Montessori addition trays: hands-on mathematics

add tray C using IMG_8374A 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.adding tray jewels IMG_8361This 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.

adding tray set out IMG_8362The 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.

peg & pompom paper plate addition to 10These 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.cutlery noodle additionThis 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.sticker addition red sort trayThis 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. peg addition black 4 hole trayNumber 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.gold & silver start additionThe 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?

 

 

 

Teaching toddlers to count: 1 to 5 workjobs and Montessori style tray activities

Here are some more counting activities for toddlers and preschoolers who are learning to count from 1 to 5. If your child has learnt the number order by rote (ie. can count out loud to 5) and is beginning to develop one-to-one correspondence (matching one verbal number to each object being counted) then they are ready to start simple hands-on counting activities like these. You may even like to set out only the numbers 1 to 3 to begin with. If you are new to teaching toddlers how to count, it might be helpful to read this post first.

I ask the children to order the pie tins from 1 to 5 and sort out the golf tees by colour before counting each group and placing them into the correct pie tin. Use a number strip for young children to follow until they know the number order without help.

Kinesthetic learners (and all young children) love the hands-on style of these activities and despite the fact that  this group is far from my favourite set of tray activities, I included them to show you how a quick search around the house will furnish you with plenty of materials to set up your own.

This is one of the first counting activities I introduce. The shapes are sorted by type, matched to the example at the start of the row and counted into the bottle tops. Beginners will often just fill up the bottle tops without having any idea of the numbers, but I simply have them read the number and count the objects as we take them out and pack them away.

Unfortunately this workjob doesn’t photograph well but the shiny silver contact paper and blue jewels are very attractive to little ones. The box comes from a packet of plastic food wrap. The jewels are placed into plastic shot glasses which are numbered from 1 to 5.

I bought these secondhand metal goblets for our pretend play home corner because they are unbreakable. Pegs of many varieties slide nicely over the thin sides. Placing dots under the numerals means that children who do not recognise their numbers can count how many dots there are until they can recall the numeral name.

All my young ones have enjoyed hammering golf tees and other items into these polystyrene foam blocks covered with loose weave hessian-like fabric. The red washers come from a set of many shapes and sizes raided from Grandad’s shed with the numerals marked on them in permanent marker.

Chip and dip trays are handy for many different activities.These wooden numbers came from a baby puzzle toy and the items are an eclectic assortment from my Montessori materials drawers.

Pegging is good for fine motor development. The child counts the number of feathers on each peg and matches the peg to the correct number of dots on the card circles left from used sticky tape rolls. The box is just the storage for the feathers and rolls.

These beads and frame are a commercially produced toy that I picked up secondhand for a couple of dollars. Keep an eye out for this kind of material at op shops and swap-meets. The tiles are from an old game I bought for $2 at a secondhand store. I threw out the game and just kept the tiles.

Another commercially produced toy picked up for a couple of dollars with baby food jar lids for the numbers.

Montessori style toddler activities: transferring and one to one correspondence

Egg cartons are a cheap and readily accessible option with clear depressions for each object. A large object to transfer such as these stones or wooden eggs will keep a toddler well occupied.

One-to-one correspondence is an important foundational maths skill. Here are some ideas I have used with my older babies, toddlers and into preschool years.

What is it?

  • Saying one number to one object as you count (therefore the “one to one” correspondence.)
  • Children often begin learning to count by saying numbers out loud while pointing or touching objects, without those numbers actually matching up with the objects being counted.
  • Children also count the same object more than once or skip objects entirely.

    These super sized marbles are a favourite material in our house, even for the older children. They fit perfectly into this mini-muffin tray.

    Making activities:
  • One to one correspondence activities should be self-correcting; there are exactly the correct number of objects for the receptacle. Any left over or running out before all the spaces are filled signals to the child that there has been an error.
  • Start with large, non-slippery objects that fit easily into a scoop or are transferred by hand and move on to activities that require greater fine motor control.
  • Even older babies can experiment with one-to-one correspondence. Babies love to put things in containers and tip them out again. A freezer popsicle tray is fabulously enthralling for a child at this stage. They work especially well if no more than one object can fit in each segment, but this is not essential.

Popsicle tray and wooden dolly pegs. It’s surprising how something this simple can hold a young child’s attention.

A basic activity for babies.

Extending activities:

  • Keep interest by changing the way objects are transferred; by hand, with  spoons, scoops, tongs then tweezers.
  • Change the material to be transferred; stones, pompoms, pegs, jewels, plastic animals or anything else you can think of. Keep in mind the age of the child and be wary of choking hazards.
  • Change the receptacle used; bowls, baskets, tins, containers, iceblock trays, egg cartons, jars or any other container with a definite number of depressions.

Pompoms come in many different shapes and sizes and are a safe material for little ones. The worst mine have ever done is suck on them or pull them apart.

Using their hands to transfer large, easily grasped objects is a great beginning for babies.

This tray came out of our fridge. It is meant to hold eggs but to my knowledge has never actually done so!

Be careful with jewels. They are very attractive but also feel nice to suck and babies and toddlers do tend to out them in their mouths.

