Counting up to 10

Spring Counting Pack

I made a spring counting pack for Zany with lots of montessori based tasks, she really appreciates a bit of colour and prettiness. The pack has got about 5 activities in it all based on numbers one to 10. However some of the activities can be used in multiple ways such as the number cards and the flower making mats, which allows you to use pom poms, buttons or playdough. If you would like to purchse the pack you can head on over to my Teacher Pay Teachers store. Simply click on the widget:

 

There are number of different activities like sequencing, one to one correspondence a game and the Montessori Memory Game which is excellent for recall of numbers and amounts.

set up on tray

This is the number sequencing task, where you have to put the flowers in the correct order accorging to their number by glueing them on a strip.
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This is the completed task, with all of the flowers glued in the correct order.

The next task in the pack was to make a booklet of ladybirds with the nubers one to ten, zany had to add the correct amount of spots to each ladybird.

Dynamic Addition

Dynamic Addition in Montessori means exchanging or carrying on numbers during an addition sum. This process as with all Montessori concepts starts with the concrete material in this case the Golden Beads and then moves to abstract materials using simply pen and paper and no manipulatives. In between there are various other materials that can be used to aid this process such as the stamp game, and the small or large bead frame.

Nuh has been able to perform quite large addition sums since his was about 5 using this method, and moved to abstract at about 6. However I have found that he constantly needs refreshing on these concepts otherwise he forgets. I think that this is because Montessori Maths uses a spiral approach to teaching and not true mastery. It is something that I am thinking deeply about at the moment any way. This is a piece of work completed with the manipulatives notice how he is not carrying the numbers on by writing them on the sheet. This is because he can simply count how many units, ten bars, hundred squares and thousand cubes he has by changing them out for each other as required.

We use the stamp game paper for Dynamic addition sums, as it is easy and is colour coded if you need that, Nuh does not I have used black and white versions and he can perform the sums the same. He definitely has a solid grasp of place value, even if he does not recognise that term for it. It is important I feel to note that when beginning carrying forward or dynamic addition you start with the Golden bead material then slowly move to abstract using smaller sums than in the thousands. So you might start by using sums that only include 10's and units, alternatively you can start by only exchanging one column at a time, so the units. When this is accomplished with ease you can then add in exchanging of the 10 column, then 100. The point is to start slow and build up, don't just go straight in with a full exchange of all three columns.

Moving towards Abstraction 

The stamp game uses coloured wooden squares with a value printed on them, instead of counting out beads to make your addend you simply count out the number of tiles you need to each column. In the example below, Nuh has two addends 3456 and 1235, he needs to find the total obviously. It is good practise to use a ruler between the two addends, however we used the lid of the box and a clipboard to differentiate.

When both addends are laid out it is time to put them together, just like you do with the golden beads.  You can then count each column starting with the units and make the necessary exchanges:

Notice how the units column has more than 10, Nuh counted up to 10 then moved the 10 tiles to one side, he then put them back in the box and retrieved a 10 blue tile.

Now all the exchanging is complete, in this instance just one exchange, he can write his answer on the paper.








Abstraction 

In the picture below he completed this work without manipulatives, so he has written the number that he is carrying forward in each column. He has a solid grasp of the fact that once you have more than 10 in any column you must carry forward.

Montessori Order of Maths Presentations 3-6

This is the rough order of the Maths presentations for Montessori 3-6, I say rough because you will always get a slightly different take depeding on which album you follow. This post was prompted by a chance conversation with a friend who was not sure how to proceed with Montessori Maths, I remember this all too clearly at the start of my Home Ed journey as Montessori is not like anything I had ever come across before. Matters are also complicated if you cannot set out a full range of materials through lack of space or for any other reason. To understand Montessori maths you need to know that the Maths materials are grouped into categories some sequential and some paralell. The reason for the paralell or spiralling nature of Montessori Maths is that there is some obvious overlap of concepts and some concepts and exercises need knowledge from another group in order to progress.

Group 1: Numbers 1 - 10


The first section of Montessori Maths in my Album, deals exclusively with numbers 1 - 10. It starts out with the number rods, this includes the concept of one more and one less. Next you would present the number symbols and use them with the rods. After that you would progresses to using counters or objects with symbols this is mainly one to one correspondance work and you can use virtually anything for counting. Finally in this  work you would complete the making of 10, 9, 8, 7, 6 etc... you would also complete subtraction of the numbers 1 - 10.
In summary this section involves one to one correspondence, sequencing the symbols 1 to 10 correctly, recognising  and learning the symbols for numbers 1 - 10 and adding and subtracting numbers 1 through 10. Basically knowing the number facts 1 -10 this is the foundation of the decimal system. This group is sequential and the child must have totally mastered the concepts before proceeding to the next group.

This is the only time that you would focus soley on one area of maths, all throughout the rest of the album you would normally work on two or three different concepts like the Decimal system, linear counting and addition. However there is a caveat with the next group.

