Transcript KS3 Place Value & Types of Number

LO To assess my understanding of place
value and types of number.
Key Words: Explain, Justify,
Communicate
RAG
17/07/2015
Starter Activity
Have a look at the ‘Heard the Word’ Grid
Are there any key words which you know
the meaning of now which you didn’t know
before?
Level
Place Value and types of number
3
I can round
whole
numbers to
the nearest
10, 100 or
1000.
4
I can identify factors of
two-digit numbers
Identify square
numbers up to 15 x 15
I know simple tests for
divisibility for 2, 3, 4, 5,
6, 8, 9
I can find the factors of
a number by checking
for divisibility
5
I can recognise
and use
multiples, factors,
common factor,
highest common
factor, lowest
common multiple
and primes.
I know and can
use the order of
operations,
including
brackets.
I can check the
reasonableness of
results with reference
to the context or size of I can round a
numbers
number to one
decimal place.
I can use the multiples
of 4 to work out the
multiples of 8.
6
I am able to
carry out
calculations with
more than one
step using
brackets.
7
When making
estimates I can
round to one
significant figure
and multiply and
divide mentally.
8
I can use laws
of indices in
multiplication
and division.
I can use
I understand the standard form
effects of
I am able to
to make
make and justify multiplying and sensible
dividing by
estimates and
estimates for
numbers
approximations between 0 and 1 calculations
of calculations.
involving
I am able to use multiplication
I am able to find prime factor
and division.
decomposition
prime factor
to find the HCF
decomposition
and LCM of a
of a number.
pair of numbers.
Key Words
Factor
Multiple
Prime Number
Square Number
Indices
Estimate
Standard Form
Never
heard
before?
Heard of but
not sure what
it means?
Know what it means and can explain it in context
Jot down your ideas here...
Level 4
Is this number divisible by 3?
How do you know?
Level 3
Round this
number to the
nearest 10 and
then to the
nearest 100.
Is this number divisible by 7?
How do you know?
144
Level 5
Is this number a square
number?
How do you know?
Level 3
Level 4
Level 5
144
Level 5
Write down all of the
factors of each of
these numbers.
How do you know that
you haven’t missed
any out?
Level 5
What is the highest
common factor of these
numbers?
How do you know?
Level 5
What is the lowest
common multiple of these
two numbers. How do you
know?
48 & 60
Level 7
Show how you can use prime factor
decomposition to find the Highest
Common Factor and the Lowest
Common Multiple of 48 and 60
Level 6
Express each of these
numbers as a product of
its prime factors.
Level 5
Level 5
Level 5
48 & 60
Level 6
Level 7
Level 4 Question
Answers & Working Out
A girl worked out the cost of 8 bags of
apples at 47p a bag.
Her answer was £4.06.
Use estimation to say whether you
think she is right or wrong.
Explain your answer.
Level 5 Question
a)
Round 2.75037 to 1 decimal place
b) Write down a number that would
be 3.4 when rounded to 1 decimal
place.
Answers & Working Out
Level 5 Question
Answers & Working Out
Kate says that 2 + 3 x 5 = 21
Is Kate right or wrong?
Explain your answer.
Level 6 Question
Give your answer correct to 4 significant
figures. Show all your working out.
Answers & Working Out
Level 7 Question
Multiplying makes numbers
bigger. When is this statement
true and when is it false?
Division makes things smaller.
When is this statement true
and when is it false?
Answer & Working Out
Level 7 Question
Answers & Working Out
Level 8 Question
Answers & Working Out
Convince me that
a) 37 x 32 = 39
b) 37 ÷ 3-2 = 39
c) 37 x 3-2 = 35
Level 8 Question
a) Write 734.6 in standard form
b) Write 6.3 x 10-3 as an ordinary
number.
c) Sir Isaac Newton was a
mathematician, physicist and
astronomer. In his work on the
gravitational force between two bodies
he found that he needed to multiply
their masses together.
Work out the value of the mass of the
Earth multiplied by the mass of the
Moon.
