## Hands-on maths; multiplying, clocks & time, sequencing and skip counting.

Here are the last couple of tray activities for our hands-on maths this term. While I have changed the way we are using the trays (Yes – again!) it has worked well to have the concepts we are covering in our Math-u-see books available for hands-on practise using concrete materials. As the children work through their books they are able to stop and spend extra time on a new skill using the trays if it is not immediately grasped from the instruction DVD that goes with the written material.

Curtain rings and flat wooden beads work well to illustrate the concept of “lots of” or “groups of” as the children learn basic multiplication skills.

These clock and time cards printed out from the internet start with a set of just the hours, then minutes, then half hours and finally a mixture of all 3. I googled clock/time worksheets and printed them before cutting them up. There are lots of options available online.

Learning to sequence numerals is made easy with the use of a number strip to follow. Initially the children use only the numerals 1 to 5 then up to 10, then 30 and so on. Eventually the number strip is removed as well.

Skip-counting and money concepts can be learnt by marking each interval with paper triangles and laying out real coins. I happen to have a bunch of one and two cent coins stashed away so we use those as well, although I do make sure the children know they are no longer legal currency.

## Hands-on maths; rounding numbers

Free printable number strips below.

While I have a moment I thought I’d continue to post about our maths activities with free printables for each activity.

Using a number line to teach children the concept of rounding to the nearest 10, 100 or 1000 helps to make the concept a little clearer. I printed out these number strips and used a hole punch to make holes above each number. The children select a number card, poke a golf tee into the hole closest to that number and then count the holes or hops it takes to reach the nearest 10/100/1000 in each direction. The smaller the number of hops, the closer the number and therefore they know which way to round; up or down.

This skill requires a firm grasp of number order and an understanding of place value in order for a child to be successful. The printable strips start with a blank space so that they overlap slightly and can be laid out in one long number line 0 to 100, 100 to 1000 and 1000 to 10000.

number-line-for-rounding-to-10s

number-line-for-rounding-to-100s

number-line-for-rounding-to-1000s

## Hands-on maths; ordinal number

(Free printable ordinal number cards below)

For a child who has a strong grasp of numbers and number order, ordinal number is a simple concept. Applying the labels of first, second, third etc. is something that children are exposed to in their everyday life. Every child is familiar with the phrase “Me first!”

This activity tray takes the concept of ordinal number and gives children practise in using it to label the order of runners in a race, months of the year and days of the week.

For your free printable ordinal number cards and awards click here: days of the week & months of the year and here: race track & position ribbons.

For more hands-on maths ideas see my free printables for addition, subtraction, and solving for the unknown.

## Hands-on maths; subtraction activity trays

(Free printable subtraction cards below)

Today I am continuing with my hands-on maths series (addition here, solving for the unknown here) with subtraction activities for hands-on learning. This (above) is what the “activity centre” looks like on my shelves. I would love to have it all spread out on individual trays but there is just not enough room. A simple plastic box and re-purposed desk organiser do the job and the children take out the materials they wish to use for the day.

You can use any materials you like but it is helpful if there is some way to clearly show that they have been subtracted or taken away. I have out wooden craft pictures that are turned over as they are subtracted, miniature fruit erasers that stand up and are then laid down as they are taken away, double sided 2-colour counters, Duplo blocks and some random plastic connecting pieces that clearly have 2 different sides. You can have the children physically move the pieces or put them in a separate container or some other method of showing that they are subtracted but I think it is good to be able to still see how many have been taken away as it helps with self-correction of errors.

The children choose one set of subtraction cards at a time to work on, beginning with the easier subtract 1 or 2 cards and then moving on to the more difficult combinations once they are able to do these without needing manipulatives. The aim is to have these basic maths facts committed to memory or so quickly worked out mentally that higher level mathematical skills based on them are not slowed down by having to work out the simpler steps. For your copy of my free printable subtraction cards click here: vertical-subtraction.)

## Solve for the unknown – hands-on maths

Here are the free printable cards for you to use with the solving for the unknown activities from this post.

solving-for-the-unknown-totals-of-2-3

solving-for-the-unknown-totals-of-4

solving-for-the-unknown-totals-of-5

solving-for-the-unknown-totals-of-6

solving-for-the-unknown-totals-of-7

solving-for-the-unknown-totals-of-8

solving-for-the-unknown-totals-of-9

solving-for-the-unknown-totals-of-10

## Addition tray activities for hands-on maths

After my earlier post on addition tray activities I have had some requests for a copy of the addition cards so here are your free printable vertical addition problems ready to print and laminate.

## Hands-on maths; solving for the unknown tray activities

(Free printables below!)

Success in higher level maths requires mastery of basic addition, subtraction, multiplication and division concepts. The answers need to come quickly, without requiring mental effort to work them out, otherwise the more difficult problem solving is slowed considerably and errors result. Working through simple problems over and over cements the answers in children’s heads and helps them stay in long-term memory. Lets face it though, page after page of the same kind of problems in a maths textbook can be… well.. boring!

My solution is to gather a range of attractive materials and allow the children to complete problems repeatedly, but in a way that means they hardly notice it is the same skill over and over.

These are our ‘solving for the unknown’ trays and like the addition trays, the cards are in sets. This cards all have the same end total, for example 0+_=3, 1+_=3, 2+_=3 and 3+_=3. Containers of the same number as the answers are filled with 2 distinctly different types of materials to illustrate the problem shown on the cards. The children can start with the smaller numbers and work on them until they no longer need manipulatives and can compute them almost instantly before moving on to the larger numbers.

