What sorts of things can a parent teach their child at home?
There are three parts to Maths : Number & Algebra; Measurement & Geometry; and Statistics. I spend most time with my kids on ‘Number’ as a good grounding in this helps all areas. Number is also easy to quiz and teach in short bursts at home with minimal preparation time.
Number & Algebra
Practice counting to 100, forwards and backwards
Try naming the number before and the number after a number between 0 – 100 – e.g tell me what number comes after 63 , tell me what number comes before 40.
Learn doubles for numbers up to ten – e.g knowing that double 2 is 4 and double 3 is 6.
Learn that when you add numbers you can swap them around and get the same answer, e.g 2 + 3 = 5 and so does 3 + 2.
Learn pairs of numbers that add up to 5: e.g 3 + 2 and 4 + 1
Learn pairs of numbers that add up to 10: e.g 9 + 1 and 6 + 4
Learn how to make the ‘teen’ numbers: e.g 10 + 7 = 17 and 10 + 3 = 13
Use a mix of pictures and maths symbols to show an equation – e.g a drawing of 3 eggs + a drawing of 2 eggs = a drawing of 5 eggs. Start building familiarity with the plus, minus, times and fraction symbols.
Recognise a pattern and carry it on, e.g 2, 4, 6, ....what comes next and why?
Geometry and Measurement
Sorting out objects by shape, colour, temperature, texture etc – get an old bag of buttons and try out different ways of grouping them.
Following and giving instructions for movement that involve distances, directions and half or quarter turns – eg, face the library, take fourteen steps forward then do a half turn to the right. You can always make this into a fun game with a blindfold – heck you could even trick them into heading to bed!
Describe position relative to a person or object using terms like: next to, behind, in front of, between, to the left. Sketch simple maps.
Reflecting and turning shapes (rotation by half and quarter turns), repeating the same shape across a border (translation) – many girls love doing fancy borders on their pages so this can be a handy starting point for getting them thinking about shapes.
Statistics
Making sense of simple data – eg bar graphs, pictographs.
Possible outcomes – eg, heads and tails – toss a coin for who is doing the dishes and let your kids think about the odds.
Mathematics: Years 3 & 4 (Ages 7 & 8)
What sorts of things can a parent teach their child at home?
Number & Algebra
Practice counting to 1000 forwards and backwards – obviously it’s a bit painful to listen to your darling do this all the way from zero, so instead just do bits and pieces e.g lets see if you can count from 760 to 820.
See if your child can name the number ‘one more than’ and ‘one less than’ numbers that are between 0 and 1000.
Work on counting in groups of ten and a hundred e.g. 347, 447, 547... or 26, 36, 46, ...
Try adding and subtracting in groups of ten or a hundred e.g. 346 – 10 = 336 and 346 – 100 = 246
Revise basic addition facts from 0 + 0 = 0 up to 9 + 9 = 18 (i.e. 4 + 1 = 5 and 8 + 6 = 14 and 9 + 3 = 12 are all basic addition facts). This can be made fun by timing them and giving short quizzes. Boys especially often love a bit of competition! These are the 36 Addition Basic Facts - aim for them to be able to instantly recall these facts when asked by the end of Year 4.
2+2=4 3+3=6 4+4=8 5+5=25 6+6=12 7+7=14 8+8=16 9+9=18
2+3=5 3+4=7 4+5=9 5+6=11 6+7=13 7+8=15 8+9=17
2+4=6 3+5=8 4+6=10 5+7=12 6+8=14 7+9=16
2+5=7 3+6=9 4+7=11 5+8=13 6+9=15
2+6=8 3+7=10 4+8=12 5+9=14
2+7=9 3+8=11 4+9=13
2+8=10 3+9=12
2+9=11
Show them that when you add numbers you can swap them around and get the same answer, e.g. 2 + 3 = 5 and so does 3 + 2. Show them the inverse nature of adding and subtracting – e.g, if 6 + 7 = 13 then 13 – 7 = 6.
Fill the gaps – eg. 13 - ? = 8. Again you can do short quizzes.
Place value – teach them how many ones, tens and hundreds are in whole numbers up to 1000 e.g 345 is 3 hundreds, 4 tens and 5 ones.
Fractions – they need to know that the top number is the count and the bottom number is the size of the parts eg. 4/3 has 4 bits and each bit is made by breaking a whole into 3. Teach them that whole numbers can be written as fractions e.g 5 can be written as 5 over 1. You can start on some adding of fractions when they have the same bottom number – e.g. 1/8 + 2/8 = 3/8.
Practice writing an equation using correct symbols – get them familiar with symbols like + and =
The professional advice is not to teach the formal algorithims (writing out and solving sums the way we used to – in columns, carrying numbers etc) until children have a good understanding of place value.
Show them how numbers can be partitioned and practice doing this to solve a variety of problems : 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14. Practice strategies for solving mathematical problems - see the numeracy strategies at the bottom of the page for some guidance on this.
Challenge them to continue on a pattern such as: 3, 5, 7...
And 5, 10, 15...What would 7th one be?
Measurement & Geometry
Use devices and units to measure length, area, volume, mass, angle, temperature and time – do a bit of home baking and DIY!
Geometric language: describe shapes and have them describe shapes using terms like: side, corner, face, centre, edge, larger, smaller.
Making 3D shapes from nets – build a cube!
Compass directions, co-ordinates – you could get really keen and head off orienteering otherwise this is a good car topic – which way are we heading etc. See if they can understand a map grid.
How many mirror lines a shape has – eg a square has 4, what a shape will look like if turned a half turn around its centre?
Statistics
Knowing the difference between “Category” (grouping) and “Whole number” data – e.g recording how many cars drive by of each colour is grouping so it is category data. Recording exactly how long each class member’s pencil is would be whole number data.
Get familiar with graphs –e.g. Pie graphs and bar graphs, pictographs. Discuss what they tell you – e.g. a big piece of the pie is shaded in for white cars so this tells me more people drive white cars than the other colours.
Probability – is something likely – what is the chance of rolling a 6? “equally likely” to throw an even or odd number and “not very likely” to throw a 6 and “no chance” of throwing a 7.
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