Autumn Algebra & Place Value
sc
Hegarty
B1- Sequences
I Can …
Practice
1
Describe and continue a sequence diagrammatically
Find the next
two terms
2
Predict and check the next nth term (the nth position)
What is the
20th terms?
3
Represent sequence in Tabular & graphical forms
Draw this sequence in a
Table and graphically
4
Continue a numerical linear sequence (arithmetic sequence)by
identifying the term-to-term rule (common difference)
Find the term to term rule
60, 74, 88, ___, ___
1.5, 1.2, 0.9, ___, ___
5
Explain the term-to-term Rule of numerical sequences in full sentences
using mathematical words.
How many sequences can you create beginning with 1,
2,
Write the term-to-term rules in words
6
Continue numerical non-Linear sequence (geometric sequence or not
with a common difference)
Find the next two terms
i) 1, 2, 4, 8, ___, ___ ii) 1, 3, 6, 10, ___, ___
7
Find missing term within sequences
Find the missing terms:
i) 6, __, 14, __, 22, __ ii) 8000, ___, ___, 6500, ___
8
Recognise special sequences: square numbers, cube numbers,
Fibonacci sequence, triangular numbers
List the first 5 cube numbers,
List the first 5 Fibonacci numbers
SC 1: Describe and continue a sequence
diagrammatically
Example
add 2 more triangle to the end
+3 +3
+3
add 1 triangle to each side
+2
+3
•
•
+3
+4
+4
+5
Add 1 more triangle than previous to the
right side
Add 1 grey more triangle than previous to
the right side
Describe what is happening in the sequence and draw the next two terms
How many circle, lines or squares in each term. Predict how many for the next 2 terms
SC 2: Predict and check the next term
Example
3, 5, 7
9
11
6, 12, 18
a) How many hexagon in each term in this sequence?
b) How many will there be in the next term? 24
c) How many will there be in the 5th term? 30
d) Draw the terms to check your prediction.
SC 3: Represent sequence in Tabular & graphical forms
Example
A sequence can be represented in multiple ways:
1
2
3
1) Complete the table
a)
b)
 Numerically
 Pictorial
c)
 in a Table
d)
(1,4) (2,7) (3,10)
2) Complete the table and represent these sequence of a graph
a)
 Graphically
b)
SC 4: Identifying the term-to-term rule (common
difference)
1) Find the term-to-Term rule:
Example
2) Find the term to term rule
Linear Sequence have a common difference between each
terms:
3) Find the term to term rule and complete the table
Term-to-term rule: +4
Term-to-term `
rule  -7
`
-7
11 4
`
`
-7 -7
SC 4: Continue a linear sequence
1)
SC 6: Non Linear Sequence
Linear Sequence: Arithmetic Sequence
-6, 1, 8, 15, 22
+7 +7 +7
Non-Linear Sequence:
Does not have a common difference
Geometric sequence:
2, 4, 8, 16, 32
2) Use the term to term rule to find the next two terms
x2 x2 x2
Special sequences:
Square numbers
1, 4, 9, 16, 25
+3 +5 +7 +
triangle sequence
1, 3, 6, 10, 15
+2 +3 +4 +5
3)
SC 7: Find missing term within a linear sequences
1) Find the missing terms
Example
8
14 – 6 = 8
+3
+4
20
+6 +6
6
+4
19 - 7
=12
+6
26-14
12 ÷ 2 = 6
=12
19 - 4 = 15
11 15
+4
32
+4
12 ÷ 3 = 4
2) Use these numbers to make as many linear sequence with terms:
SC 8: Special Sequences
Good to know- Learn by heart
Fibonacci Numbers
Challenge: Find The 10th term
Position to term Rule
Hegarty
B2- Algebraic Notation
I Can …
Practice
1 288
Use function machine (number) to find output
Find the
Output:
2
Use inverse operation on function machine to find input
Find the
Input:
3 157
158
Use correct algebraic notation for adding, multiplying and
dividing
𝑺𝒊𝒎𝒑𝒍𝒊𝒇𝒚
𝑖) 𝑎 + 𝑎 + 𝑎 =
=
4
Use function machine (algebra) to solve equations
Find in the
Input/output
5
Identify the functions needed to produce the outputs
Find the
Function:
6 155
178
Substitute values for the variables to calculate the value of the
expression.
Substitute n = 5 into the expression:
ii) 2 × 𝑎 × b =
iii) a ÷ 𝑏
Find the first three term of sequence 3n + 2
B2- Algebraic Notation
I Can …
Practice
Solution
1
Use function machine (number) to find output
Find the
Output:
2
Use inverse operation on function machine to find input
Find the
Input:
3
Use correct algebraic notation for adding, multiplying and dividing 𝑺𝒊𝒎𝒑𝒍𝒊𝒇𝒚
𝑖) 𝑎 + 𝑎 + 𝑎 = 𝟑𝐚 ii) 2 × 𝑎 ×= 𝟐𝐚𝐛
𝒂
iii) a ÷ 𝑏 =
𝒃
Use function machine (algebra) to solve equations
Find in the
Input/output
4
5
Identify the functions needed to produce the outputs
Find the
Function:
6
Substitute values for the variables to calculate the value of the
Substitute n = 5 into the expression:
expression.