The materials are attractive and any cards they can already do they simply tell me the answer to and set aside so that they are not wasting time practising combinations they already know.

Not all learners love hands-on activities. My 7 year old book work lover is happily working through page after page of these same problems in her maths text. She finds manipulatives frustrating and thinks that they slow her down. When she meets a problem that she cannot do in her head or on paper, she pulls out the relevant materials and works it through until she can move on – in her book. Children have different learning styles and maths is one subject that can easily be adapted to suit.

Free printable problem cards for solving for the unknown:

solving-for-the-unknown-totals-of-2-3

solving-for-the-unknown-totals-of-4

solving-for-the-unknown-totals-of-5

solving-for-the-unknown-totals-of-6

solving-for-the-unknown-totals-of-7

solving-for-the-unknown-totals-of-8

solving-for-the-unknown-totals-of-9

solving-for-the-unknown-totals-of-10

## Learning Styles & hands-on learners

(Free printable vertical addition cards below.)

Catering for a variety of learning styles can sometimes be a challenge for homeschoolers. If you have a number of children you have probably worked out by now that not every curriculum works well for all students and that as wise educators we need to adjust our approach to suit the learning styles of our children. That said, I believe that ALL children must learn to sit still and concentrate as a necessary life skill, regardless of whether they find that easy or difficult. The difference is that requiring all learning to take place in the same way (bookwork for example) will make life very unpleasant for you and your hands-on kinaesthetic learners.

We have started school for the year and the past week has been full of the usual teething problems that a new year and new programme presents. I started my 3 youngest students on a completely hands-on mathematics programme this term. After trialling it for a week, my 7 year old daughter has gone back to purely bookwork, using manipulatives only when absolutely necessary to understand a concept. She loves to work in books, especially brand new ones and it was killing her to have her maths book just sitting there while she was being forced to work through problems with manipulatives when she’d much rather do it on paper or in her head. My 7 year old son has settled on a midway compromise; one day of bookwork followed by one day of hands-on experiences to back up the concept being covered.

My 4 year old does not get a choice – he will be working with concrete manipulatives because I believe that at his stage of development this is the most successful method for developing a good handle of the basic mathematical concepts and skills he needs as building blocks for higher level concepts.

So in light of all that, here are some of the hands-on trays that we are using this year for maths, with more to come in subsequent days if and when I get a chance to photograph them!

Our addition trays have 2 kinds of materials to make it visually clear that we are counting out 2 separate groups before adding/joining them together to work out how many there are altogether. The cards are in sets that only work on adding 1 number at a time, for example 0+3, 1+3, 2+3, 3+3, 4+3, 5+3, 6+3, 7+3, 8+3, 9+3 and 10+3.

I printed and laminated the cards and provided felt pens (textas) to write the answer or wooden numbers to “build” the answer for those who prefer not to have to write. (For free printable vertical addition cards click here.)

I also added several types of containers so that the materials could be set out in pairs to contain them and illustrate the problem being worked on. These included stiff cardboard cupcake liners, disposable tinfoil pie tins and these white dishes.

These hands-on Montessori style trays complement the Math-U-See curriculum that we choose to use in the early years and provide the extra practise needed by some in order to grasp the new concepts.

## Blessing Buddies and “What’s in the Box?” for holiday routines

Our little one is enjoying the new and exciting Christmas tray activities that have been arriving each day with the Blessing Buddies. Even during the holiday period, a flexible routine is essential for toddlers. While we break out of our usual day-to-day activities, I still try to make sure that my 2-year-old has some structure to her day and she enjoys doing her table activities after breakfast while her siblings work on their crafts and gifts throughout December.

This tinker tray of loose parts was a hit today as she used it to decorate the felt Christmas tree. After decorating our actual Christmas tree recently she understood exactly what this concept was all about. Of course they don’t all end up back in the tray quite the same way at the end!

Gingerbread men “cookies” to decorate plus a Christmas tree ice block sorting tray to use with the oversized tweezers or spoon. We will make gingerbread biscuits some time soon so this will make more sense to her after that experience.

While not too Christmassy, she loves these mini erasers so I have made them available for decorating the coloured rice Christmas tree, again with oversized tweezers to help with hand strength for pencil grip later on.

The Blessing Buddies have decided it’s too difficult to bring a new activity each day with so many nighttime commitments at the moment so for today’s blessing they set up a “What’s in the Box?” cupboard instead. They will add some new activities to it during December but  it gives the children more time to play with and enjoy the special Christmas activities (plus it takes the pressure off me to remember to hide a new one each night!) The other children like to use some of the same activities for table time as well.

So “What’s in the Cupboard?”

The craft at the moment is hand-sewing designs onto plain red tea-towels from Ikea which we will use as gifts. Even our 4 year old is managing a decent running stitch.

## Invitation to play

Once again our pretend play home-corner had become a sadly neglected play choice. Time for a change! Toy rotation is a marvellous thing – I simply packed away the play materials that have been out for some time and pulled out a few items the children haven’t seen in a while. Placing them out in an attractive invitation to play makes all the difference. Even the older children were itching to get in there and have a play once these “new” items were in view and the little ones are now happily “cooking” away.