For older children using small objects that require greater fine motor control adds a little more challenge. Combining one-to-one practice with beginning counting is the next step.

Multiplication: Learning your times tables

Most of us will remember the days of practising our times tables over and over again until they came without a  second thought. As much as children often detest learning this skill it is nonetheless a very important mathematical foundation that will underlay so many of the more difficult maths concepts later on. If these simple multiplication equations are not mastered it will slow progress and make maths just that little bit harder.

With his in mind, here are some activities to drill the times tables that make it just a little bit more fun and will be especially helpful to those kinesthetic learners who need the hands-on experience to really lock these facts into their memories. They can be used as workjobs, shoebox tasks, Montessori style tray activities, work stations or simply as part of your every day maths programme.

This is an egg holding tray from my refrigerator with a cheap set of plastic ping-pong balls from the $2 shop. The multiplication problem is written on each ball with the answers in each circle on a piece of card taped to the back. The balls are simply matched up to the correct answer. (Children usually have no problem with 0, 1 or 10 times any number, so if there are not enough spaces I leave these equations out of the set.)

A paper plate has the answers written around the edge with multiplication problems slid into the end of plastic pegs. Children work out the sum and slide the peg on to the correct place.

The 7 times table is written onto wooden pegs with the answers on coloured contact stuck around the edge of a plastic container. Pegs are stored in the container when the activity is complete.

Small slots are cut into the top of each egg carton segment with the answers to the 8 times table written on each. Fat shaped popsticks (paddle-pops) have the sums written on each and are poked into the corresponding hole. The last segment has a larger hole to place al the sticks when the activity is complete.

Popsticks with answers are matched to the 9 times table written on an icecream container lid.

An empty container (lunchbox etc.) plus some pattipans and card circles are all that is needed for this activity. The patti-pans have the answers and the card circles have the 4 times table written on them.

Ziploc activity bags for toddlers and preschoolers

Noodle threading is always fun, just remember to tie one on the end to stop all the others sliding off while children are threading. When they have had enough of threading they can pretend to cook the noodles for dinner.

Ziploc activity bags are simply self-contained activities for toddlers, preschoolers and young children that include everything necessary for the child to complete the activity. Thus named because they are often stored in Ziploc plastic bags that are readily available from the supermarket. These bags have a plastic zip-style closing system that is easy for young children to manipulate, however we haven’t found them to be very long-lasting. Shoe boxes, trays or other containers are of course equally suitable but not so easily transported. Press-loc or snap-loc plastic bags are not as good because young children are not able to re-seal them independently, but if you don’t mind a few seconds to close each bag when they are done, they seem to last longer.

The kind of activity you can include is endless and their uses wide and varied. Some Mothers save them for school time activities while the older children require their attention. Others use them to take on holidays, while travelling in the car or when visiting with friends. They are useful for meals out in a restaurant, at home for mat time, blanket time, highchair time or table time activities. Whenever you need to keep a young child happily occupied these can be whipped out for hours of entertainment.

So what do you put in them? Almost anything really. Ideally they wouldn’t contain anything too messy if you want them to be easily transportable, but for home use anything goes.

Department stores have packs of paper shapes in the scrapbooking section which are great for gluing.

  • Glue stick and paper shapes for gluing

    When young toddlers first start to draw, tape one page at a time onto the table or highchair tray. For two reasons – it won’t keep slipping around and every page of the colouring book will not end up with a single blue line down the middle!

  • Drawing
  • Playdough
  • Stamping (stamp pads and ink stamps)
  • Lacing, threading or beading
  • Puzzles
  • Books
  • Construction toys
  • Pattern blocks
  • Stickers and sticker books
  • Small tea sets and mini teddies

    Finger puppets work best when the characters represent well knows stories that the children have heard you tell before.

  • Finger puppets
  • Mini whiteboard and eraser
  • Small chalk board and duster

    Simple stacking pegs are interesting once toddlers have the dexterity for it. This one kicked in at about 2 years when they could handle the quite stiff pegs.

  • Peg boards
  • Board games
  • Dot-to-dots and mazes
  • Colour-by-number
  • Stencils

You could include learning activities for basic maths and language skills. Starter Styles are a maths activity that cover a variety of beginning language and mathematical skills.

There are heaps of brilliant websites and blogs with an abundance of ideas for Ziploc bag activities;

Chasing Cheerios is one of my favourites with lots of wonderful toddler activities.

Natural Parents Network has some good ideas, including coloured pasta beading, pasta sorting, mini-books and stickers, lid sorting, playdough, cut and glue collage bag, and mini-playmats with cars and things.

Intrepid Murmurings has preschooler activity bags here.

There are lots of ideas for what they call “tote bags” here – just scroll down. They get better as they go.

Materials and storage for workjobs and Montessori tray activities

Plastic Chinese food containers fit neatly into my drawers and are a cheap and easy storage system for the items I use to make home-made workjobs and Montessori tray activities.

