## Montessori multiplication trays: Hands-on mathematics

Wooden peg-board (the kind you use to hang tools from in the garage) is a cheap and simple alternative to purchasing a multiplication board.

Continuing on with my mathematics tray ideas this week (introduction and addition trays here, subtraction trays here), here are some multiplication ideas for learning times tables. We made our own homemade Montessori multiplication board using pegboard wood for a cheap alternative. For another easier method using a rubber bath mat, see this post. While the Montessori multiplication boards are an excellent idea, my children found it quite tedious placing the beads into each little hole every time, preferring to use the blocks from our Math-U-See sets, MAB’s or other manipulatives instead.

Whichever way you choose to present multiplication, make it visual, tactile and concrete to begin with, before moving to abstract concepts. The following tray ideas are for children who already understand the concept of multiplication and simply need some more practise of their basic facts (their times tables) in order to commit them to memory.

Threading beads onto pipe cleaners (bend the ends to keep the beads from slipping off) is a home-made alternative to the Montessori bead materials. They become the manipulatives, with the multiplication problems written on popsicle sticks. The popsticks are laid out, making sure that the word “start” and all the answer sides are upright. The child turns over the “start” stick and uses the bead strings to solve the problem on the other side. They find the answer to that problem on the next stick and turn it over to reveal a new sum on the other side and continue on in the same way until they reach the “finish” stick. If at any time they turn over the finish stick before they have completed all the other sticks, it indicates they have made an error along the way.

Wooden MAB’s (multi-based arithmetic blocks) are the “old fashioned” mathematics manipulative that I grew up with. They can be used in place of bead chains for many math concepts. Here they are set out for learning the 10 times table (multiplying by 10’s.) The sum is on the left and the small circles show a running total, with the large circle answer at the end of the chain. A small pad is included for recording the answers.

These plates are actually set up for skip counting in the photograph, however with the addition of some multiplication problems, lend themselves very well to practising times tables.

Popsicle sticks with answers are matched to multiplication problems on an icecream container lid.

Popsicle sticks with the problem are slid into slots with matching answers on the egg carton.

A cheap (yet difficult) puzzle was a fun way to practise. Answers are written on the back board to match the puzzle piece with the corresponding problem. The puzzle must be difficult enough that the child cannot easily cheat by just following the picture, rather than working out the sums. (Not that any of your children would ever do that!!)

Plastic balls with problems are matched to the answers in an iceblock tray.

Pegs with problems are pegged on to the answer segment on the container, which doubles as a storage place.

Dice are thrown (you need 3) to create any combination of addition, subtraction or multiplication problem and the answer is covered on the board. The idea is to continue until all answer squares have been covered. This is for children who already have a fairly good mastery of their basic number facts and tables.

Each square container holds 4 little plastic shot glasses for practising the 4 times table. Jewels are counted into each glass and totalled to find the answers.

A plastic lunchbox filled with pattipan answers to match problems on circle.

The correct number of flags are inserted into the castles, with the castles showing how many groups.

Pegs are slid on to the matching answers on the paper plates. A manipulative is needed for working out the problems unless the child is able to complete them mentally.

Ping pong ball problems are matched to the answers in an egg holder from the fridge.

## Montessori subtraction trays: Hands-on mathematics

These Montessori style hand-on subtraction activity ideas are great for preschoolers and young children who need plenty of experience with concrete materials to consolidate basic mathematical skills. (See my last post for more info.)

As with the addition trays, the subtraction facts that  the child has already memorised are added to the screw-top jar to provide a visual indicator of their progress.

Initially, the subtraction problems are split into sets; subtract 0, subtract 1, subtract 2 and so on and only 1 set is 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. As with addition, learning to take away 0, 1, 2, and 10  is very easy, so starting with these gives the child a boost of confidence as they quickly master the first sets, filling that jar almost immediately.

The subtraction materials are set out as above. The first and last plate are deliberately different from the second to provide a visual reminder of the relationship between the two. Subtraction must be done in order (numbers are not interchangeable as they are for addition and multiplication problems) so the child first counts out the number of objects they are starting with into the first plate. The smaller plate shows what has been taken away (removed, subtracted etc.) and what is left on the first plate is scooped over to the final plate, providing the answer.

When the novelty of the plate tray wears off, I present the subtraction problems the child has not mastered in different formats to provide extra practise and revive interest in the activity.

Subtraction problems on pegs are pegged onto the side of the container with the correct answer. The counters are the manipulative. Provide more than one container or a multi-sided container if you want a broader scope of answers.

These subtraction cards are a set from Kmart that we were given. A dry erase marker can be used to mark the answers on the cards. The “glass” slippers are wedding favours. My girls love this activity just because they get to handle the tiny shoes! An attractive material will draw them in every time. Add an interesting story to the tray (How many spare slippers Cinderella keeps in her closet?) and you will have them begging to have a go.

