What is Place Value?

What is Place Value_ (1)

Place value is the value of each digit in a number.  But what is the difference between a digit and a number? Well, a digit is a single number which forms part of bigger number whereas number is the collection of the group of digits.   So, if we take 563, the 5, 6 and 3 are the separate digits but, combined in this order, they make the number 563.  Place value is the understanding that the 5 represents 5 hundreds, the 6 is 6 tens and the 3 is 3 units.  As can be seen:-


What makes this hard initially is the pesky zero!  Look at these numbers







I am sure, as adults, we can agree they are all different.  But imagine being a child where you are still learning about numbers and being faced with this.  Suddenly, it is really very complicated.  By the time children are in primary 2 they are being asked to understand numbers in the hundreds.  Often in writing they can circle the biggest number or sequence a set of numbers.  They can identify the digit in the hundreds, tens or units columns.  Worksheet assessments will show all this clearly.  But as soon as you start playing with numbers and discussing them with children they can often demonstrate a shaky understanding of the concept.

Asking children to count or skip count (counting in jumps, i.e. 3, 6, 9, 12…) can demonstrate they stumble when they need to jump from one decade to the next (29 to 30, 59 to 60) or to the next hundred (99 to 100, 299 to 300).  When asked to write a number they may struggle to know exactly what column each digit should be in, writing 563 as 50063 for example.  Or when asked which number comes first out of 57 and 302 they may say 57 as the 5 is bigger than the 3, it didn’t relate to the value of where the digit sat.

If children do not fully understand the concept of place value in their early years then as they progress to harder mathematical concepts in primary 3 or 4 is all of a sudden can prove difficult. They need to understand this key concept to be able to add and subtract bigger numbers, to use times tables, negative numbers and more.

Every single child I work with for maths tuition have 1 single thing in common.  They all have a misunderstanding of place value.  Helping the child start to understand that 563 is the same as 500+60+3 helps them break it down and play with it.  We use a range of techniques and resources to help children understand this.  Once understood, children can then use this knowledge to add and subtract, multiply and divide and are less likely to make errors in their work.

The Journey Begins

Thanks for joining me!  Today we start the website and the blog.  But how exactly did I get into tutoring? Well, here is a little about me.

I was born and raised in the Muirhouse in Edinburgh back in the 1980’s.  Have you seen Trainspotting?  Well that is where I am from.  It isn’t a bad thing though, it taught me the grit and determination I have needed to succeed in whatever I have put my hand to.

My parents valued education, indeed my father was a teacher, yet I left school at 16 years old.  I was not, and to this day am not an academic.  However, in my early 20’s I gave up a job in a law firm to go to college and then onto the University of Edinburgh to study primary teaching.  I am now back at the University of Edinburgh, this time studying a Masters in Learning for Sustainability.  It was daunting to go back to uni when I am no academic, a Masters degree is for learned people, no?  However, I recently met a lecturer called Dr Sam Harrison who has completed his doctorate, runs a great sustainability residential project up north and was quite frank in saying he is no academic (though he really knows his stuff).  He is the first person who made me think maybe this wee lass from Muirhouse might just find her way through academia!

But back to the matter at hand, how I ended up a tutor.  My studies taught me that it is essential that learning is engaging and meaningful.  Indeed, my best grades at university have been those where could see a meaningful reason to study and take enjoyment in doing so.  The subjects I struggled with were those that were dull, where I was expected to learn facts and figures but could not see how they might relate to real life.  As a teacher (I am currently teaching a wonderful primary 6 class on a Wednesday) and now as a tutor, I keep that in mind.  With over ten years experience I still hold true to the philosophy that learning must be real, meaningful and most importantly, fun!

To me, tutoring gives me the best parts of teaching.  I get to work closely with children and their families to help them progress.  I get to challenge them and help them achieve things they never felt possible.  The children themselves are inspirational and it is a wholly rewarding job.  The biggest compliment I get is when parent’s say the confidence their child is developing eclipses that of the single curricular area and carries over into their entire lives.  Children seem happier, more confident and are willing to challenge themselves.

Good company in a journey makes the way seem shorter. — Izaak Walton