass using the line as the diameter 3 Draw a perpendicular line to the radius that connects to the edge of the circle 4 Measure the perpendicular line with the ruler and record your results
17
Measurement Tools
Lesson Activity 1 What is a common feature of the Measurement Tools?
2 List different math concepts you can demonstrate with each of the measurement tools.
Open Activity 1.notebook on the USB storage device you received to complete the following activity: 3 Use the SMART Notebook ruler and compass to create a geometric construction by following the instructions below. 1. Draw a horizontal line (0째) using the ruler, and then draw two points on the line
2. Draw a circle using one point as a center point, and the other point as the radius point (use the distance between the two points as the radius) 3. Draw another circle using the second point as the center point and the first point as the radius point. Your diagram should look similar to this:
4. Draw a line through the points where the two circles intersect using the ruler. What do you notice?
5. Connect the two initial points to the point above them where the two circles intersect. What kind of shape do you get? Hint: measure the lengths of the sides.
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SMART Notebook Math Tools Learner Workbook
SMART Notebook Math Tools: Advanced Shapes Using Shapes in SMART Notebook Math Tools In this section you will learn how to manipulate curved lines and shapes with the added math options included in SMART Notebook Math Tools. You will also learn how to use irregular polygon shapes.
19
Advanced Shapes
Creating Advanced Shapes and Using Manipulation Tools
SMART Notebook software helps your students get the most out of your math lessons by enabling you to create geometric shapes, virtual manipulatives and diagrams. With SMART Notebook Math Tools you can create polygons of any shape, size or form, and perform various math functions with selected shapes and lines.
Manipulating Advanced Shapes SMART Notebook Math Tools includes additional math options for certain shapes and curved lines that you’ve created. You can manipulate shapes and curved lines by pressing and dragging their vertices. You can also display the interior angles and side lengths of certain shapes, and watch these values update automatically as you edit the shape.
Exercise 6: Math options for curved lines 1 Use the Lines tool to create a curved line 2 Change the properties of the line, such as the color, thickness and style NOTE: The Save Tool Properties option is not available for curved lines. 3 Select Show/Hide Vertices from the object drop-down menu 4 Press and drag the red circles (vertices) on the line
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SMART Notebook Math Tools Learner Workbook
Exercise 7: Math options for shapes 1 Use the Shapes tool to create a triangle 2 Change the properties of the triangle, such as the color, thickness and style 3 Select Show/Hide Vertices from the object drop-down menu 4 Select Show/Hide Interior Angles from the object drop-down menu 5 Select Show/Hide Side Lengths from the object drop-down menu 6 Press and drag the red circles (vertices) of the triangle
NOTE: The lengths of the triangle sides correlate to the default metric (cm) units on the ruler.
Extension Which SMART Notebook shapes have special math options? Do they all have the same options?
Options Shape
Show/Hide Vertices
Show/Hide Interior Angles
Show/Hide Side Lengths
Shape Division
Triangle
Yes
Yes
Yes
No
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Advanced Shapes
Shape Division With SMART Notebook Math Tools you can divide a circle, square or rectangle into separate, equal pieces to teach and demonstrate fractions.
Exercise 8: Creating Fraction Strips Fraction strips are great learning tools for students. SMART Notebook Math Tools enables you to create your own fraction strips, of any size, to use as virtual manipulatives.
1 Use the Shapes tool to create a rectangle. Ensure the long sides of the rectangle are vertical. 2 Clone the rectangle several times to create the unit fractions you want to display 3 Select Shape Division from a rectangle’s drop-down menu to divide it into two parts 4 Note the fractions displayed inside each part 5 Divide the other rectangles into different parts to create the desired fractions 6 Press and drag a row to use as a fraction strip
TIP: You can also divide squares created with the Regular Polygon tool and circles created with the Measurement Tools.
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SMART Notebook Math Tools Learner Workbook
Irregular Polygons You can create different polygon shapes to demonstrate a math concept, such as finding the area of a given shape. SMART Notebook Math Tools enables you to create irregular polygons by marking points on a page.
