## 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.

## 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.

## Hands-on maths; skip counting

I like to keep much of our early mathematical skills as hands-on as possible. If an area will need to be drilled over and over again until mastery is achieved, then it is far more interesting for my children to do that using Montessori style tray activities rather than repetitive book work. Learning addition and subtraction facts, multiplication tables and the like are great examples of this. Lots of work is necessary, but it need not be all written bookwork.

This week my 6-year-old son needed to polish up on his skip counting. I pulled out some plastic Easter eggs and wrote the 2, 5 and 10’s on each hump of the caterpillar, poking a pipecleaner through the first one to make the caterpillar’s head. He placed each in order and recited them to me once finished. Next time I will remove a couple and get him to say them (including the missing numbers) until he can eventually say them all without any numbers as prompting.

## Homeschooling 6-year-olds; Writing

Diary writing is a wonderful way to teach writing skills with young children. The topic is relevant and interesting to them (all about themselves!!) and it provides a wonderful keepsake in the years to come. All aspects of spelling, grammar and punctuation etc. can be covered as the child writes and it includes copywork practice which I believe is essential for learning strong writing skills.

If you are not familiar with the concept of copywork and the reasoning behind it, the basic ideas is that children’s writing will best develop as they see excellent writing modelled. As they copy correct spelling, punctuation and other building blocks that successful writers use, they become familiar with these skills and are then able to put them into place in their own writing. (Google Charlotte Mason copywork for more information on this concept.)

The modern idea of children just “having a go” as they spell phonetically means that they are seeing incorrect “pictures” of wrong spelling, reinforcing these mistakes in their memory, rather than the correct spelling that they will see in copywork activities.

Once or twice a week I have my 6-year-olds draw a picture of a significant event that has occurred recently and then tell me about it. As they speak, I write down their words, leaving a line between each line of my writing. As I write, we discuss concepts such as:

• punctuation; capital letters and full stops
• spelling (I may have them tell me how to spell a sight word they are familiar with)
• phonics (I might ask how to write the “sh” sound in a word for example)
• descriptive words (is there a more interesting way to say “good?”)

Diary writing for children who are not yet forming letters correctly:

Another way to use diary writing  that also works on reading skills and letter/word recognition is to have the child dictate a single sentence to you about the drawing they have made. You write the sentence into their diary book, leaving a full line blank between each line that you write and also write it a second time onto a separate strip of paper. The child then cuts the separate strip up into single words (word recognition is a concept in itself, as well as requiring scissor skills) which are then mixed around out of order. They must then match these words back up to the ones you have written on the page and glue them underneath, re-reading with your help to ensure it makes sense and is matched correctly.

For my son who struggles with fine motor control, pencil grips are a must. He also cannot copy the words underneath my writing, but traces over the top instead. I let him use good quality gel pens with a pencil grip at times because they make a nice dark line without much pressure being required and he likes them – anything to encourage writing!

When young children are doing any kind of writing, correct pencil grip is important. The longer they practise writing with incorrect grip, the harder it is to correct later, just like any other habit. For those who struggle, a good quality pencil grip is a must. It should be very soft and molded to keep fingers in the correct place. Our favourite has flaps like wings that spread out over the top of the thumb and pointer finger, stopping children from sliding their fingers up and over the top of the pencil grip in a fist style. Be wary of purchasing cheaper brands. I did so this year, being very happy to find 5 grips in a packet for the same price of just one I had bought previously, however these turned out to be made of a much firmer rubber and the children do not find them comfortable to use.

Other writing activities that my year 1 homeschoolers participate in:

• handwriting book. (Individual letter practice because learning to make letters the correct shape and starting at the right place is still important. Most children at this age are still making mistakes with this and again, we don’t want bad habits to form and have to be re-learnt later.)
• copywork. (Bible verses, character related, good quality literature examples.)
• finger strength building activities. (Plenty of time on activities that require fine-motor skills such as hand sewing, threading beads, Lego, playdough etc.)
• free time to choose drawing and writing. (They have desks in their bedrooms well-stocked with a variety of papers, envelopes, notepads, drawing and writing tools that they have access to during room time after lunch each day. They are always drawing or writing notes, cards and letters to friends and family. My reluctant writer has spent anything up to 30 minutes a day for several weeks now filling every single line of an A5 notepad with squiggly lines – his “writing.” Nothing I could have set for him would ever have got him to spend this long using a pencil!)
• writing in family birthday and thank you cards and letters to friends and relatives

That’s about it for writing in year one for us. With this foundation in place I know from experience that they will go on to successful writing in the future.

What do you do for writing in your homeschool?

## Homeschooling 6 year olds – reading

Teaching a child to read in the early years is not as daunting as it at first seems. There are so many different methods out there and honestly, a child that does not have any developmental issues will learn using any of them – just pick one and go for it! Some will need a little more time with the same materials but will get there in the end and others may need you to find them something that addresses their particular needs. Of course, reading excellent literature to children on a daily basis is so important for their development in this area.

The methods I use work for me and have adapted easily for the little ones in my house who needed a little more time. I have already discussed how to lay the foundations for teaching reading in teaching children to read – where to begin so I’ll leave that for now.

Moving on from ear training, a good phonics programme is a must, some sight word practise is helpful and a good quality set of early readers is useful.

