numeracy leaders teachers Aug 17, 2023

Have you ever noticed that when a student counts there are critical flash points that indicate if they have a deep understanding of the patterns within of our number system? 

In Foundation you might see a student struggling with 44,45,46,47,48,49....(pause for 4 seconds)... 40 'ten'.

A common challenge for Year 1 and 2 students is: 107,108,109 (pause for 4 seconds)...200.

In this blog I wanted to share some of the strategies I use to help students to overcome this issue.

Firstly, I want to share with you a little about why this problem arises.

Moving forwards or backwards over any place value part is challenging. We call this 'bridging'. It is a skill students struggle with from very early in their counting journey, all the way through to Year 5 and 6 when they are required to count in decimal parts.

Bridging requires a really deep understanding of the unit we are counting by and the counting pattern that underpins this count (this is closely related to an understanding of place value).

Jumping from 109 to 200 is common thinking mistake amongst novice counters.

It is mostly because they haven't generalised the idea that the 1-99 counting pattern repeats within each hundred.

In my instruction I want to help them to see this pattern,

So, once we get to 100, I then count alongside them... I say "1 hundred and" over and over as they count from 1-99 to help them see that it is the same pattern that they already know, except they have to say "one hundred and" in front

(Correct me if I am wrong US teachers, but I think this is different for you, as you don't use 'and', you just say 'one hundred one') .

In Australia, we include the 'and', so my instruction goes like this...

Me: One hundred and

Them: 1

Me: One hundred and

Them: 2

Me: One hundred and

Them: 3

Me repeating the same count (one hundred and) over and over, quickly helps them to see that the only thing that is different in the count from 100-199 is we need to say "one hundred and" in front of the numbers 1-99...

Then, if they get to 109...and get stuck you can say...

"what comes after 9? 10... ok. So put your '1 hundred and' in front of '10' and keep the count going..."

We then move to do the same with numbers 200-300, then 300-400 etc.

Me: Two hundred and

Them: 1

Me: Two hundred and

Them: 2

Me: Two hundred and

Them: 3

Me Two hundred and

Them: 4 etc

This all happens in one lesson because I want them to see the 'big picture' of counting. It is short, sharp explicit instruction and it is one of my favourite lessons to teach as so many 'light bulbs' go on amongst students! 

I walk into the lesson and say 'by the end of today you will be able to count to 1000'. Many students look at me in disbelief, remembering how long it took them to learn how to learn to 99... but I say... maths is all about patters, we are going to see the patterns today!

When we help our students to be aware of the patterns, it is so powerful!

This week I encourage you to ask a student in your class what is the next number after any of the following numbers (49, 109, 1199, 10 099, 1.09- depending on where they are at in their counting journey)… and see how confident they are in bridging to a new place value part. This will tell you a lot about their understanding of place value and our number system.

This is a perfect example of a mini timely assessment, that won't take long, but will immediately guide your instruction! Formative assessment...tick... responsive teaching...tick!

Have a great week!


Want to learn more from Dr Ange Rogers? Click here to find out about her 'Quality Place Value Assessment in Years 3-6 Mini Course'

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