Exercise 9: Finding the Area of a Polygon Students often encounter challenges when trying to find the area of an irregular polygonal shape. SMART Notebook Math Tools enables you to demonstrate this concept by creating and manipulating irregular polygon shapes of different sizes and shapes. 1 Select the Grid - large background from the SMART Notebook Gallery and insert it into your page 2 Use the Irregular Polygon tool to create your shape, using the grid as a guide 3 Determine the area of the shape by counting the square units enclosed by the shape 4 Demonstrate how to determine the area by separating the shape into rectangles using the Irregular Polygon tool 5 Determine the sum of the separate areas and compare with your initial findings
Extension Illustrate another method of separating the shape into rectangles to determine the area
23
Advanced Shapes
Regular Polygons Tool You may notice that the most common shapes you create in your lessons are regular polygons. With SMART Notebook Math Tools you can manipulate regular polygon shapes the same way you manipulate irregular polygon shapes. You can change the shape of the polygon by its vertices, show the lengths of the sides, and display the interior angles.
Exercise 10: Creating Tessellations with Regular Polygons SMART Notebook Math Tools enables students to manipulate regular polygon shapes to learn and review basic geometric concepts. You can use regular polygons to introduce students to tessellations. This enables students to explore space conservation and repetitive shape patterns.
1 Create a regular triangle polygon 2 Clone the triangle and join the two triangles together side-on-side 3 Continue to clone and join triangles together until you can see a pattern with no overlapping or gaps 4 Create a square and repeat steps 1–3 5 Display the interior angles of the triangles and squares 6 Note the angles at each vertex of both patterns. What do you notice about the sum of the angles? 7 Determine what other regular polygons can form a tessellation
Extension Try to create a semi-regular tessellation, like the following image, by using two or more different regular polygons using the same guidelines.
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SMART Notebook Math Tools Learner Workbook
Lesson Activity 1 What are some manipulatives you currently use in your lessons? How can you recreate them as virtual manipulatives with the Shapes tool?
2 How do you currently insert or create diagrams in your lesson?
3 What are some fraction concepts you can demonstrate with the shape division function?
4 List some advantages of creating shapes with the Shapes tool.
Open Activity 2.notebook on the USB storage device you received to complete the following activity: 5 Draw a floor plan of your classroom using the Shapes tool • Include a scale and legend • Include dimensions of the room and each item in the room • The drawing must contain a triangle, circle, quadrilateral and another shape of your choice • Find the area and perimeter of each item in the room
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SMART Notebook Math Tools Learner Workbook
SMART Notebook Math Tools: Equations Working with Equations In this section you will learn how to convert mathematical handwritten expressions and equations to text. You will also learn how to edit and solve equations, and add mathematical symbols and equations to a SMART Notebook page.
27
Equations
Working with Equations
Handwriting Recognition for Mathematical Symbols SMART Notebook Math Tools enables you to write equations on the page using the tools of your interactive product. SMART Notebook Math Tools recognizes many numbers, letters, symbols, operators and functions and converts your written equation to typed text that you can edit.
Exercise 11: Writing equations 1 Use a pen tool to write an equation on the SMART Notebook page 2 Select the equation 3 Press the equation's menu arrow, and then select Recognize Math Ink from the drop-down menu NOTE: Selecting Recognize Math Ink will enable you to solve and graph your equation.
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SMART Notebook Math Tools Learner Workbook
4 If the equation appears correctly, press the green circle with the checkmark
NOTE: Converting some written expressions and equations to Math Ink automatically converts the expressions to numerical solutions. Math Ink can convert expressions involving numbers (added or subtracted) in a vertical column, or single variable equations in the form “x =�. Math Ink replaces the handwritten expression with the numerical solution, similar to how most calculators operate.
SMART Notebook Math Tools recognizes many characters, including numbers, operators, Roman letters, Greek letters, and other mathematical symbols. SMART Notebook Math Tools also recognizes many mathematical functions. NOTE: For a full list of recognized symbols and functions, see Appendix C: Math symbols and functions supported by SMART Notebook Math Tools.
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Equations
Solving Equations SMART Notebook Math Tools is a fully functional calculator. You can use SMART Notebook Math Tools just as you would use a traditional calculator. The difference is that you enter numbers, operations and functions by writing on your interactive product.