Give your answer in standard form.
Mass of Earth
= 5.98 × 1024 kg
Mass of Moon = 7.35 × 1022 kg
Answer & Working Out
Level
3
I can round
whole
numbers to
the nearest
10, 100 or
1000.
4
I can identify factors of
two-digit numbers
Identify square
numbers up to 15 x 15
Place Value and types of number
I know simple tests for
divisibility for 2, 3, 4, 5,
6, 8, 9
I can find the factors of
a number by checking
for divisibility
5
I can recognise
and use
multiples, factors,
common factor,
highest common
factor, lowest
common multiple
and primes.
I know and can
use the order of
operations,
including
brackets.
I can check the
reasonableness of
results with reference
to the context or size of I can round a
numbers
number to one
decimal place.
I can use the multiples
of 4 to work out the
multiples of 8.
6
I am able to
carry out
calculations with
more than one
step using
brackets.
7
When making
estimates I can
round to one
significant figure
and multiply and
divide mentally.
8
I can use laws
of indices in
multiplication
and division.
I can use
I understand the standard form
effects of
I am able to
to make
make and justify multiplying and sensible
dividing by
estimates and
estimates for
numbers
approximations between 0 and 1 calculations
of calculations.
involving
I am able to use multiplication
I am able to find prime factor
and division.
decomposition
prime factor
to find the HCF
decomposition
and LCM of a
of a number.
pair of numbers.
My own reflection on my
learning in this unit of work.
To be a better learner I
could………………..
To move my learning on I need
to
To move my learning on I need
to improve my understanding
of………………….
Here come the answers.
Highlight or tick the relevant statement on
the learning journey.
To the nearest
10 = 140
To the nearest
100 = 100
144
Level 4
This number is divisible by 3
because 144 ÷ 3 = 48
This number is not divisible by 7
because 7 x 20 = 140 and
7 x 21 = 147
Level 4
144 is a square number
because 12 x 12 = 144
Level
3
Round whole
numbers to
the nearest
10, 100 or
1000.
4
Identify factors of twodigit numbers
Identify square
numbers up to 15 x 15
Place Value and types of number
5
Recognise and
use multiples,
factors, common
factor, highest
common factor,
lowest common
multiple and
primes.
6
To be able to
carry out
calculations with
more than one
step using
brackets.
7
When making
estimates round
to one
significant figure
and multiply and
divide mentally.
8
Use laws of
indices in
multiplication
and division.
Use standard
Know simple tests for
form to make
To understand
divisibility for 2, 3, 4, 5,
the effects of
To be able to
sensible
6, 8, 9
make and justify multiplying and estimates for
dividing by
Know and use the estimates and
calculations
Find the factors of a
numbers
approximations between 0 and 1 involving
number by checking for order of
operations,
of calculations.
multiplication
divisibility
including
To be able to use and division.
Check the
prime factor
brackets.
To be able to
reasonableness of
find prime factor decomposition
to find the HCF
results with reference
Round a number decomposition
and LCM of a
to the context or size of to one decimal
of a number.
pair of numbers
numbers
place.
Use the multiples of 4
to work out the
multiples of 8.
Level 5
Level 4
Factors of 48
1 & 48
2 & 24
3 & 16
4 & 12
6&8
Factors of 60
1 & 60
2 & 30
3 & 10
4 & 15
5 & 12
6 & 10
12 is the highest
common factor because
it is the biggest number
which is a factor of both
48 and 60.
48 & 60
Level 7
HCF –2 x 2 x 3 = 12
LCM –2 x 2 x 2 x 2 x 3 x 5
Level 5
240 is the lowest common
multiple of 48 & 60
48, 96,144, 192 , 240
60, 120, 160, 240
Level 6
2 x 2 x 2 x 2 x 3 = 48
24 x 3 = 48
2 x 2 x 3 x 5 = 60
22 x 3 x 5
Level
3
Round whole
numbers to
the nearest
10, 100 or
1000.
