Hands-on maths; solving for the unknown tray activities

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(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

 

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Learning Styles & hands-on learners

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(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.

img_2659We 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.

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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!

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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.

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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.)

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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.