# Math Connections Set 1 and 2

When I was teaching math it seemed like you could never have enough worksheets for kids to do.  To me it was very helpful to have practice problems that were fun for the kids to complete.  Math worksheets that combined solving math problems with getting the punchline of a corny joke or riddle were always a hit with my students.

In Math Connections Set 1 I created an app that provides an endless supply of math practice sheets.  The app is designed to look like a spiral ring notebook sitting on a table.

Problems numbered from 1 to 10 are presented on the left and answers are shown on the right.  Each answer is associated with a letter.  At the bottom of the page there is a riddle or joke.  The punchline is hidden by numbers but as the student solves the math problems, the punchline is revealed.

Math Connections Set 1 is designed for elementary age students.  The types of problems generated by the app are in these categories:

• Addition of Positive Integers (0-12)
• Addition of Positive Integers (10-100)
• Subtraction of Positive Integers (10-100)
• Multiplication Facts (0-12)
• Powers of Two
• Square Root
There are over 100 jokes or riddles in Math Connections Set 1
In Math Connections Set 2 a different set of jokes and riddles are used.  Set 2 has problems that are appropriate for Middle School and High School level students.  In both Set 1 or Set 2 the level can be selected by tapping an icon on the scoreboard. In Set 2 the problems are in these categories:

• Variables and Expressions
• Variable Expressions with Powers
• Operations with Integers (+/-)
• Simplifying Expressions
• Powers of Two with Variables
• Square Root with Variables

Math Connections Set 1 and Set 2 are available with a volume discount for educational institutions. These apps can be purchased worldwide exclusively through the Apple App Store.  The apps are also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of any of these apps. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’ website for more information about this and other iOS and tvOS apps for education.

# Critical Thinking Activities

The development of problem solving skills and critical thinking abilities is currently a high priority in K-12 schools.  Curriculum development experts and experienced teachers who lead inservice programs recognize the need for emphasizing these important areas of learning. Helping students learn how to think and how to learn is perhaps the most important skills that 21st century educators can and do embrace.

Unfortunately in many cases critical thinking activities are overlooked or considered to be something extra to do — something beyond the basics, but many teachers realize that critical thinking skills are basic.  Critical thinking skills are actually a ‘critical’ component of a sound curriculum.

The Critical Thinking Skills app provides 10 different activities that challenge students to use, develop and improve their problem solving and critical thinking abilities.

In the app a column of buttons on the left side of the screen launch the corresponding activity.  Shown above is a sample screen from the Hundreds Chart Patterns activity.  The set of activities include the following:

1. Hundreds Chart Patterns
2. What’s the Rule?
3. Find a Match
4. Cube Patterns
5. Dot Designs
6. Isometric Designs
7. Design Patterns
8. Reflections
9. Sum Patterns
10. Number Line

# Pioneers in Math and Science

New apps for iOS and tvOS Devices:

It is reported that Newton once said , “If I have seen further than others, it is by standing upon the shoulders of Giants”.  The Pioneers in Math and Science series of apps for iOS and tvOS devices explores the lives and contributions of several giants in astronomy, physics, philosophy, biology and mathematics who lived before and after Newton.

In Galileo Galilei • The Father of Modern Science, a timeline feature is used to introduce students to the fascinating life of Galileo.  It discusses his early education and explains that as a young man Galileo’s father moves the family to Florence which at the time was a major center for artistic, literary and scientific studies.

The timeline feature is interactive and students can request more information about any of the highlighted years but tapping the year.  The arrows at either end of the time allow students to scroll through the time period.

Illustrated information screens pop up to help students learn about Galileo’s accomplishments.  Students will find it inspirational that many of the things that fascinated Galileo as a young man became a major focus of his studies and lead to mathematical and scientific breakthroughs for him later in his life.

In Isaac Newton – Mathematician • Physicist • Astronomer, students explore the many Newton’s achievements including those related to the nature of white light.  Newton discovered that sunlight was actually made up of many different colors.  He should this by holding up a prism near a window in his laboratory and projecting a spectrum of colors.

René Descartes • Philosopher • Mathematician presents the work of the man who linked algebra and geometry and laid the foundation for modern mathematics.

Descartes work in philosophy formed the basis for the modern scientific method.  He wrote about his skepticism regarding what he could experience through his senses and encourage people to seek knowledge through reason, mathematics and science.

