Year 7F – Autumn 1 – Making generalisations about the number system 1
Big Idea:
Context:
Aligning with OCL curriculum has increased the level of challenge and the expected base level of knowledge that students in Y7 are expected to have. As a result, addition
and subtraction have been taken out of the SOW but this should be checked through the daily review. Much of the content in this half term is building on the knowledge
students have already acquired in primary school. Many of the concepts will not be new but the expectations around rigour of language used and the rigour of reasoning
will provide the challenge for students and some gaps will need to be filled in. Different base number systems and binary should be new to students and teachers should
make links to different number systems and computing. This half term should be viewed as an opportunity to consolidate basic knowledge in number and the challenge
should be driven by language used and reasoning.
Key vocabulary - Definition
Assessment
Integer – A whole number
Week 2
Decimal – A number that has a decimal point followed by digits to show a value of
- Multiplying and dividing by powers of 10
less than 1
- Writing in binary
Base – The number of digits in a number system
- Reading analogue clock face
Binary System – A number system with two digits: 0 and 1
- Comparing time in different quantities
Commutative Law – The law that says that the order of addition does not matter
- Find the amount of time between two different points
Multiple – The result of multiplying a number by an integer
Week 4
Square number – The result of multiplying an integer by itself
- Multiplying 2 and 3 digit integers
Cube number – The result of multiplying an integer by itself twice
- Multiplying decimals
Square root – The inverse operation of squaring
- Dividing integers with decimal answers
Power – The number of times a value should be used in a calculation
- Dividing decimals
Associative Law – The law that says that how calculations are grouped does not
- Finding powers
matter when adding and subtracting or multiplying and dividing
- Finding square and cube roots
Distributive Law – The law that states that multiplying a number by a group of
Week 6
numbers is the same as doing each multiplication separately
- Multiples of a number
Priority – To be completed first
- Lowest common multiples
Factor – An integer which can divide into a number without leaving a remainder
- Factors of a number
Prime number – An integer with exactly two different factors
- Highest common factors
Highest common factor – The highest integer that is a factor of two or more
- Order of operations
numbers
Lesson
Lesson focus and objectives
Pre-requisite Knowledge
Misconceptions
Exit Ticket Questions
1.1
Place value
Numbers position on a number line When multiplying by 10 you add Place these calculations in
To know:
a zero
ascending order
- The place value columns of hundredths,
When dividing by 10 you take
32 ÷ 100
tenths, ones, tens, hundreds etcaway a zero
3200 ÷ 1000
- That multiplying by a power of ten moves
Moving the digits the wrong
0.0033 x 100
digits from their place value columns to the
way when multiplying/dividing
0.033 x 1000
left
-
1.2
1.3 S
2.1
2.2
That dividing by powers of ten moves digits
from their place value columns to the right
- How to compare calculations that are
multiplied by powers of ten
Different base number systems
To know:
- That the base of a number system is the
number of digits in a number system
- That we use a base 10 system for counting
and calculation and a base 60 system for
time
- How to write base 10 numbers in binary
Time
To know:
- How to read an analogue clock face
- How to convert between 12 hour and 24
hour time
Converting time
To know:
- How to convert between seconds, minutes,
hours and days
- How to compare amounts of time in
different quantities
- How to choose the most suitable unit of
measurement for a given amount of time
Measuring time
To know:
- How to find the time between two points in
the same day
- How many days there are in each month
- How to find the time between any two
points in time
Lesson 1.1 (Place value)
Struggling to put numbers into
Binary
10 in binary = ten
a) Write the number 28 in
binary
b) What is 101 + 1000?
Write your answer in
base 10
Never seeing/using an analogue
clock
12pm = midnight
12am = midday
1) What time does the
clock face show
1.5 minutes = 1 minute 50 secs
Mistakes when
multiplying/dividing by 60
Converting time (2.1)
1.5 minutes = 1 minute 50 secs
Mistakes when
multiplying/dividing by 60
All months have 30 days
2) Write 3:45pm in 24
hour clock
3) Write 04:20 in 12 hour
clock
1) Convert 100,000
seconds into days,
hours, minutes and
seconds
2) Which is bigger: 5,000
minutes or 3 days?
1) How much time has
passed between
10:23am and 8:01pm?
2) How much time passed
between 3:15pm on
28th August and
12:10pm on 10th
September?
2.3 S
Multiplying integers
To know:
- That multiplication is commutative
- How to multiply 2 and 3 digit numbers using
partitioning (grid method)
Addition being commutative
Times tables
Multiplying and dividing by 10
3.1
Multiplying decimals
To know:
- How to multiply and divide by powers of ten
- That multiplying a number by a number less
than 1 decreases its value
- How to multiply an integer by a decimal
- How to multiply a decimal by a decimal
Multiplying integers
Multiplying and dividing by powers
of 10 (autumn 1)
3.2
Dividing integers
To know:
- That division is not commutative (fact)
- How to divide integers with integer answers
- How to divide integers with decimal answers
NNJR
Dividing decimals
To know:
- That when we multiply the divider and the
dividend by the same value the answer
remains unchanged (fact)
- How to divide integers by decimals
- How to divide decimals by decimals
Powers
To know:
- That a square number is the product of an
integer multiplied by itself (fact)
- That a cube number is the product of an
integer multiplied by itself twice (fact)
Times tables
Multiplication and commutativity
3.3 S
4.1
4.2
Mistakes around using column
method
Partitioning 3 digit numbers
incorrectly
Missing zeroes when
multiplying the 10s and 100s
(eg. 30 x 700 = 2100)
Not lining up with regards to
place value when adding
Not dividing by 100 when
multiplying two decimals (eg.
