More Widgets

Once I got started designing the Math Widgets series I realized it was going to be a lot of fun.  The study of mathematics is an immensely broad topic and for kids who are really into math it is wonderful if a teacher can provide enrichment experiences that introduce new ideas and concepts that go beyond “what’s on the test”.  The Math Widgets series is a collection of tools with these kids and teachers in mind.

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Math Widgets III explores some special concepts in number theory.  For example, the Multibase Abacus piques one’s interest in alternative number systems.  What if we only had 8 fingers instead of 10?  Would we use a base 8 system?  With the Multibase Abacus students can investigate base 8 and any other base from 2 to 10.

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On the Multibase Abacus, numbers are represented by tapping beads to add or subtract values from the columns of various place value systems.  In the example below we are showing a base 5 system.  Starting on the right we have the ones place labeled with 50.  Moving to the left we have 5’s, 25’s, 125’s, 625’s etc.  Tapping one of the column labels results in a bubble showing the value of the place in base 10.  In the quiz mode students are challenged to represent randomly selected numbers in randomly selected bases.  Quite a few skills come into play when trying to answer the questions posed by the Multibase Abacus, including: estimation, addition, subtraction, multiplication and using exponents.

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Clock Arithmetic is another topic in math that is perfect for an enriched curriculum.  Whenever we divide two integers there is always a remainder (sometimes it’s zero).  Clock Arithmetic is a widget that encourages student’s to explore this concept which is known as Modular Arithmetic.  In programming languages there is a special operator used to signify the modulus function.  If a=7 and b=3 then in computer code a%b returns 1 since one is the remainder when 7 is divided by 3.  Sometimes the word ‘mod’ is used instead of the “%” symbol to describe this calculation, for example 15 mod 12 is equal to 3.  In the example below, tapping the 2 is the correct response.

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Once in a while, but rarely, you might find a newspaper article about a mathematician solving a problem or finding a proof that has been elusive for hundreds of years.  For example, the conjecture  that no three positive integers ab, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known to have infinitely many solutions since antiquity.  First conjectured by Pierre de Fermat in 1637, this theorem had been the focus of study by mathematician for centuries and was finally proven in 1995 by Andrew Wiles.  Goldbach’s Conjecture has never been proven. It was first posed in a letter from Goldbach to Euler in 1742.  The conjecture posits that every even integer greater than 2 can be expressed as the sum of two primes.  Use the Goldbach’s Conjecture widget to explore this idea by finding the primes whose sum is the given even numbers.

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The Hexagon Arithmetic Widget is a six number system that uses emojis as the symbols.  Counting moves in a clockwise direction around the hexagon.  The object is to complete the addition table using logic to figure out the pattern.

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Math Widgets I, II and III are offered exclusively by the iTunes App Store and sell for $1.99 each.  Educational discounts are available for schools.  Please visit our website for more information about these and other apps for education.

 

Math Widgets & Math Widgets II

There are two definitions for the term widget.  First, a widget is a small gadget or mechanical device that performs a useful function. In this context, the term is often applied to a device where the actual name is unknown or unspecified.  Second, a widget is an application, or component of an interface, that enables a user to do something special, for example perform a useful function or access special information.  Math Widgets fit both definitions.  The Math Widgets apps are collections of math tools that provide opportunities to explore a variety of important math concepts.  Some of the concepts extend the K-8 math curriculum laterally and therefore these apps are particularly useful for teachers who are looking to provide enrichment.

