Colour-coded maths guides

Thirteen A4 sheets. Each one starts with a worked example, then leaves the same template blank to fill in. Print at 100% with background graphics switched on.

Colour-coded maths guidesPrintable templates where the colour of a digit tells you what it is worth. Colour-coded maths guidesPrintable templates where the colour of a digit tells you what it is worth.What the colours meanThousandsone counter is worth 10004Hundredsone counter is worth 1007Tensone counter is worth 104Onesone counter is worth 17Tenthsone counter is worth 0.14Hundredthsone counter is worth 0.017Fractions use two of the same colours34The number on top is the numerator.It counts how many pieces you have.The number underneath is the denominator.It says how many equal pieces the whole was cut into.Using these sheets1Work the example at the top of the page togetherIt is already filled in, so it shows exactly what a finished answer looks like.2Fill the blank templates underneathWrite each digit in the box that matches its colour. The colour is the reminder of what it is worth.3Check by reading the colours backSay the value aloud — "two hundreds, four tens, six ones" — before reading the number.Printing in black and white? Every colour also has its own pattern, so the columns stay distinct.Colour-coded maths guidesKey
Place value to 999One colour for each column, so a digit carries its value wherever it moves. Place value to 999One colour for each column, so a digit carries its value wherever it moves.Worked example: three hundred and forty-sevenHundredseach worth 100Tenseach worth 10Oneseach worth 1347digitswhat itlooks like300+40+7= 347Now you tryWrite each digit in the matching column, then draw the blocks underneath.526Hundredseach worth 100Tenseach worth 10Oneseach worth 1480Hundredseach worth 100Tenseach worth 10Oneseach worth 1209Hundredseach worth 100Tenseach worth 10Oneseach worth 1Colour-coded maths guidesSheet 1
Thousands, tenths and hundredthsThe same colour system, extended either side of the decimal point. Thousands, tenths and hundredthsThe same colour system, extended either side of the decimal point.Worked example: two thousand four hundred and six point three fiveThousandseach worth 1000Hundredseach worth 100Tenseach worth 10Oneseach worth 1Tenthseach worth 0.1Hundredthseach worth 0.01240635The zero is doing real work here. It holds the tens column open so the 2 stays in the thousands.2000+400+0+6+0.3+0.05Now you tryEach column to the right is ten times smaller than the one before it.1 508.7in wordsThousandseach worth 1000Hundredseach worth 100Tenseach worth 10Oneseach worth 1Tenthseach worth 0.1Hundredthseach worth 0.013 090.42in wordsThousandseach worth 1000Hundredseach worth 100Tenseach worth 10Oneseach worth 1Tenthseach worth 0.1Hundredthseach worth 0.01640.05in wordsThousandseach worth 1000Hundredseach worth 100Tenseach worth 10Oneseach worth 1Tenthseach worth 0.1Hundredthseach worth 0.01Colour-coded maths guidesSheet 2
PartitioningSplit a number into the value of each digit — the step every written method depends on. PartitioningSplit a number into the value of each digit — the step every written method depends on.Worked example44 000+2200+660+554 265 = 4 000 + 200 + 60 + 5Splitting a number this way is what makes column methods work — you only ever add matching colours.Now you tryBreak each number into its parts, then write the addition underneath.3 807+++written as an addition5 920+++written as an addition1 040+++written as an addition2 306+++written as an additionColour-coded maths guidesSheet 3
Column additionDigits only ever add to digits of the same colour. Anything over nine moves left. Column additionDigits only ever add to digits of the same colour. Anything over nine moves left.Worked example: 268 + 157HundredsTensOnes268157+42511Small carried digits go above the next column to the left —in a different colour so they are never mistaken for the sum.8 + 7 = 15Write 5 in the ones, carry 1 into the tens.1 + 6 + 5 = 12Write 2 in the tens, carry 1 into the hundreds.1 + 2 + 1 = 4Now you tryOnly ever add digits of the same colour. Carry into the column to the left.HundredsTensOnes374248+HundredsTensOnes529386+ThousandsHundredsTensOnes14652738+ThousandsHundredsTensOnes35071896+Colour-coded maths guidesSheet 4
Column subtractionWhen a column will not subtract, exchange one counter from the colour to its left. Column subtractionWhen a column will not subtract, exchange one counter from the colour to its left.Worked example: 432 − 156HundredsTensOnes432156−27631212You cannot take 6 from 2, so exchange one ten forten ones. Cross the digit out and rewrite it above.12 − 6 = 62 − 5 will not work either, so exchange againfrom the hundreds: 12 − 5 = 7.3 − 1 = 2Exchanging never changes the number — 432 is still 432 when it is written as 3 hundreds, 12 tens and 2 ones.Now you tryCross out and rewrite above when you exchange. Work from the ones column left.HundredsTensOnes623287−HundredsTensOnes805349−ThousandsHundredsTensOnes40521678−ThousandsHundredsTensOnes73002941−Colour-coded maths guidesSheet 5
