What is Place Value?

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

1

10

1.0

100

10.01

1001

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.