Year 5 Maths Handy Revision Guide (Autumn Term)

Year 5 MathsHandy Revision Guide (Autumn Term)

Multiplying by 10, 100 and 1000When we multiply by 10 the number becomes 10 times bigger. Thedigits move one place to the left.HT12 x 10UThHTUTo multiply by10 move eachdigit onedecimal placeto left and addzero as a placesaver whenneeded. Tomultiply by 100move each digittwo decimalplaces left.12 X 100When we multiply by 100 the digits move 2 places to the left andso on.TOP TIPSThe easy way to multiply whole numbers by 10, 100, 1000 is to addzeroes.(X 10 add 1 zero) e g. 33 X 10 330(X 100 add 2 zeroes) e.g. 41 X 100 4100(X 1000 add 3 zeroes) e.g. 71 X 1000 71,000For decimal numbers (which are not whole) hop the decimal pointto the right always remembering we are making the numberbigger.1 place to the right for X 10e.g 38.9 X 10 3892 place to the right for X 100 e.g. 8.12 X 100 8123 place to the right for X 1000 e.g. 9.13 X 1000 9130

Dividing by 10, 100 and 1000When we divide by 10 the number becomes 10 times smaller. Thedigits move one place to the right.When we divide by 100 the number becomes 100 times smaller.The digits move two places to the right,HT130 10UThHTU8800 100TOP TIPSThe easiest way to divide whole numbers which end in zeroes is totake off the same number of zeroes as you are dividing bye.g.3700 100 37 (take off 2 zeroes)770 10 77 (take off 1 zero)For numbers which do not end in zeroes the easiest way to hop thedecimal point to the left always remembering we are making thenumber smaller.1 place to the left for 10 e.g. 379 10 37.92 places to the left for 100 e.g. 889 100 8.89

FactorsThe factors of a number are the numbers which divide exactlyinto it (‘Fit’ into it) without a remainder.To find factors don’t just guess by randomly thinking of numbers,work through the numbers in order.Example:The factors of 16 are 1, 2, 4, 8 and 16The pairs of factors of 12 are 1 x 12, 2 x 6, 3 x 4MultiplesA number adding onto itself again and againe.g. multiples of 2 would be 2, 4, 6, 8, 10, 12, 14 etc.multiples of 5 would be 5, 10, 15, 20, 25, 30, 35 etcTOP TIPMultiples are More , Factors Fit

Square Numbers and Square RootsA number multiplied by itself is a square number. They are squarenumbers because they can be drawn in the shape of a square. Theopposite of a square number is called a square root.SquaresSquare Roots1² 12² 44² 165² 256² 367² 498² 649² 8110² 100 1 4 16 25 36 49 64 81 100 1245678910Cube Numbers and Cube RootsA number multiplied by itself and then by itself again e.g. 2 X 2 X2 is a cube number. The opposite of a cube number is called acube root.At Year 5 we only need to learn the first 3 cube numbersCubeCube Roots1³ 12³ 2 x 2 x 2 83³ 3 x 3 x 3 27³ 1 ³ 8 ³ 27 123

Prime NumbersA number which has only one pair of factors itself and 1 is a primenumber. Nothing divides into a prime number apart from 1 anditself. The first prime number is 2. It is the only even primenumberThese are the first 10 prime numbers.2, 3, 5, 7, 11, 13, 17, 19, 23, 29Prime FactorsWe find the prime factors of a number using a factor tree.For example find the prime factors of 12.Start with the number in the middle of the page.Write down a pair of factors as the first branches1262If the number is prime leave it alone and put a circle round it (likea stop sign). If not write it as a pair of factors using morebranches.126322Continue until all the numbers at the end of the branches areprime numbers.The prime factors of 12 are all the numbers with circles aroundthemSo 12 2 x 2 x 3

RoundingWhen we round to the nearest 10 we need to look at theunits column to see if we need to round up or downExample:Number of people at Hall Grove School is 374, to thenearest 10 is 370.When we round to the nearest 100 we need to look at thetens column to see if we need to round up or downExample: Number of people at Hall Grove School is 374, tothe nearest 100 is 400When we round to the nearest 1000 we need to look at thehundreds column to see if we need to round up or downExample: Number of people in Windlesham is 8374, to thenearest 1000 is 8000Remember : If the number we are looking at is 5 or above weround up.Example: 285 to the nearest 10 is 290Decimal numbers can be rounded to the nearest whole number,Example:5.78 to the nearest whole number is 632.89 to the nearest whole number is 3312.06 to the nearest whole number is 12