Let’s take a look and the first Math Widgets app.  This app is available for both iPad and Apple TV and includes four widgets: Slide Rule, Fraction Action, Integers and Coordinate Grid.

screen_1With the advent of calculators and computers, obviously the need for a slide rule has diminished, if not, virtually vanished, but what fun for kids to learn the basic idea of a slide rule by manipulating a virtual slide rule on their iPad or Apple TV.  In addition to representing the meaning of two fundamental math concepts: adding and subtracting,  the slide rule gives teachers an opportunity to discuss some of other historical tools used to help people do math for example the abacus or Napier’s Bones.  (See Abacus Deluxe and Napier’s Bones)

screen_2The operation of the Slide Rule widget is straightforward. The widget presents a problem in the middle of the screen and challenges the student to show the answer using the slide rule.  Addition and subtraction problems are presented.

screen_4The Integers widget uses a number line to help students understand operations with positive and negative numbers.  A problem is presented and the student is challenged to slide the marker to show the answer.  When slid in a positive direction a blue bar appears on the number line.  A red bar is used to show movement in the negative direction.  By using this app student will develop a better understanding of basic operations with integers.

screen_3Fraction Action provides an interactive widget for learning about equivalent fractions.  A fraction is randomly selected and displayed as a numerator over a denominator. It is also shown as parts of a circle.  The challenge for the student is to move the indicator along the fraction ruler to select the equivalent fraction.

screen_5The Coordinate Grid widget is designed to help students learn to locate points on a standard Cartesian plane.  The x and y axes and the quadrants are labelled.  The student is given a coordinate pair and is challenged to find the corresponding point on grid by moving a slider.

The first Math Widgets app seemed so useful that I thought I would do another one so I developed Math Widgets II.

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Math Widgets II has 4 widgets:  Multibase Chart, Arrow Math, Tinker Totals and Peg Puzzle Party.  While studying number systems other than Base 10 might not be a critical part of the standard elementary curriculum, it is a fun enrichment idea for teachers who are looking to extend the curriculum for certain students. Multibase Chart provides an interesting experience in representing numbers using different bases.

screen_2In this example the computer has challenged the student to represent 19 in Base 8.  The red slider has be moved to isolate all the possible two digit numbers in Base 8.  Since 2 x 8 + 3 = 19, the correct answer is 23.   The correct answer is located at column D, row C.  Tapping this cell results in a positive reinforcement message and increase in score.

screen_3Success in mathematics and many other areas of study involves the skill of being able to follow a specific set of instructions.  Arrow Math provides an opportunity to practice two skills, the ability to carefully follow a set of instructions and also the meaning of an inverse operation.  Arrow Math provides teachers with a visual way to talk about inverse operations which are important in the study of mathematics.  When using this widget ask students questions such as ‘What is the inverse of moving to the right?’ or ‘What is the inverse of moving down and left?’.

screen_4The Tinker Totals widget creates number puzzles where the object is to arrange number given into the cells of a pattern so that the numbers along each line add to the same sum.

screen_5Peg Puzzle Party is a logical thinking puzzle where the challenge is to end up with the least number of pegs on the board.  A move consist of pick a peg and jumping over another peg to land in an open space.  When a peg is selected the available moves are highlighted in green.  Peg Puzzle Party is a fun way to exercise your brain and can be used to help students develop strategic thinking skills.

Math Widgets and Math Widgets II are offered exclusively by the iTunes App Store and sells for $1.99.  Please visit our website for more information about these and other apps for education.

 

Mouse Maze Math

Some apps are just really fun to develop.  Mouse Maze Math is one of those apps!  For me the idea of programming a mouse to run through a maze is an old one.  I used to kid my programming students that we were going to see who could build the smartest mouse.  We would set out to  write programs where we used graphics to define a maze and then added a section of the program that would control a little red blip that represented the mouse.  The object was to write a program that would navigate the maze and eventually get the red blip to move to the yellow blip that represented the cheese.

Computers have come a long way since the days that I was working with 7th and 8th graders at the first computer lab in Ventura County.  I read in the news today that Apple’s new Mac Book Pro is 6.8 million times faster than the original one.  That’s pretty amazing and Mouse Maze Math is pretty different from what was possible back in the days when floppy disk drives were a new thing.mousemaze_title

Mouse Maze Math challenges students to answer arithmetic problems as they give navigation instructions to a mouse to enable it to run through the maze. It is available for iPads and Apple TV.  In the iPad version students tap  green arrows cause the mouse move in one of four directions: left, down, right or up. In the Apple TV version a student can either use the Siri Remote by swiping and tapping or use a game controller to control the mouse.

