Developing Mathematical Thinking In Number : Place Value

1. Developing Mathematical Thinking In Number : Place Value

2. 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.

3. 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

4. Progression

5. 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 Pictorial: 0 1 2 3 4 5 What would you like to count? How many cars did you count? Create a number rich maths environment.

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

7. Counting challengesThe English language can be confusing for children learning number names Is there a consistent pattern in English vocabulary ? Do the number names 11-20 link to number names 1-10?

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

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

10. 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

11. A very brief history of zero 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

12. 3 3 0 0 7 7 Begin to understand place value and use it to compare numbers, partition numbers and in calculating. • 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 37 is 30 + 7 3 tens and 7 units

13. Understanding and using decimal notation and place value in decimal fractions. £1.27 1.27

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