1. SIS Curriculum Framework 2012-13 (Scope and Sequence document)
YEAR: 8 UNIT: Area and Volume (5 weeks) Date completed: May 2012 (VS) Updated:
Themes Learning Outcomes Assessment Key words and subject skills
Main Ideas Essential KU&S Strategies
Essential Questions
Possible further KU&S How students will
demonstrate their
KU&S
Assessment for Learning: Keywords:
In this unit, students Core:
Perimeter/Area/Cm2
will investigate about 1. Find
areas
and
perimeters
of
rectilinear
shapes
Peer assessment of Trapezium
2. Calculate
the
area
of
a
trapezium
and
composite
shapes.
scavenger hunt Pi /Circumference /Diameter/ Radius
perimeter, area and 3. Find
the
circumference
of
a
circle
from
radius
and
Follow-me cards Scale factor
volume for different diameter.
Volume /Capacity /Litres
kinds of shapes 4. Find
the
area
of
a
circle
and
compound
shape
from
Assessment of Learning: Cubic centimeters
radius
and
diameter.
Stack
5. Recognise
standard
3-­‐D
shapes
and
represent
them
Questions on flipcharts Prism
using
nets.
Extension sheet Cross section
6. Find
the
volume
of
a
prism.
Worksheets
Extension:
Skills Framework:
7 Use
the
inverse
to
find
the
radius
and
diameter
from
the
Prior Knowledge
circumference.
Presenting conclusions and supporting with
8 Find
areas
of
enlarged
shapes
by
using
the
square
of
the
evidence
scale
factor
and
reverse.
Students should be able to
9 Use
the
volume
to
find
missing
lengths
of
prisms
apply the skills they have Making a judgment
10 Find
surface
areas
of
prisms
and
pyramids
learnt in the Area/Perimeter
unit from year 7 Justifying and articulating ideas
Remaining open to feedback
Using ICT to investigate
Showing resilience and perseverance

2. Learning Themes Development Resources
Objectives Main Ideas
Essential Questions
1. 1. Find
areas
and
Students re-cap area and Follow-me cards WS11
-­‐
(30 mins) perimeters
of
rectilinear
perimeter of rectangles, These can be used as either a whole class activity Area_and_Perimeter_Fo
shapes
squares and triangles. or making a physical loop in pairs. llow_Me_Cards
2. 1. Find
areas
and
To solve problems involving Starter problems Flipchart:
(20 mins perimeters
of
rectilinear
area and perimeter See flipchart. Pick and choose as appropriate FC1 - 3 Tasks
shapes
each)
Task 1: Find rectangles with the same area as
perimeter

3. Task 2: Find shapes with the same perimeter
Task 3: Find the area of a compound shape using
subtraction
3a. 2. Calculate
the
area
of
a
Students can estimate areas of Area of a trapezium, Irregular shapes Worksheet:
(1 hour) trapezium
and
irregular shapes WS1
-­‐
Estimate
Area
of
composite
shapes.
Students are given a worksheet and some bold a
TRAPEZIUM
squared paper. They can overlay the worksheet
and count squares/half-squares to give a rough Flipchart:
answer FC1 - Estimating
Explain task to students. irregular areas
Extension – if they appear to already know a
formula, have them work out the areas and
compare/discuss with those who are estimating.
Can they explain the formula? Or derive it?
Pathway A – no, add build on task
Pathway B – keep task
Link to others 10 ticks worksheet
Add CFW’s task