In Charles Darwin • The Science of Evolution a map of the world is used to show the voyage of exploration of the HMS Beagle.  This five year journey around the world gave Darwin the information he needed to develop his Theory of Evolution.

Each of the apps in this series feature a quiz so that student can demonstrate comprehension of the reading material and other special features such as a speech where the text from the diagrams, quizzes or scrolls can be read aloud to students.

Galileo Galilei • The Father of Modern ScienceIsaac Newton – Mathematician • Physicist • AstronomerRené Descartes • Philosopher • Mathematician and Charles Darwin  • The Science of Evolution and other  apps in this series are available with a volume discount for educational institutions. These apps can be purchased worldwide exclusively through the Apple App Store.  The apps are also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of any of these apps. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’ website for more information about this and other iOS and tvOS apps for education.

# Math Decoder

Most people who are involved in education and have studied educational psychology know the name, Jean Piaget.  Piaget’s Theory of Cognitive Development, defined and described stages of development: sensorimotor, pre-operational, concrete operational and formal operational.  Many math curriculum materials are designed to fit with these developmental stages that roughly correspond to age groups:  sensorimotor (0-2), pre-operation stage (2 to 7), concrete operational (7 to 11), and formal operational (11+ and adulthood).  The availability of computers and educational software may have shifted some of these age groupings toward the younger ages since very young children are often using iPads and other devices to explore and learn concepts with assistance of highly interactive educational games and experiences.  Apps can be very engaging and often create multimedia learning environments that motivate students through positive reinforcements such as praise, points, stars, trophies or virtual stickers.

The manipulative approach to teaching math is based on the cognitive development theories of Piaget, Bruner and others.  Software designed to support these theories, for example my Hands-On Math Series, brings the manipulative approach to the computer screen by creating interactive representations of mathematical objects.  Math Decoder is designed in a similar way so that the student is able to move numbered tokens into place to show his or her answer.

Math Decoder presents random numbers in a grid that is similar to the familiar tic-tac-toe board.  Problems are given using shapes that reference the position of the numbers in the grid.  To give an answer students must determine which numbers are referenced by the shapes and then perform the arithmetic operation.

Using Math Decoder helps build mental math skills.  It involves abstract thinking because the symbols are used to represent numbers in way that is similar to how variables are used in algebra.  I designed Math Decoder to be a quick exercise that teachers and parents can assign to students when they have a few minutes of time.  Challenge students to earn a trophy.  It’s fun!

Math Decoder is available with a volume discount for educational institutions. Algebra Portal AR can be purchased worldwide exclusively through the Apple App Store.  It also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of Algebra Portal AR. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’ website for more information about this and other iOS and tvOS apps for education.

# Algebra Portal AR

Apple’s new ARKit has opened the door to new kinds of app experiences.  My new app, Algebra Portal AR, creates virtual rooms filled with information about important terms and key concepts related to the Algebra I curriculum.  What is really exciting about the Algebra Portal is students stand up, walk around and experience a totally immersive environment that is filled with illustrated examples that are used to explain some of the fundamental ideas of algebra.

The floor Algebra Portal is a standard Cartesian plane with the x and y axes labelled.  Teachers could develop lesson experiences that involve students walking into the portal and then moving to a specific (xy) position to learn about a particular topic from the algebra curriculum.

When a wall inside the Algebra Portal is tapped a menu of terms is displayed.  If a term is selected detailed information about the topic is displayed with examples.

Students and teachers will be amazed when they create virtual rooms filled with information about key terms and concepts from the middle school and high school algebra curriculum.

Explore algebra in a new way with the Algebra Portal AR. Use the camera view on your iPad to detect a flat surface and then tap the screen. Instantly a portal opens to a world filled with information about the terms and concepts that are part of the algebra curriculum.

In an nutshell, to use the app, students walk around in the augmented reality algebra portal where they can tap on the walls and other objects in the rooms to get more information and to hear Siri read aloud information about the selected item. Students can scroll through an extensive list of terms related to the information on the walls of the rooms, walls and objects in the portal.

Algebra Portal AR creates virtual rooms that are approximately 4 meters by 7 meters. It is best used in a well-lit open space, perhaps in a school’s auditorium or multi-purpose room. If the Algebra Portal sounds interesting to you, you might also like the Geometry Portal AR.