In the maze shown below some of the pathways are blocked by arithmetic symbols.  When these symbols are encountered a calculator-like device is displayed.

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If the student answers the problem correctly the mouse stays on the spot and the student can continue to solve the maze.

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Mazes are randomly selected and automatically displayed when the dice icon is tapped, but mazes can also be built by the students.  By dragging elements of the maze onto the grid, student are able to construct a maze.  Mazes built by students can be saved and retrieved at a later time.

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Mouse Maze Math is a fun way to practice arithmetic and also creatively use the iPad to design and construct mazes.  I’ve always believed in active teaching and active learning.  I hope teachers will enjoy using this tool with their students.  Teachers should let me know if they are interested in evaluating this app for use at their school.   I have a limited number of download codes for FREE evaluation copies of this app.   I hope that elementary students enjoy practicing basic math skills with this app and that this colorful interactive app will help them in their journey to become great problem solvers.

Fraction Builder

I submitted Fraction Builder to iTunes yesterday and it was approved in less than an hour!  It is so amazing to me what great service Apple offers to developers.  I certainly appreciate the way that the App Store provides access to my work to students and teachers all over the world.

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In most of my math apps I try to make them icon-based so that language skills are not critical for working with concepts.  Fraction Builder has a series of icons across the top of the screen.  Tapping each icon results in a specific function.

For example, tapping the red dice generates a random fraction.  Denominators range from 1 to 12.  Once the denominator is set, numerators can be any number that results in a proper fraction.

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When the question mark is tapped, a question is generated and displayed on a moveable note.  To answer the question students drag number tiles to make the fraction.  Usually it is best to start with the denominator.  If using this app in a classroom, the teacher should explain that the denominator represents the number of equal parts.  For this example, the student would first slide the three tile to the denominator position.  Next, the student should slide a one to the numerator position.  Once the numerator and denominator have been properly set, the students should tap the check mark.  When this icon is tapped the app compares the students answer to the correct answer for the question.

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A scoreboard displays student progress as they work with the app.  It shows the topic, number of questions attempted and the percent correct.  Quiz questions are based on three main topic areas:

• Naming Fractions

• Equivalent Fractions

• Comparing Fractions

Various other functions are performed when other icons are tapped.  This chart explains the other functions.notebook

I hope that teachers will let me know if they are interested in evaluating this app for use at their school.   I have a limited number of download codes for FREE evaluation copies of this app.   For some students learning about fractions is difficult.  It is my hope that this colorful interactive app will help them in their journey to master fraction concepts.

 

Classroom Spinners

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Teachers need lots of tools in their arsenal when it comes to teaching any subject, especially math.  The use of a spinner is a great way to introduce math concepts related to probability.  The Classroom Spinners app provides teachers with six different types of spinners that can be configured to have sections with color or no color.  The sections can be labelled with numbers or letter.  The sections can also be unlabelled.

Tapping the info button brings up a screen explaining the various functions of the app.

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The Classroom Spinners screen shown below is configured to have six sections.  Each section has a different color and the sections are labelled with letters.  Many different investigations of probability theory can be explored using this setup.

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For example, here are a few questions to ask the students:

  1.  What is the probability of landing on a vowel?
  2. What is the probability of landing on A,B, or C?
  3. If the last five spins were A,A,C,A,A, what is the probability of the next spin being the letter A?
  4. What is the probability of getting an B on the first spin and E on the second?
  5. If you spin 10 times about how many times would you expect the letter D to occur?

