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3/3 Multiples
Level 3
PROMPT sheet                                                                    Multiples are the number sequences
                                                                                that make up the tables

3/1 Place value                                                         Example
                                                                        The multiples of 2 are:
The position of the digit gives its size                                2      4       6       8                10       ...




                                              .
                                                                        The multiples of 5 are:



                                                           hundredths
        thousands

                    hundreds




                                                  tenths                5     10       15      20               25       ...
                                      units
                               tens




                                                                        The multiples of 10 are:


                                              .
                                                                        10    20       30      40               50       ...

        4             3         5      2            6          1

                                                                        3/4 Fractions

Example
                                                                            1                    numerator
The value of the digit ‘4’ is 4000
The value of the digit ‘3’ is 300
                                                                            2                    denominator

                                                                             This means 1 part out of every 2
3/2 Recognise negative numbers
                                                                        Example 1
       These can be seen on a thermometer


                                                                                 1                       5
                                                                                  2      =              10
                                                                                  These fractions are all ½
                                                                                   1         2     3    4            5
                                                                                     2       4     6    8        10
                                                                        Example 2

 The numbers below freezing (00) are negative                                                      2
                                                                                                   3
       Number line to work out sums
                                                                                This means 2 part out of every 3




                          3 – 5 = -2                                              2
                                                                                         =
                                                                                                            4
                                                                                  3                         6
3/5 Decimals                                           3/7 Division facts from a multiplication


         Decimals and money                            Any multiplication sum can be written as 2
                                                       division sums
£3.00 means 300p
£3.50 means 350p                                                      14 x 5 = 70
£3.05 means 305p


Remember
                                                       70 ÷ 14 = 5                  70 ÷ 5 = 14
A calculator does not know if the numbers you put in
are money so £3.50 will look like 3.5



         Ordering Decimals                             3/8 Balancing a sum

1.23 m       1.6 m        1.65 m        1.3 m          left hand side is equal to right hand side

1.23 m       1.60 m       1.65 m        1.30 m                          3 x 4 = 12
 Make the number of digits the same, it is easier to
                   order them                             This can be used to find missing numbers
Smallest                                  Largest
1.23 m       1.30 m           1.60 m        1.65 m                     3 x 4 = 3 +
                                                                         12 = 3 + 9
                                                                      So     = 9
3/6 Know the 3, 4 and 6 times tables

1    x   3   =   3            1     x   4   =   4
2    x   3   =   6                                     3/9 Add 2 digit numbers mentally
                              2     x   4   =   8
3    x   3   =   9            3     x   4   =   12
4    x   3   =   12           4     x   4   =   16     Partitioning
5    x   3   =   15           5     x   4   =   20                      36 + 19
6    x   3   =   18           6     x   4   =   24
7    x   3   =   21           7     x   4   =   28
8    x   3   =   24           8     x   4   =   32     30 + 6 + 10 + 9          36 + 10 + 9
9    x   3   =   27           9     x   4   =   36
                                                       = 40 + 15              = 46 + 9
10   x   3   =   30           10    x   4   =   40
                                                       = 55                   = 55
                 1    x   6   =    6
                 2    x   6   =    12                  3/9 Subtract 2 digit numbers mentally
                 3    x   6   =    18
                 4    x   6   =    24                                   63 - 26
                 5    x   6   =    30
                 6    x   6   =    36                  Partitioning          Counting on from 26
                 7    x   6   =    42
                 8    x   6   =    48                  63 – 20 – 6             (26) + 4 + 33
                 9    x   6   =    54                  = 43 - 6                      = 37
                 10   x   6   =    60                  = 37
3/11 Solve problems                                   3/13 Methods for multiplying

         When to multiply and when to divide                                 38 x 3
         When to round up and when to round down
                                                      Column method
Here is an example
                                                                                           38
                                                                                           2 3 x
                                                                                          114
There are 17 children in the playground.
Each bench in the yard can seat 3 children.           Grid method
How many benches will be needed?                                                  30           8
                                                                                3 90          24
                  17 ÷ 3 = 5 r 2
         We need to divide to share the children                           90 + 24 = 114
         around the benches
         We need to round up to 6 benches for the     Partitioning method
         remaining 2
                                                                                         38 x 3
Here is another example                                                                = 30 x3 + 8 x 3
                                                                                       = 90    + 24
Dan made 47 cakes.                                                                     = 114
He sells them in boxes of 6.
How many full boxes will we have?                     To multiply by 10
                                                      Move all the digits along one place to the left.
                  46 ÷ 6 = 7 r 4                      Remember to put a zero in the units.

         He needs to divide to share the cakes into                    H        T         U
         boxes                                                                  3         0
         He needs to round down to 7 boxes because
                                                                       3        0         0
         he needs to have 6 cakes in each box

                                                                           30 x 10 = 300

3/12 Written method for addition                      3/13 Methods for dividing

       Line up the digits in the correct columns
                                                                              25 ÷ 3
e.g.    132 + 239                 H   T U
                                  1   3 2             8 x 3 = 24             So 25 ÷ 3 = 8 r 1
                                  2   31 9 +
                                  3   7 1
                                                      To divide by 10
3/12 Written method for subtraction                   Move all the digits along one place to the right.


