Year 5 & 6 Maths
What sorts of things can a parent teach their child at home?
Number & Algebra
Now is the time to get those times tables sorted from 0 x 0 = 0 up to 9 x9 = 81.
1x1=1
1x2=2 2x2=4
1x3=3 2x3=6 3x3=9
1x4=4 2x4=8 3x4=12 4x4=16
1x5=5 2x5=10 3x5=15 4x5=20 5x5=25
1x6=6 2x6=12 3x6=18 4x6=24 5x6=30 6x6=36
1x7=7 2x7=14 3x7=21 4x7=28 5x7=35 6x7=42 7x7=49
1x8=8 2x8=16 3x8=24 4x8=32 5x8=40 6x8=48 7x8=56 8x8=64
1x9=9 2x9=18 3x9=27 4x9=36 5x9=45 6x9=54 7x9=63 8x9=72 9x9=81
1x10=10 2x10=20 3x10=30 4x10=40 5x10=50 6x10=60 7x10=70 8x10=80 9x10=90 10x10=100
Playing a CD in the car can help! It is important that they actually understand what they are doing – a good idea is to replace the word ‘times’ with ‘groups of’ e.g. How many pens would there be if I had 3 groups of 4? What about 5 groups of 4? Teach them that 8 times 7 is 8 groups of 7 and could be worked out by adding 3 groups of 7 (3 x 7= 21) to five groups of 7 (5 x 7=35 )and 21 + 35 = 56. When doing division replace ‘divided by’ with “shared among” – again to help them understand what it is they are memorising/working out.
Once the times tables are mastered – try reversing to check that they understand the relationship to division – e.g. knowing 6 x 4 = 24 so 24 divided by 4 = 6.
Counting in ones, tens, hundreds, thousands, ten thousands, e.g. 554, 654, 754 ... Practice taking one off or adding one on – e.g. if there are 43560 people in a town and one leaves, how many are there now? If ten thousand is removed from a set of 701000 how many are left? (= 691 000).
Practice writing numbers up to 1000000
Learn to count in tenths e.g. 4.6, 4.7, 4.8 ....
Place value – identify how many tenths, ones, tens, hundreds and thousands are in a number but also they need to understand ‘nesting’ – e.g. that nested in the thousands are hundreds, tens and ones (2467 has 24 hundreds, 246 tens, 2467 ones). To work out 2000 – 700 it is easier to think of it as 20 hundreds – 7 hundreds = 1300. Once they have nesting understood, you can teach them how to write out traditional sums (algorithims) for adding and subtracting multiple digit numbers.
Multiplying and Dividing by 10 – e.g. 420 divided by 10 = 42; 68 divided by 10 = 6.8; 65.6 times 10 = 656
Try working out adding and subtracting problems in their head using a range of strategies (see the Numeracy Strategies at the bottom of this page). See if they can do this with three digit numbers and with simple decimals (one decimal place, i.e. tenths).
Some strategies you could show them:
603 - 384 could be solved using place value: 60 tens subtract 38 tens is 22 tens (220) take away one = 219
923 - 587 could be worked out by what is called 'rounding and compensating' - round the 587 to 600, work out 923 - 600 = 323 then add 13 to the answer to compensate for the fact that took off 13 too many due to the rounding. Try using a number line to record what they are doing.
841 - 695 could be worked out by reversing 695 + ? = 841. 100 takes you up to 795, 5 more up to 800 and 41 up to 841 so the answer is 100 + 5 + 41 = 146
13 x 6 can be worked out by adding 10x 6 to 3 x 6 (this is called the distributive property).
14 X 9 can be worked out by breaking it up into 2 x (7 x 9). This is called the associative property)
36 divided by 9 can be worked out by asking what times 9 = 36 (this is called the inverse property).
Fractions:
Practice writing fractions in numbers and words. Revise that the top number is how many parts and the bottom number is the size of each part. Practice putting them in order from smallest to largest when the bottom number is the same – eg put these in order from smallest to largest 3/5, 1/5 and 4/5 )= 1/5, 3/5, 4/5. Try putting them in order smallest to largest when the top number is the same – eg order 4/8, 4/5, 4/7 and 4/3 (=4/8,4/7,4/5,4/3)
Two thirds of 24 can be worked out as 24 divided by 3 times 2 = 16
Practice writing equivalent fractions (show the same portion – e.g. 20 out of 40 and 10 out of 20 are equivalent. Limit this to equivalent fractions that involve doubling or halving – eg. ¾ and 6/8 are equivalent.