I use Letterland for phonics. It was developed to help children who were struggling and was so successful it came into mainstream education. Initially I introduce 1 new letter a day using the abc book, with both its alphabet name and sound, and we spend 5 minutes reading the little story and finding a bunch of items starting with that sound. On the following day we review the sounds and letter names previous learnt before introducing a new letter. At the end of 26 days, with daily reviews of sounds already covered, our 3 year olds will usually know around 20 of the 26 sounds, many of the letter names and be able to work out the rest of the sounds using the Letterland character’s names to prompt them. Not bad for 10 minutes a day.

The 4 and 5 year olds go on to initial sounds experiences, alphabet activities and 3 letter words. (Put “preschool” in the search bar to find my many posts for preschool activities that include alphabet charts, spinny spellers, Duplo 3 letter words, Montessori trays etc.) Our focus this year is now sight words and more advanced digraphs – the sounds that letters make when they get together. Letterland has the cleverest stories to explain these changes.

For example, “H” is Hairy Hat Man who hates noise and whispers his soft “h” sound and the letter “S” is Sammy Snake who hisses his “s” sound. When Sammy stands behind Harry in words his hissing is so loud that Harry turns and says “sh” which is why you can hear a “sh” sound when you see “sh” in words such as shop and ship. Easy isn’t it! Once the children have heard these stories they rarely forget them and they provide very easy prompts when working on decoding words for reading. Even my older children can sometimes be prompted in their reading or spelling of a difficult word with the reminder of one of the more advanced Letterland stories.

For beginner readers who find reading akin to pulling teeth, putting the readers aside and focussing on building a bank of sight words may be helpful. I type out all the words necessary to read their first Bob Book and we use those for sight word games, flash card drills and other simple activities until they are known by sight. That way, when the child attempts to read the actual book, they are able to breeze through and wonderingly say at the end “I read it!” rather than feel like pulling out their hair (or is that just me?) as they laboriously sound out 1 word after another.

In the sight word mastery file above, the words are moved from pocket to pocket as the child reads them successfully. If they forget the word it goes back to pocket 1 and starts again. That way, by the time words make it into the review envelope they have been read correctly 6 days in a row and are probably quite well known by then – enough to be recognised in the book later.

The Montessori pink series  starts with simple phonetic words that are matched to pictures. It is an independent activity that requires no supervision other than me listening to the words being read once they have matched all the pictures. In graded sets that get gradually harder, these are free to print out and there are heaps of free resources for them on the web.

There are so many more ideas for teaching reading but these are a few that we have used repeatedly over the years during a short period of one-on-one time with each child, coupled with a little independent work on a daily basis. One they have that lightbulb moment they will be off and running and you will need to restrain yourself from telling them to put that book down and go out and play!

## Homeschooling 6 year olds – maths

It is fairly well understood in the preschool years that children need many hands-on experiences as the best grounding for mathematical understanding. However, it is too easy to fall into the trap of thinking that as soon as a child starts school he or she must “hit the books.” There is still a need to manipulate, play and explore concrete materials in the early years and rushing too fast into abstract concepts (ie. “on paper” solutions) to mathematical concepts can hinder a child developing true understanding.

So, with this in mind, do I use a maths programme for my 6 year olds? Yes, but as a spine from which other maths experiences flow. It helps me to know that I am not missing any skills along the way. Those children who have a good grasp of number concepts can skip through very quickly and often will plead to just write out their answers in the book rather than use manipulatives. If I can see that they truly grasp the skills (understanding the why and how of each problem) then they go ahead. Learning styles do differ after all and not everyone needs the manipulatives. However, other children will need to go through basic concepts such as one-to-one correspondence with manipulatives over and over and over and over again!

In the early years we use Math-U-See because it does include manipulatives, has a DVD lesson format which means the children are not dependent on me to give them one-on-one teaching to explain each lesson and has a clean and simple set-out with a good progression from skill to skill. Early writers are given enough space to write large numbers and opportunities to use their manipulatives throughout. When more practise is required, I provide Montessori style hands-on activity trays until the concept is thoroughly grasped before the child continues on in the book.

Reluctant writers and maths:

When a child has difficulty with fine motor control and writing skills it can slow them down in all their subject areas. Maths however is one area that can be easy modified to eliminate this problem. Ask yourself – “Am I teaching handwriting or maths?” Do you want your child to progress in maths or hate every minute of it because they have to sit there laboriously writing numbers in their painfully slow style?

My son would take ages to complete this page if he had to write the answers down, plus I would struggle to read them anyway! Given this inexpensive box of wooden letters, he can work through the problems, calculating some in his head, putting out manipulatives for others and using the wooden numbers to “write” the answers. Quick and easy and demonstrating his understanding of the subject at hand, rather than his handwriting ability.

When more experience is needed with a concept, he works on Montessori style trays such as the one above, giving him lots and lots of repeated practise of the same skill over and over again until it becomes second nature. We made up little stories about customers in restaurants who were sometimes greedy (according to the numbers on the spoons) and he enjoyed choosing the food (jewels) to serve.

With the combination of bookwork plus hands-on trays, my 6 years olds feel that they are doing real “school” like their older brothers and sisters and all ability levels are being catered for. One is zipping through the book at a great rate (she LOVES book work!) and the other is taking a more leisurely course with lots of hands-on experiences along the way. Individual children,  individual abilities, individual learning styles. This is one of the reasons why we homeschool after all isn’t it?

Next up: Homeschooling 6 year olds – reading and writing