Materials used in this group are: Number rods, sandpaper numerals, counters and numbers, spindle box,

Group 2 : The decimal system

As the  decimal system  is based on 10 all the knowledge accquired in group 1 will now be used to understand the hierachy and system functions of the decimal system. Simple computations will also be covered in this section. When the learning of the decimal system is well underway you will introduce the Third Group, so you will begin giving paralell exercises.

Materials used in this group are the Golden Bead Material, large number cards, stamp game, dot board

Group 3:Linear counting

Linear counting involves learning the number and values 1 -1000 it also covers skip counting. Learning values up to a thousand will greatly assist with the childs understanding of the larger numbers involved in the decimal system.

Materials used in this group are: short bead stair, teen boards, snake game, 100 chain, 1000 chain, 100 board, squaring chains 1 - 10, cubing chains 1 -10 

Group 4: Arithmetic Tables

The fourth group teaches the child to memorize the arithmetic tables, this again is a paralell group and can start to be introduced in the later stages of the decimal system and linear counting.

Materials used in this group are: dot board, addition strip board, subtraction strip board, addition snake, addition charts, subtraction charts, multiplication bead, mulitplication board, multiplication charts, unit division board, division charts.

Group 5 - Abstraction 

This group again is paralell and overlaps with the other groups and is often referred to as the 'passage to abstraction'. In this group the child will start to recognise that they can complete the calculations more efficiently without the materials, however in order for this to be accomplished they need to understand the process of each form of arithmetic and know the tables of each operation. So they know the number facts for 1 -20 inside out and can quickly subtract or add any number 1 -20, similarly they must know their times tables. It is important to note that at the start of this work they may only know the addition tables as they may still be working on the subtraction tables from group 4.

Materials used in this group are: Small bead frame, Wooden heirarchial Material, Large bead frame, Racks and Tubes.

Group 6: Fractions 

Typically this group is started when the passage to abstraction has begun

Materials used in this group are: Red fraction circles, fraction lables.

I hope that this helps.xx

Static Addition

Static Addition

We have been working on static addition for some time, we started out with the golden beads using multiple add ends. I followed the Karen Tyler album for these lessons. You start these lessons using multiple add ends, so you start adding numbers in the thousands together first.

This is one of the sums that Nuh did at the beginning of this process, when he was still using the golden bead material:

I used to write out the sum for him on paper using the correct colours for thousand, hundreds etc.. I know you are meant to use the number cards for this but I prefered to do this as it makes more sense to me, especially as we will be moving onto written sums eventually.

I cannot remember how long we did the static addition like this for, it was a good few weeks though. Once he felt that he had mastered it, he asked to do the sums with out the manipulatives. This is known as moving from concrete to abstract and is the goal of the album. I purchased some static addition sums from the Montessori Printshop. They were cheap and good value for money, I feel.

Numbers 1 to 5

I have decided to start teaching Zuh some basic Maths concepts, she is still only 4 1/2 so I will only be doing Maths and Adab/Habit training, no phonics or anything else.

Some of the first lessons in the Karen Tyler Maths album relate to the numbers one through ten. The first lesson deals with quantity, then symbol, then quantity and symbol together. I didn't really document this with Nuh, but Alhamdillah, Zuh is chomping at the bit (sensitive period) for numbers and counting. So I am going to document activities as we go, I didn't bother buying the official Montessori counters, and wooden number symbols. Instead I used some wooden numbers from 'The Range' and a variety of objects for counting, I will now reuse these with Zuh. One of the cheapest and best counters in my humble opinion are the glass nuggets you buy in the garden centre, I do believe you can buy them in a lot of pound shops as well. I like these because they are not too fancy as to be distracting but they are lovely and tactile and my kids anyway seem to love them.

Zuh can already count out individual objects 1 - 20 but can only recognise number symbols 1, 2, 3 and 4. So obviously I will be concentrating on teaching her the symbols for each number one to 10 this will involve lots of counting, which she loves.

Lesson 1

Even though the Zuh can recognise the numbers 1 - 4 I wanted to give her something that she can easily accomplish for her first lesson ( self esteem building and all that, also as this was her first ever lesson I wanted it to be a success)  so I thought we would do three activities around this. The first activity was to correctly identify the symbols for 1 through to 4. I made sure that she could recognise them without any mistakes, so I did a simple presentation by laying each number out and naming it, then I pointed to them into sequential order and asked her to identify them. Lastly I mixed them up so that they were out of sequential order and then pointed to them and asked her to identify the number. She did all of the above without any problem.

I then let her decorate the numbers.

Next I took an activity straight from the Karen Tyler Album involving stickers and counting. Basically you set up a piece of paper with the numbers on that you are presenting, and some stickers on a tray. The task was to simply put the correct amount of stickers in the correct number column. Simple but effective.

Lesson 2

This lesson was all about 5, I wanted to focus on this number individually as she sometimes confuses it with 2. So I did not do a traditionally Montessori presentation of 3 numbers, we just did 5. I started the lesson by reviewing yesterday's learning. I then got out the wooden number 5, I placed it in front of her on the tray and said "this is the symbol for 5", I then got her to trace the number with her finger and say 5. Next I got her to decorate the number 5.