4. 3b. 2. Calculate
the
area
of
a
Students are able to see how All about trapeziums Flipchart:
(1 hour) trapezium
and
the formula is derived, and FC2 - All about
composite
shapes.
hence calculate the area of a Students should work in groups of three for the Trapeziums
trapezium. main part of the lesson. All students are
responsible for the work, but the following tasks FC3 - Proofs
In groups, student think about could be assigned: FC4 – creating shapes
how they can use what they with fixed area
already know to help them find • Recorder: Records all important information on the
the area. They are then record sheet.
prompted, if required, to • Measurer: Double checks all measurements and
calculations.
consider methods to formalize • Reporter: Shares all pertinent information with the
the derivation. class (Flipchart page 1)
These roles are important because they hold each
student in the group accountable.
Teacher displays page 2 of flipchart, a standard
trapezium. Students are then asked to find a
“method’ for finding the area. Work your way
through the images and ideas on the chart – using
it as little as possible so that the students are not
being too guided. Let them come up with their own
ideas.
Prompt Q: “What other shaped could help you?”
Extension: the more algebraically able students
would benefit from considering more than one
deconstruction method – some images are shown
on pageof the flip chart. Can they make up their
own?
To conclude: students can now work out the
areas on the original sheet, and compare their
estimates.
Alternative (Pathway A)
Getting students to prove the formula for the area
of parallelogram, kite and trapezium

5. 4 1. Find
areas
and
Building spreadsheet using ICT Tasks Student
(1 hour – perimeters
of
rectilinear
simple formulae Task 1 1 – Paper size
shapes
each task) 5. Recognise
standard
3-­‐D
Paper sizes template
shapes
and
represent
Working out the ratio of different paper sizes and to 2 – Surface area
them
using
nets.
realize that the sum of all paper sizes equal to the template
6. Find
the
volume
of
a
orginal size A0 3 – Volume template
prism.
Task 2 Teachers
9 Use
the
volume
to
find
missing
lengths
of
Surface Area investigation FC1 – ICT tasks
prisms
To calculate the maximum surface area 1 – Paper size solution
10 Find
surface
areas
of
2 – Surface area
prisms
and
pyramids
Task 3 solution
Using surface area to calculate the maximum 3 – Volume solution
volume
5a. 3. Find
the
circumference
Measure the circumference Apple Pi (1) Resources:
(1 hour) of
a
circle
from
radius
and diameter of various (Students should be asked to bring in flat Lengths of string (long)
and
diameter.
circular objects circular, or cylindrical objects prior to the Circular objects to be
lesson) measured
Calculate the ratio of Warm-up: Ask students to measure width and Calculators
circumference to diameter length of their desks. Then ask them to work out Rulers
the distance around it.
Discover the formula for the Q: What unit did you use? Why? Worksheet:
circumference of a circle Why did some measurements differ? What do we WS1 - Apple Pi
call this measurement? (for gentle sets) Recording
Discovery by measuring & Main Part: Divide into groups of 4, each with a Flipchart:
pattern spotting in order to main role: FC1 - Apple Pi
determine relationships.
• Task Leader: Ensures all students are participating; Link:
lets the teacher know if the group needs help or has NCTM site
a question.
(includes some
• Recorder: Keeps group copy of measurements and
calculations from activity. thoughts on discussion
• Measurer: Measures items (although all students Qs)
should check measurements to ensure accuracy).
• Presenter: Presents the group’s findings and ideas
to the class. (On Flipchart)
Students should measure the "distance around"
and the "distance across" of the objects that they
brought to school. Students should be allowed to

6. select which unit of measurement to use. However,
instruct students to use the same unit for the
distance around and the distance across.
The recorder put the information on the Apple Pi
worksheet and the team works out the last column.
Discuss with class (on the flip chart). Compare
averages.
Discussion Questions:
- Why did we use the ratio of circumference to diameter for
several objects? Wouldn’t we have gotten the same result
using just one object?
- Were any of the ratios in the last column not close to 3.14?
If not, explain what might have happened.
- Describe some situations in which knowing the
circumference (and how to calculate it) would be useful
Extension: Have students plot the diameter of
those objects along the horizontal axis of a graph
and plot the circumference along the vertical axis.
Consider line of best fit and the gradient…..
Conclusion: Questions on flipchart to assist
assessment.
Pathway B – keep, good
5b. 3. Find
the
circumference
Measure the radius and Apple Pi (2) Resources:
(1 hour) of
a
circle
from
radius
diameter of various circular Circular objects
and
diameter.
objects using appropriate units Starter: Estimate the area of the circular objects Calculators
4. Find
the
area
of
a
circle
of measurement that they have brought to class. Using the Scissors
and
compound
shape
worksheet, students should individually complete Compasses
from
radius
and
Discover the formula for the the first two columns. (Differentiated methods Rulers
diameter.
shown on Flip if req’d) Centimeter grid paper

