Download Math- terminology

Maths Terminology
Mental calculation requires strategic thinking. If students are to develop their ability to think strategically,
then it is important that a common language is taught and plenty of opportunities are provided for practice.
The following terms should be introduced to students and the associated concepts explored, practised and
extended so that the language forms an integral part of every number exploration.
Terminology
Subitise
Comment
Building on Knowledge
Meaning to suddenly know, subitise is taken from the Latin word
subito. Subitising is an important skill that lays the foundation for
many later mathematical concepts. Perceptual subitising means
looking at a single group of objects and knowing just by looking at
them how many there are. Conceptual subitising builds on this
skill: for 6 and 2 thrown on two dice students can be encouraged
to subitise the 6 and count on 2 more.
Count on
Requires that students understand altogether as the joining of
groups of objects or numbers and that we can count on from the
numbers other than 1 and thus break the counting sequence.
Touching and counting every object does not practise early
addition skills. Students need to realise that it is more efficient to
subitise than count on.
How does knowing count on 1, 2 or 3
help you with 50 + 30?
How does knowing count on 1, 2 or 3
help you with 70 - 20?
Double
Doubles lay the foundation for more sophisticated strategies such
as ‘near double’, are often part of number splitting strategies and
provide a direct link to the concept of halving when working with
subtraction.
How does knowing your doubles facts
help you with 60 – 2?
How does knowing your doubles facts
help you with 70 – 35?
How does knowing double 3 = 6 help
with double 33?
How can we apply doubling strategies
to situations involving measurement
(e.g. time, length etc)?
Rainbow
Facts
Also known as build to 10 they identify all the pairs of numbers
that add to 10. Rainbow facts lay the foundation for
understanding friendly numbers and the later bridge through 10
strategy. The concept can be extended to include pairs of
numbers that add up to 1, 100, 1 000 etc.
What number pairs add to 1, 100,
1 000 etc.?
How do rainbow facts help us with
subtraction?
e.g. 100 – 70 = 30
Turnarounds
Refers to the commutative property of numbers in addition.
Students need to understand that the order in which numbers are
added makes no difference to the answer but it does make a
difference to the ease of adding the numbers. For example, for 2 +
6 it is faster to turn the numbers around and then count on 2 from
6. The concept of turnarounds also applies to multiplication.
How does knowing your turnarounds
for addition help you with
multiplication?
Near double
Sometimes described as ‘double + 1’ or ‘double – 1’. Near double
allow students to build on a known strategy, a process that
becomes very important as students learn to extend their number
facts.
How does knowing 6 + 7 is near to
6 + 6 help with 60 + 70?
Adding zero
It might seem obvious that adding zero to a number leaves it
unchanged but it is necessary to ensure students have developed
this understanding.
What is the outcome when we
multiply by 0?
Friendly
Numbers
Numbers ending in 0 are called friendly because they are very
easy to add a single digit number to. It helps lay the foundation
for the bridge through 10 and compensation strategies.
How does being able to work easily
with numbers ending in 0 help us
with calculations like 9 + 7 or 80 + 50?
TERMINOLOGY cont’d
Bridge through Builds on knowledge of friendly numbers and rainbow facts.
For example, to use bridging to add 9 + 4, the 4 is split into 1 +
10
3 giving 9 + 1 + 3. The rainbow pair 9 + 1 makes 10, and 3 is
easily added to the friendly number 10 to make 13. Strategy
can easily be extended into 10s, 100s and beyond e.g. 90 + 50
becomes 90 + 10 + 40. (See Compensating)
How does being able to bridge through
10 help us with 130 – 50?
How does being able to bridge through
10 help us with 39 + 26?
Adding 9
Relating + 9 to 10 – 1 makes it easier for students to make
connections with their understandings about friendly numbers.
What thinking could I use to help me
with + 90 or + 100?
Landmark
Numbers
The term given to numbers such as 25, 50 and 100. Knowing
that double 25 is 50 makes computing double 26 easy. Also
facilitates discussion around mathematical facts such as 75 + 25
= 100. Concept can also be linked to percentages and fractions.
What are the landmark fractions and
percentages?
Number
Splitting
Numbers can be split in many ways to make computations
easier e.g. 26 + 37 could become
26 + 4 + 33, allowing
students to strategise with reference to rainbow facts and
friendly numbers. Numbers can also be split for other
operations e.g. 13 x 4 could become (10 x 4) + (3 x 4)
How can we use number splitting to
help us complete calculations involving
the other operations?
Compensating
Making
friendly
numbers
Rounding, estimating and number splitting are the foundation
for the strategy of compensating when adding or subtracting.
Rounding 51 to the friendly number 50 makes it easier to add
17. For an exact answer, compensation in the form of adjusting
is required. The 1 taken off must now be added back. Rounding
and adjusting is one of the most frequently used compensation
strategies. (See Bridge through 10)
Changing
operations
Inverse
operations
Halving/
doubling
Students may find it easier to think addition when subtracting
or think multiplication when dividing. For example, 13 – 8,
students can think 8 add what makes 13?
Using developed doubling and halving strategies, students can
be encouraged to simplify more complex calculations. For
example, students could work out 17 x 4 by thinking 34 x 2
What sequence of numbers can be
halved down to 1?
Partitioning
Refers to the myriad of ways that numbers can be divided into
parts. There are standard place value partitions such as 582 =
500 + 80 + 2, but 582 can also be viewed as 58 tens + 2 ones or
even 382 + 200. The partition 382 + 200 is far more helpful
when calculating 582 – 198.
In what ways can partitioning be used
to make calculations easier?
Commutative
Law
The commutative law says that when you add or multiply
numbers the order doesn’t matter – you can swap numbers
over and still get the same answer, e.g. 2 + 3 = 3 + 2 = 5 or 2 x 3
=3x2=6
See Turnarounds
Associative
Law
The associative law says that it doesn’t matter how you group
the numbers (which you calculate first) when you add or when
you multiply, e.g. (2 + 4) + 5 = 6 + 5 = 11 or 2 + (4 + 5) = 2 + 9 =
11
Distributive
Law
The distributive law says that when you add up some numbers
then do a multiply or you multiply separately than add them,
you will get the same answer e.g. 2 x (5 + 2) = (2 x 5) + (2 x 2)