Transcript maths number workshop

Aims of session
•
To explore the language and skills learnt in
Rushen Primary School relating to
number.:
• number bonds,
• partitioning,
• times tables,
• decimals,
• fractions,
Number bonds
•
Number bonds - a pair of numbers to make a total.
•
Children start of with number bonds to 10 such as 1 + 9 =10 and
all other pairs, as well as in the inverse 2 + ? = 10.
•
Other number bond patterns - all addition and subtraction facts
to 10 ie 3 + 4,
•
facts to 100 (starting with those that end in 5 or 0),
•
facts to 1000 (starting with multiples of 50 or 100)
•
fraction bonds to make 1.0 ie 0.2 + 0.8, fractions to make 1.
Would be expected to be able to do these
quickly to be confident so that they know them
with instant recall.
Partitioning
• Partitioning - separating values within
a number.
-
Partition 25 means separate into 20 (2
tens)and 5 (5 units or ones).
Use of names - units / ones, tens,
hundreds, thousands, ten thousands,
hundred thousands, million, tenth,
hundredth, thousandth.
Can be written under place value columns
or written as 20 + 5 = 25.
Understanding place value and meaning of
numbers is a vital skill.
Times Tables / Multiplication facts.
• Start off learning two times tables, build
up to 5 and 10. By Year 5 should really
know all times tables facts (10x10) and
the related division facts, - vital tool in
many other areas of maths.
Basics: Children learn to count in equal
steps from 0 and then we slowly
introduce the language 2 lots of, always
using apparatus until concepts are
secure, then building onto abstract
thinking.
• Decimals used to show values less than
Decimals
one - can be known as a decimal
fraction.
First introduced with measures and money,
contexts children know. e.g. £1.50,
where the 0.50 is less than a pound and
is five lots of ten, we link this concept to
the tenths column to the right of the
decimal point.
Extend to hundredths and then
thousandths.
Be able to add, subtract multiply and divide
Fractions - what are they?
Part of a whole.
1
2
A number written with the top part (the numerator)
telling how many you have.
and the bottom part (the denominator) telling you how
many parts the whole is divided into,
Language of fractions
•
•
Language of fractions is used all around children,
“here’s my half.” “I’ll cut this cake into equal parts
for the four of us.” etc
We would encourage correct use of terms from
early on - not “my half is bigger than yours!”
Simple fractions
Simple fractions are the common fractions
such as
1
1
1
1
1
1
2
3
4
5
8
10
Equivalent fractions
• Equivalent fractions are fractions that are
equal in size but have a different
denominators or numerators.
1
2
=
2
4
There are many more, use of fraction wall.
Mixed Numbers & Improper fractions
Mixed numbers and improper fractions show
values where there are more than one whole
being shown.
Two and a half pieces is the same as 5 halves
=
1
5
2
2
2
Changing fractions to a common
denominator
When fractions are to be ordered or added
than they need to have the same denominator
(link to equivalent fractions)
3
1 1
1
7
4
8 2
4
8
becomes 6 1 4
8 8 8
2
8
7
8
8 is the common denominator as all
denominators are in the times table. If this is
not obvious then multiply the denominators to
find a common denominator.
Ordering fractions
To order fractions of the same denominator
we need to look at the numerator.
6
1
4
3
7
8
8
8
8
8
Smallest to largest
1
3
4
6
7
8
8
8
8
8
Ordering fractions
To order fractions with different denominators
we need to convert all fractions to the lowest
common denominator.
3
1 1
1
7
4
8 2
4
8
becomes 6 1 4
8 8 8
2
7
8
8
7
Smallest to largest
1
2 4 6
7
and then 1
1
1
3
8
8 8 8
8
8
4
2
4 8
Ordering
fractions
Finding fractions of an amount or
quantities.
As a fraction is a division of a whole then we
use division to find a fraction of amounts.
Finding a half means dividing by 2 - to make
two equal sized groups.
1
4
÷4
1 ÷ 3
1 ÷ 5
3
5
ie divide by the denominator.
Finding fractions of an amount or
quantities.
To find fractions such 2/3 then we need to find
a third and then multiply this by 2.
2 of 12 = 1
3
3
is 4 x 2 = 8
Finding fractions of an amount or
quantities.
To find fractions such 2/3 then we need to find
a third and then multiply this by 2.
2 of 12 = 1
3
(12 ÷ 3) is 4 then x 2 = 8
3
Divide by denominator and then multiply this by
the numerator.
Showing fractions as decimals and
vice versa.
•
1 is equal to 0.5 as it is half of 1 or a whole one.
2
•
1 is equal to 0.25 as it is quarter of 1 or a
whole.
4
•
Other decimal equivalents are explored and
later on fractions are expressed as decimal by
making them out of 100 - or using a calculator.