       Line up the digits in the correct columns
                                                                       H        T         U
e.g. 327 - 119                    H   T   U                                     3         0
                                      1   1
                                  3   2    7                                              3
                                  1   1    9 -
                                  2   0    8                                30 ÷ 10 = 3
3/14 Classify 2D shapes




              A           B                C                  D                     E




           Triangle     Square        Rectangle          Parallelogram         Trapezium




              A           B                C                      D                 E




         Reflective   Reflective      Reflective         NO reflective          Reflective
         symmetry     symmetry        symmetry           symmetry               symmetry


3/14 Classify 3D shapes




  Cube       cuboid           triangular prism         cylinder       sphere      cone       square-based
                                                                                               pyramid




 All have a curved surface                         All are prisms – same shape through the length



    Pyramids go to a point
3/15 Nets of 3D shapes                  3/16 Shapes in different orientations

                                         These are the same shapes – just moved round


                            CUBE




                                        These shapes have been reflected – flipped over

                                        In a HORIZONTAL mirror line


                            CUBOID




                                        In a VERTICAL mirror line




                         SQUARE-BASED
                          PYRAMID
                                        In a 450 mirror line
3/17 Describe position and movement               MEASURES OF LIQUID(Capacity)
                                                  5 millilitre spoon
       LEFT             RIGHT



ANTICLOCKWISE             CLOCKWISE
                                                  1 litre = 1000ml




                    Clockwise 900 or ¼ turn




                    Anticlockwise 900 or ¼ turn

                                                  3/19 Other units of measure

                                                  PERIMETER is the distance round the outside
                                                  of a shape
                    Half turn                     Perimeter of this shape = 12cm




3/18 Use standard units

MEASURES OF LENGTH
 1cm = 10mm



                                                  AREA is the number of squares INSIDE
                                                  Area of this shape = 5cm2
1 metre = 100cm
1 kilometre = 1000m
                                                                      1
MEASURES OF WEIGHT
1 gram




1kilogram = 1000g
ANGLE is the amount of turn                   3/21 Construct pictogram
This angle is 300
                                              This question is about the number of bags of
                                                    sugar you could buy with £10

                                                                            Sugar
                                                                  K ey:                = 4 bags




                                                     Ye a r                         N um ber of bags



                                                               Sugar        Sugar         Sugar        Sugar
                                                     1995




3/20 Gather information                              1999      Sugar        Sugar         Sugar        Sugar




To record the number of birds in the garden
                                                    Do not forget the KEY
      Type of        Tally        Number of
       bird                         birds
     Blackbird                                3/22 Venn Diagram
                                     10

      Blue-tit                                 These are used to record and sort information
                                        4

      Starling
                                        2

      Sparrow
                                        3

       Other
                                        1




3/21 Construct bar chart                             Shapes with                       Shapes with
                                                     right angles                       equal sides


Leave gaps between the bars                   3/22 Carroll Diagram


          10                                                    Number                            Number
           9                                                      of                                of
                                                                 Boys                              Girls
           8
  Number 7                                    Brown eyes               11                              12
   of Y7 6
   pupils
    late 5                                     Blue eyes               4                                3
           4
           3
           2
           1                                  3/23 Extract information from bar charts,
           0                                       pictograms and tables
                 M   T   W    T     F

