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# Progression in Number and Place Value

Created on 13 March 2013 by ncetm_administrator
Updated on 30 June 2014 by ncetm_administrator

# Progression in Number and  Place Value

## Introduction

This suite of videos demonstrates children developing understanding and fluency with number. Children from across the primary school can be seen developing confidence in understanding and applying key concepts, such as inverse relationships and place value.

## Counting in steps of one and ten

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

## Partitioning in different ways

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

## Using resources to develop fluency and understanding

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

## Partitioning

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

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29 March 2017 17:50
When children's misconceptions are addressed straight away, it makes it so much easier for them to make sense of new information as it will be adapltable to the knowledge they already have.
19 May 2016 15:25
When using resources for addition and subtraciton to develop their fluency and understanding the opportunity to explore misconceptions is great, and is allows children to develop an understanding of what they need to change to achieve the end goal.
11 March 2014 10:29
The use of place value counters is really interesting and a great taxtile resource.
06 November 2013 17:26
Looking at the addition of 2 digit numbers I never teach children to just put the bundles of ten together and the ones together and then to count them all as I feel this is not helping them to progrss their mental methods. I do lots of counting in tens from different points with equipment as a visual then we count on from the first number in tens then ones as this better supports what they do in their head to calculate. What does everyone else think?

I love the videos though loads of very clear teaching and fantastic use of resources!
26 September 2013 17:51
Place counters have transformed the way I teach mathematics!! Thanks NCETM :)
24 June 2013 09:13
Thank you for taking the time to share your thoughts and offer suggestions. The videos are not intended to demonstrate all the steps in progression and I agree concrete resources are important and the videos illustrate some such as pegs, bead strings and straws. I think various types of partitioning should continue side by side and the fourth video clip above we see older children doing this and also using both canonical and non canonical partitioning to support understanding of decomposition for subtraction. The important thing is that children maintain conservation of number when partitioning. There is also benefit of using a variety of resources side by side where one can support the other.

I agree that there is a danger that the 100 square can be taught as a trick, although taught well it can be a powerful image to draw attention to relationships and pattern in number. I think resources and representations in mathematics used by teachers who see with clarity the mathematical structures and concepts embedded in them can provide pupils with access to understanding the mathematics. The primary purpose of a representation is primarily to help children "understand" the mathematics, rather than just "do" the mathematics. There is a significant amount if research that identifies that one one of the key tools of an effective mathematics teacher is their ability to create and select representations in mathematics according to how they represent the concept they are seeking to teach.

Teaching mathematics is complex and I am grateful to the teachers who worked hard in single lessons to capture a variety of resources and activities in order that we might provide illustrations of how things might be approached. There is more than one way to teach mathematics and the New Curriculum encourages teachers to make their own decisions in how to organise the curriculum and try innovative ideas.
I really like your idea of the egg boxes as a tens frame and I am sure will use the idea.

We are now on to phase 2 of the video project, so more things to come!
24 June 2013 08:54
You can buy trays of 6x5 then cut them up into 3 trays of 2x5 to make ten frames. If it were possible to attach pictures or videos, I could show you pictures and videos of Nursery pupils using them to subitize numbers to10, as well as stating then demonstrating (by putting in another block or removing one) numbers one more than or one less than any number within 10. I have also used them with Reception pupils to get them to show 15 as being a full 10 and 5 ones, leading on to 20 and beyond, and understanding (and checking by counting) that 60, for example, will be 6 full egg boxes of 10.
23 June 2013 17:54
From the video it would appear that the partitioning has been taught in the wrong order: pupils should be taught to partition numbers to 10 and master these prior to being introduced to place value and partitioning numbers into tens and ones. When partitioning numbers we are breaking them up into (two) parts. e.g. 5 can be broken up into parts of 2 and 3, and this should be prior to addition and subtraction, which are operations on numbers. Partitioning of numbers into two parts can also include 0 and this can be done with very young children in Nursery and Reception when they are ready.

Much of the work appears to involve children at the pictorial and abstract stage, whereas they should first encounter all these topics with apparatus so that they learn in a concrete-pictorial-abstract sequence. The wrong answers that the children gave were all as a result of moving them to the abstract too quickly before giving them enough concrete experiences using apparatus. If we want our pupils to master number then we need to give them opportunities to work with appropriate apparatus and not go straight to the symbolic.

The stick was being used as a representation of the number line, which includes all real numbers - the teacher was pointing at the marks, not the blocks between the marks; surely a number track would be more appropriate at this level as it includes only integers?

The use of straws was good and children need to do lots of bundling and unbundling of tens. Egg boxes as ten frames would be really useful here as well. The order of introducing the Dienes blocks was back-to-front: children should meet the ones first, then make a ten stick, then replace the ten ones together with one tens stick, rather than meet the tens stick then relate that to the ones. Lots of work with unifix cubes prior to the Dienes blocks is essential as lower ability children do not necessarily abstract the concept that one tens stick is ten ones stuck together.

I would never use a 100 square. I feel that it is a trick to use when we have failed to teach place value correctly. As you go 'down' numbers get bigger and when you get to the end of line you jump to the start of the next one - first encounter with discontinuous functions? Listen to some of the things the pupils are saying and you might understand why I would not use one.