Structure of HSNP Numeracy - Four Levels of Proficiency

Division 1 Mental and bus stop division

Objectives  Use multiplication facts to work out divisions  Use mental strategies to work out divisions with ‘friendly’ numbers  Divide two- and three-digit numbers by single-digit numbers  Divide three- digit numbers by two-digit numbers  Express remainders as fractions

For this unit you will need: Division bingo at http://www.topmarks.co.uk/Flash.aspx? f=BingoMultiplicationv9, Remainders after division bingo at http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_reso urces/848/remainders.swf

Watch out for pupils who:  do not know their multiplication facts and so can’t make use of them to solve divisions;  try to partition numbers into 100s, 10s and 1s to divide (as they would for multiplication), rather than into a multiple of 10/100 of the divisor and the rest, e.g. partition 372 into 300, 70 and 2 to divide by 4 rather than in 360 and 12;  do not know halves of odd numbers of multiples of 10/100, e.g. 70 and 90, 700 and 900 and so can only halve numbers with even digits.

HSNP © Hamilton 2013 Shining Term 1 Division 1 Session 1 Objectives: Use multiplication facts to work out divisions; Use mental strategies to work out divisions with ‘friendly’ numbers

Teacher input with whole class  Play Divisions bingo at http://www.topmarks.co.uk/Flash.aspx? f=BingoMultiplicationv9. Choose ‘random divisions missing number’ and ask pupils to choose five numbers to write on their whiteboards. Click to show each question. Pupils ring the answer if they have it. Keep a record of the questions. The first to ring all five numbers wins.

 Now play Remainders after division bingo at http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_r esources/848/remainders.swf. Pupils again choose five numbers, but this time ring them if they have the remainder after each given divisions. Paired pupil work  Pupils work in pairs to write 11 divisions, each with a different remainder from 1 to 11. Each division must have a different divisor! They compare their list of divisions with a neighbouring pair. Teacher input with whole class  Write the following divisions on the board and ask pupils to discuss how they might solve them: 420 ÷ 5, 448 ÷ 8, 872 ÷ 4, 560 ÷ 7, 4200 ÷ 6  Draw out strategies such as dividing by 10, then doubling to divide by 5, and halving 2/3 times to divide by 4/8. Pupils solve each.

HSNP © Hamilton 2013 Shining Term 1 Division 1 Session2 Objectives: Divide two- and three-digit numbers by single-digit numbers; Express remainders as fractions Teacher input with whole class  Write 96 ÷ 6 on the board. Ask pupils if there are more than ten 6s in 96. Subtract 60 from 96 and write 10 at the top. How much is left? How many 6s in 36? Write 6 at the top and subtract 36. Agree that there is no remainder. 10 + 6 = 16 6 ) 96 - 60 36 - 36 0  Repeat for 115 ÷ 8. Agree that there is a remainder of 3. Paired pupil work  Write the following divisions on the board: 92 ÷ 4, 55 ÷ 4, 85 ÷ 6, 93 ÷ 8, 100 ÷ 7, 127 ÷ 5, 87 ÷ 3, 150 ÷ 6, 159 ÷ 3, 191 ÷ 7, 106 ÷ 8  Pupils take it in turns to choose a division and work out the answer. They start off with 10 points. They score the remainder, but if the division leaves no remainder, they lose a point. E.g. 52 ÷ 4 = 13, so they lose a point, but 55 ÷ 4 = 13 r 3, so score 3 points. The person with the highest score when you ask them to stop, wins. If they run out of divisions, they can make up their own! Ask them to keep a record of all the divisions with answers.

Teacher input with whole class  Ask pupils what the answer was to 106 ÷ 8. Agree that the remainder was 2 and remind pupils how we can also divide this 2 by 8 instead of 2 leaving it as a remainder, to give the fraction /8, which can be simplified to ¼. Ask pupils to write the remainders to the other divisions as fractions, simplifying where possible.

HSNP © Hamilton 2013 Shining Term 1 Division 1 Session 3 Objective: Divide three-digit numbers by two-digit numbers  Write 896 ÷ 26 on the board. Ask pupils to list multiples of 26 to 10, using the previous multiples of 26 to help them, e.g. adding 26 and 52 to give three lots of 26, doubling four lots of 26 to give 8 lots of 26. Are there are more than ten 26s in 796? More than 20? More than 30? More than 40? Pupils use this list of multiples to help. Subtract 780 from 896 and write 30 at the top. How much is left? How many 26s in 116? Use your list of multiples to help. Write 4 at the top and subtract 104. Agree that the remainder is 12. 30 + 4, r12 34 r12 26 ) 896 - 780 116 - 104 12  Repeat for 715 ÷34. Paired pupil work  Write the following numbers on the board: 456 756 432 945 634  Pupils take it in turns to choose a number and divide it by a number between 10 and 50 of their choice – the number may not be a multiple of ten! If the answer is between 10 and 20 they win 10 points, if the answer is between 20 and 30 they win 20 points and if the answer is between 30 and 40 they win 30 points, otherwise they score nothing! Ask them to keep a record of all the divisions with answers.

Teacher input with whole class  Discuss how pupils could check their work. Draw out using multiplication and adding on the remainder. Pupils check three of their divisions using multiplication.