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Developing Mathematical Thinking In Number : Place Value

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Aim of presentation To encourage staff reflection on approaches to teaching number. To stimulate professional dialogue. To use as a CPD activity for staff individually or collegiately.

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Experiences and Outcomes I have explored numbers, understanding that they represent quantities, and I can use them to count, create sequences and describe order. MNU 0-02a I have investigated how whole numbers are constructed, can understand the importance of zero within the system and can use my knowledge to explain the link between a digit, its place and its value. MNU 1-02a I have extended the range of whole numbers I can work with and having explored how decimal fractions are constructed, can explain the link between a digit, its place and its value. MNU 2-02a

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Progression

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Pictorial: Progression Using practical materials and sets of objects when beginning counting and using numbers. Emphasise the link between the number words and the objects. One-to-one correspondence What would you like to count? How many cars did you count? Create a number rich maths environment.

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Subitising This is an important early developmental step. It is the ability to recognising a small number of objects without counting.

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Counting challenges The English language can be confusing for children learning number names Gaelic wordLiteral Meaning Japanese word Literal Meaning English Word 10 deich10 Ju Ten 11 aon dheug Ju-ichi Ten-oneEleven 12 dà dheug Ju-ni Ten-twoTwelve 13 trì deug Ju-san Ten-threeThirteen 14 ceithir deug Ju-shi Ten-fourFourteen 15 cóig deug Ju-go Ten-fiveFifteen 16 sia deug Ju-roku Ten-sixSixteen 17 seachd deug Ju- shichi Ten-sevenSeventeen 18 ochd deug Ju-hachi Ten-eightEighteen 19 naoi deug Ju-kyu Ten-nineNineteen 20 fichead20 Ni-ju Two-tenTwenty Is there a consistent pattern in English vocabulary ? Do the number names link to number names 1-10? Is there a consistent pattern in English vocabulary ? Do the number names link to number names 1-10?

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Language : Counting up and down ? Consider counting up in 10s from 6 What direction are the numbers going when counting up?

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Language : Counting up and down ? Is this better for pupils experiencing at the first level? Consider counting up in 10s from 6 What direction are the numbers going now when counting up? Vocabulary – counting on, counting back

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Starting from 0 ? Which 100 square emphasises the Early Level – key concept of counting on and back from a given number including crossing the decades ? e.g. 18,19, 20, 21, 22

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It took the human race about years to come up with the notion of 0. This being the Indians around 500 AD. Zero was first thought of in the context of writing numbers down eg to distinguish between 4, 40, 400, Zero was introduced as a place holder. Zero is particularly useful in calculations – allowing the alignment of digits under column headings. eg think about trying calculations without converting Roman numerals to our number system A very brief history of zero

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37 is tens and 7 units We can use partitioning in calculations. Some pupils may think this, others may require to jot this thinking down (30 +2) + (40 + 6) Begin to understand place value and use it to compare numbers, partition numbers and in calculating.

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Understanding and using decimal notation and place value in decimal fractions £1. 27

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Next steps What information will you share with colleagues? What might you or your staff do differently in the classroom? What else can you do as to improve learning and teaching about number What impact will this have on your practice?

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