Place value is so much more than just what digit is in each place.  It’s about the value of those numbers and how it relates to other numbers.  That sounds simple, but is actually hard to help kids develop.

This video is from a live training I did inside the Build Math Minds Facebook Group about a post that one of our members asked about how to help kids understand the value of multi-digit numbers instead of just the ‘place’ a digit is in.

Our textbooks do a disservice to place value because it is seen as this isolated skill.  We just do a lesson on place value. Those lessons are often just skills around place value.  But as I go through what we’re talking about today, I want you to be thinking about the ‘why.’   Why is it so important that kids understand that the 4 in 42 is worth 40?

So much of mathematics connects together, but it’s not taught in that way.  In this video I’ll talk about how we can build place value and how it connects to building your students’ number sense.

Watch the video or read the transcript below:

Here are links to products/activities mentioned in this vlog.

 Flexibility Formula Course

John Van de Walle’s and friends book, Teaching Student-Centered Mathematics PreK-2

Our language doesn’t help kids understand place value

One reason kids in the U.S. struggle with place value is that our number names don’t help kids see the value.  In some other languages, the number name for eleven is ‘ten-one’ so from the time the kids are counting they understand that the digits ‘11’ have a value of ‘ten-one’.  

So what are some things we can do to help our kiddos understand the value of multi-digit numbers?  You can emphasize the value by renaming the numbers when you are counting and explain to kids that you are ‘saying it silly’ to help them understand the value of the digits.  But that is just one way you can help them.

I believe Place Value and number sense go hand-in-hand to build students’ flexibility with numbers.

Place value is connected to the 4 Number Relationships

If you have been around here much, you know number sense is my thing, number sense is my jam. I really believe in building our students flexibility with numbers and that happens when we build their number sense and place value; understanding place value is a part of that number sense. 

There are four number relationships that come from John Van de Walle’s and friends book, Teaching Student-Centered Mathematics PreK-2.  They talk about how we need to develop these four relationships around all numbers up to 20. And I believe we need them for all numbers, even fractions, decimals. 

I go into lots of detail in my Flexibility Formula Course about these number relationships and how it builds flexibility for kiddos. So I’m not going to go too in depth, but I thought it would be cool to take a look at these four number relationships and how they really do help build place value for our multi-digit numbers:

• Spatial Relationships is about helping kids visualize quantities and how those quantities relate to each other.  There were lots of comments in the Facebook post about using Base Ten Blocks or some prefer DigiBlocks over Base Ten blocks, Dimes and Pennies, but my personal favorite is to use anything where you are Bundling/Unbundling because kids get to see the tens being built and that helps them they see it as 1 ten AND ten ones.  That’s hard for kids to see when you are using dimes & pennies.  Back when Box Tops were actually physical box tops, I encouraged teachers to collect those and have their class be the counters of those.  Now that those are all electronic, I would encourage you to collect the pop tabs on cans, have your students count all that get collected, and then donate them to a local Ronald McDonald House.
• One/Two More & Less is about instantly knowing what is 1 more or 1 less than a number and 2 more or 2 less.  That then becomes One/Two TENS More & Less and One/Two HUNDREDS More & Less, etc.
• Benchmarks of 5 & 10 is seeing how quantities related to 5 and to 10.   The benchmarks then become multiples of those.  So we want kids to see 53 as 3 away from 50 and 46 is 40 and a 6 but it’s also 4 more to the next Benchmark of 50.
• Part-Part-Whole is when kids understand that a whole can be broken into parts and it stays the same and that parts come together to create a whole.  We want kids to see 53 as a 50 and a 3 but it’s so much more than that.  Make sure to investigate all the ways you can decompose and compose numbers using 10s and 1s.  53 can be 40 and 13, 30 and 23, etc.  Because this is what they end up doing as they move into subtraction with regrouping.  Think about what happens when you do the algorithm for 53 – 19, we call it regrouping or borrowing, but basically you are unbundling. You are taking that 53 and helping kids understand that they can turn it into a 40 and a 13, because that’s easier to subtract the 19 from. 

Place value isn’t just about helping kids to identify the digits in their value, it’s just an overall building an understanding of what numbers are, how those numbers relate to other numbers, and then using that understanding to operate flexibly with those numbers. 

Think about everything that kids could do, if they understand how they can break apart numbers, especially along place value.  Addition and subtraction becomes so much easier if they can.  If they have built this understanding of multi-digit numbers around place value and number sense, it helps them to be able to think flexibly with numbers when they go to operate with them, then they’re not just reliant upon an algorithm or steps and procedures. 

If you want to see more about how building an understanding of place value and number sense impacts students’ fluency with mathematics throughout elementary and how to help build these ideas, go to https://buildmathminds.com/starterkit to request my Building Elementary Math Fluency Starter Kit.  The starter kit focuses heavily on building this understanding of numbers and operations for basic addition and multiplication facts but shows how that understanding transfers into multi-digit operations as well. 

I hope this has helped you build your math mind so you can build the math minds of your kiddos.

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