Multiplying with a gridThe colours carry over from partitioning: tens along one edge, ones along the other. Multiplying with a gridThe colours carry over from partitioning: tens along one edge, ones along the other.Worked example: 24 × 36Split both numbers into tens and ones, then multiply every row by every column.306204×60012012024600 + 120 + 120 + 24 = 864Estimate first: 24 is about 25 and 36 about 35, so the answer should land near 875.Now you tryWrite your partitioned numbers in the coloured headings first.45 × 23×estimateadd the four answers68 × 52×estimateadd the four answersColour-coded maths guidesSheet 6
The fraction wallOne whole, cut nine different ways — the reference sheet for every fraction below. The fraction wallOne whole, cut nine different ways — the reference sheet for every fraction below.Cut the same whole into more pieces and each piece gets smaller.1 whole1halves1/21/2thirds1/31/31/3quarters1/41/41/41/4fifths1/51/51/51/51/5sixths1/61/61/61/61/61/6eighths1/81/81/81/81/81/81/81/8tenthstwelfthsLine any two rows up to compare. Two quarters reach exactly as far as one half, so they are equal.Use the wall to answer theseWhich is larger, 2/3 or 3/5?How many twelfths make 3/4?Write two fractions equal to 1/2.Which is smaller, 1/8 or 1/10?Colour-coded maths guidesSheet 7
Equivalent fractionsThe top and the bottom always travel together — that is the whole rule. Equivalent fractionsThe top and the bottom always travel together — that is the whole rule.Worked example: 2/3 written in sixths23=46× 2× 2Whatever you multiply the top by, multiply the bottom by the same amount. The value does not change.2/34/6Same shaded length, different number of pieces.Now you tryFill the missing number, then write what you multiplied or divided by.14=12what did you do?35=20what did you do?27=6what did you do?912=3what did you do?Colour-coded maths guidesSheet 8
Adding and subtracting fractionsYou can only add pieces that are the same size. Everything else is preparation. Adding and subtracting fractionsYou can only add pieces that are the same size. Everything else is preparation.Worked example: 1/2 + 1/31Check the bottomsHalves and thirds are different sizes, so they cannot be added yet.2Find a number both go intoBoth 2 and 3 divide into 6, so rewrite each fraction in sixths.3Add the tops onlyThree sixths plus two sixths is five sixths. The bottom stays at 6.1/21/33/62/636+26=56You never add the bottom numbers.Now you try14+13=rewrite both with the same bottom number+=25+310=rewrite both with the same bottom number+=34−16=rewrite both with the same bottom number−=56−14=rewrite both with the same bottom number−=Colour-coded maths guidesSheet 9
Simplifying fractionsDivide the top and the bottom by the largest number that goes into both. Simplifying fractionsDivide the top and the bottom by the largest number that goes into both.Worked example: simplify 18/241824÷ 6÷ 634nothing divides into both 3 and 4,so this is fully simplifiedFactors of 181 2 3 6 9 18Factors of 241 2 3 4 6 8 12 24the largest number in both lists is 6Dividing by a smaller common factor still works — it just takes more steps. 18/24 to 9/12 to 3/4.Now you tryList the factors of each number, ring the largest they share, then divide by it.1230=factors of 12factors of 302045=factors of 20factors of 453648=factors of 36factors of 484270=factors of 42factors of 70Colour-coded maths guidesSheet 10
Multiplying and dividing fractionsMultiplying goes straight across. Dividing is the same thing with the second fraction flipped. Multiplying and dividing fractionsMultiplying goes straight across. Dividing is the same thing with the second fraction flipped.Multiplying: straight across23×35=615=25tops × topsbottoms × bottomsthen simplifyDividing: keep, flip, multiplyKeepthe first fraction exactly as it isFlipthe second fraction upside downMultiplystraight across, as above34÷25=34×52=158flippedTurn mixed numbers into improper fractions before you start. 2¼ becomes 9/4.Now you try12×45=simplified37×23=simplified23÷16=simplified58÷34=simplifiedColour-coded maths guidesSheet 11
Fractions, decimals and percentagesOne value, three notations — and the three conversions that move between them. Fractions, decimals and percentagesOne value, three notations — and the three conversions that move between them.The same amount, said three waysFractionDecimalPercentageHow much of the whole1/20.550%1/40.2525%3/40.7575%1/50.220%1/100.110%1/30.333…33.3%ConvertingFraction to decimaldivide the top by the bottom3 ÷ 8 = 0.375Decimal to percentagemultiply by 1000.375 × 100 = 37.5%Percentage to fractionput it over 100, then simplify24% = 24/100 = 6/25Now you tryComplete every row.FractionDecimalPercentage3/50.465%7/20Colour-coded maths guidesSheet 12