7. area of a circle Blank A4
Main Part: Students cut a circle template into
Estimate the area of circles sectors (or construct on blank A4 if more able) and Worksheets:
using alternative methods use to gradually form an approx. parallelogram – WS2 - Areas of
follow flip chart. (read through before to plan Circular things
how much you’ll use it – the more able may not WS3 – Circle template
need guiding quite so much) WS6 – 10cm circle
Discovery by measuring & Arrive at formula for Area of Circ
pattern spotting in order to Link:
determine relationships. Discussion Questions (on flip): NCTM site
(Includes some
- In your opinion, why did we use the properties of a thoughts on discussion
parallelogram to discover the area formula for circles?
Qs)
-When would it be necessary to know the exact area of a
circle? When would an estimate be sufficient? Explain your
thinking.
- Why did we approximate our answers for area? Can
the area of a circle ever be exact?
-
Conclusion: Questions on flipchar
5c. 3. Find
the
circumference
Students will discover a Square circles Worksheet:
(1 hour) of
a
circle
from
radius
relationship between the (alternative to Apple pi 1) WS4 - Square Circles
and
diameter.
diameter of a circle and it’s WS5 – pi investigation
4. Find
the
area
of
a
circle
circumference To begin: using rulers, students complete the info Flipchart:
and
compound
shape
for squares on the worksheet. FC2 - Square circles
from
radius
and
Identify various units of measure
diameter.
based on their appropriateness for Then ask them to do the same for the circles, this Materials:
each shape and size.
will prompt a discussion on how to measure Counters
Draw conclusions about the
circumference…. Coins
relationship of side/perimeter in Paperclips
squares and diameter/circumference Practical: M&Ms if you wish
in circles based on collected data. Hand out alternative units of measure to be used (M&Ms, String
paper clips, coins, identical beads, etc.). Be sure there are
Through physical representations, enough. You may wish to discuss how each unit of measure
develop the idea of a constant that can be used, or you may prefer that the students discover
relates a circle’s diameter and this on their own. FLIPCHART shows how this could be
circumference, namely pi. done. The teacher can also discuss with students how they
may have to estimate portions of a unit if the measure is not
exactly an integer. Allow students to find a second measure
of the squares and both measures of the circles using at least
one non-traditional unit of measure.

8. Collecting data:
Once students have filled in the activity sheet, the teacher
records sample on flipchart. (or on own copies of ‘What
changes?’ worksheet). At this point, the teacher should lead
the students into identifying a relationship between a
square’s perimeter and its side. Many students will know that
Perimeter = 4 × Side, or P = 4s, but try to get students to
think of the 4 as a constant that is equal to P ÷ s. It is
important for students to see that this relationship is the same
regardless of the square’s size or unit of measure, which
makes it a "constant." A discussion of constant versus
variable may be necessary here.
Same is done for circles leading to the discover of a
constant(Pi)
Assessment:
Student to write a paragraph about what they discovered
today – allow opportunity to share. In pairs, students find
circles around school and challenge each other to find the
circumference. Confirm by measuring with string?
Problem at end of flipchart to consider.
6. (1 hour) 3. Find
the
circumference
Students demonstrate that 3 in a row game Worksheet:
of
a
circle
from
radius
they can calculate area and WS1 – 3 in a row
and
diameter.
circumference of circles, given Page 1 of worksheet is the Game Board (Game board and
4. Find
the
area
of
a
circle
a radius or diameter. Page 2 is to be cut up in to playing cards cards needed for each
and
compound
shape
Page 3 are answers pair)
from
radius
and
Game format. Students are
diameter.
given ‘answers’ and asked to Game: Playing card are shuffled face down. In
fit them to the correct circle pairs, students take it in turns to pick a card from
the pile and cover up the relevant circle on the
board. If they can’t find a match, the card goes on
the bottom of the pile. The aim is to get three in a
row to win.
Ext: Impose a time limit, controlled by the teacher.
No calculator, practice estimation
7. (1 hour) Extension
Students solve complex Extension Tasks - Circles Worksheet:
7. Use
the
inverse
to
find
problems involving the area WS1
–
answer
sheet
to
the
radius
and
diameter
from
the
circumference.
and perimeter of circles Task 1: Compound Shapes circle
problems
Let the students do these without instruction and WS2
–
Compound
see how they problem solving- asking questions of shapes
them. Some could share solutions.