𝒊) 𝟓𝟐 = 𝟐𝟓 𝐢𝐢)𝟐𝟎 − 𝟓 = 𝟏𝟓 𝒊𝒊𝒊) 𝟐 × (𝟓 + 𝟒) = 𝟏𝟖 𝒊𝒗) 𝟐 × 𝟓 + 𝟖 = 𝟏𝟖
Find the first three term of sequence 3n + 2
SC 1: Use function machine (number) to find output
1. Complete the one step / two step function machine
Example
One step FM
2. Complete the three step function machine
Two step FM
3.
4.
SC 2: Use inverse operation on function machine to find input
1. Use inverse function to find the input for one step FM
Example
3
2. Use inverse function to find the input for two step FM
1
(𝟓 − 𝟐) x 4 = 12
3. Write down the input z when y = 17
Sequence: multiply by 2 then add 6
Position
1
2
3
4
6
term
8
10
12
14
16
 Term-to-term rule + 2
In algebra, we use particular
Algebraic Notation: Good To Know
notation or different calculations.
Identify:
True for all
values of
a&b
SC 3: Use correct algebraic notation for + ̶ X ÷,
1) Simplifying by collecting like terms
Example
Collecting Like Terms
2) Find equivalent terms by simplifying
Multiplying algebraic Terms
3) Simplify fractions
𝐚
𝐚 ÷𝟑=
𝟑
Dividing algebraic Terms
3÷𝐚=
𝟔×𝐚
𝟔𝐚 ÷ 𝟑 =
= 𝟐𝐚
𝟑
𝟑
𝐚
4) Spot the mistake
SC 3: Use correct algebraic notation for + ̶ X ÷,
Match the notation on the left to the description on the right
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
15
SC 4: Use function machine to solve equations
1. Complete the Function machine to solve these equations:
Example
Using Inverse Function Machine to Solve equations
2. Use Function machine to solve these equations:
3. Write down an expression for the output y when the input is 𝒙
4. Complete the function machine so that 𝒚 = 𝟒(𝒙 = 𝟓)
5. Think of a number, double it, add 4. The answer is 24.
Use function machine to find the original number:
𝒙 = 𝟑𝟒
SC 5: Find the function needed for the output
Find the rule
Example
Problem Solve to identify the function
14
3
2. Find the missing function
+10
10
𝟓 × 𝟐 = 𝟏𝟎
→ 𝟏𝟎 +10 = 𝟏𝟎
𝟐𝒙 + 𝟏𝟎 =
Completer the function machine using inverse
BIDMAS:
-4
X2
𝑦=2 𝑥−4
-4
÷2
𝑦=
𝑥 −4
5
3. Find the missing function
SC 6: Substitute values for the variables to
calculate the value of the expression
Example
1. Evaluate these expression by substitution a =2
 Replace 𝒙 with 5
2. If a= -2 and b = 6. Find the value of these expression:
i)
2a + b
iv) 4ab
ii) 6a -b
iii ) 3a – 2b
v) a + 3ab
vi) a² + b²
2. Find missing terms of sequence
sc
Hegarty
B3- Equivalence
I Can …
1
Understand the meaning of equality
2
Solve one step equation using + /- using family fact
3
Solve one step equation using x / ÷ using family fact
4
156
5
6
Identify like terms
Understand the meaning of equivalence
157
Simplifying Collecting like term
Practice
SC 1: Understanding equality
Equality: Both side of an equation are equal (have the same value)
equal
Equality: Left Side = Right Side
8+3=7 +4
8+2≠7+4
8 x 3 = 12 + 9 + 3
1) Which of these are not equal?
2) Write integers in the box to make the calculation correct. Provide 2 different solutions
SC 2: Solve one step equation using + /- using family fact
1) Draw the bar model for these equations
Example
Addition family fact:
7 + 3 = 10
3 + 7 = 10
10 − 3 = 7
10 − 7 = 3
2) Use family fact to solve these equations
𝑥 + 14 = 20
14 + 𝑥 = 20
20 − 𝑥 = 14
𝟐𝟎 − 𝟏𝟒 = 𝒙
𝑤+9=𝑡
9+𝑤 =𝑡
𝒕 −𝒘=𝟗
𝑡−9=𝑤
3) Ken thinks of a number.
He subtracts 78 from his number and gets the answer 137.
Show this information as an equation and solve the equation to find
Ken’s number.
How else could you represent the information?
SC 3: Solve one step equation using x/÷ using family fact
1) Draw the bar model for these equations
Example
Multiplication family fact:
4 × 6 = 24
6 × 4 = 24
24 ÷ 6 = 4
24 ÷ 4 = 6
4 × 𝑎 = 28
a × 4 = 28
28 ÷ 𝑎 = 4
𝟐𝟖 ÷ 𝟒 = 𝒂
4×𝑏 =𝑎
b×4=𝑎
𝒂÷𝒃=𝟒
𝑎÷4=6
2) Use family fact to solve these equations
a) 2𝑥 = 10
𝑏) 5𝑥 = 187
𝑑)
= 10
𝑒)
=2
𝑐) 12 = 4𝑥
𝑓) 4 =
3) Marta thinks of a number.