Algebra Portal AR is available with a volume discount for educational institutions. Algebra Portal AR can be purchased worldwide exclusively through the Apple App Store.  It also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of Algebra Portal AR. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’ website for more information about this and other iOS and tvOS apps for education.

# Hide and Seek AR

Kids love to play Hide and Seek.  Hide and Seek AR is similar to the popular game with a new twist:  The players use the app to hide and find geometric shapes in an augmented reality environment.

Hide and Seek AR is a two player game.  The game begins when the first player closes his or her eyes while the second player uses the iPad to hide three geometric figures in the augmented reality environment.  When three shapes have been hidden, the first player passes the iPad to the second player whose task is to find the objects before time’s up (3 minutes).

It’s a great way to introduce elementary age students to the names of geometric figures.  Both 2D shapes and 3D solids are used in the game.  Synthetic speech is also used so students can hear directions and also the names of the geometric figures.

A list of geometric figures is shown at the bottom of the screen.  Students can scroll through the list by swiping left or right. A variety of shapes are available in different colors.

 cube cylinder hexagon rectangle sphere circle polyhedron pyramid square star trapezoid triangle

Students can place a shape in the Augmented Reality by tapping places on the screen.  The virtual objects ‘magically appear’ and can be viewed from various angles by walking up to and around the object.

Hide and Seek AR is easy to use.  Buttons are used to control most of the activity.  The app would be appropriate for most elementary age students.

Hide and Seek AR is available with a volume discount for educational institutions. Hide and Seek AR can be purchased worldwide exclusively through the Apple App Store.  It also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of Hide and Seek AR. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’ website for more information about this and other iOS and tvOS apps for education.

Other apps that use Augmented Reality are:

# Molecules AR

Molecules AR creates an Augmented Reality experience for view atoms and molecules in 3D.  While using the app students can tap icons to display the hydrogen, carbon, nitrogen or oxygen atom.  Protons, neutrons and electrons appear about 1 meter in front of the iPad came and can be experienced by moving forward, backward or around the virtual image.

To learn more about the atomic structure, students can tap the notebook icon to display information about the composition of the selected atom.

At the bottom of the screen there is a slider that allows the student to scroll through a list of atoms and molecules:

 hydrogen atom (H) carbon atom (C) nitrogen atom (N) oxygen atom (O) oxygen molecule (O2 ) nitrogen molecule (N2) water molecule (H2O) carbon dioxide molecule (CO2) ammonia molecule (NH3) methane (CH4) ethane (N2H6) acetylene molecule (C2H2) hydrogen cyanide (HCN) ethylene molecule (C2H4) formaldehyde molecule (CH2O) nitroxyl molecule (HNO)

Once selected a 3D model of the atom or molecule appears about 1 meter in front of the camera in the augmented reality viewer.  The model can be rotated on its x, y or z axis.  In addition students can walk up to the molecule and view it from different perspectives.

Molecules AR is available with a volume discount for educational institutions. Molecules AR can be purchased worldwide exclusively through the Apple App Store.  It also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of Molecules AR. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’website for more information about this and other iOS and tvOS apps for education.

Other apps that use Augmented Reality are:

# Geometry AR

When used in a curriculum based application, an Augmented Reality experience really pulls students into the subject matter.  There is a certain ‘magic’ about seeing and manipulating shapes that only you can see.  Geometry AR is an educational enhanced viewer for 2D and 3D geometric objects.  Here’s a screen shot illustrating an ellipse.

Notice the xyz control in the bottom right corner.  This icon causes the 3D shape to start rotating on the selected axis.  This enables the student to view the shape in unlimited orientations.  Students can view the various faces of geometric shapes.  Tapping the center of the icon causes the shape to stop rotating.

Using the slider students can selected a variety of 2D and 3D shapes. Optionally they can tap the dice to get a random selection. Tapping the notebook causes textual information about the shape to be displayed.

If sound is optionally activated the text from the notebook is read aloud to the student.

Geometry AR is available with a volume discount for educational institutions. Geometry AR can be purchased worldwide exclusively through the Apple App Store.  It also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of Geometry AR. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’website for more information about this and other iOS and tvOS apps for education.

