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## Montessori addition trays: hands-on mathematics

A strong foundation in basic mathematical skills will set children up for later success. Too many children learn how to complete math problems by following a formula or method that they simply do not understand. They pass the tests, but when the difficulty of the problems increases, or they are presented in a different format than the one they are used to, the child flounders.

Teaching children using concrete materials (items that can be seen and handled) before moving to abstract concepts (problems worked out on paper) is absolutely vital to make sure they understand the connection between the methods they are using and how and why they work.

The Montessori method for mathematics is brilliant, especially for young children. It is very systematic and progresses from skill to skill in small steps, with each stage building on the one before to ensure understanding and mastery is gained before moving to the next step in the ladder. Concepts that are not covered in your standard state school math book are intentionally introduced and explained in a way that can easily be grasped by even very young children.

Many children seem to simply absorb these small skills along the way, almost accidentally, but the children who struggle with maths are usually the ones who never intuitively grasped the shortcuts, mental methods and other little tricks and understandings that their more successful peers just seemed to somehow “get” without direct instruction.

One of the foundational skills that later math problems build on is adding, subtracting, multiplying and dividing small numbers. Many children will make mistakes when solving a more advanced problem, simply because they make a basic error with one of these simple calculations. Spending time in the early years ensuring that children master their basic maths facts is a must for success and speed later on.

Here is a Montessori addition tray and some other Montessori inspired ideas for teaching young children to add small numbers, mastering their addition facts as they complete them.This is how our addition tray looks on the shelf. Only one child at a time is using it, so it is set up in such a way as to mark their individual progress. Every week or so I “test” their mastery of the addition facts and those problems that they are able to solve mentally (without thinking time) are placed into the screw-top container. They are pulled out for occasional review, but no longer need daily practise. This provides some intrinsic motivation as they see the pile in the dish growing smaller and smaller and the container getting fuller and fuller. They love it when we exclaim over how many they know now.

Initially, I split the facts into sets; plus 1, plus 2, plus 3  and so on and only have 1 set out at a time.  Once they know the sets fairly well individually, we combine the lot, taking out the ones they have mastered and working on what is left. Obviously, learning all the plus 0, plus, 1 plus 2 and plus 10 facts is very easy, so starting with these gives the child a boost of confidence as they quickly plow through the first sets, filling that jar almost immediately.

The activity is set out in the child’s workspace like this. The correct number of jewels are counted into the first and second dish, before both sets are scooped together into the final dish for them to find the answer by counting. It provides a very clear visual display of what happens when you add two numbers together.

Because some children will take a long time to recall all of the addition facts, I give them lots of different kinds of materials to count and present the problems in different ways. Here are some of the Montessori inspired, hands-on workjobs  that I have used with both my own children as we homeschool and in a classroom situation when I was a teacher.

These pegs are labelled with the addition facts and the pompoms serve as the counting material. Once the child has found the answer, the peg is clipped onto the correct segment of the paper plate. It is self-checking as there is only one peg for each segment – any double-ups means that they need to redo those pegs to discover the correct answer. The holder for the pegs is the centre from a used roll of masking tape.This was a favourite with my children. As always, making up a funny story to go with the activity turned it into something really fun. Those greedy restaurant patrons were at it again and the children had to figure out who’s cutlery was whose and put it into the correct cup. Only one knife, spoon and fork should be in each cup, so again, any double-up means that the child needs to redo the problem. The noodles serve as the counting material.This activity is very quick to make. The sticker cards are the manipulatives with problems written onto card strips. Once solved, each strip is placed into the segmented dip tray in top of it’s answer. Number stickers on the base of the 4 segment tray determine where each problem card is placed. The pegs are slipped onto the sides to count and solve the problem.The silver stars have the problem and the gold stars hold the answers. The child counts the jewels to solve the addition sum and matches the silver star to it’s mate.

Presenting attractive materials and a variety of experiences will make learning these basic skills enjoyable for your child and set them up for success in the future.

Other posts you may find useful:

Montessori tray activities for toddlers

Montessori counting trays 1 to 5

Homeschooling with toddlers and preschoolers

Teaching children to read – where to begin?

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