How to Use the Montessori Pythagoras Board: Multiplication Lessons and Extensions
The Montessori Pythagoras Board is a multiplication material used in elementary classrooms to help children explore times tables, patterns, square numbers and the relationships between multiplication facts. Rather than simply memorising answers, children can use the board to see how multiplication works visually.
I often use the Pythagoras Board after children have worked with the multiplication bead board, bead bars and multiplication charts. It is especially useful when a child knows some multiplication facts but still benefits from seeing the patterns and relationships between them.
This activity facilitates group work because it takes up so much room and because children like asking others for help so that they can complete the row.
In this task card, students have to put all the products on the board that are more than 30.
What Is the Montessori Pythagoras Board?
The board is a 10 x 10 grid. Along the top and left are the numbers 1-10. There are numbered tiles which are the products for each equation. The child places the product in the correct place. The board can be used alongside the bead bars where one child makes the product with the bead bars and the other child puts the product on the board with the tile. This is an excellent tool for helping students see patterns such as the commutative property.
When Should I Introduce the Pythagoras Board?
In Montessori we have many different multiplication resources. Not every resource will resonate with each child. This is usually not the first Montessori multiplication resource I use, however if you have an older 9-12 child who has transferred from traditional education I have sometimes found it a good multiplication resource to use alongside the checkerboard.
If you are following a more traditional Montessori sequence, the child will usually already have experience with the multiplication bead board, finger charts, bead chains and multiplication with bead bar
How to use the Montessori Pythagoras Board?
- Lay out the number tiles in order.
- Connect the board to earlier multiplication materials if needed.
- Choose one multiplication table to explore.
- Find and place the products for that row.
- Invite the child to notice patterns.
- Continue with another row or allow the child to complete the board.
- Provide a control chart for self-checking.
Some children may like to fill in the whole board. I provide a control or answer chart for children to use for this purpose, some of my students like to 'hide' the control chart and only refer to it when they really need to!
What Can Children Learn From the Pythagoras Board?
Multiplication facts
We know that learning basic facts are vital to help children solve more complex maths problems. The pythagoras board can provide one way to do this.
The commutative property
Show that:
3 × 4 and 4 × 3 give the same product. The child can see the symmetrical across the diagonal.
Square numbers
The diagonal is a natural place to notice 1, 4, 9, 16, 25 etc.
Patterns in multiplication tables
Children can look for:
- even/odd patterns
- repeated endings
- relationships between tables
- doubling patterns
- multiples
Extending the Pythagoras Board
I have made a set of task cards to help extend the use of the pythagoras board it includes ideas such as:
- Find all products greater than 30.
- Find all square numbers.
- Find products that appear more than once.
- Compare the 3 and 6 times tables.
- Find all even products.
- What do you notice about the diagonal?
- Find examples of the commutative property.
- Cover a row and predict the missing products.
Want Some Pythagoras Board Follow-Up Work Ready to Go?
I made these task cards because I wanted children to do more with the Pythagoras Board than simply fill it in and put it away.
There are 35 cards altogether and they encourage children to look more closely at multiplication facts, square numbers, the commutative property and the patterns they can see on the board.
I like using them for independent or partner work once a child is familiar with the board. They give a bit of structure without turning the material into another worksheet.
Frequently Asked Questions About the Montessori Pythagoras Board
What is the Montessori Pythagoras Board used for?
The Pythagoras Board is mainly used to explore multiplication facts and the relationships between them. I also find it really useful for helping children notice square numbers, repeated products and patterns between the different multiplication tables.
Does the Pythagoras Board help children learn their times tables?
Yes, but I would not use it simply as a way to make children memorise facts. One of the things I like about Montessori maths is that we can give children opportunities to see why the maths works before expecting automatic recall.
The Pythagoras Board gives children another way to practise multiplication while still being able to see the patterns and relationships between the numbers.
What should children use before the Pythagoras Board?
There is no single moment when every child must start using it. If you are following a fairly traditional Montessori sequence, children will usually already have had experience with materials such as the multiplication bead board, bead chains, bead bars and multiplication charts.
I am also happy to bring it out when I think it will help a particular child make a connection. Montessori sequences are useful, but the child in front of us matters too.
What can children do after they have completed the board?
This is where I think the board becomes much more interesting. Ask children to look for patterns rather than simply completing it over and over again.
They might find the square numbers, compare two multiplication tables, look for products that appear more than once, find examples of the commutative property or explain something interesting they notice.
Not Sure Where This Fits in the Montessori Maths Sequence?
Montessori maths has a lot of materials, and when you are teaching 6–12 it can sometimes be difficult to remember what comes before something, what comes next, and which lessons you have not yet introduced.
I made a free Montessori Maths Scope & Sequence to help with exactly that. I use it as a guide rather than a checklist because children do not all move through maths in exactly the same way.
Get the Free Montessori Maths Scope & Sequence →
Continue Exploring Montessori Maths
If you are working on multiplication and number understanding, you may also find these useful:
- Which Montessori Math Resource is right for me? Montessori maths is wonderfully hands-on, but the number of materials, lessons and follow-up activities can feel overwhelming, this blog post can help you navigate it!
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