She divides her number by 7 and gets the answer 42
Write this information as an equation.
Solve your equation to find Marta’s number.
Draw a bar model
32
𝑥
SC 4: identifying like terms
1) Which term are like terms:
Example
To find like terms:
1) cover coefficient
2) rearrange the variables in alphabetical order.
3) If the combined variables look the same, then they 2) State which terms
are like terms
𝟑𝒙𝟐 𝟑𝒙𝒚
𝟐𝒚𝒙
𝟑𝒙𝟐 𝟑𝒙𝒚
𝟐𝒙𝒚
 Like terms
2) Group like terms together
Equivalence: two expression have the same value
(Writing the same expression in different ways)
Equality verses Equivalence
𝟐 𝒙 + 𝟒 ≡ 𝟐𝒙 + 𝟖
𝟐𝒙 + 𝟒 = 𝟒𝒙
Only true when 𝒙 = 𝟏
true for all values of 𝒙
1) Each of these expression should sum to 15 m
Equivalence: Writing the
expression in a different way:
2) Which 2 expression are equivalent to 𝟑𝒙 + 𝟔
6 + 3𝑥
3 𝑥+2
3(𝑥 + 6)
𝒙+𝒙+𝒙+𝒙
→ 𝟐𝒙 + 𝟑𝒙
→ 𝒙 + 𝟒𝒙
→ 𝟔𝒙 − 𝒙
3) Complete the table
equivalence of substitution:
If 𝒙 = 𝟒 𝒕hen 4 can replace
the 𝒙 in an equation
2𝒙 + 6
 2 x 𝟒 + 6 = 14
4) W𝐫𝐢𝐭𝐞 𝟒 𝐞𝐱𝐩𝐫𝐞𝐬𝐬𝐢𝐨𝐧 𝐞𝐪𝐮𝐚𝐥 𝐭𝐨 𝟐𝟒𝒙 + 𝟒
SC 6: Simplifying Collecting like term
1) Simplify by collecting like terms
2) Write three expressions with 5 terms that simplifies to:
𝟐𝒙 − 𝒙𝒚𝟐 + 𝟒
3) Identify which answer is correct
s
Hegarty
B4 – Place Value
Practice
I Can …
1
13
45
write and represent the numbers up to million in several ways
Complete these representations to show the same number
2
3
4
5
14
13
Identify place value
convert integers between numeral and words
work out the intervals and complete a number line
round to the nearest 10, 100, 1000
Write down the value of 5 in : 305, 052, 867
Write Two hundred and three thousand, fifty-four
6
130
137
14
46
14
46
410
7
8
9
17
Round to 1 significant figure
There are 2000 students in a school. What I the maximum
and minimum student possible?
Round to 1 sf: 2940, 0.0249
Compare and sort numbers using symbols <≤>≥=≠
Order a list of numbers
Put in ascending Order:
Find the range from a group of values
Find the range of these numbers:
68 63 79 111 104
Find the median from the list of these numbers:
68 63 79 111 104
What as a power of 10:
1000 × 102 × 10−3 × 100 =
Write in standard form:
2.5 × 106 × 2.2 × 104 =
10 409
Find the medium from a list of values
11 121
125
12 122
123
writing multiple of 10s in the form 10𝑛
writing and interpreting numbers in standard Form
Example
1 403 021 603
SC 1: I can represent numbers in multiple ways
Complete these representations so they all show the same number.
One billion, four hundred and three million, twenty-one thousand, six hundred and three
1,403,021,603 = 1,000,000,000 + 400,000,000 + 3,000,000 + 20,000 + 1,000 + 600 + 3
Represent these numbers in multiple format
a) 1 073 080 529
b) Eighty-eight million, eighty-eight thousand, five hundred and twelve
c) Half a million
Example
Example
1 403 021 603
SC
SC 1:
1: II can
can represent
represent numbers
numbers in
in multiple
multiple ways
ways
Complete these representations so they all show the same number.
Zero
point 7 = 1,000,000,000 + 400,000,000 + 3,000,000 + 20,000 + 1,000 + 600 + 3
1,403,021,603
1. Represent this numbers in multiple format
2. Put in expand form
3. Complete the number bond
Example
1) State the value of 6 in 630, 604.6  600,000, 600 and 6th
2) State the place value of 7 in : 7, 354, 708.172  million, hundred, hundredth (100th)
3) Write down half million more than 600, 128  500,000 + 600, 128 = 1, 100, 128
Write down the numbers that are:
a) Three million more than 917 000 000
b) The sum of three hundred million and 700 000 000
c) 30 000 000 more than nine hundred and sixty million
d) The difference between one billion and seventy-five million
SC 2: identify place value
Example
SC 3: convert between numerals and words
Eighty-eight million, eighty-eight thousand, five hundred and twelve  88,088,512
10, 703, 009, 009.22  Ten billion, seven hundred and 3 million, nine thousand and nine point two-two
Write in figures:
a) Thirty-five thousand million
b) One and a half billion
c) Two hundred and three thousand
d) Half a million
e) One billion, ten thousand and one
f) Seven thousandths
g) Seventeen thousandths
h) Seven hundred thousandths
i) Zero point three five
j) Seventy-two hundredths
k) Nought point nought seven
l) Nought point nought three
m) Two hundredths
n) Fifty hundredths
o) One tenth
Write in words:
a)
1, 234, 567.