4
Identify factors of twodigit numbers
Identify square
numbers up to 15 x 15
Place Value and types of number
5
Recognise and
use multiples,
factors, common
factor, highest
common factor,
lowest common
multiple and
primes.
6
To be able to
carry out
calculations with
more than one
step using
brackets.
7
When making
estimates round
to one
significant figure
and multiply and
divide mentally.
8
Use laws of
indices in
multiplication
and division.
Use standard
Know simple tests for
form to make
To understand
divisibility for 2, 3, 4, 5,
the effects of
To be able to
sensible
6, 8, 9
make and justify multiplying and estimates for
dividing by
Know and use the estimates and
calculations
Find the factors of a
numbers
approximations between 0 and 1 involving
number by checking for order of
operations,
of calculations.
multiplication
divisibility
including
To be able to use and division.
Check the
prime factor
brackets.
To be able to
reasonableness of
find prime factor decomposition
to find the HCF
results with reference
Round a number decomposition
and LCM of a
to the context or size of to one decimal
of a number.
pair of numbers
numbers
place.
Use the multiples of 4
to work out the
multiples of 8.
Level 4 Question
Answers & Working Out
A girl worked out the cost of 8 bags of
apples at 47p a bag.
47p rounded to the nearest 10 is 50p
50p x 8 = £4.00
Her answer was £4.06.
Use estimation to say whether you
think she is right or wrong.
Therefore the apples must have cost
less than £4.00 not more.
Explain your answer.
Level 5 Question
Answers & Working Out
a)
2.8
Round 2.75037 to 1 decimal place
b) Write down a number that would
be 3.4 when rounded to 1 decimal
place.
Any number between 3.35 and 3.44
Level
3
Round whole
numbers to
the nearest
10, 100 or
1000.
4
Identify factors of twodigit numbers
Identify square
numbers up to 15 x 15
Place Value and types of number
5
Recognise and
use multiples,
factors, common
factor, highest
common factor,
lowest common
multiple and
primes.
6
To be able to
carry out
calculations with
more than one
step using
brackets.
7
When making
estimates round
to one
significant figure
and multiply and
divide mentally.
8
Use laws of
indices in
multiplication
and division.
Use standard
Know simple tests for
form to make
To understand
divisibility for 2, 3, 4, 5,
the effects of
To be able to
sensible
6, 8, 9
make and justify multiplying and estimates for
dividing by
Know and use the estimates and
calculations
Find the factors of a
numbers
approximations between 0 and 1 involving
number by checking for order of
operations,
of calculations.
multiplication
divisibility
including
To be able to use and division.
Check the
prime factor
brackets.
To be able to
reasonableness of
find prime factor decomposition
to find the HCF
results with reference
Round a number decomposition
and LCM of a
to the context or size of to one decimal
of a number.
pair of numbers
numbers
place.
Use the multiples of 4
to work out the
multiples of 8.
Level 5 Question
Answers & Working Out
Kate says that 2 + 3 x 5 = 21
Kate is wrong
You have to multiply first
3 x 5 = 15
2 + 15 = 17
Is Kate right or wrong?
Explain your answer.
Level 6 Question
Answers & Working Out
Give your answer correct to 4 significant
figures. Show all your working out.
12.18 ÷ 1.03 = 11.8252427184466
11.83 to four significant figures
Level
3
Round whole
numbers to
the nearest
10, 100 or
1000.
4
Identify factors of twodigit numbers
Identify square
numbers up to 15 x 15
Place Value and types of number
Know simple tests for
divisibility for 2, 3, 4, 5,
6, 8, 9
5
Recognise and
use multiples,
factors, common
factor, highest
common factor,
lowest common
multiple and
primes.
6
To be able to
carry out
calculations with
more than one
step using
brackets.
7
When making
estimates round
to one
significant figure
and multiply and
divide mentally.
8
Use laws of
indices in
multiplication
and division.
