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Stage
Subject
Secondary
mathematics
Year
Term
7
Multiplication grids
Module contents
Module focus
Curriculum focus
Investigating the connections between multiplication, division and area.
Learning objectives
By the end of the lesson pupils will:

be able to calculate the area of a rectangle using multiplication and
division.
Learning outcomes
Most pupils would be expected to:

mentally calculate the area of a rectangle from given dimensions in tenths
and units and solve equations by calculating the dimensions from a given
area of a rectangle.
Pupils making slower progress will:

calculate the area of a rectangle from given dimensions in tenths and
units using the visual support of a 10 x 10 grid.
Pupils making faster progress will:

mentally calculate the area of a number of rectangles with different
dimensions and accurately write equations to demonstrate their
calculations.
References
Strategy Framework references
Calculations
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Mental methods and rapid recall of number facts


Consolidate the rapid recall of number facts, including positive integer
complements to 100 and multiplication facts to 10 X 10, and quickly
derive associated division facts.
Consolidate and extend mental methods of calculation to include
decimals, fractions and percentages, accompanied where appropriate
by suitable jottings; solve simple word problems mentally.
Shape, space and measures
Measures and mensuration

Know and use the formula for the area of a rectangle; calculate the
perimeter and area of shapes made from rectangles.
The Framework for teaching mathematics can be found at:
www.standards.dfes.gov.uk/keystage3/respub/mathsframework/forewo
rd/
National Curriculum references
Ma2 Number and algebra
Calculations
Pupils should be taught to:
Mental methods
Number operations and the relationships between them
a add, subtract, multiply and divide integers and then any number;
g recall all positive integer complements to 100 [for example
37=63=100]; recall all multiplication facts to 10 x 10, and use them to
derive quickly the corresponding
division facts;
i develop a range of strategies for mental calculation; derive unknown
facts from those they know; add and subtract mentally numbers with
up to two decimal places
(for example, 13.76 + 5.21, 20.08 + 12.4); multiply and divide numbers
with no more than one decimal digit (for example, 14.3 x 4, 56.7 ÷ 7),
using factorisation
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when possible.
The National Curriculum programme of study can be found
at:www.nc.uk.net/nc/contents/Ma-3-2-POS.html.
Use of ICT
Teacher use of ICT
This module will give you the opportunity to:

use dynamic geometry software to demonstrate how to calculate the area
of a rectangle.
Requirements
Hardware



A computer
Data projector and large screen display and/or interactive whiteboard
(IWB)
ICT suite
Software

Dynamic geometry software, such as The Geometer's Sketchpad
You can download the viewers needed for these files on the Software
downloads page.
Lesson preparation
A key element of this module is a lesson for you to adopt and adapt to
meet the needs of your class. It is designed to help you evaluate the
impact of using ICT for learning and teaching. Display and discuss the
objectives and key vocabulary for this lesson with the pupils.
Some example lesson resources have been created for you to use and
can be found in the Download resources section. Review the
resources before the lesson and adapt if necessary. Ensure your
computer, large screen display or IWB and resources are set up before
the lesson. If you are able to use an ICT suite ensure pupils can
access the file Areas of rectangles from their individual computers. If
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you do not have access to an ICT suite, e nsure you have printed
sufficient copies of the worksheet Areas of rectangles_puzzle sheet
for your pupils to use in the main part of the lesson.
Vocabulary
area, divide, division, factor, inverse, multiplication, multiply, product,
rectangle, scale
Health & Safety
All standard safety procedures with computers need to be in place.
Information can be found at www.ictadvice.org.uk.
ICT skills guidance
The guidance in this section supports the ICT skills described in the
Module contents.
Pupils' prior knowledge and skills
Pupils should already:


o
o

know how to consolidate multiplication facts up to 10 x 10;
be able to derive quickly:
division facts corresponding to tables up to 10 x 10;
squares of multiples of 10 to 100 (e.g. 60 x 60);
be able to calculate the area of simple compound shapes that can be split
into rectangles.
Starter
Open the resource Areas of rectangles and display the page units x
units. Vary the dimensions of the rectangle by using the select tool and
dragging the point D. As snap points has been selected, point D can
only be positioned at integer values.
Ask pupils to suggest the dimensions of rectangles that have an area
represented by, e.g. 36 cm2. Invite pupils to the board to drag the
points of the rectangle to make different rectangles and create
equations based on their number fact, e.g. 6 x 6 = 36 and 36 ÷ 6 = 6 or
3 x 12 = 36 and 36 ÷ 3 = 12.
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Using the line tool, draw a line to divide the rectangle and demonstrate
partitioning within the calculation, e.g.(2 x 6) + (4 x 6) = 36. Now use
examples of common mistakes in multiplications (e.g. 7 x 8, where
pupils often incorrectly calculate 7 x 7 and then add 8) by partitioning
(for 7 x 8, drag a 7 x 8 rectangle and highlight the extra row of 7).
Establish that the area of each square within all of the rectangles
represents 1cm2. It is important to ensure that pupils are aware that
the actual areas of the shapes when represented on the projected
image are NOT measured to scale. However they are accurate if the
page is printed.
Main
Move to the page tenths x units and ask pupils what is different about
the scale. The dimensions of the rectangle can be varied by using the
select tool and dragging the point D. The accuracy has been fixed such
that only tenths multiplied by units are displayed.
Explain that the y-axis has been magnified and establish that each of
the rectangles on the grid represents an area of 0.2 cm 2. Move the
point D to represent an area of 0.6 cm x 1 cm and then drag the point
to the right, increasing the units by one each time. Ask pupils what they
notice about the area of the rectangle and record their findings on the
board.
You might like to ask questions, such as:


Each time the length BC increases by one unit, by how much does the
area increase?
What are the similarities between the multiples of 0.6 and the multiples of
6?
You might like to ask more open questions, such as:

How could you represent an area of 4.8 cm2 ?
Invite pupils to the board to drag the point D to satisfy this condition.
Ask pupils to open the file Areas of rectangles_puzzle sheet at their
computers. Pupils requiring more support could also have access to
the file Areas of rectangles. Alternatively, if you are not working in an
ICT suite, give out the worksheet Areas of rectangles_puzzle sheet
and a copy of a blank 10 x 10 grid.
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Ask pupils to work through the tasks on the worksheet. Encourage
pupils to discuss their strategies with each other as they are working,
for example generating the sequences of the multiples, or using their
understanding of place value.
Go through the questions with pupils. Ask pairs of pupils to explain
their reasoning in response to the 'challenge' question.
Plenary
Move to the page tenths x tenths and ask pupils what is different about
the scale. As snap points has been selected, the point D can only be
positioned at exact values.
As the projection is deceiving, discuss the size of a rectangle, say 0.2
cm by 0.5 cm. Ask pupils to sketch a rectangle of this size. Discuss
how mathematical sketches are often exaggerated, as it is unrealistic
to draw such small shapes accurately. Using a similar strategy as
before, explore rectangles of different dimensions and their resulting
areas.
Assessment
In assessing for learning you should consider the following points.
1. Ensure objectives are expressed in language that pupils understand.
2. Give pupils clear success criteria related to these objectives.
3. Give pupils opportunities to discuss their successes and challenges
focusing on the objectives.
4. Provide oral and written feedback to pupils.
5. Encourage pupils to explain their thinking and reasoning in a secure
environment.
6. Provide time for pupils to reflect upon what they have learned and
understood and identify any difficulties.
You can find information on assessment for learning at:
www.standards.dfes.gov.uk/keystage3/respub/afl_ws.
Adaptation
Lower attaining pupils will benefit from having access to some
rectangular arrays of multilink cubes and a blank 10 x 10 grid. Focus
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the teaching towards developing partitioning skills as a means to
support pupils’ strategies when learning multiplication facts. Encourage
pupils to use the software to relate the area of each part to the
calculation. Ask questions such as:


How can you use doubling to obtain the answer to 6 x 7 if you already
know the answer to 3 x 7?
Does a rectangle that measures 3 cm x 5 cm have a larger area than one
that measures 4 cm x 4 cm?
Higher attaining pupils should be encouraged to use the software to
solve problems involving decimal values of area and perimeter. Pose
problems such as:


How many different rectangles can you generate with an area of 13.5 cm2
?
Is it possible to generate rectangles with a perimeter numerically equal to
its area? Can you explain your findings?
Evaluation
Lesson reflection
These prompts are designed to help you reflect on how the use of ICT
affected your teaching and pupils’ learning.
Prompts for reflection:
1. How did the use of ICT:
o
help pupils to make better progress towards achieving the learning
objectives?
o
affect the pace of learning?
o
affect pupils’ motivation, interest and time spent on task?
o
affect your ability to differentiate your teaching and personalise pupils’
learning?
2. What knowledge or skills have you gained and extended in teaching this
lesson?
3. What adaptations would you make to the lesson and its resources to suit
the needs of your class?
You may wish to create a record of your evaluation and save it as
evidence of your professional development. If so, you can download a
template containing these prompts and spaces for your responses.
This document is part of a range of materials designed to help teachers teach using ICT.
For more information, log on to www.teachernet.gov.uk/supportpack
Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
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Materials evaluation
These prompts are designed to help you consider why, how and when
you would incorporate these lesson activities and resources into your
curriculum and teaching plans.
Prompts for evaluation:
1. What are the benefits of using these teaching and learning approaches
and resources to achieve the subject objectives?
2. How do the suggested activities fit with your existing curriculum and
teaching plans?
3. What adaptations would be required to the activities or resources to suit
the needs of your class?
4. Are there any requirements for ICT equipment, other resources, space,
etc. that might limit how and where the lesson is taught?
You may wish to make a note of your thinking for your own records
and to share with your colleagues. If so, you can download a template
containing these prompts and spaces for your notes.
Download module
Download module
You can download a module pack containing the lesson plan,
resources, supplementary information and extension activities using
the link below. The pack is in a zipped file to minimise file size, but
unless you have a broadband connection, the download may be slow.
To extract the files within the module pack you will need either Winzip
or Microsoft Windows Extraction Wizard. This software is freely
available and can be downloaded from the Software downloads
page.
This document is part of a range of materials designed to help teachers teach using ICT.
For more information, log on to www.teachernet.gov.uk/supportpack
Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.