Making connections with place value (F-3)

As you probably know, I am very passionate about developing high quality place value instruction in schools. I think if we can help students develop a deep understanding of place value, it lays strong foundations for their future understanding in mathematics as a whole.

When I work with schools on place value, I encourage teachers to think about the connections they can make between place value and other areas of the curriculum. There are many connections, but sometimes it takes a little bit to see them- it is a little like a 'magic eye’ you sometimes can’t see them unless you look really closely! In this week’s blog I want to share some of the connections I see between place value and other mathematical content.

While many schools teach place value in Term 1, we tend to move on to teaching other areas of the curriculum in the remaining terms and sometimes place value is 'forgotten'. Place value is an abstract construct that requires a great deal of understanding, and is key to developing number sense, so the more connections we can make back to the work we introduced at the start of the year- the better.

Of course, it is very important that we are embedding the place value skills we have taught in Term 1 through our retrieval practice routines for the rest of the year. We want our students to develop fluency around these skills.

For example, if we explicitly teach our Year 3's reading and writing large numbers using the 'place value houses' pattern (one of my favourite place value lessons to teach) (see the relevant Clickview video I created for support on introducing this idea), we must provide many opportunities for students to practice this skill over the course of the year. This may be in the form of a Daily Review or other retrieval routines. If we do not do this, the skill of reading and writing large numbers will not transfer into our student's long term memory and we will find ourselves having to re-teach this in Year 4 (this is why the maths curriculum seems crowded- because we are trying to re-teach and fill gaps that have not been taught to mastery in previous years).

Retrieval Practice is one thing, however, David Ausubel's research talks about the importance of meaningful learning. We don't just want our students to have boxes of disconnected knowledge, ideas or skills sitting in their mind. We want them to assimilate their existing knowledge, make connections and create a deep understanding of concepts and ideas.

For example, if we are in Year 1 and we are looking at place value, one focus may be comparing numbers to determine which is larger or smaller. We could look at 16 and 61 and discuss the reasons why 61 is larger. For many novice learners coming to learn about place value, the positional property, where the value of each digit changes according to where it is located, is confusing. For them, both numerals have the same digits, so they appear to be the same value. 

It is not until they come to appreciate that '16' has 1 ten and 6 ones and '61' had 6 tens and 1 one, that they can begin to accurately compare.

Another important area of the Year 1 curriculum is in the measurement strand where we:

AC9M1M01
compare directly and indirectly and order objects and events using attributes of length, mass, capacity and duration, communicating reasoning

For me this is the perfect opportunity to bring back the resources we used to compare numbers in place value, but in the context of measurement.

You can see in these photos, how I asking the students to use streamers to measure their foot length, then using materials and resources we have used previously in the year in our place value instruction (number lines and bead strings) to make connections back to previous ideas. 

 Asking questions such as:

What number does your streamer reach on the number line? 

How many beads are the same length as your streamer?

Link back the ideas, resources and language we have previously explored.

Another example is in Year 2 when we look at Number Line in place value. Later in the year we can again look at number lines and link this with our work on fractions.

In Year 2 we look at:

 AC9M2N03
recognise and describe one-half as one of 2 equal parts of a whole and connect halves, quarters and eighths through repeated halving

While typically we think about exploring fractions in relation to shape (pizzas or pies), number lines provide the perfect opportunity to work on partitioning. This can then connect our work on place value and fractions.

Exploring 'halving' of number lines, then using place value to determine the value of marks on the number lines is a very important skills for students to develop. It allows them to see the connection between learning that 'half of 10 is 5' and how this applies to a number line. As you can see below I like to teach further connections by exploring half of 0-10, 0-100 and 0-1000 number lines at the same time. This also helps students to see that they don't need to learn every maths fact that exists, if they know half of 10 is 5, that helps them with half of 10 tens (100) which is 5 tens (50) and half of 10 hundreds (1000) which is 5 hundreds (500) . 

One last example of a connection we can make with place value is through renaming.

In Year 3 we look at:

AC9M3M03
recognise and use the relationship between formal units of time including days, hours, minutes and seconds to estimate and compare the duration of events

 This provides the perfect context to explore renaming.

When we rename the value of the number does not change. So we can rename 45 as 3 tens and 15 ones, and the value remains as 45.

We do this all the time (pun intended) in time.

We rename 120 seconds as 2 minutes.

We rename 7 days as one week

We rename 365 days as one year (non leap year).

So when we are looking at this measurement description in Year 3, we can and should be referring back to our work in place value on renaming.

Asking things such as:

Which is longer 2 days and 4 hours or 50 hours? Let's start by renaming the 2 days and 4 hours as just hours.

In this blog I have provided three simple examples of ways we make connections across the mathematics curriculum to help our students make links and develop a deeper understanding.

I encourage you this week to take a few moments to consider where you might be able to make connections for your students in your planning. Seeing and hearing ideas in a slightly different way or using a familiar representation in a new context is an excellent way to help our students to anchor their knowledge to prior knowledge and create longer and stronger knowledge.

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