Simplify Symbolically:
Simplify Numerically:
Exercise 12: Solving expressions and equations 1 Write an expression or equation 2 Select the expression or equation 3 To display a series of steps for reducing or converting the expression or equation to its lowest form, press the menu arrow, and then select Math Actions > Solve Symbolically 4 To generate the numerical solution, press the menu arrow, and then select Math Actions > Solve Numerically NOTE: SMART Notebook Math Tools can solve some equations numerically but not symbolically, and it can solve some equations symbolically but not numerically. If a solution type isn’t available, you’re unable to select it in the menu. 5 To find an equation’s zero value, press the equation’s menu arrow, and then select Math Actions > Find Zeroes
6 To find an equation’s minimum and maximum values, press the equation’s menu arrow, and then select Math Actions > Find Extrema
Find Extrema: no min - values nomax - values
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SMART Notebook Math Tools Learner Workbook
Exercise 13: Numerical Calculations A great feature of SMART Notebook Math Tools is the integration of the calculator function to solve written expressions and equations. You can write expressions and equations in digital ink and display the solutions all in the same work space, without having to use other applications.
1 Write the expression as shown to the right 2 Press the expression's menu arrow, and then select Recognize Math Ink 3 Press the expression's menu arrow and select Math Actions > Solve Numerically 4 Press the expression's menu arrow and select Math Actions > Solve Symbolically. This simplifies the expression to the lowest or fraction form.
Simplify Numerically: 0.583 Simplify Symbolically:
Exercise 14: System of Equations You can use SMART Notebook Math Tools to solve sets of equations containing variables. Just write your system of linear equations, stacked one on top of the other, and SMART Notebook Math Tools can generate a solution for the variables to satisfy all equations.
1 Write the system of linear equations as shown above 2 Highlight and group the linear system 3 Press the linear system's menu arrow and then select Recognize Math Ink 4 Press the linear system's menu arrow and select Math Actions > Solve Numerically
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Equations
Equation Editor SMART Notebook Math Tools enables you to add and edit equations on a page using numbers, letters, symbols, operators and functions with an Equation Editor. You can also use this feature to make annotations for equations, formulas and diagrams.
See Appendix D: Equation Editor for SMART Notebook Math Tools for a description of the available options.
You can also use the Equation Editor to add equations that aren’t supported by Math Ink’s handwriting recognition. NOTE: You can copy and insert equations from Microsoft™ Equation Editor or MathType™ software.
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SMART Notebook Math Tools Learner Workbook
Adding and Editing Equations Although SMART Notebook Math Tools can convert written math expressions and equations to text, it may not recognize some symbols written or aligned in the expressions. To resolve this issue, SMART Notebook Math Tools includes an Equation Editor which enables you to enter math symbols and templates as text. 1 Open the on-screen keyboard 2 Press the Equations button on the Math toolbar 3 Press an area of the SMART Notebook page to insert your equation. The Equations toolbar and text box appear. 4 Type your equation using the on-screen keyboard 5 Insert symbols or templates by pressing the corresponding bar or palette on the Equations toolbar TIP: You can use either the TAB key or the INSERT key to move the insertion point in the equation. 6 Press the Select button on the toolbar to switch from the Equation Editor to your SMART Notebook page To edit your equation, simply double-click the equation to open the Equation Editor. NOTE: To change the size of your equation, select the equation and then press and drag the resize handle.
Extension Find the symbols and templates in the Equation Editor to create the following equation:
Can you use the Equation Solver to solve this equation?
33
Equations
Annotating equations Input
Output
Rule for Function Discriminant <0 =0 >0
2 complex roots 2 equal real roots
2 distinct real roots
SMART Notebook Math Tools includes braces, brackets, arrows, and other templates that are perfect for adding annotations to equations. There are four templates in the fences palette of the Equation Editor that are particularly useful for the following types of annotations.
Input
Output
Rule for Function
The Equation Editor also enables you to enter text as you create your equations. This function is useful for labeling and adding descriptors to equations when creating lesson notes or templates. NOTE: You are unable to change the font setting or use the Spacebar in the Equation Editor. Certain words that contain math function words, such as rectangle, do not display properly. The Equation Editor automatically inserts spacing around math function words, making it difficult to display certain words. It is recommended that you insert braces, brackets, arrows, and other templates with the Equation Editor, and insert text using the SMART Notebook Math Tools text tool.
Extension List examples of instances when you would want to add annotations to equations using the Equation Editor.
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SMART Notebook Math Tools Learner Workbook
Lesson Activity 1 List some ways you can use the symbols and templates from the Equation Editor in your lesson.