Add and subtract fractions that have the same number on the bottom – e.g. ¾ + ¾ = 6/4 = 1 2/4
Try changing improper fractions to mixed numbers – e.g. 17/3 = 5 and 2/3
Learn the decimals and percentages that equal simple fractions (halves, quarters, fifths, tenths) and use these to solve simple percentage of amount problems such as: What is 50 % of 18? (=9) What is ½ as a decimal? (= 0.5)
Patterns e.., 4, 8, 12, 16... and 4 , 7, 10 , 13 ...
Measurement & Geometry
Measurement – know that units have to be the same size and fill a length, space or time with no gaps or overlaps.
Get familiar with these units and try picking which is the best to measure something with:
Distance: metres, centimetres, millimetres, kilometres
Area: square centimetres, square metres
Volume: Cubic centimetres, cubic metres
Weight: Kilograms and grams
Angles: Quarter and half turns
Temperature: Degrees Celsius
Time: Seconds, minutes, hours, days
Work out area of rectangles (length times width) and the volumes of cuboids (length times width times depth)
Shape:
Group shapes by number of sides, know what parallel means, what a right angle is (e.g. a trapezium has one pair of parallel sides.
Number of mirror lines
Rotational symmetry (e.g. a square maps onto itself 4 times in a full turn).
Know that a prism is a shape that has a fixed cross section – e.g. triangular prism, cylinder. Think of a loaf of bread.
Reading Maps – use co-ordinates e.g. D3, compass directions.
Compare a ‘transformed’ shape with its original and describe how it has been changed – whether it has been reflected (flipped over), enlarged (made bigger or smaller), rotated (turned) or translated (moved across or up and down).
Statistics & Probability
Statistics – posing questions, thinking about what data would be needed and how it could be analysed.
Tally charts, frequency tables, pictographs, bar graphs, strip graphs, pie charts, dot plots, stem and leaf graphs, line graphs
Which type of display is best for which data e.g. pie charts and strip graphs are good for showing proportions while pictographs and bar graphs highlight the difference in frequencies of categories.
Probability – expected outcomes and experimental outcomes
Number & Algebra
Now is the time to get those times tables sorted from 0 x 0 = 0 up to 9 x9 = 81.
1x1=1
1x2=2 2x2=4
1x3=3 2x3=6 3x3=9
1x4=4 2x4=8 3x4=12 4x4=16
1x5=5 2x5=10 3x5=15 4x5=20 5x5=25
1x6=6 2x6=12 3x6=18 4x6=24 5x6=30 6x6=36
1x7=7 2x7=14 3x7=21 4x7=28 5x7=35 6x7=42 7x7=49
1x8=8 2x8=16 3x8=24 4x8=32 5x8=40 6x8=48 7x8=56 8x8=64
1x9=9 2x9=18 3x9=27 4x9=36 5x9=45 6x9=54 7x9=63 8x9=72 9x9=81
1x10=10 2x10=20 3x10=30 4x10=40 5x10=50 6x10=60 7x10=70 8x10=80 9x10=90 10x10=100
Playing a CD in the car can help! It is important that they actually understand what they are doing – a good idea is to replace the word ‘times’ with ‘groups of’ e.g. How many pens would there be if I had 3 groups of 4? What about 5 groups of 4? Teach them that 8 times 7 is 8 groups of 7 and could be worked out by adding 3 groups of 7 (3 x 7= 21) to five groups of 7 (5 x 7=35 )and 21 + 35 = 56. When doing division replace ‘divided by’ with “shared among” – again to help them understand what it is they are memorising/working out.
Once the times tables are mastered – try reversing to check that they understand the relationship to division – e.g. knowing 6 x 4 = 24 so 24 divided by 4 = 6.
Counting in ones, tens, hundreds, thousands, ten thousands, e.g. 554, 654, 754 ... Practice taking one off or adding one on – e.g. if there are 43560 people in a town and one leaves, how many are there now? If ten thousand is removed from a set of 701000 how many are left? (= 691 000).
Practice writing numbers up to 1000000
Learn to count in tenths e.g. 4.6, 4.7, 4.8 ....