9. Flipchart:
FC1 – Problems
Task 2: Nrich Problems FC2 – Nrich problems
Flip chart (links embedded) & worksheet. PP1 – Circle problems
These are quite challenging!!
8a.
Identify the names of three The Hunt for 3D Shapes Worksheets:
(1 hour) 5. Recognise
standard
3-­‐D
dimensional geometric shapes (gentle)
shapes
and
represent
(cube, rectangular solid, square
Pathway C them
using
nets.
Warm-up WS1 - Scavenger Hunt
pyramid, prism,sphere, cone and Brainstorm the names of all the 3D shapes they WS2 - Scavenger Hunt
cylinder).
know- ensure all are written on IWB. Peer assessment
Identify the number of faces,
edges and vertices. Scavenger Hunt: In groups of 4-6, issue
Assignment worksheets. Group members should
Find 3D objects in real life and share our ‘shapes’ then follow instructions on the
describe them. sheet.
Students engage in a team Presentations: to the rest of the group. Peer
hunt to identify common 3D assessment sheets available.
objects and explain properties.
8b. 5. Recognise
standard
3-­‐D
Students understand the Riddle me this Worksheet:
(1 hour) shapes
and
represent
properties of 3D shapes (gentle) WS3 - Riddle me this
them
using
nets.
Pathway C Go through examples on the worksheet. Note that
Riddle describing a shape the first two lines describe the shape and the next
two, how it moves.
Give students a while to compose their riddle then
collect them in. Share out randomly in order to
challenge others in the class.
8c. 5. Recognise
standard
3-­‐D
Students understand that 3D 3D shapes Resources:
(1 hour) shapes
and
represent
shapes can be constructed from Printed nets (selection
them
using
nets.
2D nets Task: NETS on links below)
Students come into the class where there are A4 Squared paper
Exploration lesson where coloured printed sheets, scissors and tape on each Isometric paper
Extension
students are provided with a grouped table. No intro, the teacher just says, “Ok! Scissors
variety of nets and just ‘left to Let’s see what you can make me!” tape
10. Find
surface
areas
of
prisms
and
pyramids
it’
Be prepared with challenging platonic solids and Links:
be ready to assist/pair up those who are struggling. Applet 2D to 3D
Discuss, comment and classify. Encourage Printables

10. students to walk around and see what other have
made, and to ask questions. Extension nets to
print
Extension: Students set each other problems
from, “Make a cube with edge 3 cm” to “Make me a
4 cm square based pyramid with height on 5 cm”
9. (1 hour) 6. Find
the
volume
of
a
Roughly estimate the Filling Boxes! Folding Boxes! Links:
prism.
volume/capacity of everyday Cubes applet
objects Warm up- What is my VOLUME?
Estimation task. Discuss and deal with any Flipchart:
Understand how to calculate misunderstandings. FC1 - Estimating
the volume of a cuboid Volume
Project on IWB – cubes applet and familiarize
Understand ho doubling length studetns with how if works (if necessary) Resources:
will increase the volume by a cm2 cubes (or
factor of 8. Activity1: Following the ‘Filling Boxes worksheet, multilinks)
students use cm cube to assist them in answering 8.5 x 11” paper – 2 per
Understand and apply the the questions. Be sure to place enough centimeter student.
formula for the volume of a cubes that students can measure the length, width,
cuboid and height of their prisms, but not so many that Worksheets:
they can completely fill their prisms. WS1 - Filling Boxes
Use origami to create a three- WS2 - Folding
dimensional prism from a two- Activity 2: Have students make the origami cuboid instructions
dimensional sheet of paper – according to written instructions. Ready –made
find the volume. models may help. Assign groups carefully so that
you have one spatially aware student in each.
Discussion: How can the volume can be
determined without completely filling the cuboid
with cubes?
Summarize: Key concepts at the end of class.
Ask volunteers to explain how they approximated
the volume of the box using centimeter cubes. The
first two rows from the table in Question 2 will
reinforce the concept that doubling all three
dimensions will result in a box with a volume that is
eight times as large.

