Does Your Child Really Understand Place Value? Montessori Place Value Questions for Ages 6–12

Teaching place value in Montessori is about much more than children being able to name units, tens, hundreds and thousands. Montessori maths materials such as the Golden Beads and Stamp Game give children a wonderfully concrete introduction to our base-ten number system, but children can sometimes become very competent at using the materials without fully understanding the value of the numbers they are manipulating.

In the Montessori elementary maths curriculum, children are introduced to large numbers and the four operations relatively early. It is quite common for a six-year-old to be adding four-digit numbers using Montessori materials. But there is an important difference between knowing how to complete an addition equation and having a secure understanding of place value. A child might know that they need to add the digits in the tens column, for example, but do they understand that they are actually adding tens? Can they recognise that 6 tens has a value of 60, that 5 hundreds represents 500, or that 490 can also be thought of as 49 tens? These deeper place value concepts become increasingly important as children move into larger numbers, mental maths, rounding, multiplication, division and decimals.

In this post I’ll look at some of the place value understanding that can sit underneath Montessori maths work, how you can check whether a child really understands the value of a digit, and ways to strengthen that understanding using Montessori place value materials and follow-up activities.

Our Montessori equipment is great for teaching place value. 

In Montessori we start quite early with 'big' numbers for example it is not uncommon for a 6 year old to be adding two four digit numbers together. However students aren't always able to articulate the place value of what they are adding. I'll give you an example if I gave the equation 

  4567

+2321

--------

to a student  and asked them what they were doing they would probably say 7 + 1 for the units, then 6 + 2 for the tens, then 5 plus 3 for the hundreds. This is different to saying 60 + 20 for the tens or 500  + 300 for the hundreds

Simply put value is about understanding the meaning of a certain number. In the number 4325 the 3 is in the hundreds place so its value is 300. 

Place Value also has other underlying concepts for example

- Is the student aware of embedded place value? For example 490 is 49 groups of ten or the number for 32 groups of ten is 320.

- Is the student aware of how a number such as 3489 can be broken down into its place value amounts e.g. 3000 + 400 + 80 + 9

- Is the student able to use place value to see patterns, for example 100 more than 2534 is 2634. Another 100 is 2734 and so on.

 

When could you teach this?

• This works best when naturally integrated alongside equipment. For example when you are giving a child an equation stop and ask them what the number means. 
• If this isn't practical when you are conferencing with a student you could talk to them then about it. 
• Having task cards with specific questions on them is also helpful. Students could alternate between traditional equation card questions and place value questions

 

My advanced place value task cards have questions like those above to help students learn these concepts. 

They work best with the stamp game or with the golden beads. However you can use them with any place value equipment you have. 

Where Does Place Value Fit in the Montessori Maths Sequence?

Place value is one of the foundations of the Montessori maths curriculum. Children begin by building quantities and understanding our base-ten number system with concrete materials such as the Golden Beads, before gradually moving towards more abstract place value work, written calculation and mental strategies.

If you are wondering what should come before or after this work, you can download my free Montessori Math Scope and Sequence for ages 3–12. It gives you an overview of the major maths concepts across the 3–6, 6–9 and 9–12 cycles and can help you see how place value connects with operations, fractions, decimals and later abstract mathematics.

Remember that a scope and sequence is a guide rather than a checklist. Children may move backwards and forwards between materials as they develop understanding, and the aim is always to respond to the child in front of you.

More Montessori Place Value and Maths Ideas

• Teaching Place Value Properly in Montessori – explore how Montessori materials can help children understand the structure of our number system rather than simply memorising place values.
• Teaching Maths Strategies in a Montessori 6–12 Class – look at how place value, partitioning, reversing and other strategies develop alongside Montessori materials.
• Teaching Rounding in Your Montessori Class – extend children's place value understanding into estimating and rounding larger numbers.
• A Montessori Scope and Sequence Is Not the Law – a useful reminder about balancing curriculum planning with following the child.

Once children understand what each digit represents and can confidently build, read and manipulate larger numbers, they are much better prepared for increasingly abstract work with the four operations, decimals and problem-solving.