This is especially useful when we use money or measures suchas length or mass 2.76 to the nearest pound is 34 m 35 cm can be rounded to 4 m, to the nearest metreNegative NumbersNumbers don't just stop at zero. When you count backwards fromzero, you go into negative numbers.Positive numbers are more than zero.Negative numbers are less than zero.Use a number line to order negative numbers. For instance, it iseasy to see that -2 is a higher number than -5 because it isfurther to the right on the number line.

Solving Word ProblemsIn mathematics there are many ways of saying the same thing.SymbolWords Used Addition, Add, Sum, Plus, Increase, Total-Subtraction, Subtract, Minus, Less, Difference,Decrease, Take Away, Deduct Multiplication, Multiply, Product, By, Times, Lots Of Division, Divide, Goes Into, How Many TimesWhen solving word problems.First Read the question carefullyUnderline the key words – look for the clue words (e.g. total)Write down the CalculationSolve the answerCheck - does it make sense?

FractionsA fraction is a part of a whole. There are two numbers to everyfraction:The top number of the fraction is called the numerator. Thebottom number is called the denominator.Fractions of AmountsTo find a fraction of a quantity:Divide the quantity by the denominatorMultiply the answer you get by the numeratorTo find2of 15, for example:5Divide 15 by 5 (the denominator): 15 5 3Multiply the answer 3 by 2 (the numerator): 3 x 2 6So 2/ 5 of 15 is 6To find1of 66, for example:6Divide 66 by 666 6 11So1of 66 116

Properties of TrianglesIsosceles triangles have 2 equal sides and 2 equal angles.Scalene Triangles have no equal sides and no equal angles.Equilateral Triangles have 3 equal sides and 3 equal angles.A Right Angled Triangle has an angle of 90 (a right angle)

COMMON FRACTIONS, DECIMALS ANDPERCENTAGESFraction121314341103101100Equivalent Decimal0.5Percentage50%0.3333 .33.333 %0.2525%0.7575%0.110%0.330%0.011%

Year 5 MathsRevision Practice (Autumn Term)These examples are to help you put the revision notes into practice.You do not need to do them all. Perhaps a grown up could make upsome more examples for you. Answers are available.1

Multiplying and Dividing by 10, 100 and 1000Calculations1. 30 x 10 .8. 3.3 x 10 .2. 210 x 10 .9. 8800 x 100 .3. 3.45 x 10 .10. 110 10 .4. 0.3 x 10 11.2600 100 .5. 56 x 100 12.39000 100 6. 777 x 10 .13.4800 100 .7. 459 x 100 .14.730 100 .15. 6.5 10 Write the missing numbers.1. 100 x2. 5800 3. 43 x4.5. 687 x10 200 430 100 4 68 7002

Word Problems1. Sudley Primary school is having a fun run. Each child inYear 5 runs 10 laps of the field. If each lap is 0.3 kmhow far does each child run?2. If 100 wooden beads weigh 4100g, how much doeseach wooden bead weigh?3. A doctor spends on average 0.5 hours seeing apatient. Approximately how long does it take thedoctor to see 10 patients?3

Factors, Prime Numbers, Square Numbers, Cube Numbers,Multiples1. Think up all the factors for:a.6(4 factors)b.12(6 factors)c.15(4 factors)2. Write the prime numbers up to 20 (there are 8 in total)3. What is unusual about 2, compared with all the other primenumbers?4. Join up the numbers to their correct square numbers andcomplete the original number (the square root) in the column tothe right.Square number819149254121161001443664Square sum2x25x56x612 x 129x91x13x38x87x711 x 114x410 x 105. What is 2 cubed ? 6. What is 3³ ? 4Square root

7. What is 1³ ? 8. Find all multiples of 4 up to 48 .9. Find all multiples of 6 up to 72 .10. Look at the list of numbers37891011Which numbers are divisible by 3? .Which numbers are even numbers? .Which numbers are factors of 30? Which numbers are prime numbers? .Which numbers are square numbers? Which number is a cube number? .Which numbers are multiples of 5? Is 1 a primenumber ?52596

Rounding1.2.3.4.5.6.7.8.9.10.3766 to the nearest 100 is .3766 to the nearest 10 is 3766 to the nearest 1000 is .43.87 to the nearest whole number is . 2.51 to the nearest pound is .2m 50cm to the nearest metre is 5.33 to the nearest whole number is .12.8 to the nearest whole number is .4.22 to the nearest whole number is .69.5 to the nearest whole number is .Ordering Numbers1. Order these numbers from lowest to highest:a)201, 210, 21, 2009, 299b)– 7, 1, 0, 6, – 5, – 3, 10, 11c)901, 199, 99, 9009, 109Negative Numbers and Temperature1. The temperature rises by 15 degrees from -4 C. What is thenew temperature?2. The temperature falls from 11 C to -2 C. How many degreesdoes the temperature fall?3. The temperature is 6 C. It falls by 8 degrees. What is thetemperature now?4. Put the temperatures in order coldest to warmest.16 C, 18 C, -23 C, -25 C, -13 C, 12 C, 20 C6

5. Which of these temperatures is lowest?i) -4 C or -2 Cii) -8 C or 8 Ciii) -16 C or -17 Civ) -5 C or -6 CFractions of AmountsCalculate :¼ of 28 .½ of 56 .⅛ of 64 .Measuring LinesUse a ruler to measure these lines (be careful with the units)a.b.c . .mm .cm .mmUse a ruler to draw a line 65 mm long start from the dotd .7

Year 5MathsRevision Practice (Autumn Term)SOLUTIONSThese examples are to help you put the revision notes intopractice. You do not need to do them all. Perhaps a grown upcould make up some more examples for you. Answers areavailable.1

Multiplying and Dividing by 10, 100 and 1000Calculations1. 30 x 10 300 .8. 3.3 x 10 33 .2. 210 x 10 2100 .9. 8800 x 100 880,000 .3. 3.45 x 10 34.5 .10. 110 10 11 .4. 0.3 x 10 3 11.2600 100 26 .5. 56 x 100 5600 12.39000 100 390 6. 777 x 10 7770 .13.4800 100 48 .7. 459 x 100 45,900 .14.730 100 7.3 .15. 6.5 10 Write the missing numbers.1. 100 x2. 5800 3. 43 x4.5. 687 x10 200 430 100 458200010400 68 700 1002 0.65

Word Problems1. Sudley Primary school is having a fun run. Each child inYear 5 runs 10 laps of the field. If each lap is 0.3 kmhow far does each child run?0.3 x 10 3km2. If 100 wooden beads weigh 4100g, how much doeseach wooden bead weigh?4100 100 413. A doctor spends on average 0.5 hours seeing apatient. Approximately how long does it take thedoctor to see 10 patients?0.5 x 10 5 hours3

Factors, Prime Numbers, Square Numbers, Cube Numbers,Multiples1. Think up all the factors for:a.61,2,3,6b.121,2,3,4,6,12c.151,3,5,15(4 factors)(6 factors)(4 factors)2. Write the prime numbers up to 20 (there are 8 in total)2,3,5,7,11,13,17,193. What is unusual about 2, compared with all the other primenumbers?Only Even Prime Number4. Join up the numbers to their correct square numbers andcomplete the original number (the square root) in the column tothe right.Square number819149254121161001443664Square sum2x25x56x612 x 129x91x13x38x87x711 x 114x410 x 105. What is 2 cubed ? 8 6. What is 3³ ? 27 4Square root931752114101268

7. What is 1³ ? 1 8. Find all multiples of 4 up to 48 4,8,12,16,20 etc .9. Find all multiples of 6 up to 72 6,12,18,24,30, etc.10. Look at the list of numbers3789101125Which numbers are divisible by 3? 3, 9, 96 .Which numbers are even numbers? 8,10, 96 .Which numbers are factors of 30? 3, 10 Which numbers are prime numbers? 3,7, 11 .Which numbers are square numbers? 9, 25 Which number is a cube number? 8 .Which numbers are multiples of 5? 10, 25 Is 1 a primenumber ?NO596