Title of Unit:
Historical Mathematics
Year
9
Term
Any
Duration
6 lessons
Unit Description: Students will be researching the life and work of 4 different mathematicians and work through activities based around their work in order to see how
their work feeds into the school maths that they learn.
Prior learning
Number, Formulae,
Surface Area,
Volume, Area,
Density,
Sequences,
Probability, Ratio.
Phase A
Matching exercise.
Mathematicians with
the dates they were
active.
Content & Range Objectives
4.1 Geometric reasoning
Investigate Pythagoras' theorem, using a
variety of media, through its historical and
cultural roots.
3.1 Equations, formulae, expressions and
identities
Use formulae from mathematics, substitute
numbers into expressions and formulae; derive
a formula.
2.7 Calculator Methods
Use a calculator efficiently and appropriately to
perform calculations, knowing not to round
during intermediate steps of a calculation; use
the function keys for powers and roots
Phase B
Phase C
Students will do research in groups of selected
mathematicians. They will then present what they have
learnt about these mathematicians to the rest of the class.
Students then spend a series of lessons doing rich tasks
and investigations into some of the work that these
mathematicians did, seeing how it links to what they learn
in school.
Level
5/6
Key Process Objectives
Classify and visualise properties and
patterns
Generalise in simple cases by working
logically
Draw simple conclusions and explain
reasoning
Misconceptions:
Do students know the difference between
AD and BC and the new system of CE and
BCE.
Knowing the difference between
area/surface area and perimeter
Knowing the difference between significant
figures and decimal places
Understand the meaning of square root as
being x1/2
Counting the units between the dots
Units of area and perimeter
Key Vocabulary
Consecutive Ratio Sequence Predict
Relationship Pattern Strategy
Represent Analyse Interpret
06/03/2016
1
Quiz on the work that
the different
mathematicians did.
Debate on who is the
most important
mathematician.
Connecting to……
Sequences,
Pythagoras, Golden
Ratio, Formalising
maths and Proofs.
Possible crosscurricular links with
science.
Resources:
Phase A:
Match Cards and “Who are the Mathematicians” powerpoint,
washing line.
Phase B:
Fibonacci Lesson:
Steps problem, Rabbit Breeding Problem & Golden rule
Pascal Lesson:
Probability and Pascal’s triangle worksheet, Patterns and
Properties of Pascal’s triangle worksheet.
Pythagoras Lesson:
Pythagoras worksheet, access to NRICH website.
Archimedes Lesson:
Task sheet, Maths Watch lesson PP presentation, Tracing
paper, Hodder Edexcel text book, Scissors, Ruler, Calculator
Phase C:
Quiz sheets.
Suggested Assessment Criteria
APP sheet attached
Peer Assessment Sheet to be used for presentations.
Bexley LA
Title of unit
Phase
A
Historical Maths
How will the pupils learn?
e.g. tasks/activities, starters, plenaries etc
Starter:
Powerpoint with loads of names on it. Students
then need to pick out the mathematicians.
8
Year
How will the learning
emerge?
e.g key questions,
assessment points,
assessment criteria
Term
Any
How will this be adjusted?
Support
Extension
Resources needed:
Match cards, “Who are the
Mathematicians” powerpoint,
washing line.
Trial and error and
discussion.
Main section:
Students receive a set of cards. They need to
match the names of mathematicians to their
dates.
Notes
e.g. practical resources,
ICT, homework …
Group the
mathematicians
into 2 groups. CE
versus BCE.
Discussion: What did each of the
mathematicians do/discover?
Assign a mathematician to a group of students.
Students then go away to research their
mathematician (possibly for homework).
Include some blank
cards with missing
dates.
Include cards
outlining
mathematicians’ work
for matching.
Research Instruction sheet
Plenary:
Put mathematicians in the right order on a
timeline- possibly use a washing line across a
classroom.
B
All lessons will have the same structure.
Activities can be found after the lesson outline.
Starter:
Students to present in groups the results of their
research into their mathematician, reminding
the class of where they were on the timeline.
Peer assessment/evaluation
of presentation.
