Springboard Digital User Guide– Students & Parents

SpringBoard Digital User Guide– Students & Parents – Math Tools

Overview ...... 2 Welcome to SpringBoard Digital User Guides...... 2 Algebra Tools ...... 3 1. Navigating to the Algebra Tools ...... 3 2. Using the Input/Output and Graphing Calculator Algebra Tools ...... 4 3. Using the Algebra Tiles Tool ...... 7 Desmos Calculators...... 10 1. Navigating to the Desmos Calculators ...... 10 Geometry Tools ...... 11 1. Navigating to the Geometry Math Tools ...... 11 2. Using the Geometry Tools...... 12 3. Using the Protractor ...... 13 Number Concept Tools...... 15 1. Navigating to the Number Concepts Tools:...... 15 2. Using the Number Concepts Tools ...... 16 3. Using the Ruler...... 18 4. Using Number Lines...... 19 Probability and Statistics Tools...... 22 1. Navigating to the Probability and Statistics Math Tools...... 22 2. Using the Probability and Statistics Tools...... 23 3. Using the Spinner Tool ...... 25 4. Using the Random Number Tool...... 27 5. Using the Number Cubes Tool...... 29 WIRIS...... 31 Desmos Graphing Calculator ...... 32

Overview Welcome to SpringBoard Digital User Guides

In this guide for Math Students, you will learn to use the Math Tools in four important Math subjects. You’ll also learn more about GeoGebra tools and the Desmos graphing calculator by visiting suggested links/websites.

Space for notes:

Algebra Tools

Using the Algebra Tools, you can: • model equations being solved with Algebra Tiles • create tables and graphs using the Input/Output table or the Graphing Calculator • build an equation to add to work using the Equation Editor

1. Navigating to the Algebra Tools

1. Click My Bookshelf on the dashboard and open the math e-book.

2. Select any question and click on the + sign. When the answer space opens, click on the Math Tools Suitcase. The first tools that appear are the Algebra Tools.

There are other math tools in the suitcase. Read the Geometry, Number Concepts and Probability and Statistics Math Tools Guides to learn more about those tools.

2. Using the Input/Output and Graphing Calculator Algebra Tools

1. Select the Algebra Tool needed. In this question, a table is needed. Choose the Input/Output Tool.

2. The problem asks for certain x-values, -3, -2, -1, 0, and 1, to be included in the table. Clicking on the settings icon that allows the list to be edited.

Hint: To see the tool window full screen, click on the four-way arrows in the top corner of the tool window.

3. The problem asks for the function to be graphed on grid paper. The visual on SBD can be used for assistance with this task. The required x-values can be added to the table by clicking below the last value. Values can be added using the computer keyboard or the input options on the screen.

4. Determine the related y-value for each x-value added to the table. As the related y-values are added to the table, points representing each ordered pair shown in the table appear on the graph.

5. To determine whether the answers added to the table are correct, graph the function to model a second representation of it. Click on the plus sign and choose “f(x)expression”.

6. The computer keyboard or the screen input tools can be used to type the function into the space provided. Notice that the function is graphed through the points plotted using the table function. The values are correct!

3. Using the Algebra Tiles Tool

1. Choose the Algebra Tiles tool.

2. In this question, the equation to be solved is 6x + 3 = 5x + 10. This equation does not require the use of x2 tiles but x tiles and unit tiles are needed as shown below.

3. The equation can be shown above the tiles using the toggle button beneath the tool pane.

4. Use the Algebra Tiles to assist in solving the equation. Do this by removing the same number of x tiles and unit tiles from both sides of the pane by dragging them off the pane toward the bottom.

5. To determine the solution to the equation, look at the tiles left behind after all of the x tile and unit tile pairs are removed. In this case x = 7. Be sure to check the solution by substituting the solution into the original equation.

There are many uses for the Algebra Tools in SBD. In addition to the tools outlined in this guide, the Equation Editor can be used to create different types of equations to add to your work.

Explore the Algebra Tools and share your findings with your class!

