Year 5 Maths
Handy Revision Guide (Autumn Term)
Multiplying by 10, 100 and 1000 When we multiply by 10 the number becomes 10 times bigger. The digits move one place to the left. H
T
12 x 10
U
Th
H
T
U
To multiply by 10 move each digit one decimal place to left and add zero as a place saver when needed. To multiply by 100 move each digit two decimal
12 X 100
When we multiply by 100 the digits move 2 places to the left and so on. TOP TIPS The easy way to multiply whole numbers by 10, 100, 1000 is to add zeroes. (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 = 71,000 For decimal numbers (which are not whole) hop the decimal point to the right always remembering we are making the number bigger. 1 place to the right for X 10 e.g 38.9 X 10 = 389 2 place to the right for X 100 e.g. 8.12 X 100 = 812 3 place to the right right for for X 1000 e.g. 9.13 X 1000 = 9130
Dividing by 10, 100 and 1000 When we divide by 10 the number becomes 10 times digits move one place to the right.
. smaller
The
When we divide by 100 the number becomes 100 times smaller. The digits move two places to the right,
H
T
130 ÷ 10
U
Th
H
T
U
8800 ÷ 100
TOP TIPS The 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 the decimal 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
Factors
The factors of a number are the numbers whi ch divide exactly into 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 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
Square Numbers and Square Roots
A number multiplied by itself is a square number. They are square numbers 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 2! = 4 4! = 16 5! = 25 6! = 36 7! = 49 8! = 64 9! = 81 10! = 100
"1
= "4 = "16 = "25 = "36 = "49 = "64 = "81 = "100 =
1 2 4 5 6 7 8 9 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 a cube root. At Year 5 we only need to learn the first 3 cube numbers Cube Cube Roots 1# = 1 2# = 2 x 2 x 2 = 8 3# = 3 x 3 x 3 = 27
#"1
= #"8 = #"27 =
1 2 3
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 number These 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 3
2 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 them So 12 = 2 x 2 x 3
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 nearest 100 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 the hundreds column to see if we need to round up or down Example: Number of people in Windlesham is 8374, to the nearest 1000 is 8000
Remember : If the number we are looking at is 5 or above we round up. Example: 285 to the nearest 10 is 290
Decimal numbers can be rounded to the nearest whole number, Example: 5.78 to the nearest whole number is 6 32.89 to the nearest whole number is 33 12.06 to the nearest whole number is 12
This is especially useful when we use money or measures such as length or mass £2.76 to the nearest pound is £3 4 m 35 cm can be rounded to 4 m, to the nearest metre Negative Numbers
Numbers don't just stop at zero. When you count backwards from zero, 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 is easy to see that -2 is a higher number than -5 because it is further to the right on the number line.
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 Times
When 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?
Fractions
A fraction is a part of a whole. There are two numbers to every fraction:
The top number of the fraction is called the numerator. The bottom number is called the denominator. Fractions of Amounts
To find a fraction of a quantity: Divide the quantity by the denominator Multiply the answer you get by the numerator To find
2 5
of £15, for example:
Divide 15 by 5 (the denominator): 15 ÷ 5 = 3 Multiply the answer 3 by 2 (the numerator): 3 x 2 = 6 So 2/ 5 of £15 is £6 To find
1 6
of £66, for example:
Divide 66 by 6 66 ÷ 6 = 11 So 1 of £66 = 11 6
Properties of Triangles Isosceles 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 AND PERCENTAGES Fraction 1
Equivalent Decimal 0.5
Percentage 50%
2
1
0.3333….
33.333…%
0.25
25%
0.75
75%
0.1
10%
0.3
30%
0.01
1%
3 1 4
3 4
1 10 3 10 1 100
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.
1
Multiplying and Dividing by 10, 100 and 1000 Calculations
1. 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 x 2.
= 5800 ÷
3. 43 x 4. 5. 687 x
10 = 200 = 430
÷
100 = 4 = 68 700
2
…………………………
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 the doctor to see 10 patients?
3
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 number 81 9 1 49 25 4 121 16 100 144 36 64
Square sum 2x2 5x5 6x6 12 x 12 9x9 1x1 3x3 8x8 7x7 11 x 11 4x4 10 x 10
5. What is 2 cubed ?………………………… 6. What is 3! ?…………………………
4
Square root
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
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 square numbers? …………………………………………………………… Which number is a cube number? ………………………………………………………………….. Which numbers are multiples of 5? ………………………………………………………………… Is 1 a prime number ?