Main section:
Teacher to briefly explain the activity that
relates to the mathematicians’ work.
Students then work on the activity throughout
06/03/2016
2
Bexley LA
the lesson. Each activity is designed so that
students should be able to work independently
from the teacher.
Plenary:
Discussion- what have students learnt today?
Where would we see this mathematician’s work
again? Are there any links with any other class
work?
Pascal:
Lower ability task:
This is an activity that can be used over a whole
lesson with less able students or as a starter/
homework with more able students.
It is an investigation into the patterns and
properties of Pascal’s triangle.
Higher ability task:
This is an activity aimed at higher ability
students to investigate the link between Pascal’s
triangle and probability. It will take a full lesson.
It can be used with lower ability groups if you
stop after the first instruction box.
Pythagoras:
Rich task for Pythagoras is tilted squares,
adapted from an nrich problem.
06/03/2016
Students will complete the
worksheet by following the
instructions and try to spot
the patterns/ sequences
that emerge on their own.
They might know the
names of these sequences
or they might need to find
them out.
Students may need
help understanding
the structure of the
triangle and how it
is set up.
Task 4 might need
to be removed.
When used as a
starter/homework,
students can use it to
start thinking about
more complex
sequences.
Each student will need their
own worksheet as there is a
table to fill in at the bottom.
Students will follow the
instructions on the
worksheet to find for
themselves the link
between Pascal’s triangle
and probability.
The activity could
be restricted to the
first instruction box
or the first 2
instruction boxes.
The worksheet
could be split into
smaller activities for
lower ability
groups.
Extension
investigation question
is given at the end of
the worksheet.
Each student will need a
worksheet.
It may also be helpful to give
them a pyramid template to fill
in Pascal’s triangle.
Assessed by presentation
from the pupils and from
the outcomes of the rich
task.
Teacher support is
included in the rich
task to give the less
able pupils a hint.
Teachers of more
able classes may wish
to show the problem
in its simplest form
and not distribute the
Each student will need their
own worksheet for rich task.
The original problem can be
viewed and shown to the class
on the website nrich.maths.org
3
Bexley LA
Fibonacci:
Rich task(s) is/are set for students to work on in
groups or individually. Rabbits, Steps or Fibs
Tasks. Use ppt to introduce π, Ф and get
students then to explore the golden ratio.
Students to feedback their findings to the class
different groups could express their findings…
Archimedes:
Rich task can be found on slides 21-24 of the
attached powerpoint (Phase B- Archimedes)
The earlier slides in the powerpoint can be used
in previous lessons to intrioduce the concepts
needed in order to fully understand the rich
task.
06/03/2016
question sheet.
and search tilted squares.
Teacher gives students a
chance to get started then
thro’ questions like:
Steps- Draw a diagram to
get an idea of what is
happening?
Rabbits- Use the table or
flow chart diagram to help
you. What do you notice
about the total number of
rabbits at the end of the
month? How could you
continue the pattern
without drawing anymore
rabbits? What do you notice
about your number pattern?
Steps and Rabbit
tasks
Fibs
HL: Where in nature do we see
the Golden Ratio?.. worked
examples
Follow the powerpoint
(slides 21-24).
Learning will emerge
through discussion that
follows.
Lower ability
students can
conduct a small
scale investigation
where different
objects with
different surface
areas and volumes
are submerged in
water, then collect
and measure the
amount of water
displaced, plot the
results, then
discuss their
findings
More able students
can carry out the
same experiment, but
take it a step further
by fixing and
modifying parameters
(surface area,
volume, density of
the object), collect
their results in tables,
then use scatter
graphs and other
mathematical tools
such as sequences to
interpret their
findings
Buckets, Foil, Paper clips,
water.
4
Bexley LA
C
Discuss links between mathematicians and
relate these links to the timeline.
Discussion
Debate: Who was the most important
mathematician and why?
Quiz to find out what the students recall from
the presentations and the activities.
06/03/2016
Students argue that
the mathematician
that they
researched is the
most important.
Check answers of quiz.
Students argue that a
mathematician other
than the one they
researched is the
most important.
Quiz sheets.
5
Bexley LA