TA Maths Course Session 3: Division

Aims of the session: To build understanding of mathematics and its development throughout KS2 To have a stronger awareness of how to support struggling learners and stretch those who are secure To enhance subject knowledge of the pedagogical approaches to teaching mathematics

Division At the heart of success of this topic is clearly mastery of times tables. The more fluent a student is at their tables, the easier they will find division. Practice those times tables at every opportunity. Remember: Lining up to assembly (and hopefully other teachers will follow suit). Getting changed for PE, etc. Parents! They can really support the regularity of practice (daily?)

Grouping and Sharing 12 ÷ 3 = 4 Grouping – we know how many are in each group but not how many groups there will be. The answer is the number of groups. Sharing - we know how many groups there are but not how many are in each group. The answer is the number in each group. Grouping

Bar Model? I had 32 sweets and I shared them between 4 children. How many did each child get? I had 32 chocolate bars and they came in packs of 4. How many packs did I get?

Building the Journey Year 3 Pupils can derive associated division facts e.g. if 6 ÷ 3 = 2, then 60 ÷ 3 = 20 Pupils develop reliable written methods for division, progressing to the formal written methods of short division. Year 4 Pupils can derive associated division facts e.g. if 28 ÷ 7 = 4, then 2800 ÷ 7 = 400 Pupils practise to become fluent in the formal written method of short division with exact answers Year 5 Divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context. Year 6 Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context. Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context.

Activities to support multiplication and division on a number line Give children opportunities to share and group objects. Different representations…

Ella has 48 plasticine legs to make animals for a display How many cows could she make? How many beetles could she make? How many spiders could she make?

An image for 56  7 Either: How many 7s can I see? (grouping) Or: If I put these into 7 groups how many in each group? (sharing)

The array is an image for division too 5 6 7 8 5 6 7 8

363 ÷ 3 = 1 2 1 3 6 3 3

364 ÷ 3 = 3 6 4 3

364 ÷ 3 = 1 2 rem 1 3 6 4 3

345 ÷ 3 = 1 1 5 3 4 5 3 1

Year 4 The journey is now about fluency with short division. Although not explicit, three-digit divided by one-digit seems a sensible goal by the end of the year. There should be exact answers (no remainders). Do you have "tricks" to ensure there are no remainders?! 462 ÷ 2 725 ÷ 5 537 ÷ 3 474 ÷ 6 738 ÷ 9 100 10 1

Divisibility rules A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8. A number is divisible by 3 if the sum of the digits is divisible by 3. A number is divisible by 4 if the number formed by the last two digits is divisible by 4 A number is divisible by 5 if the last digit is either 0 or 5 A number is divisible by 6 if it is divisible by 2 AND it is divisible by 3 A number is divisible by 8 if the number formed by the last three digits is divisible by 8. A number is divisible by 9 if the sum of the digits is divisible by 9. A number is divisible by 10 if the last digit is 0

Year 5 Division moves up to four digits, with the emphasis on manipulating the remainder. Manipulation includes: simply recognising it exists! understanding how to get a fractional answer understanding how to get a decimal answer Note: the decimal and fractional answer could easily be taught "as a process", but the emphasis must be on understanding. Again the student who "masters" the manipulation quickly, must have their division enriched by appropriate problem solving opportunities.

Dividing by 6 happens when putting eggs into boxes?! Year 5 Dealing with remainders (needs differentiating carefully) These three examples have been chosen to illustrate various outcomes that might happen. Scaffold the manipulation of the remainder carefully over the year, as and when different groups are ready for the next step. e.g. 7143 ÷ 5 3466 ÷ 8 3416 ÷ 6 1000 100 10 1 Dividing by 6 happens when putting eggs into boxes?!

Year 6 Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context. Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context. 12 5 4 2 1 12 5 4 2 1 Careful then writing recurring decimals...

Deeper thinking Students need experience of a variety of problems which give rise to multiplication and/or division Questions in context – not straight worded questions

Deeper thinking

Where now? Reflect on the addition and subtraction journey. What are the most important messages you are going to take away? *