Plant and Animal Cells

Cell structures and functions are fascinating.  Like a complex machine microstructures in cells work together to support life.  Chloroplasts are tiny factories found in plant cells that are powered by solar energy and convert that energy into chemical energy that in turn is able to support all life on earth.  The Plant and Animal Cells app introduces students to chloroplasts and many other fascinating structures found in plants.

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In addition to plant cells, the app presents the key structures and functions in animal cells.  For example, the nucleus or control center of the cell.  The nucleus regulates the functions of other microstructures in the cell.

While using the app students will read about cell structures in both plant and animal cells.  Teachers will like the comprehension quizzes that are available for each topic. For example a fill-in-the-blanks style quiz prompts students to key in the missing word in a sentence.

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A true/false and multiple choice style quiz can also be selected as a follow-up to studying using other parts of the app.  Percentage scores for each quiz are reported on the screen.

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The section on cell reproduction explains the key steps in the process.  A diagram is used to help students understand the various stages.

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Plant and Animal Cells is available with a volume discount for educational institutions. Plant and Animal Cells 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 Interactive Plant and Animal Cells. 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.

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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.

 

Hands-On Math Hundreds Chart

Hands-On Math Hundreds Chart

When I was teaching elementary math in Southern California one of my favorite teaching aids was the hundreds chart.  I would burn up my photocopying budget reproducing hundreds charts so my students could color patterns showing the multiples of 2, 3, 5 or 7.  It really comes as no surprise to me that Hands-On Math Hundreds Chart is one of my favorite apps.  No longer is necessary to provides students with paper hundreds charts.  Using the app students just pick a color and a marker and then away they go marking patterns on the chart.

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The interface is intuitive.  The markers function like objects and can picked up and moved.  To complete remove an object simply drag it off the chart.

A Teaching Tool

So what can you do with a hundreds chart?  Which concepts can you teach?  One of the first activities to do with young students is skip counting.  Pick a color and a type of marker.  To count by 3’s, for example, begin by tapping the cell labelled ‘3’ and then continue to 6, 9, 12, 15, etc.  Eventually a pattern begins to emerge.  Perhaps some of your students will discover that the pattern for 3 creates diagonal lines.  Encourage students to use math vocabulary in describing their hundreds chart explorations.

But more can be done with a hundreds chart.  Marking patterns to show multiples of a given number is a great way to practice and learn multiplication tables and it is easy for teachers to check students work with just a glance at the iPad screen.  But there must be more that can be done with a hundreds chart.

Least Common Multiple

The reason the Hands-On Math Hundreds Chart app has 8 colors and 6 shapes is so that overlapping patterns can be created on the chart.  When kids start overlapping patterns things get really interesting, mathematically speaking.  Understanding Least Common Multiple, in my mind, is an essential skill for success in mathematics.  Using Least Common Multiple (LCM) students can reduce fractions to simplest terms.  LCM is the smallest positive integer that is evenly divisible by two other numbers, a and b.

Let’s define a as 3 and b as 5 (which also happen to be two prime numbers, but more on that later).  Here’s what the chart will look like after a pattern for 3 has been marked with a red square.

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Now let’s overlay the pattern for 5 with a blue circle.  Things are starting to get interesting…

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At this point a teacher would want to ask the students to find all the numbers that got both marks, the red square and the blue circle.  I would recommend that the students mark these numbers with a yellow highlight (transparent yellow square).

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Wow! Look at that the yellow highlighted numbers also make a pattern.  This numbers are the common multiples of 3 and 5.  Now study the chart and find the smallest number in this set.  15 is the LCM of 3 and 5.

Find the LCM of other numbers.  Just tap the eraser to completely erase the chart. Oh, and remember, if you only want to remove one marker just slide it off the chart.

A Classic Lesson

The first 4 prime numbers are 2, 3, 5, and 7.  In mathematics, the sieve of Eratosthenes is a pattern that reveals the prime numbers.  To investigate the pattern on the Hands-On Math Hundreds Chart, begin by marking the pattern for the number 2 and then we will mark 3, 5, and 7.  The procedure involves skipping the first number in the series and then marking out all the multiples.  So, skip 2 and then more out 4, 6, 8, 10, etc.  The chart should look something like this:

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Use a different color for each number.  Now mark out the pattern for 3, but remember to not mark 3 since it is also prime.  Continue by marking the patterns for 5 and 7.  If a number is already marked just skip it.  Since the next prime is 11 and 11² is 121 so not on the chart and we don’t need it for this experiment.

When the marking procedures are finished, the chart should look like this:

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The numbers that did not get marked are prime numbers.  All the marked numbers are composite numbers.

Get Creative!

There are lots of ways to make math fun using Hands-On Math Hundreds Chart.  Make up your own problem sets so that when the problems are answered correctly a picture is created.  For more information about this app click here.

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