b)
1, 303, 220, 000
c)
9, 095, 002, 003
d)
23. 789
e)
0.45
f)
2.035
g)
9.10
SC 4:work out the intervals and complete a number line
Fluency
1)
Estimate where the arrow is
Fully label the following number lines
0
20
20
0
20
0
Can you work out the values of the intervals for the following number lines
1)
00
60
60
0
0
0
60
60
0
Reasoning
1)
-12
2)
3)
Problem Solving
Compare the two number lines below. What's the same?
What's different?
1)
9
Can you work out the interval for the following number line?
Give a reason for your answer.
10
Why count the number of spaces in between the marks on a
number line, rather than the marks?
Can you create 4 different number lines
with different scales that have a start
point of 0 and an end point of 30?
Challenge – can you create one where the
interval is a decimal?
28
0
20
2)
3)
Can you create a question using a
number line where the answer for the
interval would be 2.5?
Can you come up with 3 questions you
could ask about the number line below?
7
25
Mark 7.45, 7.48 and 7.425
on the number line
I can work out intervals on a number line
Fluency
1)
Estimate where the arrow is
Fully label the following number lines
0
5
10
15
20
25
0
8
4
12
-10
30
-20
-20
-40
20
10
0
-60
0
1) Can you work out the values of the intervals for the following number lines
Interval =10
Interval =20
00
10
30
40
50
60
0
20
20
40
Interval = 12
Interval = 15
0
15
30
60
45
0
24
12
Reasoning
1)
-12
28
1)
3)
20
40
60
48
60
Can you create 4 different number lines
with different scales that have a start
point of 0 and an end point of 30?
There are lots of different answers. Ask your teacher to check.
Challenge – can you create one where the
interval is a decimal?
There are lots of different answers. Ask your teacher to check.
9
2)
Both intervals are 7, but the second number line is not the 7 times table
2)
20
Problem Solving
Compare the two number lines below. What's the same?
What's different?
0
36
16
Can you create a question using a
number line where the answer for the
interval would be 2.5?
Can you work out the interval for the following number line?
Give a reason for your answer.
There are lots of different answers. Ask your teacher to check.
10
Why count the number of spaces in between the marks on a
number line, rather than the marks? The spaces give you the
E.g. Fully label the number line, work out the interval etc.
3)
Can you come up with 3 questions you
could ask about the number line below?
No, you need 2 numbers to be able to work out the interval
correct interval.
7
25
0.06 0.07
0.01
0.068
0.2
0.4
0.08
0.10
0.6
Example
Round to nearest 10
Round to nearest 100
SC 5:round to the nearest 10, 100, 1000
The school kitchen wants to order enough jacket potatoes
for lunch. Potatoes come in sacks of 100. How many sacks
do they need for 766 children?
A number rounded to the nearest 10 is 550.
What is the smallest possible number it could be?
Example
Round to 1 sf
SC 6:Round to 1 significant figure
Estimate the answer
To one significant figure, the population of Scotland is given
as five million.
What is the greatest possible population of Scotland?
What is the least possible population?
Example
SC 7:Compare and sort numbers using symbols <≤>≥=≠
𝟔𝟒𝟏 < 𝟔𝟓𝟎𝟎. 𝟎𝟎𝟏
𝟔𝟒𝟓𝟎. 𝟎𝟎𝟒 > 𝟔𝟒𝟎𝟎. 𝟎𝟏𝟎
𝟔𝟒𝟓𝟎. 𝟎𝟎𝟒 ≠ 𝟔𝟓00.001
Example
Arrange in order from smallest: 201, 197, 210, 192, -208
Put in ascending order: 0.5, 0.45, 0.435, 0.46, 0.501
SC 8:Order a list of numbers
Solution
Arrange in order from smallest: 201, 197, 210, 192, -208
Put in ascending order: 0.5, 0.45, 0.435, 0.46, 0.501
SC 8:Order a list of numbers
Type equation here.Example
SC 9: Find the range from a group of values
SC 10:Find the median from a group of values
3 numbers with no mode, mean 7
and range 4 
Find Range
Find Median
SC 11:writing ordinary numbers in the form 10𝑛
Fluency
Write the following numbers as a power of 10
a) 100
b) 10,000
c) 1,000
d) 1,000,000
e) 0.1
f) 0.00001
g) 0.01
h) 0.0000001
e) 10−1
f) 10−3
g) 10−6
h) 100
Write the following as an ordinary number
a) 103
b) 104
c) 108
d) 101
Choose the largest number from each of the following pairs of numbers
a) 103 and 10,000
b) 1,000 and 104
c) 0.01 and 10−1
d) 0.1 and 10−5
Reasoning
1)
Problem solving
For each of the following statements, decide whether the statement is true
or false. If a statement is false, explain why.