Use standard
form to make
To understand
the effects of
To be able to
sensible
make and justify multiplying and estimates for
Find the factors of a
dividing by
calculations
number by checking for Know and use the estimates and
numbers
order of
approximations between 0 and 1 involving
divisibility
operations,
of calculations.
multiplication
Check the
including
To be able to use and division.
reasonableness of
prime factor
brackets.
To be able to
results with reference
find prime factor decomposition
to find the HCF
to the context or size of Round a number decomposition
and LCM of a
numbers
to one decimal
of a number.
pair of numbers
place.
Use the multiples of 4
to work out the
multiples of 8.
Level 7 Question
Answer & Working Out
Multiplying makes
numbers bigger.
When is this
statement true and
when is it false?
False when:Multiplying a positive number by a negative number
e.g. 2 x – 3 = -6
Multiplying by a number between 0 and 1
e.g. 8 x 0.2 = 1.6
Multiplying by 0
e.g. 10 x 0 = 0
True when:Multiplying a negative number by a negative number and
multiplying by a number greater than one.
Division makes things
smaller. When is this
statement true and
when is it false?
False when:Dividing a negative number by a negative number
e.g. -6 ÷ - 3 = 2
Dividing a negative number by a positive number.
e.g. -8 ÷ 2 = -4
Dividing by a number between 0 and 1
e.g. 8 ÷ 0.2 = 40
True when:Dividing a positive number by a negative number
e.g. 8 ÷ - 4 = -2
Dividing a positive number by a number greater than one.
42 ÷ 6 = 7
Level
3
Round whole
numbers to
the nearest
10, 100 or
1000.
4
Identify factors of twodigit numbers
Identify square
numbers up to 15 x 15
Place Value and types of number
Know simple tests for
divisibility for 2, 3, 4, 5,
6, 8, 9
5
Recognise and
use multiples,
factors, common
factor, highest
common factor,
lowest common
multiple and
primes.
6
To be able to
carry out
calculations with
more than one
step using
brackets.
7
When making
estimates round
to one
significant figure
and multiply and
divide mentally.
8
Use laws of
indices in
multiplication
and division.
Use standard
form to make
To understand
the effects of
To be able to
sensible
make and justify multiplying and estimates for
Find the factors of a
dividing by
calculations
number by checking for Know and use the estimates and
numbers
order of
approximations between 0 and 1 involving
divisibility
operations,
of calculations.
multiplication
Check the
including
To be able to use and division.
reasonableness of
prime factor
brackets.
To be able to
results with reference
find prime factor decomposition
to find the HCF
to the context or size of Round a number decomposition
and LCM of a
numbers
to one decimal
of a number.
pair of numbers
place.
Use the multiples of 4
to work out the
multiples of 8.
Level 7 Question
Answer & Working Out
Convince me that
a) 37 x 32 = 39
an x am = an+m
b) 37 ÷ 3-2 = 39
c)
37 x
3-2 =
35
an ÷ am = an-m
Level
3
Round whole
numbers to
the nearest
10, 100 or
1000.
4
Identify factors of twodigit numbers
Identify square
numbers up to 15 x 15
Place Value and types of number
Know simple tests for
divisibility for 2, 3, 4, 5,
6, 8, 9
5
Recognise and
use multiples,
factors, common
factor, highest
common factor,
lowest common
multiple and
primes.
6
To be able to
carry out
calculations with
more than one
step using
brackets.
7
When making
estimates round
to one
significant figure
and multiply and
divide mentally.
8
Use laws of
indices in
multiplication
and division.
Use standard
form to make
To understand
the effects of
To be able to
sensible
make and justify multiplying and estimates for
Find the factors of a
dividing by
calculations
number by checking for Know and use the estimates and
numbers
order of
approximations between 0 and 1 involving
divisibility
operations,
of calculations.
multiplication
Check the
including
To be able to use and division.
reasonableness of
prime factor
brackets.
To be able to
results with reference
find prime factor decomposition
to find the HCF
to the context or size of Round a number decomposition
and LCM of a
numbers
to one decimal
of a number.
pair of numbers
place.
Use the multiples of 4
to work out the
multiples of 8.
