How to teach 2-digit place value

In December last year I had the pleasure of meeting, chatting and presenting alongside US based maths consultant Robert Kaplinksy when he visited Melbourne. Robert has an excellent website called Open Middle that is wonderful for working on problem solving skills with F-8 students. As well as being super knowledgeable and passionate about maths education, he is most importantly a lovely person.

I first virtually 'met' Robert a couple of years ago when I completed his 'Ed Consultants Lab' workshop. This workshop came at the perfect time for me, as I had reached the point where I felt I needed expert guidance on expanding my consulting business, but (ironically) finding people to learn from in the Education space was very difficult.

As a side note, if you are an Education Consultant, I highly recommend checking out Robert's course (it is opening again on January 24, 2025).

Moving from working in schools or universities to being a consultant opens a whole new world and can be a daunting step. For me, learning from someone who has (and continues to be) working successfully in this space, about the short-cuts and pitfalls was incredibly valuable.  

After completing this workshop, one of my goals was to share my place value work with teachers not only across Australia but also across the world. Place value is the basis of our international number system, so it is a constant across the globe and something everyone needs to teach!

I have kept in contact with Robert over the years, asking a few 'consultant-related' questions along the way, and he has always been very generous with his advice and time. So, you can imagine how excited I was to present alongside him at a symposium in November last year. It really was a 'pinch me' moment!

Around that time I was super chuffed to be invited by Robert to create a mini workshop for his ‘Grassroots’ website.

Grassroots Website

Grassroots offers an impressive collection of workshops from education leaders in all curriculum areas in both Primary and Secondary contexts. It presents both ‘mini’ workshops which take approximately 2-3 hours to complete, and  ‘regular’ workshops which are 13-20 hours.

With the guidance and support of Robert and his wonderful team, over the course of this year, I have been putting together a mini workshop called “How to teach 2-digit place value”. 

The process to create the mini workshop made me realise how much I have honed my knowledge and understanding of place value teaching and learning over the years.

To create the workshop I worked with Robert to refine my content into a simple, coherent and practical series of lessons.

The workshop is designed for teachers who are introducing their students to 2-digit place value for the first time. So, in Australia this is anywhere between Foundation and Year 2 (with our 5-8 year olds).

The course is structured as follows:

Lesson 1: Why are my students not remembering what I have taught them in place value?

Have you ever taught place value and then come back to the ideas a few weeks later and it is like you are teaching something completely new? This happened to me over and over again when I taught my Year 1/2 students. At the time I didn't have any idea how of the complexities of place value for my students. I just kept thinking "I have taught this, why have they forgotten?".

So, in this lesson I go through what is place value and why the combination of it being an additive, positional and multiplicative system makes it so complex for novice learners.

Lesson 2: How do I know if my students are ready to learn place value?

We all know maths in hierarchical, however it takes a great deal of pedagogical content knowledge and experience to break down concepts and understand what pieces need to be in place before we move onto more complex ideas.

There are several key early number skills that I make sure are in place before I begin teaching place value. Counting skills, recognising numerals, subitising, making equal groups, and part-part whole are a few that are key. In this lesson I go through the link that these skills have to place value, and why a strong foundation makes you teaching of place value so much easier!

Lesson 3: Which numbers should I have students learn first?

We know that the order and sequence we teach skills in mathematics is critical.  In this lesson I discuss the models we often use to introduce 2-digit place value. Some models are more difficult than others (hello Base 10 blocks), and should be used after students have had experience with grouping items into tens themselves (e.g., with counters, unifix, straws etc). I also discuss the importance of starting with regular 2-digit numbers- such as 45- which follows the pattern of 4T (tens) then 5 (ones). Other examples are 67, 89 and non-examples of regular 2-digit numbers are 34 and 27. This lesson explores the regular and irregular numbers and how we can introduce them systematically to our students.

Lesson 4: Which numbers should I skip and come back to later?

Within the teaching of 2-digit place value (in English) there are numbers which are more challenging than others (teen numbers!). Being aware of these difficulties and having the language and models to explain these clearly is critical to ensure our students are avoiding common misconceptions like writing fourteen as '41'! In this lesson I share how we deal with teens (not teenagers but teen numbers- but if you have any advice on 'teenagers' I would welcome it! :))

Lesson 5: How can I best ensure my students remember place value?

 Retrieval practice is so important in our teaching and learning. One of the reasons our students seem to 'forget' place value is we are not providing them with enough opportunities to practice the skills we are teaching them. Another really important part of teaching place value is ensuring we are covering all of place value. My 6 aspects of place value provide a structure that helps to ensure we are teaching a variety of skills, which helps students to begin to see and make connections, assisting in their long-term retention of ideas and concepts. This lesson presents the 6 aspects and explains what skills we should be teaching within each aspect.

Lesson 6: How can I fit this into my already full math(s) program?

I understand that Place value is only one part of the maths curriculum you are teaching. However, I would argue that it is the most important part! So, if there is going to be an area that we need to spend more time on, it is place value! When I taught in the Year 1/2 classroom, we would teach place value for 3 weeks at the start of the school year. At the time, I thought this was a long time to teach place value. Looking back this was because I didn't have the PCK to appreciate how complex and how much time was actually required to embed the place value ideas. I now advocate for 6 weeks of place value instruction from Years 1-6 at the start of the year- one week on each of the 6 aspects. But even this is not enough...we need to constantly be coming back to place value ideas and skills throughout the year. This lesson explains some simple ideas to ensure we are providing opportunities for our students to retrieve their place value knowledge throughout the school year.

So that is a quick summary of my Grassroots mini workshop. If you are interested in taking the workshop you can click here to find out more information. The workshop will take you about 2.5 hours in total, but is broken up into short snippets of information, and quick practical tasks to complete. It costs $45USD, which as of today is around $68.59AUD. 

If you are in the US, the workshop provides you with one Graduate Level Professional Development Credit to the University of the Pacific - Benerd College and the University of Massachusetts Global (which I think is such an awesome initiative to reward teachers for online course completion!)

I am very thankful to Robert Kaplinsky for giving me the opportunity to share my knowledge and passion with teachers across the world, and I am proud to be the first Australian consultant on the Grassroots platform! 🦘

This week I encourage you to think of a professional goal to work towards in the coming year. Setting and working towards goals is an important part of us developing and pushing ourselves out of our comfort zone. I can vouch for the dopamine high I experienced when after many, many hours of work I achieved my goal and saw my workshop on the Grassroots website! It was definitely worth the hard work!

Have a great week!

Ange🎲🎓

 P.S. You can download the PDF version of this blog to print or share with colleagues here.