Our Mental Maths Passports

One of the three aims of the national curriculum states that pupils (of all ages, not just primary children) will: become fluent in the fundamentals of mathematics., so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. 

At St George's we are committed t ensuring that children are equipped for this challenge.

We have designed 6 mental maths passports so that we can report on your child's development in this area.  these are available to download at the bottom of this page.

Our approach to teaching mental maths fluency is detailed below. 

  1. It is all about Teaching.  Mental strategies must be taught and modelled.  Practise without teaching will not promote good progress.  Teachers must ensure that teach strategies patterns and connections daily.  Practise is children’s chance to apply this.

  2. Concept is Key.  Fluency is about understanding the concept not learning new facts.  This promotes understanding and effective learning. Examples include:

2A.  Counting - once I have learnt 0-10 and understand the base 10 number system, I can apply this to accelerate through teen numbers and then 20-30 etc.   Teen numbers present challenges but if we teach the concept (twelve is 10 and 2 with a special name) children use their prior knowledge to accelerate their progress.

2B.  Number bonds and pairs.  If I understand the concept of a number bond, I have the fundamentals of the commutative law and the link between addition and subtraction.  So

5 + 1 = 6          1 + 5 = 6

6 - 1 = 5           6 – 5 = 1

I also note the pattern Odd + Odd = Even (need to check if this is a rule!)

Knowing bonds to 6 is the foundation for learning bonds to 7.  What happens if my total increases by 1 (to 7)?  How can I adapt the number calculations/bonds?

 

2C.  Times Table. 

Multiplication and division are a related concept and should be taught as so (also remembering to stress links with repeated addition and subtraction).  As children learn tables and note their patterns, they also develop conceptual understanding (Even x Even = Even etc).  Children must be taught to use known facts when they learn a new times tale.  In principle this means when I start the x 7 table they will already know:

0 x 7                           7 ÷ 0

1 x 7        7 x 1             7 ÷ 1            7 ÷ 7

2 x 7        7 x 2             14 ÷ 2          14 ÷ 7

3 x 7        7 x 3             21 ÷ 3          21 ÷ 7

4 x 7        7 x 4             28 ÷ 4          28 ÷ 7

5 x 7        7 x 5             35 ÷ 5          35 ÷ 7

6 x 7        7 x 6             42 ÷ 6          42 ÷ 7

 

 

10 x 7      7 x 10           70 ÷ 10         70 ÷ 7

 

I might know (depending n the order that I have been taught):

8 x 7 (I would teach this related to my knowledge of x2 and x 4) and associated facts

9 x 7 (I would teach this related to my knowledge of x3 and x 6) and associated facts

 

I need to know

7 x 7 Reinforce square numbers and associated facts

11 x 7 Reinforce 11 x 7 = (10 x 7) + (1 x 7) and associated facts

12 x 7 Reinforce 12 x 7 = (10 x 7) + (2 x 7) and associated facts

 

  1. Daily Counting is an expectation to develop fluency.

Our passports have explicit counting aims.  Counting starts at different places and travels forwards and backwards.  It is oral and recorded.  For example, if we arecounting in 7s, I might ask children to complete the grid below to show understanding.

 

-11

 

 

 

 

 

 

38

 

 

 

 

 

 

87

 

 

  1. Teaching must always start with a reference to concrete and pictorial representation.  This applies from EYFS to Year 6.  Models and Images are the central aspect of our teaching and fundamental to mastery approaches to learning.  We have an exhaustive range of teaching resources to promote this.  Some examples are::

Concrete Resources

Pictorial Resources

Numicon

Multiplication Grids

Deans

Number Lines

Ten Frames

Decimal, percentages and fraction tiles

Counters and concrete objects

Array creators

Counting Beads

Dice, dominoes etc,

 

  1. Build on Prior Knowledge.  Children do not start again when they look to develop fluency.  they build on prior knowledge.   For example:

  • All addition and subtraction regardless of how large or small the digit value is, relates back to number bonds.  278 + 42 would use 8+2 as the starting point.  27.8 + 4.2 is an extension of this fluency (I have created 10 tenths making a whole).

  • Area of rectangles is linked to arrays.

  • Fractions and percentages apply division.

3/5 of £275  relies on noticing 5 x 50 = 250 and 5 x 5 = 25.

700g + 15% relies on 700 ÷ 10 and knowing 5% is simply half of 10%

Files to Download

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