2 How did you create annotations before using the Equation Editor?
Open Activity 3.notebook on the USB storage device you received to complete the following activity: 3 Complete the Trigonometry Formula Sheet using the Equation Editor and Equation Solver: 1. Label the sides of the right angle triangle 2. Complete the formulas for the Pythagorean Theorem and trigonometric functions 3. Use the Pythagorean Theorem to complete the chart
Trigonometry adjacent hypotenuse opposite
Pythagorean Theorem
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SMART Notebook Math Tools Learner Workbook
SMART Notebook Math Tools: Graphing Working with Graphs In this section you will learn how to add Number Lines, Cartesian graphs and Quadrant graphs to your SMART Notebook file. You will also learn how to create graphs using tables and equations.
37
Graphing
Generating Graphs
Custom Graph Builder SMART Notebook Math Tools enables you to add a Cartesian graph, quadrant graph or number line to a page.
Extension Add a Number Line, Cartesian and Quadrant graph to a page using the Graph Wizard. List the custom options for each graph. • Number Line
• Cartesian
• Quadrant
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SMART Notebook Math Tools Learner Workbook
Manipulating Graphs You can customize the title, size, position and grid lines of the graphs and edit the start point, end point, labels and gridlines of its axes.
Top
Top
Vertical
Vertical
Horizontal
Show/Hide Point Labels Horizontal
Show/Hide Lines
Show/Hide Line of Best Fit
Show/Hide Numbers
Show/Hide X/Y Labels and Title
Zoom in
NOTE: If no icons appear below the graph, press the
Zoom out Display Different Section
button in the graphâ&#x20AC;&#x2122;s bottom-right corner.
39
Graphing
Exercise 15: Adding Data You can plot points directly to a graph to display collected data. SMART Notebook Math Tools enables you to generate and customize Cartesian and quadrant graphs by adding coordinate points.
Student test scores and hours of study
Hours
Test Scores
Test Scores
of Study
Hours of Study
1 Press Graphs on the Secondary toolbar 2 Select Quadrant 3 Select the graph, and then edit its properties 4 Plot points by double-pressing the graph TIP: You can display the coordinates of a point on the graph by pressing once on the point. Double-pressing the point removes it from the graph. 5 Press the Show Points Labels button 6 Press the Line of Best Fit button
Extension Using the line of best fit from the previous scatter plot, estimate the test score of a student who studied for 25 hours.
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SMART Notebook Math Tools Learner Workbook
Exercise 16: Shapes in a Graph If you want to demonstrate transformations of an object on a coordinate plane, you can use SMART Notebook Math Tools to draw the object on a grid and show geometric transformations such as translations and reflections.
1 Press the Graphs button on the Secondary toolbar 2 Select Cartesian 3 Press the Irregular Polygons button on the Secondary toolbar 4 Draw an object by pressing on different coordinates on the graph 5 Select the shape, and then select Reflect Shape > Reflect Over X=0 from the drop-down menu 6 Select the reflected shape, and then edit its properties 7 Press and drag the object to perform a translation TIP: You can also snap the vertices of the object to the grid. 1 Select the object and display the vertices by selecting Show/Hide Vertices from the object drop-down menu. 2 Select and drag a vertex. A red horizontal and vertical guide line indicates when the vertex point is on a grid line.
Extension Explain how you would use the graph to demonstrate the following types of transformations: • Reflections
• Translations
• Rotations
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Graphing
Dynamic Graphing SMART Notebook Math Tools enables you to create a graph from an equation, a graph from a table of values, and a table of values from a graph. If you edit the equation or values, the graph automatically updates to reflect the changes.
. NOTE:You can display the data of up to two graph tables/equations on one graph.
Extension List some different math concepts that require you to use graphs in your teaching.
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SMART Notebook Math Tools Learner Workbook
Exercise 17: Generating a Graph from a Table You have a set of coordinate points that you want to display graphically for your students. SMART Notebook Math Tools enables you to create a table of values and generate a graph based on these values. Hours Test of Study Scores
Test Scores
Student test scores and hours of study
Hours of Study
1 Press the Graph Tables button on the Secondary toolbar 2 Select the number of rows that you want in the table 3 Type values for the first set of data into the table's cells TIP: You can write the numerical data in the cells of the graph table, and then select Recognize Graph Table Content from the table drop-down menu. SMART Notebook Math Tools converts the written data to Math Ink. 4 Select the graph table 5 Press the table's menu arrow, and then select Math Actions > Generate Graph from the drop-down menu NOTE: If you update the information in the tables, SMART Notebook Math Tools automatically updates the graph. If you update the information in the graph, SMART Notebook Math Tools automatically updates the tables.