Level 8 Question
Answer & Working Out
a) Write 734.6 in standard form
a) 7.346 x 102
b) Write 6.3 x 10-3 as an ordinary number.
c) Sir Isaac Newton was a mathematician, physicist
and astronomer. In his work on the gravitational force
between two bodies he found that he needed to
multiply their masses together.
Work out the value of the mass of the Earth multiplied
by the mass of the Moon.
Give your answer in standard form.
Mass of Earth
= 5.98 × 1024 kg
Mass of Moon
= 7.35 × 1022 kg
b) 0.0063
5.98 x 7.35 = 43.953
1024 x 1022 = 1046
43.953 x 1046
= 4.3953 x 1047
Level
3
Round whole
numbers to
the nearest
10, 100 or
1000.
4
Identify factors of twodigit numbers
Identify square
numbers up to 15 x 15
Place Value and types of number
Know simple tests for
divisibility for 2, 3, 4, 5,
6, 8, 9
5
Recognise and
use multiples,
factors, common
factor, highest
common factor,
lowest common
multiple and
primes.
6
To be able to
carry out
calculations with
more than one
step using
brackets.
7
When making
estimates round
to one
significant figure
and multiply and
divide mentally.
8
Use laws of
indices in
multiplication
and division.
Use standard
form to make
To understand
the effects of
To be able to
sensible
make and justify multiplying and estimates for
Find the factors of a
dividing by
calculations
number by checking for Know and use the estimates and
numbers
order of
approximations between 0 and 1 involving
divisibility
operations,
of calculations.
multiplication
Check the
including
To be able to use and division.
reasonableness of
prime factor
brackets.
To be able to
results with reference
find prime factor decomposition
to find the HCF
to the context or size of Round a number decomposition
and LCM of a
numbers
to one decimal
of a number.
pair of numbers.
place.
Use the multiples of 4
to work out the
multiples of 8.
Self Assessment
• Collect back your assessment task and the
purple sheet.
• Have a look at your learning journey. Your peer
has ticked the skills that you have demonstrated
in this assessment.
• Pick an un-ticked skill as your target and write
EBI next to it.
• Complete the self assessment boxes on the
purple sheet.
To be a better learner I could................
Less Helpful Comments
More Helpful Comments
Work Faster / do more
Be neater
Try the harder ones
Stay on task.
Clearly show my working out.
Put my hand up to ask a question
when I don’t understand.
Talk less
Make sure that when I am talking
to the people on my table, I am
talking about the Maths.
Listen more when the teacher is
talking.
Contribute answers and
questions during the explanation
part of the lesson.
Level
3
I can round
whole
numbers to
the nearest
10, 100 or
1000.
4
I can identify factors of
two-digit numbers
Identify square
numbers up to 15 x 15
Place Value and types of number
I know simple tests for
divisibility for 2, 3, 4, 5,
6, 8, 9
I can find the factors of
a number by checking
for divisibility
5
I can recognise
and use
multiples, factors,
common factor,
highest common
factor, lowest
common multiple
and primes.
I know and can
use the order of
operations,
including
brackets.
I can check the
reasonableness of
results with reference
to the context or size of I can round a
numbers
number to one
decimal place.
I can use the multiples
of 4 to work out the
multiples of 8.
6
I am able to
carry out
calculations with
more than one
step using
brackets.
7
When making
estimates I can
round to one
significant figure
and multiply and
divide mentally.
8
I can use laws
of indices in
multiplication
and division.
I can use
I understand the standard form
effects of
I am able to
to make
make and justify multiplying and sensible
dividing by
estimates and
estimates for
numbers
approximations between 0 and 1 calculations
of calculations.
involving
I am able to use multiplication
I am able to find prime factor
and division.
decomposition
prime factor
to find the HCF
decomposition
and LCM of a
of a number.
pair of numbers.
My own reflection on my
learning in this unit of work.
To be a better learner I
could………………..
To move my learning on I need
to
To move my learning on I need
to improve my understanding
of………………….