Tapping the sigma icon will display a table of the Experimental Outcomes:

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In this experiment the letter C was randomly selected 4 times.  The Theoretical Probability for any given letter is 16.7%.  What do you think will happen to the Experimental Outcome for the letter C if 90 more spins are performed?  Theoretically, how many times will C occur if  the experiment is run 1,000 times?

Classroom Spinners is a useful tool for teachers to have in their tool bag.   Check it out and let me know what you think.

 

 

 

 

 

 

Star Maze

Star Maze extends my series of visual problem solving challenges and is for iOS and tvOS devices.  Like Slip Sliders, Critter MatesThe Bird Puzzle, The Menagerie and The Hungry Rat, Star Maze is based on a grid where the object is to control a character’s movement to solve a visual challenge.  In Star Maze the characters position can be switched with a blocker and this feature is critical to solving some of the puzzles.  The character can move in any of the four directions, left, down, right or up but only stops when it encounters a wall or a target (star).

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Working to solve the Star Maze puzzles helps to develop logical thinking skills because the sequence in which the moves are made effects how many moves it takes to solve the puzzle.  The goal is to collect all of the stars in the least number of moves.  Star Maze differs from Slip Sliders because in Star Maze the character can switch positions with a blocker.  A blocker is a fixed wall in the maze that can only be moved by changing positions with the character.   In the screen shot show above the owl is the character and the black square is the blocker.

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Obviously by moving the owl straight up you can capture the first star, but now what?  Moving right and down doesn’t help much, but what about switching the character and the blocker.  Tap the switch icon and now the puzzle board looks like this:

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Now by moving straight up again, another star can be captured.

Solving the Star Maze puzzles can be fun and relaxing.  There is an Apple TV version so you can play Star Maze on your big screen TV with the whole family in the comfort of your living room. Star Maze is also available for iOS devices in the iPad family.  Try it out and let me know what you think?

If you like puzzles you might like Star Maze.   For $0.99 you get the iPad and Apple TV versions.  For more information about the Star Maze app, please visit our website. The app is available at iTunes.

Slip Sliders

Slip Sliders is the latest in my series of visual puzzles for iOS and tvOS devices.  Slip Sliders joins Critter Mates, The Bird Puzzle, The Menagerie and The Hungry Rat as visual puzzles designed to help develop logical thinking skills.

I’ve always enjoyed puzzles and so having the opportunity to design them is particularly rewarding.  For Slip Sliders, I needed a set of icons that could be paired up as part of solving the puzzle. Using Adobe Illustrator and Photoshop I created a set of birds.  It works great to draw the images large (512px x 512px) and then shrink them to the size of the icons.  By the way, I liked the birds so much I made a couple of coffee cups using the images.  The icons slide based on a particular set of rules.  They move in the one direction (left, down, right or up) until they hit an obstacle.  One of the tricky parts about solving the Slip Sliders’ puzzles is that sometimes you will need to create the obstacles in order to be able to change the direction that the slider can move.

Initially the puzzles are fairly simple and a solution can be achieved with just a few moves. Show below is how the first puzzle looks on an Apple TV.  Obviously the solution is simple, just move each of the birds on the left to the right and they will find a mate.  The birds on the left are sliders and therefore they can be moved.  The birds on the right stay in a fixed position and are the targets.

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In the second puzzle things get a little more difficult.  The birds cannot just simply be moved down because the first two need to switch columns.  I like this type of problem because the are multiple solutions.  If you are a teacher and use problems like this with your students you will find that one benefit is that several students can share different answers and it is not just the first student who finds a solution that gets the reinforcement.

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As you progress through the puzzles by tapping the right arrow, the puzzles get even more challenging.  For example, in the puzzles shown below from an iPad screen, how are you going to get the slider to stop on the red bird show in approximately the middle of the screen?

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If you like puzzles you might like Slip Sliders.   For $0.99 you get the iPad and Apple TV versions.  For more information about the Slip Sliders app, please visit our website. The app is available at iTunes.