For information about GeoGebra – CAS please visit the following site: https://www.geogebra.org/b/ogeMbIiF

For information about GeoGebra – Spreadsheet, please visit the following site: https://www.geogebra.org/b/wuiE7sPF

Desmos Calculators

1. Navigating to the Desmos Calculators You have 3 types of calcuators to choose from: 1. Click My Bookshelf on your dashboard and • Desmos Graphic Calculator open your math e-book. • Desmos Scientific Calculator • Desmos Four Function Calculator

2. Select any question and click on the + sign. When the answer space opens, click on the Math Tools suitcase. The second set of tools that appear are the Desmos Calculators.

For more information on the Desmos Graphic Calculator, please see pp 32-33.

Geometry Tools

1. Navigating to the Geometry Math Tools Using the Geometry Tools, you can: 3. Click My Bookshelf on your dashboard and • model shapes and solids open your math e-book. • plot figures and complete transformations on a coordinate grid • measure using a digital protractor

4. Select any question and click on the + sign. When the answer space opens, click on the Math Tools suitcase. The third set of tools that appear are the Geometry Tools.

There are other math tools in the suitcase. Read the Algebra, Number Concepts, and Probability and Statistics Math Tools Guides to learn more about those tools.

2. Using the Geometry Tools

1. Select the Geometry Tool needed. In this case, the problem asks for a transformation. Choose the Transformation Tool.

2. The task in this problem is to reflect a given shape. The Point and Line Segment Tools can be used to reproduce the original shape.

3. Multiple types of transformations are available to assist in solving problems. Use the one that is needed. In this case, use the appropriate Reflection Tool.

Another Geometry Tool is the protractor.

3. Using the Protractor

1. Find the Protractor in the Geometry space of the Math Toolbox.

2. Use the Protractor to measure angles within problems. As data is collected, add it to the table.

Two and three-dimensional shapes and solids can also be created using the Grapher Tool.

There are many uses for the Geometry Tools in SBD. Use

the Grapher and Transformation tools to represent

figures that can assist in solving problems. Use the Protractor to measure angles and record measurements for later use. Explore the Geometry Tools and share your findings with your class!

For information about GeoGebra – 2D and – 3D, visit the following websites: https://www.geogebra.org/b/JV45hyEh and https://www.geogebra.org/b/FN8Dev7T

Number Concept Tools

Using the Number Concept Tools, you can: • model problems involving integers • use a ruler • create number lines and tables • represent equations using a graphing calculator

1. Navigating to the Number Concepts Tools:

1. Click My Bookshelf on your dashboard and open the math e-book.

2. Select any question and click on the + sign. When the answer space opens, click on the Math Tools Suitcase. The fourth set of tools that appear are the Number Concepts Tools.

There are other math tools in the suitcase. Read the Algebra, Geometry, and Probability and Statistics Math Tools Guides to learn more about those tools.

2. Using the Number Concepts Tools

1. Select the Number Concepts Tool needed. In this question, Counters are needed. Choose the Counters Tool.

2. The task in this problem is to model the problem 5 + (-2) using Counters.

3. Use the Counters to model the problem, 5 + (-2). Drag 5 positive counters to the space and 2 negative counters

4. Use the model created in SBD to assist in solving the problem. Eliminate the zero pairs and view the quantity remaining. The answer to the problem is 5 + (-2) = 3.

3. Using the Ruler

Another Number Concept Tool is the ruler.

1. Find the Ruler in the Number Concepts space.

2. Use the Ruler and add any measurements determined to the table for later use.

4. Using Number Lines

Number Lines can be created using the Number Concepts Tools!

1. Find the Number Line in the Number Concepts space.

2. Using the Number Line Tool, add a title, label for the x-axis, minimum, maximum and interval for the number line. These labels can be turned on and off using the toggle button below the number line.

3. Enter the values needed into the table. In this question, the values found in the top row of problem 6a are added. As the values are entered into the table, points representing these values appear on the number line.

4. Use the Number Line Tool to assist in solving problems. In this question, the number line models data points in a set to assist in determine the range of the data. The greatest value on the number line is 22 and the least value is 6 so the range is 16.