Place value – identify how many tenths, ones, tens, hundreds and thousands are in a number but also they need to understand ‘nesting’ – e.g. that nested in the thousands are hundreds, tens and ones (2467 has 24 hundreds, 246 tens, 2467 ones). To work out 2000 – 700 it is easier to think of it as 20 hundreds – 7 hundreds = 1300. Once they have nesting understood, you can teach them how to write out traditional sums (algorithims) for adding and subtracting multiple digit numbers.
Multiplying and Dividing by 10 – e.g. 420 divided by 10 = 42; 68 divided by 10 = 6.8; 65.6 times 10 = 656
Try working out adding and subtracting problems in their head using a range of strategies (see the Numeracy Strategies at the bottom of this page). See if they can do this with three digit numbers and with simple decimals (one decimal place, i.e. tenths).
Some strategies you could show them:
603 - 384 could be solved using place value: 60 tens subtract 38 tens is 22 tens (220) take away one = 219
923 - 587 could be worked out by what is called 'rounding and compensating' - round the 587 to 600, work out 923 - 600 = 323 then add 13 to the answer to compensate for the fact that took off 13 too many due to the rounding. Try using a number line to record what they are doing.
841 - 695 could be worked out by reversing 695 + ? = 841. 100 takes you up to 795, 5 more up to 800 and 41 up to 841 so the answer is 100 + 5 + 41 = 146
13 x 6 can be worked out by adding 10x 6 to 3 x 6 (this is called the distributive property).
14 X 9 can be worked out by breaking it up into 2 x (7 x 9). This is called the associative property)
36 divided by 9 can be worked out by asking what times 9 = 36 (this is called the inverse property).
Fractions:
Practice writing fractions in numbers and words. Revise that the top number is how many parts and the bottom number is the size of each part. Practice putting them in order from smallest to largest when the bottom number is the same – eg put these in order from smallest to largest 3/5, 1/5 and 4/5 )= 1/5, 3/5, 4/5. Try putting them in order smallest to largest when the top number is the same – eg order 4/8, 4/5, 4/7 and 4/3 (=4/8,4/7,4/5,4/3)
Two thirds of 24 can be worked out as 24 divided by 3 times 2 = 16
Practice writing equivalent fractions (show the same portion – e.g. 20 out of 40 and 10 out of 20 are equivalent. Limit this to equivalent fractions that involve doubling or halving – eg. ¾ and 6/8 are equivalent.
Add and subtract fractions that have the same number on the bottom – e.g. ¾ + ¾ = 6/4 = 1 2/4
Try changing improper fractions to mixed numbers – e.g. 17/3 = 5 and 2/3
Learn the decimals and percentages that equal simple fractions (halves, quarters, fifths, tenths) and use these to solve simple percentage of amount problems such as: What is 50 % of 18? (=9) What is ½ as a decimal? (= 0.5)
Patterns e.., 4, 8, 12, 16... and 4 , 7, 10 , 13 ...
Measurement & Geometry
Measurement – know that units have to be the same size and fill a length, space or time with no gaps or overlaps.
Get familiar with these units and try picking which is the best to measure something with:
Distance: metres, centimetres, millimetres, kilometres
Area: square centimetres, square metres
Volume: Cubic centimetres, cubic metres
Weight: Kilograms and grams
Angles: Quarter and half turns
Temperature: Degrees Celsius
Time: Seconds, minutes, hours, days
Work out area of rectangles (length times width) and the volumes of cuboids (length times width times depth)
Shape:
Group shapes by number of sides, know what parallel means, what a right angle is (e.g. a trapezium has one pair of parallel sides.
Number of mirror lines
Rotational symmetry (e.g. a square maps onto itself 4 times in a full turn).
Know that a prism is a shape that has a fixed cross section – e.g. triangular prism, cylinder. Think of a loaf of bread.
Reading Maps – use co-ordinates e.g. D3, compass directions.
Compare a ‘transformed’ shape with its original and describe how it has been changed – whether it has been reflected (flipped over), enlarged (made bigger or smaller), rotated (turned) or translated (moved across or up and down).
Statistics & Probability
Statistics – posing questions, thinking about what data would be needed and how it could be analysed.
Tally charts, frequency tables, pictographs, bar graphs, strip graphs, pie charts, dot plots, stem and leaf graphs, line graphs
Which type of display is best for which data e.g. pie charts and strip graphs are good for showing proportions while pictographs and bar graphs highlight the difference in frequencies of categories.
Probability – expected outcomes and experimental outcomes