Extension SMART Notebook Math Tools also enables you to display data from two graph tables.
Hours of TV
Test Scores
1 Press the Graph Tables button on the Secondary toolbar 2 Select the number of rows that you want in the table
Connection Icon
3 Enter the second set of data into the table's cells 4 Select the table and link it with the existing graph by pressing and dragging the blue Connection Icon box over the graph
43
Graphing
Exercise 18: Generating a Graph from an Equation You can graph equations in 2D Cartesian coordinate systems to demonstrate relationships and determine patterns. SMART Notebook Math Tools can generate a graph for any (1 or 2) y = form equation you insert or write on a SMART Notebook page. Letâ&#x20AC;&#x2122;s demonstrate how to generate a graph from two equations. 1 Write the equation 2x+y = 4 2 Select the equation, and then select Recognize Math Ink from the drop-down menu 3 Select Math Actions > Generate Graph from the drop-down menu 4 Write another equation 3x-y = 1 5 Select the new equation, and then select Recognize Math Ink from the drop-down menu 6 Select the new equation and link it with the existing graph by pressing and dragging the blue Connection Icon box over the graph
NOTE: If you make changes to the linked equation, SMART Notebook Math Tools automatically updates the graph. You cannot generate a graph from equations that are solved or grouped.
Extension 1 Calculate five coordinate points on the graph 2x+y = 4. Record the coordinates in a Graph Table. 2 Generate a graph from the table, and then select Line of Best Fit 3 Compare your results with the graph from the equation 2x+y = 4 What is the slope of the two lines?
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SMART Notebook Math Tools Learner Workbook
Texas Instruments Emulators SMART Notebook Math Tools enables you to perform basic graphing tasks. For more advanced graphing demonstrations, you can open and operate your Texas Instruments™ emulator from SMART Notebook Math Tools. 1 Press the TI Calculators
button on the Secondary toolbar
If TI-nspire™, TI-SmartView™ 84 or TI-SmartView 73 software is installed on your computer, an icon appears with the name of your software. 2 Press this icon NOTE: The Texas Instruments emulator isn’t included with SMART Notebook Math Tools. This feature is only available if Texas Instruments software is already installed and licensed on your computer.
45
Graphing
Lesson Activity 1 How do you currently teach graphing concepts?
Open Activity 4.notebook on the USB storage device you received to complete the following activity: 2 Create a table of values to determine the coordinates of five points that lie on the graph of y = 3x+5 1. Use these five points to draw a line in a coordinate plane 2. Draw the graph of y = -2x - 10 in the same coordinate plane 3. Based on your graphs, what is the intersection point of the lines with equations y = 3x + 5 and y = -2x -10
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SMART Notebook Math Tools Learner Workbook
Additional Information Best Practices This section covers a few tips for using SMART Notebook and SMART Notebook Math Tools to deliver your math lessons.
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Best Practices
Writing Equations Consider the following when you write equations: • Write each symbol clearly and do not overlap symbols • Leave space between the characters, symbols, formulas, and equations that you write • Draw a multiplication symbol as a six-pointed asterisk (
)
• If your equation involves multiple lines, such as fractions, leave space between these lines. Do not separate a single line equation over multiple lines. • Align superscripts, such as exponents, to the right and above the adjacent character or symbol. Do not overlap characters and superscripts. • Write problems sequentially from left-to-right and from top-to-bottom • Tap the pen tool to make a decimal point with digital ink. Do not draw a tiny ball or scribble mark. • Do not use j as a variable unless you’re writing a trigonometric expression or a complex expression. Do not use i or o as variables unless you’re writing a trigonometric expression. • Do not use e as a variable unless you’re writing an exponential expression
Writing Trigonometric Equations Consider the following when you write trigonometric equations: • Enclose variables in parentheses, for example, sin (x) • Separate multiple trigonometric expressions using a multiplication sign, for example, sin(A)*cos(A)
Writing Logarithmic Equations Consider the following when you write exponents, logarithms and geometric series: • SMART Notebook Math Tools recognizes log (N) as log10N • SMART Notebook Math Tools recognizes logM as logm or logM (natural log) • SMART Notebook Math Tools supports log2M and log10M only • Write the natural logarithm (ln) as log • Write log2 as log2. Write log10 as log10. SMART Notebook Math Tools doesn't support subscripts.