There are many uses for the Number

Concepts Tools in SBD. In addition to the tools in this guide, the Graphing Calculator can be used to create graphs of equations and the Data Table can be used to create tables of data to add to your work. Explore the Number Concepts

Tools and share your findings with your

class!

For information about GeoGebra – Spreadsheet, please visit the following site: https://www.geogebra.org/b/wuiE7sPF

Probability and Statistics Tools

Using the Probability and Statistics Tools, you can: • create multiple types of graphs and plots from data • use tools such as number cubes and spinners to simulate problem situations • create tables using data • generate random numbers

1. Navigating to the Probability and Statistics Math Tools

1. Click My Bookshelf on the dashboard and open the math e-book.

2. Select any question and click on the + sign. When the answer space opens, click on the Math Tools Suitcase. The bottom set of tools that appear are the Probability and Statistics Tools.

There are other math tools in the suitcase. Read the Algebra, Geometry, and Number Concepts . Math Tools Guides to learn more about those tools.

2. Using the Probability and Statistics Tools

1. Select the Probability and Statistics Tool that is needed. There are twelve Probability and Statistics Tools available. Graphs can be created from data using eight of the tools. These tools include the Dot Plot Tool, Histogram Tool, Line Graph Tool, Scatterplot Tool, Bar Graph Tool, Box/Whisker Tool, Circle Graph Tool, and Stem and Leaf Tool.

2. The task in this question is to create a scatterplot. Click on the Scatterplot Tool. When the Scatterplot Tool opens, add labels and intervals to the x- axis and y-axis.

5. Input the data points into the table. As the data is added, the related points appear on the Scatterplot.

6. The Scatterplot can be used to answer questions and solve problems that include data.

3. Using the Spinner Tool

Another Probability and Statistics Tool is the Spinner Tool.

1. Click on the Spinner in the Probability and Statistics space of the Math Toolbox.

2. The task in this question is to spin Spinner A and Spinner B. The SBD Spinner Tool can be used for this simulation. To recreate Spinner A, complete the label and y-values columns in the table. The labels are those shown on the spinner in the book and the y-values need to be equal to create equal sectors on the spinner.

3. Click on Spin. The results are automatically added to the data table as shown below.

4. Using the Random Number Tool

Random Numbers can be generated using the Random Number Tool.

1. Click on the Random Number Tool in the Probability and Statistics space of the Math Toolbox.

2. Add the necessary information into the Random Number Tool. This information includes the number of sets of values to be generated, number of values needed per set, range of values for the sets generated and how the values should be displayed in the sets.

3. Click on Randomize. The randomized values appear in the box at the bottom of the Random Number Tool sorted by any rules that were entered into the Random Number Tool.

5. Using the Number Cubes Tool

The Number Cubes Tool can be used for simulations as well.

1. The Number Cubes Tool can be used to solve problems. To use the Nunmber Cubes Tool, click on that tool.

2. Select the number of cubes to be rolled from the drop down menu. In this case, two number cubes are chosen. Click on the roll button beneath each cube to roll it. The results of the rolls appear in the table below the number cubes.

3. The data from the Number Cube simulation can assist in solving problems.

There are many uses for the Statistics and Probability

Tools in SBD. Use the eight graph and plot tools to create graphs and plots from data. Use the Spinner and Number Cube Tools to simulate probability events. Use the Data Table to create different tables of data to add to your work. Explore the Probability and Statistics Tools and share your findings with your class!

For information about GeoGebra – Prob/Stats, please visit the following site: https://www.geogebra.org/b/B29A4c9E

For information about GeoGebra – Spreadsheet, please visit the following site: https://www.geogebra.org/b/wuiE7sPF

WIRIS

Whenever you open the (+) sign to answer a question, you can select the text editor (your first option listed as the “A”). Within a text field, you can use the WIRIS formula editor as called out below.

To learn more about use of LaTeX or click either of the links in the lower right to receive more information on how they can both be used to create expressions.

Desmos Graphing Calculator

Anytime you click the Graphing Calculator from the Math Tools pull down, you’re actually launching Desmos:

To learn more about the Desmos Graphing calculator, please visit the following website: http://learn.desmos.com/calculator