Sacred Heart Mathematics Department : Connect 3B
Unit 8 – A4 – Factors, Indices and Graphs – 10 lessons
Extension Connect 3R
Les- Lesson title
son
Use prime factor decomposition to find
the LCM of denominators of fractions in
order to add or subtract them
Find the HCF and LCM of algebraic
expressions
1
Know and use the index laws for
multiplication and division of positive
integer powers
Begin to extend understanding of index
notation to include negative powers
Begin to extend understanding of index
notation to fractional powers
Recognise that the index laws can be
applied to fractional powers
Recognise and operate with simple surds
Substitute positive and negative numbers
into linear expressions and expressions
involving powers
2
Investigate the gradient of parallel lines
and lines perpendicular to these lines
5
Plot graphs of quadratic and cubic
functions.
3
4
6
Know some of the properties of quadratic
functions.
7
Use a graphical method to solve
simultaneous equations
8
Form and solve linear simultaneous
equations
9
10
Oral objectives:
8.1 Prime factors
8.2 Indices
Objectives
Starter FrameNo
work
Find the prime factor decomposition of a number
Use prime factor decomposition to find the LCM of denominators of
fractions in order to add or subtract them
Use index notation for integer powers and simple instances of the index
laws
8.3 Laws of
indices
Know and use the index laws for multiplication and division of positive
integer powers
8.4 Substitution
Substitute positive and negative numbers into expressions involving
powers
9
10
8.6 Finding the
gradient
Given values for m and c, find the gradient of lines given by equations
of the form y = mx + c
Find the gradient of a drawn graph
25
Solve problems involving direct proportion using algebraic methods,
relating algebraic solutions to graphical representations of the equations
26
Badger
27
Use index notation for squares and
cubes
Know cubes of 1, 2, 3, 4, 5 and 10
and the corresponding roots
Use a calculator to find squares and
cubes
Use index notation for small positive
integer powers of 10
Recognise prime numbers up to 100
Find the prime factor decomposition
of a number
Badger: Yr8
Use index notation for small positive
integer powers
Simplify algebraic expressions using
index notation
Distinguish between 2n and n2
Substitute positive integers into
expressions involving small powers
Know that algebraic operations
follow the same conventions and
order as arithmetic operations
Plot graphs of the form y = mx + c, on
paper and using ICT
Recognise that equations of the form
y = mx + c correspond to straight-line
graphs
Badger: Yr8
44
Support Connect 3G
Badger: Yr8
24
Plot simple distance–time graphs and displacement–time graphs
End of unit test. Mental Arithmetic. Review Test
Badger: Yr8
10Ticks: L5, P
33
Recognise the effects of m and c in the equation y = mx + c of a straightline graph
Discuss and interpret simple distance–time graphs and displacement–
time graphs
Badger: Yr8
10Ticks: L6
10Ticks: L6
11
8.5 Equations of
straight-line
graphs
8.7 Direct
proportion and
graphs
8.8 Distance–time
and displacement–
time graphs
8.9 Interpreting
distance–time and
displacement–time
graphs
TESTING
ICT/Additional
Resources
Investigate straight-line graphs of the
form y = mx + c
Construct functions arising from reallife problems and plot their
corresponding graphs
Discuss and interpret graphs arising
from real situations
Key words:
prime factorisation, factor, factor tree, denominator, lowest common multiple, power, indices, index, simplify, substitution, equation, y-intercept, gradient, direct proportion, ratio,
origin, distance, displacement, speed