Mathematics Stage 6 – Number skills and concepts to keep practising
It is not about achieving each thing once, but regular practise – (we call it ‘hardwiring’) – So that it becomes learnt and is retained
for the long term. Being confident at and able to explain these skills is a good starting point for achieving 6. If you have any
questions or would like further explanation please come into school and speak to your child’s class teacher
1.
Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit. Round any whole number to a required degree of accuracy.
27,546,209 – ‘The value of the 5 is 500,000’
‘The value of the 9 is 9’
‘The value of the 6 is 6000’
Order 34,324,556 34,314,556 and 34,324,566
What is this number rounded to the nearest thousand? 23,435,554 becomes 23,436,000
2.
Use negative numbers in context, and calculate intervals across zero. Solve number and practical problems that involve all of the above.
What is 6 subtract 15?
What is the difference between 4 and -8?
On Monday the temperature is -17 degrees and on Friday it is 8 degrees. How much has it increased by?
3.
Multiply and divide numbers up to 4 digits by a 2-digit whole number using the formal written methods and interpret remainders in division as whole number remainders, fractions, or by rounding.
4.
Identify common factors, common multiples and prime numbers.
Common factors of 18 and 30 are 1, 2, 3 and 6
Common multiples of 2 and 3 are 6, 12 and 18 etc.
Prime numbers have two different factors. For a 2 digit number check if it is a x2, x3, x5 and x7. If not then it is a prime number.
5.
Use their knowledge of the order of operations to carry out calculations involving the four operations.
1st Brackets – 2nd Squares or square roots – 3rd Multiply and divide (left to right) – 4th Add and subtract (left to right)
e.g. (3 + 6) x 2 = 18
or 7 + (6 × 52 + 3) = 160
6.
Use common factors to simplify fractions; use common multiples to express fractions in the same denomination.
Use a common factor
to simplify
7.
Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions.
7
12
8.
Multiply simple proper fractions and simplify the answer (e.g. ¼ x ⅟₂ = ⅟₈). Divide proper fractions by whole numbers (e.g. ⅓ ÷ 2 = ⅙).
9.
Identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places
3.569 – ‘The value of the 5 is 0.5’
‘The value of the 6 is 0.06’
‘The value of the 9 is 0.009’
x move up
÷ move down
The number of zeros indicates the number of places
The number of zeros indicates the number of places
e.g. 5.67 x 100 = 567 or 53.4 ÷1000 = 0.0534
10.
Multiply one-digit numbers with up to two decimal places by whole numbers. Use written division methods in cases where the answer has up to two decimal places
11.
Recall and use equivalences between simple fractions, decimals and percentages.
12.
Solve problems involving the calculation of percentages (e.g. of measures) such as 15% of 360 and the use of percentages for comparison
13.
Express missing number problems algebraically. Use simple formulae expressed in words
e.g. There are some people on a bus. At the bus stop 9 people get off. Use the letter p to represent the number of people on the bus to begin with and write an expression to show the number of people on
the bus after the bus stop.
Answer: P = 9
14.
Generate and describe linear number sequences
Or…
If a sequence follows the rule 3n + 5
What will be the 5th number in the sequence? (3 x 5) + 5 = 20
3n-2
15.
Find pairs of numbers that satisfy number sentences involving two unknowns. Find all possibilities of combinations of two variables
How many pairs of numbers (for A and B) can you find to satisfy the number sentence (2 x a) + b = 6
a=1 b=4
16.
Use, read, write & convert between standard units of measure, converting length, mass, volume & time from smaller to larger units, and vice versa, using decimal notation to up to 3 dec places. Also convert between miles and km.
e.g.
2.5 km
=
……..m
19:38
=
7:38 pm (time)
4560g
=
………kg
1 mile
=
1.6 km
=
1600m
………l
=
4850 ml
a=2 b=2
a=3 b=0