0.3 x 0.7 = 2.1)
Not understanding that when
multiplying by a number less
than 1, the answer gets smaller.
Thinking that whenever a
number is multiplied by a
decimal, the answer gets
smaller.
Not understanding how to find
the remainder
Struggling when dividing by a
lesser known times tables (eg.
13)
Dividing integers
Multiplying and dividing by 10
Basic division skills
After finding the answer to the
calculation that’s been
multiplied by 10, thinking that
we have to divide by
10/100/1000 again (eg. 20 ÷ 2 =
10  2 ÷ 0.2 = 1)
Times tables
Multiplying integers
Multiplying decimals
Pattern spotting
43 means 4 multiplied by 4
three times (ie. 4 x 4 x 4 x 4)
Not understanding that
squaring a number does not
always give a square number
1) Explain why 3 x 8 = 8 x
3
2) Work out
a) 38 x 42
b) 136 x 84
372 x 841
Work out
a) 8 x 0.4
b) 0.6 x 0.3
c) 0.2 x 0.4
d) 8.2 x 0.04
1) 1.8 x 4.52
Work out
a) 285 ÷ 3
b) 193 ÷ 4
c) 1027.2 ÷ 8
a) 1541.8 ÷ 13
a)
Work out
a) 2.4 ÷ 0.3
b) 3.2 ÷ 0.08
a) 286.2 ÷ 0.5
1) Write down the first
ten square numbers
2) Write down the value
of 63
3) Write down the value
of 25
4.3 S
5.1
5.2
How to simplify numbers with integer
powers
Roots
To know:
- That square rooting is the inverse operation
to squaring (fact)
- How to find the square root of integers
- That cube rooting is the inverse of cubing
- How to find the cube root of integers
- How to find the nth root of special numbers
(eg 5th root of 32, 4th root of 81 etc)
Multiples
To know:
- That a multiple is the result of multiplying a
number with an integer
- How to find multiples of integers
- That the lowest common multiple of two
numbers is the lowest value that is a
multiple of both numbers
- How to find the lowest common multiple of
two integers
Lowest common multiples
To know:
- How to find the lowest common multiple of
two integers
- How to solve problems involving lowest
common multiples and time spacing
- How to solve lowest common multiples
questions involving multi-packs
Powers
Knowing square numbers
Square root means divide
Cube root means 3 time the
square root
Thinking 0 is a multiple of a
number
Thinking lowest common
multiple is always found by
multiplying two numbers
together
Multiples (Lesson 6.2)
Work out
a) √81
3
b) √125
4
a) √16
1) List the first 5 multiples
of 13
1) Find the lowest
common multiple of 15
and 12
1) Bus A departs from a
bus stop every 10
minutes. Bus B departs
from the same station
every 12 minutes. They
both depart the station
at 10:10am. When will
they next depart the
station at the same
time?
1) John is making
hotdogs. Sausages
come in packs of 8 and
buns come in packs of
12. He wants to make
at least 60 hot dogs
and he wants the same
number of sausages as
he does buns. What is
the lowest number of
packs of sausages and
buns he needs to buy?
5.3 S
6.1
6.2
6.3 S
NNJR
Factors
To know:
- That a factor of a number is an integer which
can divide into a number without leaving a
remainder (concept)
- How to find factor pairs of integers
- That a prime number is a number with
exactly two different factors
- How to identify prime numbers
Highest common factors
To know:
- That the highest common factor of two
numbers is the highest integer which is a
factor of both numbers (concept)
- How to find the highest common factor of
two or more numbers
- How to solve problems involving common
factors
Order of operations 1
To know:
- The priority of order for the operations (fact)
- How to carry out calculations involving
multiple operations
Division
Times tables
Not finding factors in pairs and
then missing factors
1 is a prime number
All prime numbers are odd
1) Find all the factors of
30
2) Find all the factors of
15
3) Find all the factors of
17
4) What is special about
the number 17?
Factors
Calling highest common factor
the lowest common factor
General arithmetic from autumn 1
and 2
Commutative laws
Likely to have been taught BIDMAS
in primary school
Division must be done before
multiplication
Addition must be done before
subtraction
1) Find the highest
common factor of 30
and 45
2) Find the highest
common factor of 24
and 18
2) Jack is tiling his
bathroom wall. The
wall measures 100cm
by 160cm. He wants to
tile the wall with
square tiles. Tiles are
available in whole
number of centimetres.
If the tiles are to be as
large as possible. What
size tile should Jack
buy?
1) Work out
a) 3 + 4 x 5
b) 4 x (10 – 2)2
-
7.1
7.2
7.3 S
How to add brackets to equations to make
them true
Order of operations 2
To know:
- The associative law
- The distributive law
- How to identify equivalent calculations using
the associative and distributive laws
- How to create equivalent calculations using
the associative and the distributive law
NNJR
Knowledge Test Redo
Powers
Order of operations
Commutative law
Thinking there’s only one way
to work out any calculation
2) Add brackets to make
the statement true
a) 9 x 3 + 4 = 56
20 – 12 x 3 + 2 = -40
1) Identify which of the
statements below are
true. Give a reason for
your answer.
a) 8 + (4 + 2) = (8
+ 4) + 2
b) 16 ÷ (8 ÷ 2) =
(16 ÷ 8) ÷ 2
c) 6 x (10 x 2) = (6
x 10) x 2
2) Write down an
equivalent calculation
to 3 x (4 + 5)