11. Extensions:
Show symbolically that when the dimensions of a
prism are doubled, the volume of the new box will
be eight times as large as the original box.
Students research another mathematical origami
model that is not a rectangular prism and share it
with the class.
Explore the surface area of rectangular prisms,
take special notice of how surface area changes as
the dimensions of a prism change
10. (1 hour) Extension
Students will understand and Scaling up Materials:
8. Find
areas
of
enlarged
use the relationship between (student to bring in a common cuboid or Common rectangular
shapes
by
using
the
square
of
the
scale
length, area and volume of cylindrical object- have a few spares) or cylindrical objects
factor
and
reverse.
similar figures. (cereal box, soda can,
Activity: Brief discussion of scale factor and what pack of gum)
Using a rectangle. Students it means. Expand if necessary. (englrmt done in Rulers or tape
will individually investigate the prev unit) measures
effect of increasing length by a
scale factor on area and Page two asks the students to visualize an Flipchart:
volume. enlarged version of their object and think about the FC1 - Scaling Up
area and volume. Worksheet:
WS1 - Scaling up
Page three sets them the challenge of investigating
what happens if it is enlarged by a factor of 3. Link:
Class should discuss their predictions before being Alternative task-nrich
encouraged to perform calculations to support their
investigation. Other scale factors should then be
investigated.
A scaffolded investigation is provided on worksheet
‘scaling up’. As students discover this relationship,
they will understand the effects of scale factors on
volume and surface area. More importantly, they
will begin to develop an understanding of why

12. square units are used for area and why cube units
are used for volume.
It is most important for students to discover this
relationship on their own. If they cannot write their
own conclusion at first, be patient. Exploring the
results for other scale factors, hearing about the
results of their classmates, and investigating other
objects may help students to grasp this important
mathematical concept.
Assessment: On the last page of the flip chart is a
statement. Have students write their response to
this, giving example if possible to support their
thinking.
Extension: (on flipchart)
Have students examine cubes with side lengths of
1 cm, 2 cm, 3 cm, 4 cm, and 5 cm. Compute the
surface area of each, and create a graph showing
the relationship between side length and surface
area. As the side length increases, what happens
to the surface area? Does it increase at a constant
rate? Describe the shape of the graph. If the side
length is n, what is the surface area? Students may
also make a similar graph comparing the side
length to the volume. If the side length is n, what is
the volume?
11a. Extension:
Problems solving task ZIN Obelisk Worksheets:
9. Use
the
volume
to
find
Task: Zin Obelisk WS1 - Zin Obelisk
missing
lengths
of
prisms
Flip chart has task (nrich link embedded) - you will
10. Find
surface
areas
of
need to print off information cards Flipchart:
prisms
and
pyramids
FC1 - Zin Obelisk
http://nrich.maths.org/5
992

13. 11b. Extension:
Problem solving tasks for more Nrich extension tasks Flipchart:
7. Use
the
inverse
to
find
able students Task: Nrich Volume – 4 Qs FC1 - Nrich Volume
the
radius
and
diameter
from
the
circumference.
Flipchart has nrich links embedded. Worksheet FC2 – Units all in a
available jumble
9. Use
the
volume
to
find
Worksheet:
missing
lengths
of
WS1 - Nrich volume
prisms
WS2 – Nrich problems
10. Find
surface
areas
of
WS3 – Cubedcan
prisms
and
pyramids
extension
WS4 – ATM handout
12
Additional resources WS1 – circumference
and area
WS2 – circumference
and area answers
WS2 – Curved surface
area and volume of
cylinders and answers
WS3 – Area and
Perimeter Compound
Figures
WS4 – Area and
compound figures