If you are setting yourself up for workjobs  or Montessori style tray activities for the first time there are unlimited numbers of materials that you could buy. Commercial Montessori products are beautiful but very expensive and particularly for the toddler and preschool ages it is relatively easy to make your own activities  for a fraction of the cost.

I generally source my materials secondhand form op shops, swap-meets and markets and buy the rest cheaply from discount variety stores or gather them from around the house. Each tray activity or workjob usually costs no more than $4.00 and many of the items can be re-used and presented with a different combination to make other “new” and interesting activities.

Some useful items to collect include the following:

Materials to count, transfer or manipulate:

  • Feathers
  • Buttons
  • Spools & film canisters
  • Jar & milk bottle lids
  • Pasta, macaroni, dried beans & rice
  • Corks
  • Sea shells
  • Popsicle sticks (popsticks)
  • Jewels & beads
  • Rocks, stones & pebbles
  • Straws
  • Fancy toothpicks
  • Golf tees
  • Stirring or cocktail sticks
  • Costume jewelry, bangles & strings of beads
  • Pipe cleaners
  • Rubber bands
  • String, twine, yarn, wool,shoe laces & cottons
  • Oversized metal or plastic needles
  • Paper bags, plates & cups
  • Plastic cutlery
  • Ribbon & bows
  • Hair clips & lackies
  • Magnets
  • Pompoms
  • Wedding favours eg. fake rings, mini doves, glass slippers etc.
  • Plastic & wooden pegs & dolly pegs
  • Dog clips, over-sized paperclips & other fasteners
  • Cardboard shapes
  • Number and letter tiles, cards & pieces from old board games
Materials for storage or presentation of trays and workjobs:
  • Glass, metal, china, cane & wooden bowls, trays, baskets & containers
  • Plastic tubs & lids
  • Cardboard tubes, boxes, egg cartons & food containers
  • Plastic containers & lids
  • Material/fabric scraps
  • Wood scraps
  • Shoe boxes
  • Ice-cube trays, dip trays & other divided containers
  • Plastic & glass jars
Utensils & tools for manipulating materials:
  • small hammers
  • Tongs, scoops, spoons & ladles
  • Tweezers
  • Measuring cups & funnels
Stationery:
  • Pens, pencils, textas, scissors & crayons
  • Glue, staplers, masking tape, sticky tape
  • Rulers, stencils, fasteners
If you have other ideas, please let me know and I will add them to the list.

Other posts you may like:

Montessori style tray activities; starting out

Montessori overview

Workjobs & learning styles

Highchair and mat activities: Montessori style practical life tong transfer activity for toddlers: Pom-poms, fruit and bugs

Over-sized pom-poms and tea bag tongs are a great starter set for tong transfer activities. The tongs are easy to manipulate and the pom-poms do not slip out.

As I have been tweaking my routine this week in readiness for our latest bundle of joy (now 3 days overdue!) I have been setting up some new tray activities for highchair time. Having toddlers on the loose while I breastfeed (especially when there are two of them) is a recipe for disaster. These activities can be used in a highchair, on a mat, for table time or for playpen time , however because I am introducing them to young toddlers and need to keep a close eye on them to begin with , I use highchair time.

Tonging is a simple practical life activity for toddlers and is excellent for fine motor control. Try to find small tongs that are not too stiff or your little ones may not have the dexterity to manage them. Tea bag tongs are easy to squeeze, as are ice tongs. Check your local opportunity shop (secondhand shops, $2 shops etc.) for supplies. Two containers and something to tong are your only other materials and usually with a bit of imagination you can find something around the house that fits the bill.

When I set up my trays I have a category for each kind of activity so that I can quickly change them over every couple of weeks without a lot of thought. Tong transfer is one category that I use and these are some of the examples I have set up in the past.

Slightly smaller pom-poms with the same easy to manipulate tea-bag tongs take the activity to the next level of difficulty.

The easiest first experiences are soft items like oversized pom-poms, cotton wool balls, balls of wool, or anything else that will not easily slip out of the tongs. Put only a few items in the container to begin with to encourage success as toddlers may quickly tire of the concentration and control needed to manage the tongs. Our “rule” with tray activities is that they should be completed before they are packed away so I want to ensure that the toddlers can be successful right from the beginning.

Larger and longer tongs are more difficult to use. These are still easy to squeeze but their length makes them more unwieldy to handle.The fruit are plastic iceblock shapes from the $2 shop.

A small set of salad tongs and a bag of plastic bugs were all that was needed for this tray.

The reality of young toddlers and tray activities is that they will have a limited concentration span and the interest shown for each activity will vary. I try to make each tray so that they can be easily completed in around 5 minutes. This means that if you want 30 minutes of highchair time to be well occupied, you will need around 6 activities. Some will be very absorbing for the child and they will complete and repeat them over and over. They will find some very challenging and perhaps even difficult and may want to spend less time on these. Reduce the amount of material on these trays accordingly. If you see that an activity is too difficult for the child to complete successfully, simply remove it and re-introduce at a later date. The perfect activity has a bit of a challenge but not so much that the child is frustrated by their inability to complete it.

Other posts you may like:

Mega marble transfer

An introduction to sorting

Bucket of giant beads transfer