# 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. With 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) The 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. The 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. Fraction 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. The 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. 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. In 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. Success 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?’. The 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. Peg 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.