5
25
96
Rounding 1. 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 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 -4°C. What is the new temperature? 2. The temperature falls from 11°C to -2°C. How many degrees does the temperature fall? 3. The temperature is 6°C. It falls by 8 degrees. What is the temperature now? 4. Put the temperatures in order coldest to warmest. 16°C, 18°C, -23°C, -25°C, -13°C, 12°C, 20°C 6
5. Which of these temperatures is lowest? i) -4°C or -2°C ii) -8°C or 8°C iii) -16°C or -17°C iv) -5°C or -6°C Fractions of Amounts Calculate : " of £28 = …………………………………. # of £56 = …………………………………. ! of £64 = ………………………………….
Measuring Lines Use a ruler to measure these lines (be careful with the units) a. _____________________________ b. ___________________ c .__________
…………………..mm
…………………..cm
…………………..mm
Use a ruler to draw a line 65 mm long start from the dot d .
7
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.
1
Multiplying and Dividing by 10, 100 and 1000 Calculations
1. 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 x 2.
= 5800 ÷
3. 43 x 4. 5. 687 x
10 = 200 = 430
÷
100 = 4
58 2000 10 400
= 68 700 100
2
……0.65……………
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 a patient. Approximately how long does it take the doctor to see 10 patients? 0.5 x 10 = 5 hours
3
Factors, Prime Numbers, Square Numbers, Cube Numbers, Multiples 1. Think up all the factors for: a. 6 1,2,3,6 b. 12 1,2,3,4,6,12 c. 15 1,3,5,15
(4 factors) (6 factors) (4 factors)
2. Write the prime numbers up to 20 (there are 8 in total) 2,3,5,7,11,13,17,19 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 number 81 9 1 49 25 4 121 16 100 144 36 64
Square sum 2x2 5x5 6x6 12 x 12 9x9 1x1 3x3 8x8 7x7 11 x 11 4x4 10 x 10
5. What is 2 cubed ?……………8…………… 6. What is 3! ?……27…………………
4
Square root 9 3 1 7 5 2 11 4 10 12 6 8
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
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 square numbers? ……9, 25……………………………………………… Which number is a cube number? …8……………………………………………………….. Which numbers are multiples of 5? ………10, 25…………………………………………………… Is 1 a prime number ?
NO
5
96
Rounding 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
3766 to the nearest 100 is …3800………. 3766 to the nearest 10 is ………3770… 3766 to the nearest 1000 is ……4000. 43.87 to the nearest whole number is 40…….. £2.51 to the nearest pound is ………… £3.00……. 2m 50cm to the nearest metre is ……3m………… 5.33 to the nearest whole number is …5………….. 12.8 to the nearest whole number is ……13……….. 4.22 to the nearest whole number is 4……………….. 69.5 to the nearest whole number is ……70…….. Ordering Numbers
1. Order these numbers from lowest to highest: a) b) c)
201, 210, 21, 2009, 299 21, 201, 210, 299, 2009 – 7, + 1, 0, 6, – 5, – 3, + 10, 11 -7, -5, -3, 0, 1, 6, 10, 11 901, 199, 99, 9009, 109 99, 109, 199, 901, 9009 Negative Numbers and Temperature
1. The temperature rises by 15 degrees from -4°C. What is the new temperature? 11 2. The temperature falls from 11°C to -2°C. How many degrees does the temperature fall? 13 3. The temperature is 6°C. It falls by 8 degrees. What is the temperature now? -2 4. Put the temperatures in order coldest to warmest. 6
16°C, 18°C, -23°C, -25°C, -13°C, 12°C, 20°C -25°C, -23°C, -13°C, 12°C, 16°C, 18°C, 20°C 5. Which of these temperatures is lowest? i) -4°C or -2°C ii) -8°C or 8°C iii) -16°C or -17°C iv) -5°C or -6°C Fractions of Amounts Calculate : " of £28 = ………28÷4=…£7…………………. # of £56 = ………56÷2=…£28………………………. ! of £64 = ………64÷8=…£8………………………….
Measuring Lines Use a ruler to measure these lines (be careful with the units) a. _____________________________ b. ___________________ c .__________
…………………..mm
…………………..cm
…………………..mm
Use a ruler to draw a line 65 mm long start from the dot d .
7
