Developing Mathematical Thinking In Number : Place Value

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.

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 

Progression

Pictorial: 1 2 3 4 50

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 correspondenceWhat would you like to count? How many cars did you count?

Create a number rich maths environment.

Subitising

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

Counting challengesThe English language can be confusing for children learning number names

Gaelic word Literal Meaning

Japanese word

Literal Meaning

English Word

10 deich 10 Ju Ten Ten

11 aon dheug 1 + 10 Ju-ichi Ten-one Eleven

12 dà dheug 2 + 10 Ju-ni Ten-two Twelve

13 trì deug 3 + 10 Ju-san Ten-three Thirteen

14 ceithir deug 4 + 10 Ju-shi Ten-four Fourteen

15 cóig deug 5 + 10 Ju-go Ten-five Fifteen

16 sia deug 6 + 10 Ju-roku Ten-six Sixteen

17 seachd deug

7 + 10Ju-shichi

Ten-seven Seventeen

18ochd deug 8 + 10

Ju-hachi

Ten-eight Eighteen

19 naoi deug 9 + 10 Ju-kyu Ten-nine Nineteen

20 fichead 20 Ni-ju Two-ten Twenty

Is there a consistent pattern in English

vocabulary ?

Do the number names 11-20 link to number names

1-10?

Language : Counting up and down ?

Consider counting up in 10s from 6

What direction are the numbers going when counting up?

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

Starting from 0 ?

90 91 92 93 94 95 96 97 98 9980 81 82 83 84 85 86 87 88 8970 71 72 73 74 75 76 77 78 7960 61 62 63 64 65 66 67 68 6950 51 52 53 54 55 56 57 58 5940 41 42 43 44 45 46 47 48 4930 31 32 33 34 35 36 37 38 3920 21 22 23 24 25 26 27 28 2910 11 12 13 14 15 16 17 18 19

0 1 2 3 4 5 6 7 8 9

91 92 93 94 95 96 97 98 99 10081 82 83 84 85 86 87 88 89 9071 72 73 74 75 76 77 78 79 8061 62 63 64 65 66 67 68 69 7051 52 53 54 55 56 57 58 59 6041 42 43 44 45 46 47 48 49 5031 32 33 34 35 36 37 38 39 4021 22 23 24 25 26 27 28 29 3011 12 13 14 15 16 17 18 19 20

1 2 3 4 5 6 7 8 9 10

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

It took the human race about 28 000 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, 400 000. 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

37 is 30 + 7

3 tens and 7 units

We can use partitioning in calculations. Some pupils may think this, others may require to jot this thinking down

32 + 46

(30 +2) + (40 + 6)

70 + 8

3 0 7

3 07

Begin to understand place value and use it to

compare numbers, partition numbers and in

calculating.

Understanding and using decimal notation and place

value in decimal fractions.

1.27£1.2

7

Next stepsWhat

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?

What impact will this have on your

practice?