a) 105 is the same as 100,000
1,000,000,000 is the same as 1010
c)
10−3 is the same as 0.01
0.0000001 is the same as 10
Fill in the question marks to make the following statements correct.
a) 10? is equivalent to 100,000
b) ? is equivalent to 10−2
b)
d)
1)
7
2) Convince me that a hundredth is the same as 0.01 which is the same as 𝟏𝟎−𝟐
c) 10? is equivalent to 0.0001
2)
Is multiplying by 𝟏𝟎−𝟏 the same as dividing by 10?
Prove your answer with some examples.
3)
Is dividing by 𝟏𝟎𝟐 the same as calculating 10% of the number?
Prove your answer with some examples?
I can convert between powers of 10 and ordinary numbers
Fluency
Write the following numbers as a power of 10
a) 100
𝟐
b) 10,000
𝟒
c) 1,000
𝟑
𝟏𝟎
𝟏𝟎
d) 1,000,000
e) 0.1
f) 0.00001
g) 0.01
𝟏𝟎
𝟏𝟎
𝟏𝟎
𝟏𝟎
𝟔
𝟏𝟎
−𝟏
−𝟓
−𝟐
h) 0.0000001
𝟏𝟎−𝟕
Write the following as an ordinary number
a) 103
b) 104
1,000
10,000
c) 108
d) 101
100,000,000
10
e) 10−1
f) 10−3
0.1
0.001
g) 10−6
0.000001
h) 100
1
Choose the largest number from each of the following pairs of numbers
a) 103 and 10,000
b) 1,000 and 104
c) 0.01 and 10−1
Problem solving
Reasoning
1)
For each of the following statements, decide whether the
statement is true or false. If a statement is false, explain
why.
True
c)
d)
1)
Fill in the question marks to make the following
statements correct.
a) 10𝟓 is equivalent to 100,000
b) 0.01 is equivalent to 10−2
a) 105 is the same as 100,000
b)
10
1,000,000,000 is the same as 10
False it should be 𝟏, 𝟎𝟎𝟎, 𝟎𝟎𝟎, 𝟎𝟎𝟎 is the same as 𝟏𝟎𝟗
10−3 is the same as 0.01
c) 10−𝟒 is equivalent to 0.0001
2)
False it should be 𝟏𝟎−𝟑 is the same as 0.001
0.0000001 is the same as 10
d) 0.1 and 10−5
7
False it should be 𝟎. 𝟎𝟎𝟎𝟎𝟎𝟎𝟏 is the same as 𝟏𝟎−𝟕
2) Convince me that a hundredth is the same as 0.01 which is
the same as 𝟏𝟎−𝟐
Students need to show all of their workings to convince.
3)
Is multiplying by 𝟏𝟎−𝟏 the same as dividing by
10? Prove
your answer with some examples.
−𝟏
True 𝟏𝟎 is equivalent to 0.1.
𝟒𝟎 × 𝟎. 𝟏 = 𝟒 and 𝟒𝟎 ÷ 𝟏𝟎 = 𝟒
Is dividing by 𝟏𝟎𝟐 the same as calculating 10% of
the number? Prove your answer with some
𝟐
examples? False 𝟏𝟎 is equivalent to 100
which is the same as calculating 1%.
Standard Form
Notes
Commutative:
:Can multiply in any order
Put all these numbers into standard form and then write them in ascending order
SC 12: working with standard form
Rounding and Estimates
Round the following
numbers to the given
decimal place.
Round the following
numbers to the given
place value.
Round the following
numbers to the given
significant figure.
a) 0.53 (1 d.p.)
a) 12 ( nrst 10)
a) 58 (1 s.f.)
b) 0.885 (1 d.p.)
b) 6.8 (integer)
b) 0.359 (1 s.f.)
c) 10.085 (2 d.p.)
c) 3527 (nrst 100)
c) 13.489 (2 s.f.)
d) 2.645 (2 d.p.)
d) 85540 (nrst 1000)
d) 0.00485 (2 s.f.)
e) 0.999 (1 d.p.)
e) 950 (nrst 1000)
e) 0.106 (1 s.f.)
f) 0.099 (2 d.p.)
ANS
f) 0.8714 (nrst 0.1)
ANS
f) 0.0999 (2 s.f.)
ANS
Rounding and Estimates
Round the following
numbers to the given
decimal place.
Round the following
numbers to the given
place value.