The same subtraction card set paired with any manipulative of your choice gives you a fresh “new” activity. This time the children were doing the problems in their heads and finding the correct bead string for the answers – good for those who find writing a chore. There is exactly the right number of bead strings so if the strings do not match the last cards this alerts the child to an error that they can find and address.

It doesn’t take too much extra time or effort to keep learning engaging and enjoyable. Have a look around your house or check out your local discount variety store for a couple of different kinds of manipulatives and you are on your way.

Posts you may find useful:

List of useful materials to collect and buy for hands-on tray activities

Building focussing and concentrating skills in toddlers

Workboxes – homeschooling multiple ages

Surviving new babies, sick kids and interruptions

## 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?

## Arsenic hour and toddler meltdowns

Arsenic hour is that late afternoon time period where the short people in the household tend to have their meltdowns. Slightly hungry in the lead-up to dinner, tired from a day full of stimulation and unable to display the self-control necessary for “keeping it together” until dinner is served, young children (especially toddlers) tend to struggle during this time and easily tip over the edge. So how can we, as Mothers of young ones, structure our day to minimise the conflict and stress that is often experienced during arsenic hour?

Start by looking at your overall day. Who is in charge? You or your child? Who is making all the choices? Evaluate your overall day in light of this and see if some or much of the conflict is simply caused by you trying to get a reluctant toddler to do something they do not want to do after making their own decisions for the majority of the day. (See “choices” for a fuller explanation.)

Look at your routine. Do you have a flexible structure to the day with a good flow of events? It should include a mixture of time with Mum, time with siblings and time alone, physical activity, quiet time, structured play times etc. (See “routines” for ideas of what to include throughout your day.)

What time are you serving dinner? Are you expecting your young child to wait until Dad comes home in the late evening and trying to feed them when what they really need is to be getting into bed? Family meal times are a priority for us and very important, but if you husband is home later than is practical, consider feeding your toddler early and bringing them back to the table when Dad arrives for finger foods, a snack or a healthy dessert so that they can participate with the family. The bonus with this is that all your mealtime/manners training can be done on-on-one with the toddler, leaving the family table free from conflict.

Bathtime can be difficult if left until after dinner. There has been seasons when I have bathed all the younger children at around 4.30pm when they are still coping relatively well and are unlikely to get into conflict situations. I can then pop them at the table, in the highchair or on their mat, with a suitable activity to keep them usefully occupied on a worthwhile task while I am free to finish dinner prep and serve them their meals.

Do not test your obedience levels during this time. What do I mean by this? Do not give directions to your toddler and expect them to obey. Rather than say, “Junior, go and get into your highchair please,” simply walk over to Junior, take his hand and cheerfully state “It’s time for highchair activities” as you walk hand in hand with him to the chair, pick him up and pop him in. When it is time for Suzie’s bath, rather than say “Suzie, go and get your PJ’s and go to the bathroom”, you grab the PJ’s and walk little Suzie to the bathroom, undressing her and plopping her in the bath. Don’t forget to give a 5 minute warning before making these announcements.

Having a good routine throughout the day, coupled with these practical suggestions will help make this time as enjoyable as any other period in the day.

Other posts you may find helpful:

Getting dinner on the table

Activities to make for babies and young toddlers

Playdough for toddlers – no biscuit cutters please!

## Flower dolls for dolls houses

The last addition to our homemade dolls houses is complete. These peg doll style pipe cleaner and bead flower girl dolls are my favourite and were so easy that this whole set took only around an hour to make.

The method is exactly the same as the peg dolls in my previous post, with the only difference being that the flower dress clothes are made from cheap artificial leis. I just cut the string and pulled the flower segments off, sliding them up the pipecleaner bodies and hot glueing them slightly apart from each other to cover the body.

Because the pipecleaners are bendy, the girls can make the people sit down in the clothes peg furniture we created or take on any manner of positions and expressions. Combined with the shoebox dolls houses, they make a wonderful travel activity and are great for room time, table time or when you are out and about and need to pack something portable to keep little ones interested.

## Magnetic pompoms

Magnetic pompoms are a great idea for table time, highchair time, mat time, while travelling with children or any other time you would like a quiet activity for your toddlers or preschoolers.

Simply buy your pompoms and hot glue gun magnets on the back. I used the free flexible strip fridge magnets that come in the mail on the back of advertising.

For a sit down activity, use a small magnetic whiteboard, biscuit or cookie tray or any other magnetic surface. They could easily be adapted for sorting by colours and/or counting or simply combined to make creative pictures on the fridge as my daughter is doing in these photos.

My original plan was to use them with the multitude of “do-a-dot” pictures that can be found on the internet, so I printed out a stack and laminated them for durability. (These pictures have circles all over them that you can dot with bingo markers or stick on small stickers for a fine motor activity.) The fridge magnets however are not strong enough to hold the pompom on to the surface through the laminate so I am going to make a second set with stronger magnets for that purpose and leave these for free creating.