Other apps that use Augmented Reality are:

# Educational Apps for Augmented Reality

With the release of iOS 11 Apple introduced several new exciting tools for developers.  One of them is a new framework called the ARKit.  ARKit is a set of tools that allow developers to create augmented reality experiences for iPhone and iPad.  3D digital objects and other information can be combined with the immediate environment.  Learning how to use this set of tools enabled me to create several new apps for iPad.

The first project is titled Solar System AR.  Once the app is launched, Solar System AR brings a 3D model of the Solar System right into a classroom or living room.

The sun and planets all rotate.  The planets revolve around the sun and the earth’s moon is shown revolving around the earth.  In addition, any planet can be selected using the slider.  Once selected, the planet appears in the augmented view.

Detailed information about each planet is displayed icons on the left side of the screen are tapped.

The length of a day on any planet is shown when this icon is tapped.

Students can find out a planet’s distance from the sun by tapping this icon.

Tapping this icon results in a table showing the dimensions of the planets in miles and kilometers.

A table showing the mass of each planet is shown when this icon is tapped.  Below is an example of one of the tables.

General information about the Solar System and specific information about each planet is available for students to read.

The Augmented Reality component of this app makes it very exciting for kids.  It is kind of a magical experience to have the Solar System appear in the immediate environment.  Students can walk around the room and move up close to any of the planets as they orbit the Sun.  Using the slider students can select any planet to study more closely.

Launch your students into the technology of the future by introducing them to the Solar System using Augmented Reality.

The Solar System AR is available with a volume discount for educational institutions. The Solar System AR can be purchased worldwide exclusively through the Apple App Store.  It also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of The Solar System AR. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’ website for more information about this and other iOS and tvOS apps for education.

Other apps that use Augmented Reality are:

# Interactive Life Cycles Explorer

I am fortunate to live on the Central Coast of California.  Every year we get to marvel at the amazing migration of the monarch butterfly.  These amazing creatures flock to eucalyptus groves in Pacific Grove, Pismo Beach and Nipomo.  Migration up and down North America is a part of their life cycle.  Even more amazing is the process of metamorphosis.  A satiated caterpillar forms a chrysalis, the organism’s cells complete disintegrate, and then reemerges as a beautiful monarch butterfly.

Interactive Life Cycles Explorer provides information about the life cycle of the monarch butterfly and five other representative animals.  Students learn the characteristics of each stage.  After studying the information about the insect’s life cycle, the student can demonstrate the knowledge of the content by taking a quiz or playing a word game.

Amphibians are amazing creatures.  They are able to live on land but spend at least part of their life cycle living in water.  Interactive Life Cycles Explorer provides detailed information about a typical frog’s life cycle.  Click on the amphibian’s icon leads the student into more detailed information.  Most of the content is illustrated with colorful graphics and the interface is designed to be like an information machine.  Sound effects are also used to add to the excitement.

Fish are an major food source for human beings, so understanding their life cycle is important topic.  This app explains a representative fish’s reproduction cycle.  Students using the app learn that fish, like many other animals, require that eggs produced by the female need to be fertilized by the male in order to develop into fish.  The will read about how in fish, usually the female produces a very large number of eggs, but most eggs do not survive to maturity.  There are many threats to fish eggs.  Changes in water temperature can stop development.  Fluctuations in oxygen levels in the water can also harm developing eggs.  Some eggs are eaten by predators or die because of a disease.

Like fish, the poultry industry is a major source of food for humans beings.  Information about the typical life cycle of birds is explained use a typical chicken’s life cycle.

For mammals, the app uses a mouse.  Mice are widely used in scientific research to study the effects of drugs, chemicals and environmental conditions, in order to better understand how these effects might affect humans.

Details about a mouse’s reproductive cycle is illustrated and labeled.  As students tap buttons they move deeper into the information and when they have finished going through the information, they can assess their mastery of information by taking a quiz or playing a word game.

Interactive Life Cycles Explorer is available with a volume discount for educational institutions. The app is available for iOS and tvOS.  Interactive Life Cycles Explorer can be purchased worldwide exclusively through the Apple App Store.  It is available through Apple’s volume purchase program.  Schools get a significant discount when purchasing multiple copies of Interactive Life Cycles Explorer. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’website for more information about this and other iOS and tvOS apps for education.

Other apps in the Interactive Explorer series are:
Interactive Earth Science Explorer
Interactive Plant Biology Explorer
Interactive Earthworm Anatomy