Round the following
numbers to the given
significant figure.
a) 0.53 (1 d.p.) 0.5
a) 12 ( nrst 10) 10
a) 58 (1 s.f.) 60
b) 0.885 (1 d.p.) 0.9
b) 6.8 (integer) 7
b) 0.359 (1 s.f.) 0.4
c) 10.085 (2 d.p.) 10.09
c) 3527 (nrst 100) 3500
c) 13.489 (2 s.f.) 13
d) 2.645 (2 d.p.) 2.65
d) 85540 (nrst 1000) 86000 d) 0.00485 (2 s.f.) 0.0049
e) 0.999 (1 d.p.) 1.0
e) 950 (nrst 1000) 1000
e) 0.106 (1 s.f.) 0.1
f) 0.8714 (nrst 0.1) 0.9ANS
f) 0.0999 (2 s.f.) 0.1 ANS
f) 0.099 (2 d.p.) 0.10
ANS
mr-mathematics.com
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B5 – FDP
I Can …
Practice
Representing Fraction and percentages as diagrams
Converting Fractions (
1
1 1 1 1 1
.
, , , , )
10 100 4 5 50 20
to decimal and percentages
Link fraction to division
Convert Complex Fractions- Decimals - Percentage-
Representing fraction and decimal on number line
Represent and interpret Simple pie chart (application)
Identify and use equivalent fractions
Sort FDP in a give order
Improper Fractions
Information: Representing Fraction decimals & Percentages
0 . 2
1
20 percent means 20 per 100 
𝟐𝟎
𝟏𝟎𝟎
1
4
0.25
1
8
0.125
1
100
0.01
1
1000
0.001
1
Decimal
1
1
10
5
0.10 0.20
Percentage
10% 20%
24%
12.5%
1%
0.1%
100%
Fraction
1.00
SC 1: Representing 10th and 100th as diagrams
1)
Exmple
2)
Multiple representation
3) Represent 120 hundredths using hundred square
4)
5)
SC 2: Converting FDP when denominator is a factor of 100
Remember factors of 100
Fraction
𝒑𝒆𝒓𝒄𝒆𝒏𝒕
𝒓𝒆𝒘𝒓𝒊𝒕𝒆:
𝟏𝟎𝟎
Fraction
Bus stop division
𝒆𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝒇𝒓𝒂𝒄𝒕𝒊𝒐𝒏
𝒏
𝟏𝟎𝟎
Numerator ÷ denominator
Place value
𝟒𝟐𝟕𝟔
𝟏𝟎𝟎𝟎
Percentage = numerator
Percentages
Decimal
Percentages
x 100
Examples i)
Fraction
Decimal
Percentage
Decimal
÷ 100
11
1000
9
𝑖𝑖)
20
𝟕
𝟏𝟎
𝟖𝟏
𝟏𝟎𝟎
15
𝑖𝑖𝑖)
500
𝟗
𝟏𝟎𝟎𝟎
𝟐
𝟓
𝟔
𝟐𝟓
0.04
60%
𝟕
𝟐𝟓𝟎
SC 3/4: Converting FDP
Division   fraction
Bus stop division method
Fraction
𝒓𝒆𝒘𝒓𝒊𝒕𝒆:
𝒑𝒆𝒓𝒄𝒆𝒏𝒕
𝟏𝟎𝟎
Place value
Equivalent fraction
Percentages
Decimal
÷ 100
Examples: Calculate as a division and write as a fraction
Decimal
Percentage
𝟔𝟒𝟑
634 ÷ 4 = 
𝟒
158.5
 4|643.0 =
158.5
𝟐𝟔𝟑
𝟒
Fraction
Division
𝟏𝟔𝟖
≡ 𝟏𝟖𝟔 ÷ 𝟔
𝟔
186÷ 𝟔 ≡ 𝟔 | 𝟏𝟖𝟔
21 ÷ 4
81 ÷ 2
162 ÷ 4
84 ÷ 8
241 ÷ 8
2947 ÷ 7
24.1
SC 4 Representing fraction, decimal and Percentage on number line
0.1 ≡ 0.10
𝟏
𝟏𝟎
≡
≡ 𝟏𝟎%
𝟏𝟎 𝟏𝟎𝟎
Complete the number lines
SC 4 Representing fraction, decimal and Percentage on number line
0.1 ≡ 0.10
𝟏
𝟏𝟎
≡
≡ 𝟏𝟎%
𝟏𝟎 𝟏𝟎𝟎
Complete the number lines
SC 5: Application – Pie chart
What fraction is shaded
a) What fraction of the kids
painted?
b) What fraction of the kids
read?
c) What percentage of the
kids danced?
a) What fraction of the kids
painted?
b) What fraction of the kids
read?
c) What percentage of the
kids danced?
