Kaprekar's Constant

 This number exploration, uses Largest, Smallest Four Digit numbers and practices subtraction. all an endeavour to find the Constant that many Four Digit Numbers end up at.

 

As the Card suggests all numbers will end up at the Constant within 1 to 7 steps.  I would challenge the students to see if there is one starting number that does not conform.

In the Classroom I would consider having 8 wall charts Labeled 1 through 7 the 8th Others!!  As Students check their four digit numbers and count the steps the record their discoveries on the appropriate chart.

Other students may wish to find out more about Kaprekar, who he was, what mathematical truths he found.

Prerequisites: Some understanding of four digit numbers and four digit substraction(or allow use of calculator) and possibly Flow Diagrams

 

Digital Roots, Patterns and Geometry

 I have long been an advocate of teaching mathematics from a known situation as well as in a context that helps students understand that mathematics is all around us.

We often do not connect Number with Geometry and Vice Versa but they are linked, intertwined, but we need to peel back a layer and see the connections.  I like the adage, "The Maths Behind The Door!" I encourage all teachers to help students find the connections.

Another area we do well, initially(Junior School) is with patterns.  We use shapes, counters and ask children to continue given patterns, create their own etc. This is a great foundation for exploring numbers later, but why do we forget patterns when exploring Number?

Digital Roots of numbers is a good way for students to practise their simple computation skills as well as look for patterns and then use them for Geometry explorations "Patterns in Circles" "Spirolaterals"

I hope these activities help you springboard the connections between Numbers, Patterns and Geometry.(There are more to come)

Indy Anna Jones and the Temple of Gloom

This activity seems logical to post as TV3 (NZ) is replaying the Indiana Jones Movies.

The idea was presented some years back at a conference I was attending, I have tweaked it for using with Teachers and Students I have worked with.

I hope you enjoy using this with your students.

Modulo Arithmetic (Clock Arithmetic) with an Art Component

 Modulo (clock Arithmetic) are Finite Number Systems, and for older students it is worth exploring a Finite System so that they may get a better understanding of an Infinite System like our Base 10(Decimal System)

Putting an Art Component with it, may encourage some reluctant mathematicians to become more interested and involved.

In the attached pics, I mention "Donald in Mathmagicland" (A Disney film 1959) I can remember showing often using 16mm film when I started teaching in '65. It gave me and my students a better understanding that maths is not just numbers but is intertwined in everything we do.

Donald in Mathmagicland

Other websites about Modulo Arithmetic for your interest and background information 

https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/what-is-modular-arithmetic

https://www.mathsisfun.com/numbers/modulo.html 

https://nrich.maths.org/4350   (this great Maths site, suggests students 14-18, I have worked with students 10+ on these activities. Often it is how the activity is approached)

Enjoy Exploring Modulo Arithmetic

An Interesting Question to follow on from a discussion about TIME

 This activity has been adapted from a Puzzle activity prepared by AIMS (Activities in Maths and Science) Fresno USA.

I can assure there are probably 3 solutions but students will come up with one or perhaps two.

Try it yourself first to see what you can come up with?

Counting Squares

Yesterday while entertaining my 6 year old grandchild we drew a picture with a number of squares on it. My question to him was 

• How many squares can you find? 
• His response was a cursory glance and counted the small squares but not the large one.
• With some help ad guidance he was able to start focusing on 1 x 1, 2 x 2, 3,x 3 squares.

I believe we need to do these types of visualisation Problems with all levels of students. 

Reaction Time

 A nice activity to help older Primary School students to check out how fast they can react, and whether through practise they can improve reaction times.

TIME: Loop Card Activity

 

Teaching the Analogue Clock!

 

I was somewhat dismayed when working with my grandchildren yesterday, that they (aged 6 and 9) could not tell the time from an analogue clock.

 

They are fairly fluent with telling the time with the digital clocks around the home, but not the Analogue. 

 

A short discussion with a quick drawn circle and placing the numbers then short and long toothpick, got them thinking about how to tell the time using this "round clock"

 

I don't believe we should discard the Round Clock at all, even though we are in a digital world, to me, it is like saying we can learn measurement by doing it all on a Tablet!

 

The Digital Clock is great for Telling The Time! but to be able to use this for measuring time needs an understanding of decimals to two places and the ability to add and subtract these decimals.

The Analogue Clock can be used to Tell The Time and it is easy to Measure Time by seeing how far the hands have moved, not much adding and subtracting required. 

 

 

Apart from Time, what else could the Analogue clock help with?

• Fractions: the obvious with 1/4, 1/2, 3/4  but what about twelfths?
• Counting in Fives: 5, 10, 15, 20.. 
• Geometry: Rotation, parts of a circle(semi-circle), degrees in a circle, angles(between hands)
  
• Finite Number System: This is called a Finite System as it goes from 1-12 and then back to 1 not like our Decimal System which is Place Value and Infinite

Whether we teach some of these higher level skills or not, what the students are getting is an intrinsic introduction to some of these.

After posting an abridged version of the above on three FB Sites:  NZ Teachers (Primary), Mathematically Speaking, Developing Mathematical Inquiry Communities (DMIC)  I was pleased to see so many posts including a number which suggested than older kids did not know how to read an Analogue clock.  I have to admit all were in favour!!!

Please check the posts out for other teaching ideas, a few websites I have attached below.

 Please Teachers, if there is not an Analogue Clock in your classroom please acquire one, and don't forget the wooden teaching clocks as well, OR get the kids to create their own!!

An Interactive Analogue and Digital

https://www.visnos.com/demos/clock?fbclid=IwAR1FB5PJEQakuEAZbriF4zVkdLNSjbzfQbNDNVUdUcVXIwtXxMZZdHKQOAs 

 

 One approach to using the Analogue Clock

https://bookunitsteacher.com/math/measurement/telling_time.htm

 

 An Australian Educator, uses a hoop

https://www.teachermagazine.com/au_en/articles/teaching-students-to-read-an-analogue-clock 

 

A New Zealand site that has teaching ideas(and worksheets) but also a Time Line of telling time including the Sundial

https://www.twinkl.co.nz/teaching-wiki/analogue-clock