Solving Multiple Line Equations SMART Notebook Math Tools can solve multiple-lined equations if you select all the equations, press the equation's menu arrow, and then select Recognize Math Ink.
Dual Page Display and Pin Page In some lesson activities, you may want to display two pages side-by-side. For example, you may want to display steps for solving a particular type of math problem on one page, and a math question for your students to complete on another page. You can display both of these pages at once using Dual Page Display. You can draw, make notes, import files and add links on either page just as you would on a single page, and you can even move objects between the two pages.
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SMART Notebook Math Tools Learner Workbook
When working in Dual Page Display, the Pin Page feature enables you to lock one page in place and use the other pane to navigate through your SMART Notebook pages. For example, when introducing new concepts, you may want to keep formulas, manipulatives or steps displayed on one page, and display various activities in the other pane. This approach enables students to refer to the new concepts or formulas or drag the virtual manipulatives onto the activity pages as needed.
Transparent Background Using the Transparent Background, you can view the computer desktop and open windows behind the SMART Notebook window and continue to interact with the transparent file. You can draw in digital ink on a transparent page and save your notes in the file. You can also display measurement tools, take screen captures and more. If an area of the screen doesn't include any SMART Notebook objects, you can select and interact with the desktop and applications behind the SMART Notebook window. The added advantage of this tool, for math lessons or demonstrations, is the availability of the SMART Notebook Measurement Tools which are not available on the Floating Toolbar.
SMART Notebook Gallery The Gallery organizes content into the following four categories: Pictures and Backgrounds, Interactive and Multimedia, Lesson Activities and SMART Notebook Files and Pages. Thumbnails in each category provide preview images of the available content. You can easily add your own background pages, clip art, multimedia and Adobe速 Flash速 content files to the My Content category.
SMART Website Many more lesson activities are available online at www.education.smarttech.com.
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SMART Notebook Math Tools Learner Workbook
Appendices Quick References The following quick reference guides are available: • Manipulating the SMART Notebook Measurement Tools • Drop-down menu options for SMART Notebook Math Tools • Math symbols and functions supported by SMART Notebook Math Tools • Equation Editor for SMART Notebook Math Tools
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SMART Notebook Math Tools Learner Workbook
Appendix A: Manipulating the SMART Notebook Measurement Tools Manipulating the Ruler You can use the SMART Notebook ruler to draw or measure straight lines in your .notebook files. You can manipulate the size, length, rotation and location of the ruler to create or measure objects of various sizes and angles.
Manipulating the Protractor You can use the SMART Notebook protractor to draw arcs and circles or to measure and display angles of objects in your .notebook files. You can manipulate the size, rotation and location of the protractor to create or measure objects of various sizes and angles.
To move the protractor To move the ruler Press the middle of the ruler, and then drag the ruler to a different position on the page. To rotate the ruler Press the top or bottom edge of the ruler, and then drag the ruler clockwise or counter-clockwise. NOTE: Displays the current rotation in degrees.
To change the measurement units Press the ruler's flip symbol. To lengthen or shorten the ruler Press the ruler's far edge, and then drag your finger away from or towards the ruler. To resize the ruler Press the ruler, press the object's resize handle, and then drag it to increase or reduce the objectâ&#x20AC;&#x2122;s size.
Press the inner section of the protractor, and then drag the protractor to a different position on the page. To rotate the protractor Press the outer circle of the protractor, and then drag the protractor clockwise or counter-clockwise. NOTE: Displays the current rotation in degrees.
To resize the protractor Press the inner circle of the protractor, and then drag away from the protractor to enlarge it or toward the center of the protractor to shrink it. To display the protractor as a complete circle Press the blue circle next to the 180Âş label on the inner circle of the protractor. To insert an angle Press the protractor. Press and drag the green circle to your desired measurement, and then press the green arrow.
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Appendices
Manipulating the Geodreieck Protractor You can use the SMART Notebook Geodreieck protractor to draw straight lines or measure angles of objects in your .notebook files. You can manipulate the size, rotation and location of the Geodreieck protractor to create or measure objects of various sizes and angles.
Manipulating the Compass You can use the SMART Notebook compass to draw arcs and circles in your .notebook files. You can manipulate the width, rotation and location of the compass to create objects of various sizes.
To move the compass
To move the Geodreieck protractor Press the inner section of the protractor, and then drag the protractor to a different position on the page. To rotate the Geodreieck protractor Press the outer edges of the protractor, and then drag the protractor clockwise or counter-clockwise. NOTE: Displays the current rotation in degrees.