Challenge
SC 6: Identify and use equivalent fractions
Example
Simplify fraction by dividing by HCF
Equivalent Fraction: multiply /divide numerator and denominator
by same value
Equivalent Fraction
SC: 7 Comparing fraction
𝟖
×
𝟖
𝟖
≡
𝟒𝟎
<
𝟓
×
𝟓
≡
𝟏𝟓
𝟒𝟎
Put in ascending order
SC 8:Order FDP
Example
Step 1 : Convert to decimal
0.42
0.44
0.429
decimal
Step 2 : Put in order
0.42 0.429 0.44
0.5 ascending order
Step 3 : Give answer in original format
42 %
𝟑
𝟕
𝟒
𝟗
0.5 original format
Improper
Fraction
Mixed
number
improper fraction notes
Convert to improper Fraction
Convert to Mixed Number
SC 9: Work with improper fraction
Convert to Number Mixed
Improper
Fraction
Mixed
number
Complete the number line
Convert to improper Fraction
Find the term-to-term rule and complete the sequence
𝟏) 𝟎. 𝟒,
𝟎. 𝟏𝟏,
𝟐) 𝟖𝟎%,
𝟔
,
𝟓
𝟏. 𝟔,
𝟐,
𝟑. 𝟏,
𝟕𝟕
,
𝟐𝟎
𝟐𝟑
𝟓
𝟒𝟕
𝟑)
,
𝟐𝟎
𝟎. 𝟏𝟖,
𝟎. 𝟐𝟓
Write division as fracti
Convert between FDP
Shade farctions
FDP on number line
Compare FDP
Do Now:
End Point:
LL) What fraction of the square is shaded?
Give your answer as 3 different fraction.
Which number is below
LW) Complete the cycle to convert:
Fraction  Decimal  Percentage
4
6
Fraction
↑
Percentages
LM) Sort in ascending order
344.01 304.41 314.04
341.04
310.44
340.14
Decimal
0.84
𝟑
𝟒
1.205
5
4
Explain how you know
What percentage of the area is shaded?
SC 9:FDP Application
Example
Factors 100?
SC: 6 Equivalent fraction
Find 3 fractions that are equivalent
End Point:
Which number is below
4
6
0.84
𝟑
𝟒
1.205
5
4
SC: 6 Equivalent fraction
SC 3: Converting Complex fractions
Example
Denominators
is not a factor
of 100
1) Use bus stop division to find decimals
0.22 …
2
= 2 ÷ 9 → 𝟗 𝟐 .𝟎 𝟎
9
2) decimal × 100 = 𝒑𝒆𝒓𝒄𝒆𝒏𝒕𝒂𝒈𝒆
𝟎. 𝟐𝟐 × 𝟏𝟎𝟎 = 𝟐𝟐%
Fraction
1
9
1
11
2
3
1
8
3
22
decimal
Percentage
𝟏
𝟏
𝟏 𝟏
𝟏
𝟏
SC 2: Converting FDP (𝟏𝟎 . 𝟏𝟎𝟎 , 𝟒 , 𝟓 , 𝟐𝟓 , 𝟐𝟎)
Example
Denominators =
Factors of 100:
1 x 100
2 x 50
4 x 25
5 x 20
10 x 10
𝑛
1) Use equivalent fraction to write in form100
3
3
5
𝟏𝟓
≡
× =
20
20 5 𝟏𝟎𝟎
2) When in form
𝑛
100
→ 𝒏𝒖𝒎𝒆𝒓𝒂𝒕𝒐𝒓 = 𝒑𝒆𝒓𝒄𝒆𝒏𝒕𝒂𝒈𝒆
𝟏𝟓
= 𝟏𝟓%
𝟏𝟎𝟎
3) Convert % to decimal by ÷ 100
𝟏𝟓 ÷ 𝟏𝟎𝟎 = 𝟎. 𝟏𝟓
Fraction
Percentage
Decimal
1
10
1
100
1
2
=
5 10
1
20
1
4
3
4
1
25
1
2
1
50
10
=10%
100
0.1
SC 2&3: FDP conversion
Example
Denominator =
Factors of 100:
1 x 100
2 x 50
4 x 25
5 x 20
10 x 10
SC 8: Division as fractions
1) Write as a fraction and simplify
Example
𝟏𝟐 ÷ 𝟑 = 𝟒
𝑎) 32 ÷ 8 =
𝑏) 27 ÷ 3 =
𝑐) 35 ÷ 5 =
d) 7 ÷ 21 =
e) 6 ÷ 30 =
f) 4 ÷ 36 =
g) 3.5 ÷ 7 =
h) 3.6 ÷ 6 =
i) 15 ÷ 0.3 =
≡
𝟏
𝟏𝟐
× 𝟏𝟐 =
=𝟒
𝟑
𝟑
𝟏 ÷𝟑=
6
24
=
3
12
0.4
2
𝑐) ⇒ 5 2 . 0 = 𝟎. 𝟒
5
=
2) Write as a division and solve
9
𝑎) ⇒
3
56 14
𝑎) 56 ÷ 8 =
=
=𝟕
8
2
b) 6 ÷ 24 =
𝟏
𝟑
𝟏
𝟒
1
𝑏) ⇒
9
3
𝑐) ⇒
5
sc
Hegarty
B1- Sequences
I Can …
Practice
1
Describe and continue a sequence diagrammatically
Find the next
two terms
2
Predict and check the next nth term (the nth position)
What is the
20th terms?