After she had decorated the number 5, I gave her a number of activities that involved counting to 5 and sequencing. First I made a sticking activity, using a grid format. Basically she had to stick the right amount of circles in each row to correspond with the number. I had originally planned to use pom poms with this task, but decided that coloured circles would be better as pom poms don't stick very well.

This is the tray set up

This is the completed activity

The next activity that I had prepared was hole punching the correct amount of holes into each card. Zuh really liked this as she has never used the single hole puncher before so it was a novel for her.

After that she completed a counting task of a one to one correspondence. The activity was to put the numbers in sequential order and then count out the correct amount of pom poms onto each card.

Finally she completed a number puzzle, where she had to look at the numbers on the bottom and put them into sequential order in order to complete the puzzle.

You can download the activities that I made for Zuh by clicking on the link below the image:

COUNTING 1 - 5

Teens

Learning about teen numbers

The Karen Tyler album, starts out with quantity. I fetched the coloured bead stair, and 9 golden bead 10 bars over to the table. Now the magic I absolutely love the way that this done, take one of the 10 bars and put it vertically in front of the child and then get the one bead from the coloured bead stair and put it next to it, and say " Ten add one is eleven". Wow so simple and so completely understandable. Repeat this with all of the teen numbers up to 19. Nuh totally got this straight away as I knew he would, Montessori maths is totally brill....

Completed work

Over subsequent days I then reinforced the concept a few more times by having Nuh replicate the work with the beads. Once he had mastered the quantity element I then wanted him to be able to identify the written numbers. I used our homemade teen boards for this and followed the presentation in the Album. (sorry no pics of this)


 I then set up a number of activities for him in order to solidify the new concepts. I made a tray using the teen number cards that I made, some animal stampers, and a few sheets of paper divided into columns. basically he had to take one of the cards turn it over and place it on the tray or in the dish, then stamp that many animals into the column. I did not put the cards in sequential order as I knew he would catch on to this quickly and stop looking at the symbol.

 Here is another activity that I created its a worksheet that reinforces the concepts, Nuh had to count the beads and the draw a line to the correct number. You can download a more ascetically pleasing version by clicking on the link below the picture.

TEEN MATCH WORKSHEET

I wanted Nuh to work on writing the number symbols for each of the teen numbers, he really dislikes writing of any sort even numbers, SubhanAllah. So I made this worksheet for him basically he had to read the number then trace it twice,then write it independently. Again I have made a better version of the sheet, click on the link below the picture

Teen, trace and write

Adding to 10

I made a tray for 'Making 9' knowing how he hates any kind of writing at the moment, I designed the task so that he would only have to choose the correct number sticker from a selection of numbers on the tray. I know he quickly identified that all of the sums would make 9, however he still then did each one on his own by counting out the objects that he had chosen for the work.

Making 9 work

Whilst Nuh was busy working, 'the Zuh' was busy attaching some magnetic letters to the fireplace and then taking them off again. Hey what ever floats your boat!

Oooh magnets!

Maths, first lessons

More than and Less than

A wonderful sister I know pointed me to a site called 'Littlest Scholars' which had this idea for teaching more than and less than. Basically you use a crocodile to teach the concept, the site had a set of free cards with numbers and the more than and less than sign for number 1 - 20. I made up the cards then using craft sticks, my trusty glue gun and some other materials I  made up some crocodiles. This is what the work looked like on the tray, I should point out that the more than crocodile on the cards would have been in the glass dish as would the other ones:

The cards with the numbers and a space to put the correct sign, a dish with the signs in and two crocodiles to remind you

I showed Nuh how to use the two crocodiles on the table to eat up the numbers and to then take one of the number cards and read it by looking at the second number first and saying is '2' bigger or smaller than '4'. If its smaller which sign to we need, so he would choose one of the cards from the dish and place it on the number mat.

Adding to 10 

I have store all my maths counting objects in some tool drawers, this allows Nuh to choose which ever object he would like to use to do his sums with. This works well as it keeps them all neat in sets of 10 but also he loves using the drawers.

I have various objects in these that he can use for sums like novelty rubbers, pegs, glass beads, pom poms, marbles.

After the debacle with getting Nuh to write out his answers I decided that I would always give him number stickers so that he could use a sticker to provide the answer on the sheet, until he is ready to write them. I made a blank addition worksheet that basically has the addition sign and equals sign on them which means i just need to fill in the numbers.

As per instructions in the Karen Tyler Maths album I am teaching him to add to 10 by tackling each number separately so we started with all the combinations that make 10, then 9, then 8 etc.....
I may be wrong but at this point you are not trying to drill them so that they remember these combinations you are simply making sure that they understand the formula for addition and that various number combinations can make the same number. I think...... please correct me if I am wrong as I am not a trained Montessori teacher.