To resize the Geodreieck protractor Press the inner circle of the protractor, and then drag away from the protractor to enlarge it or toward the center of the protractor to shrink it.
Press the arm of the compass that holds the spike, and then drag the compass to a different position on the page. To rotate the compass Press the compass' rotation handle, and then drag the compass clockwise or counter-clockwise NOTE: Displays the current angle between the spike and the pen. To widen the compass Press the arm of the compass that holds the pen, and then drag it to change the angle between the spike and the pen. To flip the compass Press the compass flip symbol. To draw using the compass Press the compass' pen tip, and then drag the compass in the direction you want to rotate it.
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SMART Notebook Math Tools Learner Workbook
Appendix B: Drop-down Menu Options for SMART Notebook Math Tools
Shapes in Graphs
Handwriting Recognition
Recognize Math Ink
Converts written math expressions to text
Reflect Over X=0
Reflects the shape over the Y axis
Reflect Over Y=0
Reflects the shape over the X axis
Reflect Over Y=X
X-coordinates and Y-coordinates change places
Reflect Over Y=-X
X-coordinates and Y-coordinates change places and are negated (the signs are changed)
Shape Manipulation
Show/Hide Vertices
Displays or hides the vertices of a shape
Show/Hide Interior Angles
Displays or hides the interior angles of a shape
Show/Hide Side Lengths
Displays or hides the sides lengths of a shape
Shape Division
Divide a circle, square or rectangle into separate pieces of equal area
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Appendices
Graphs, Tables and Equations
Recognize Graph Table Content
Converts written data to text in a table
Generate Graph
Generate and display a graph based on an equation or table
Generate Table
Generate a table of values based on points from a Cartesian or quadrant graph
Disconnect
Breaks the link between a graph and a table or equation
Simplify Numerically
Solves an expression numerically
Simplify Symbolically
Solves an expression symbolically
Find Zeroes
Finds an equation’s zero value
Find Extrema
Find’s an equation’s minimum and maximum values
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SMART Notebook Math Tools Learner Workbook
Appendix C: Math Symbols and Functions Supported by SMART Notebook Math Tools
Other Mathematical Symbols
Mathematical Symbols SMART Notebook Math Tools recognizes many symbols, including: numbers, operators, roman letters, Greek letters, and other mathematical symbols.
Mathematical Functions SMART Notebook Math Tools recognizes mathematical functions in the following categories:
Numbers â&#x20AC;˘ Logarithmic functions â&#x20AC;˘ Trigonometric functions
Logarithmic Functions Operators
log (a)
natural logarithm
log10 (a)
base 10 logarithm
log2 (a)
base 2 logarithm
Trigonometric Functions Roman Letters
Greek Letters
acos (a)
inverse cos function
asin (a)
inverse sin function
atan (a)
inverse tan function
cos (a)
cos function
cosh (a)
hyperbolic cos function
cot (a)
cot function
coth (a)
hyperbolic cot function
csc (a)
cosecant function
sec (a)
secant function
sin (a)
sin function
sinc (a)
sinc function
sinh (a)
sinh function
tan (a)
tan function
tanh (a)
tanh function
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SMART Notebook Math Tools Learner Workbook
Appendix D: Equation Editor for SMART Notebook Math Tools
Symbol palettes Template palettes Small Bar Tabs Large tabbed bar
Palette
Small tabbed bar
Empty slot Insertion point Selection
Toolbar Items
Description
Symbol palettes
Contains palettes of various math symbols
Template palettes
Contains palettes of various math templates
Small bar
Contains frequently used symbols, templates and expressions (whole equations or parts of equations)
Large tabbed bar
Contains frequently used templates and expressions (whole equations or parts of equations) relating to the tab
Small tabbed bar
Contains frequently used symbols relating to the tab
Empty slot
A dotted outline slot for text
Insertion point
A blinking marker consisting of a horizontal line and a vertical line that indicates where text or templates will be inserted
Selection
The highlighted part of the equation that is effected by any subsequent editing commands
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Appendices
Keyboard shortcuts Description
Icon
Keystroke
Fraction
CTRL+F
Superscript
CTRL+H
One point space (between text)
CTRL+ALT+Space
Thin space (between text)
CTRL+Space
Thick space (between text)
CTRL+SHIFT+Space
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