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Level 3 prompt

  • 1. 3/3 Multiples Level 3 PROMPT sheet Multiples are the number sequences that make up the tables 3/1 Place value Example The multiples of 2 are: The position of the digit gives its size 2 4 6 8 10 ... . The multiples of 5 are: hundredths thousands hundreds tenths 5 10 15 20 25 ... units tens The multiples of 10 are: . 10 20 30 40 50 ... 4 3 5 2 6 1 3/4 Fractions Example 1 numerator The value of the digit ‘4’ is 4000 The value of the digit ‘3’ is 300 2 denominator This means 1 part out of every 2 3/2 Recognise negative numbers Example 1 These can be seen on a thermometer 1 5 2 = 10 These fractions are all ½ 1 2 3 4 5 2 4 6 8 10 Example 2 The numbers below freezing (00) are negative 2 3 Number line to work out sums This means 2 part out of every 3 3 – 5 = -2 2 = 4 3 6
  • 2. 3/5 Decimals 3/7 Division facts from a multiplication Decimals and money Any multiplication sum can be written as 2 division sums £3.00 means 300p £3.50 means 350p 14 x 5 = 70 £3.05 means 305p Remember 70 ÷ 14 = 5 70 ÷ 5 = 14 A calculator does not know if the numbers you put in are money so £3.50 will look like 3.5 Ordering Decimals 3/8 Balancing a sum 1.23 m 1.6 m 1.65 m 1.3 m left hand side is equal to right hand side 1.23 m 1.60 m 1.65 m 1.30 m 3 x 4 = 12 Make the number of digits the same, it is easier to order them This can be used to find missing numbers Smallest Largest 1.23 m 1.30 m 1.60 m 1.65 m 3 x 4 = 3 + 12 = 3 + 9 So = 9 3/6 Know the 3, 4 and 6 times tables 1 x 3 = 3 1 x 4 = 4 2 x 3 = 6 3/9 Add 2 digit numbers mentally 2 x 4 = 8 3 x 3 = 9 3 x 4 = 12 4 x 3 = 12 4 x 4 = 16 Partitioning 5 x 3 = 15 5 x 4 = 20 36 + 19 6 x 3 = 18 6 x 4 = 24 7 x 3 = 21 7 x 4 = 28 8 x 3 = 24 8 x 4 = 32 30 + 6 + 10 + 9 36 + 10 + 9 9 x 3 = 27 9 x 4 = 36 = 40 + 15 = 46 + 9 10 x 3 = 30 10 x 4 = 40 = 55 = 55 1 x 6 = 6 2 x 6 = 12 3/9 Subtract 2 digit numbers mentally 3 x 6 = 18 4 x 6 = 24 63 - 26 5 x 6 = 30 6 x 6 = 36 Partitioning Counting on from 26 7 x 6 = 42 8 x 6 = 48 63 – 20 – 6 (26) + 4 + 33 9 x 6 = 54 = 43 - 6 = 37 10 x 6 = 60 = 37
  • 3. 3/11 Solve problems 3/13 Methods for multiplying When to multiply and when to divide 38 x 3 When to round up and when to round down Column method Here is an example 38 2 3 x 114 There are 17 children in the playground. Each bench in the yard can seat 3 children. Grid method How many benches will be needed? 30 8 3 90 24 17 ÷ 3 = 5 r 2 We need to divide to share the children 90 + 24 = 114 around the benches We need to round up to 6 benches for the Partitioning method remaining 2 38 x 3 Here is another example = 30 x3 + 8 x 3 = 90 + 24 Dan made 47 cakes. = 114 He sells them in boxes of 6. How many full boxes will we have? To multiply by 10 Move all the digits along one place to the left. 46 ÷ 6 = 7 r 4 Remember to put a zero in the units. He needs to divide to share the cakes into H T U boxes 3 0 He needs to round down to 7 boxes because 3 0 0 he needs to have 6 cakes in each box 30 x 10 = 300 3/12 Written method for addition 3/13 Methods for dividing Line up the digits in the correct columns 25 ÷ 3 e.g. 132 + 239 H T U 1 3 2 8 x 3 = 24 So 25 ÷ 3 = 8 r 1 2 31 9 + 3 7 1 To divide by 10 3/12 Written method for subtraction Move all the digits along one place to the right. Line up the digits in the correct columns H T U e.g. 327 - 119 H T U 3 0 1 1 3 2 7 3 1 1 9 - 2 0 8 30 ÷ 10 = 3
  • 4. 3/14 Classify 2D shapes A B C D E Triangle Square Rectangle Parallelogram Trapezium A B C D E Reflective Reflective Reflective NO reflective Reflective symmetry symmetry symmetry symmetry symmetry 3/14 Classify 3D shapes Cube cuboid triangular prism cylinder sphere cone square-based pyramid All have a curved surface All are prisms – same shape through the length Pyramids go to a point
  • 5. 3/15 Nets of 3D shapes 3/16 Shapes in different orientations These are the same shapes – just moved round CUBE These shapes have been reflected – flipped over In a HORIZONTAL mirror line CUBOID In a VERTICAL mirror line SQUARE-BASED PYRAMID In a 450 mirror line
  • 6. 3/17 Describe position and movement MEASURES OF LIQUID(Capacity) 5 millilitre spoon LEFT RIGHT ANTICLOCKWISE CLOCKWISE 1 litre = 1000ml Clockwise 900 or ¼ turn Anticlockwise 900 or ¼ turn 3/19 Other units of measure PERIMETER is the distance round the outside of a shape Half turn Perimeter of this shape = 12cm 3/18 Use standard units MEASURES OF LENGTH 1cm = 10mm AREA is the number of squares INSIDE Area of this shape = 5cm2 1 metre = 100cm 1 kilometre = 1000m 1 MEASURES OF WEIGHT 1 gram 1kilogram = 1000g
  • 7. ANGLE is the amount of turn 3/21 Construct pictogram This angle is 300 This question is about the number of bags of sugar you could buy with £10 Sugar K ey: = 4 bags Ye a r N um ber of bags Sugar Sugar Sugar Sugar 1995 3/20 Gather information 1999 Sugar Sugar Sugar Sugar To record the number of birds in the garden Do not forget the KEY Type of Tally Number of bird birds Blackbird 3/22 Venn Diagram 10 Blue-tit These are used to record and sort information 4 Starling 2 Sparrow 3 Other 1 3/21 Construct bar chart Shapes with Shapes with right angles equal sides Leave gaps between the bars 3/22 Carroll Diagram 10 Number Number 9 of of Boys Girls 8 Number 7 Brown eyes 11 12 of Y7 6 pupils late 5 Blue eyes 4 3 4 3 2 1 3/23 Extract information from bar charts, 0 pictograms and tables M T W T F