When learning about place value, an emphasis is placed on the column value of each digit. For example, the value of the digit 7 in 273 is 70. In this blog I will look at two ways to extend this understanding of place value. In the blog Seeing the Relative Size of Numbers I explain another important building block in children’s knowledge of number.
A child is asked to show 32 using dienes blocks. They get three tens and two ones. I ask the child to show me 32 in another way. Do they recognise that they can use 32 ones? Given two tens, I ask ‘How many more ones make 32? We see that 32 is also two tens and twelve ones.
This basic idea is the foundation for many place value investigations. For example, the I See Reasoning – Y5 question ‘How many ways can 0.42 be made using 0.1 and 0.01 coins?’ One of the I See Problem-Solving – LKS2 tasks also explores this idea: it’s one of the free sample tasks which can be downloaded from this page. The ‘build’ task introduces the idea of making 230 in different ways:
The main task presents this challenge:
There are ‘support’ and ‘explain’ tasks. Here’s the ‘extend’ prompt:
Of course, 423 can be made with four 100s, two 10s and three 1s. It can be made with 423 ones. There are so many combinations beyond that to be explored.
Another of my favourite types of investigations are ‘sum of the digits’ tasks – this blog gives an example from I See Problem-Solving – UKS2. Here’s how you can introduce a sum of the digits question. To start off with, present this question from I See Reasoning – Y6, but with part of the instruction covered up:
The correct answer is 102 and 98. Then the sum of the digits element of the question can be uncovered:
Children have to find ways to increase the digit sum for the 3-digit number without increasing its size too much (e.g. increasing the ones value), and how the sum of the digits for the 2-digit number can be reduced without making the number significantly smaller. Should the 9 be used in the ones column for the 3-digit number or the tens column for the 2-digit number? It’s one of my favourite tasks!
The blog Deepening Understanding of Column Value gives more ideas for how to develop children’s understanding of large quantities. I would love to hear from you if you use any of these ideas or questions in your classroom. I hope you enjoy getting to know your new class!
For information about NCETM-accredited training by Gareth Metcalfe, please visit www.iseemaths.com – bookings are being taken from Spring term 2021 onwards. Online training is available this term.