3
Represent sequence in Tabular & graphical forms
Draw this sequence in a
Table and graphically
4
Continue a numerical linear sequence (arithmetic sequence)by
identifying the term-to-term rule (common difference)
Find the term to term rule
60, 74, 88, ___, ___
1.5, 1.2, 0.9, ___, ___
5
Explain the term-to-term Rule of numerical sequences in full sentences
using mathematical words.
How many sequences can you create beginning with 1,
2,
Write the term-to-term rules in words
6
Continue numerical non-Linear sequence (geometric sequence or not
with a common difference)
Find the next two terms
i) 1, 2, 4, 8, ___, ___ ii) 1, 3, 6, 10, ___, ___
7
Find missing term within sequences
Find the missing terms:
i) 6, __, 14, __, 22, __ ii) 8000, ___, ___, 6500, ___
8
Recognise special sequences: square numbers, cube numbers,
Fibonacci sequence, triangular numbers
List the first 5 cube numbers,
List the first 5 Fibonacci numbers
Do Now
LL)
End Point
0.01, 0.05, 0.09
Fill in the gaps
a) find the next two terms
b) Use Double line to represent
sequence as fraction & percentage
LW)
𝟔
𝒘𝒓𝒊𝒕𝒆
𝒂𝒔 𝒂 𝒑𝒆𝒓𝒄𝒆𝒏𝒕𝒂𝒈𝒆
𝟓𝟎
LM) 𝑺𝒊𝒎𝒑𝒍𝒊𝒇𝒚 𝒆𝒙𝒑𝒓𝒆𝒔𝒔𝒊𝒐𝒏 𝒃𝒚 𝒄𝒐𝒍𝒍𝒆𝒄𝒕𝒊𝒏𝒈 𝒍𝒊𝒌𝒆 𝒕𝒆𝒓𝒎𝒔
𝟒𝒙 + 𝟑𝒙𝒚 − 𝟐𝒙 − 𝟔𝒚𝒙
i) How many objects (circle, squares..) in
each term 5 rectangle , 9 rectangle, 13 rectangle,
ii) How many object is in the next term.
17 rectangle,
iii) What would the next term look like?
iv) Predict How many objects (circle,
squares..) will be in the 6th term
v) Describe the Sequence (use term-toterm) Add 4 rectangle to the end
vi) Complete the table
example
Position (n) 1
Position
Position (n)
(n) 11
Number
Number
Number of..
of.. 55
of..
Rule 
2
22
3
33
4
44
5
55
6
66
99
13
17
21
25
1) Find the term –to - term Rule
2) Find the next two terms:
Connection to other topics
1) Use Function machine to find Rule
2) Represent the sequence on a table
3) Represent the sequence on graph
End Point
0.01, 0.05, 0.09
a) find the next two terms
b) Use Double line to represent sequence as fraction & percentage
Hegarty
B2- Algebraic Notation
I Can …
Practice
1 288
Use function machine (number) to find output
Find the
Output:
2
Use inverse operation on function machine to find input
Find the
Input:
3 157
158
Use correct algebraic notation for adding, multiplying and
dividing
𝑺𝒊𝒎𝒑𝒍𝒊𝒇𝒚
𝑖) 𝑎 + 𝑎 + 𝑎 =
=
4
Use function machine (algebra) to solve equations
Find in the
Input/output
5
Identify the functions needed to produce the outputs
Find the
Function:
6 155
178
Substitute values for the variables to calculate the value of the
expression.
Substitute n = 5 into the expression:
ii) 2 × 𝑎 × b =
iii) a ÷ 𝑏
Find the first three term of sequence 3n + 2
Solve with fact family
Solve with function machine
Find the value of unknown
Find the value of unknown
s
Hegarty
B4 – Place Value
Practice
I Can …
1
13
45
write and represent the numbers up to million in several ways
Complete these representations to show the same number
2
3
4
5
14
13
Identify place value
convert integers between numeral and words
work out the intervals and complete a number line
round to the nearest 10, 100, 1000
Write down the value of 5 in : 305, 052, 867
Write Two hundred and three thousand, fifty-four
6
130
137
14
46
14
46
410
7
8
9
17
Round to 1 significant figure
There are 2000 students in a school. What I the maximum
and minimum student possible?
Round to 1 sf: 2940, 0.0249
Compare and sort numbers using symbols <≤>≥=≠
Order a list of numbers
Put in ascending Order:
Find the range from a group of values
Find the range of these numbers:
68 63 79 111 104
Find the median from the list of these numbers:
68 63 79 111 104
What as a power of 10:
1000 × 102 × 10−3 × 100 =
Write in standard form:
2.5 × 106 × 2.2 × 104 =
10 409
Find the medium from a list of values
11 121
125
12 122
123
writing multiple of 10s in the form 10𝑛
writing and interpreting numbers in standard Form
Write the numbers then put it in order
327, 619
741,093
2, 936,081
542,730
2,357
327, 619
517,409
542,730
741,093
1,406,271
8,901,473
8,901,473
1,406,271
517,409
2,357
2, 936,081
Rounding
Round to nearest Whole number:
Round to 1 significant place: