Year 5 Maths Revision

8/11/2019 Year 5 Maths Revision

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Year 5 Maths

Handy Revision Guide (Autumn Term)


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H T U

Dividing by 10, 100 and 1000

When 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,

TOP TIPSThe easiest way to divide whole numbers which end in zeroes is to

take off the same number of zeroes as you are dividing by

e.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 the

number smaller.

1 place to the left for 10 e.g. 379 10 = 37.9

2 places to the left for 100 e.g. 889 100 = 8.89

Th H T U

130 10 8800 100


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Factors

The factorsof a number are the numbers which divide exactly

into it (Fit into it) without a remainder.

To find factors dont just guess by randomly thinking of numbers,work through the numbers in order.

Example:

The factors of 16 are 1, 2, 4, 8 and 16

The pairs of factors of 12 are 1 x 12, 2 x 6, 3 x 4

Multiples

A number adding onto itself again and again

e.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 etc

TOP TIP

Multiples are More , Factors Fit


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Square Numbers and Square Roots

A number multiplied by itself is a square number. They are squarenumbers because they can be drawn in the shape of a square. The

opposite of a square number is called a square root.

Squares Square Roots

1!= 1 "1 = 1

2!= 4 "4 = 24!= 16 "16 = 4

5!= 25 "25 = 56!= 36 "36 = 67!= 49 "49 = 7

8!= 64 "64 = 8

9!= 81 "81 = 910!= 100 "100 = 10

Cube Numbers and Cube Roots

A number multiplied by itself and then by itself again e.g. 2 X 2 X

2 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 numbers

Cube Cube Roots

1#= 1 #"1 = 1

2#= 2 x 2 x 2 = 8 #"8 = 2

3#= 3 x 3 x 3 = 27 #"27 = 3


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Prime Numbers

A number which has only one pair of factors itself and 1 is a prime

number. Nothing divides into a prime number apart from 1 and

itself. The first prime number is 2. It is the only even prime

numberThese are the first 10 prime numbers.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Prime Factors

We 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 branches

12

6

2

If the number is prime leave it alone and put a circle round it (like

a stop sign). If not write it as a pair of factors using more

branches.

12

6 2

3 2

Continue until all the numbers at the end of the branches are

prime numbers.

The prime factors of 12 are all the numbers with circles around

themSo 12 = 2 x 2 x 3


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Rounding

When we round to the nearest 10 we need to look at the

units column to see if we need to round up or down

Example:

Number of people at Hall Grove School is 374, to the

nearest 10 is 370.

When we round to the nearest100 we need to look at the

tens column to see if we need to round up or down

Example: Number of people at Hall Grove School is 374, to

the nearest 100 is 400

When we round to the nearest 1000 we need to look at thehundreds column to see if we need to round up or down

Example: Number of people in Windlesham is 8374, to thenearest 1000 is 8000

Remember : If the number we are looking at is 5 or above weround up.

Example: 285 to the nearest 10 is 290

Decimal numberscan be rounded to the nearest whole number,

Example:

5.78 to the nearest whole number is 632.89 to the nearest whole number is 33

12.06 to the nearest whole number is 12


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Solving Word Problems

In mathematics there are many ways of saying the same thing.

Symbol Words 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 carefully

- Underline the key words look for the clue words (e.g. total)

- Write down the Calculation- Solve the answer- Check - does it make sense?


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Fractions

A 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 Amounts

To find a fraction of a quantity:

Divide the quantity by the denominatorMultiply the answer you get by the numerator

To find5

2 of 15, for example:

Divide 15 by 5 (the denominator): 15 5 = 3Multiply the answer 3 by 2 (the numerator): 3 x 2 = 6

So 2/ 5of 15 is6

To find6

1 of 66, for example:

Divide 66 by 6

66 6 = 11

So6

1 of 66 = 11


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Properties of Triangles

Isoscelestriangles have 2 equal sides and 2 equalangles.

ScaleneTriangles have no equal sides and no equal angles.

Equilateral Triangleshave 3 equal sides and 3 equal angles.

A Right Angled Trianglehas an angle of 90 (a right angle)


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COMMON FRACTIONS, DECIMALS ANDPERCENTAGES

Fraction Equivalent Decimal Percentage

2

1 0.5 50%

3

1 0.3333. 33.333%

4

1 0.25 25%

4

3 0.75 75%

10

1 0.1 10%

10

3 0.3 30%

100

1 0.01 1%


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1

Year 5 Maths

Revision 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 up

some more examples for you. Answers are available.


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2

Multiplying and Dividing by 10, 100 and 1000

Calculations

1. 30 x 10 = ..

2. 210 x 10 = ..

3. 3.45 x 10 = ..

4. 0.3 x 10 =

5. 56 x 100 =

6. 777 x 10 = .

7. 459 x 100 =..

8. 3.3 x 10=.

9. 8800 x 100= .

10. 110 10 = ..

11. 2600 100 = .

12. 39000 100 =

13. 4800 100 = ..

14. 730 100 = .

15. 6.5 10 =

Write the missing numbers.

1. 100 x = 5800

2.

10 = 200

3. 43 x = 430

4. 100 = 4

5. 687 x = 68 700


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3

Word Problems

1. Sudley Primary school is having a fun run. Each child in

Year 5 runs 10 laps of the field. If each lap is 0.3 km

how far does each child run?

2. If 100 wooden beads weigh 4100g, how much does

each wooden bead weigh?

3. A doctor spends on average 0.5 hours seeing a

patient. Approximately how long does it take thedoctor to see 10 patients?


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4

Factors, Prime Numbers, Square Numbers, Cube Numbers,

Multiples

1. 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 prime

numbers?

4. Join up the numbers to their correct square numbers and

complete the original number (the square root) in the column to

the right.

Square sum

2 x 2

5 x 56 x 6

12 x 12

9 x 9

1 x 1

3 x 3

8 x 8

7 x 7

11 x 11

4 x 4

10 x 10

5. What is 2 cubed ?

6. What is 3!?

Square number Square root

81

91

49

25

4

121

16

100

14436

64


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5

Is 1 a primenumber ?

7. What is 1!?

8. Find all multiples of 4 up to 48 .

9. Find all multiples of 6 up to 72 .

10. Look at the list of numbers

3 7 8 9 10 11 25 96

Which numbers are divisible by 3?

.

Which numbers are even numbers?

..

Which numbers are factors of 30?

Which numbers are prime numbers?..

Which numbers are squarenumbers?

Which number is a cube number?

..

Which numbers are multiples of 5?


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6

Rounding

1. 3766 to the nearest 100 is .

2. 3766 to the nearest 10 is

3.

3766 to the nearest 1000 is ..4. 43.87 to the nearest whole number is ..

5. 2.51 to the nearest pound is .

6. 2m 50cm to the nearest metre is

7. 5.33 to the nearest whole number is ..




Ordering Numbers

1. Order these numbers from lowest to highest:

a) 201, 210, 21, 2009, 299

b) 7, + 1, 0, 6, 5, 3, + 10, 11

c) 901, 199, 99, 9009, 109

Negative Numbers and Temperature

1. The temperature rises by 15 degrees from -4C. What is the

new temperature?

2. The temperature falls from 11C to -2C. How many degrees

does the temperature fall?

3. The temperature is 6C. It falls by 8 degrees. What is the

temperature now?

4. Put the temperatures in order coldest to warmest.16C, 18C, -23C, -25C, -13C, 12C, 20C


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5. Which of these temperatures is lowest?

i) -4C or -2C

ii) -8C or 8C

iii) -16C or -17Civ) -5C or -6C


Calculate :

"of 28 = .

#of 56 = .

!of 64 = .

Measuring Lines

Use a ruler to measure these lines (be careful with the units)

a. _____________________________ ..mm

b. ___________________ ..cm

c .__________ ..mm

Use a ruler to draw a line 65 mm long start from the dot

d .


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1

Year 5

Maths

Revision Practice (Autumn Term)

SOLUTIONS

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 up some more examples for you. Answers are

available.


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2

Multiplying and Dividing by 10, 100 and 1000

Calculations

1. 30 x 10 = 300..

2. 210 x 10 = 2100..

3. 3.45 x 10 = 34.5..

4. 0.3 x 10 = 3

5. 56 x 100 = 5600

6. 777 x 10 = 7770.

7. 459 x 100 =45,900..

8. 3.3 x 10=33.

9. 8800 x 100= 880,000.

10. 110 10 = 11..

11. 2600 100 = 26.

12. 39000 100 = 390

13. 4800 100 = 48..

14. 730 100 = 7.3.

15. 6.5 10 = 0.65

Write the missing numbers.

1. 100 x = 5800 58

2. 10 = 200 2000

3. 43 x = 430 10

4.

100 = 4 400

5. 687 x = 68 700 100


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3

Word Problems

1. Sudley Primary school is having a fun run. Each child in

Year 5 runs 10 laps of the field. If each lap is 0.3 km

how far does each child run?0.3 x 10 = 3km

2. If 100 wooden beads weigh 4100g, how much does

each wooden bead weigh?

4100 100 = 41

3.

A doctor spends on average 0.5 hours seeing apatient. Approximately how long does it take the

doctor to see 10 patients?

0.5 x 10 = 5 hours


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4

Factors, Prime Numbers, Square Numbers, Cube Numbers,

Multiples

1. Think up all the factors for:

a. 6 1,2,3,6 (4 factors)b. 12 1,2,3,4,6,12 (6 factors)

c. 15 1,3,5,15 (4 factors)

2. Write the prime numbers up to 20 (there are 8 in total)

2,3,5,7,11,13,17,19

3. What is unusual about 2, compared with all the other prime

numbers?

Only Even Prime Number

4. Join up the numbers to their correct square numbers and

complete the original number (the square root) in the column to

the right.

Square sum

2 x 2

5 x 56 x 6

12 x 12

9 x 9

1 x 1

3 x 3

8 x 8

7 x 7

11 x 11

4 x 4

10 x 10

5. What is 2 cubed ?8

6. What is 3!?27

Square number Square root

81 9

9 31 1

49 7

25 5

4 2

121 11

16 4

100 10

144 1236 6

64 8


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5

Is 1 a primenumber ?

7. What is 1!?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 numbers

3 7 8 9 10 11 25 96

Which 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 squarenumbers?

9, 25

Which number is a cube number?

8..

Which numbers are multiples of 5?

10, 25

NO


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6

Rounding

1. 3766 to the nearest 100 is 3800.

2. 3766 to the nearest 10 is 3770

3.

3766 to the nearest 1000 is 4000.4. 43.87 to the nearest whole number is 40..

5. 2.51 to the nearest pound is 3.00.

6. 2m 50cm to the nearest metre is 3m

7. 5.33 to the nearest whole number is 5..




Ordering Numbers

1. Order these numbers from lowest to highest:

a) 201, 210, 21, 2009, 299

21, 201, 210, 299, 2009

b) 7, + 1, 0, 6, 5, 3, + 10, 11-7, -5, -3, 0, 1, 6, 10, 11

c) 901, 199, 99, 9009, 109

99, 109, 199, 901, 9009

Negative Numbers and Temperature

1. The temperature rises by 15 degrees from -4C. What is the

new temperature?11

2. The temperature falls from 11C to -2C. How many degrees

does the temperature fall?

13

3. The temperature is 6C. It falls by 8 degrees. What is the

temperature now?

-24. Put the temperatures in order coldest to warmest.


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16C, 18C, -23C, -25C, -13C, 12C, 20C

-25C, -23C, -13C, 12C, 16C, 18C, 20C

5. Which of these temperatures is lowest?

i) -4Cor -2Cii) -8Cor 8C

iii) -16C or -17C

iv) -5C or -6C


Calculate :

"of 28 = 284=7.

#of 56 = 562=28.

!of 64 = 648=8.

Measuring Lines

Use a ruler to measure these lines (be careful with the units)

a. _____________________________ ..mm

b. ___________________ ..cm

c .__________ ..mm

Use a ruler to draw a line 65 mmlong start from the dot

d .

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Year 5 Maths Revision