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Interactive teaching using mini-white boards in secondary mathematics

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					   Interactive
 teaching using
mini-white boards
  in secondary
  mathematics



        +
 ideas for group
      work
                           About this document.
At the time of producing this document, many teachers in secondary
classrooms were actively trying to engage students and change their
teaching styles to a more interactive approach. Mini-whiteboards seemed
to be a simple yet miraculous way of communicating students‟ ideas and
responses to move their learning forward and increase the pace of
lessons in, dare I say, an enjoyable way. Flushed with initial success
many teachers were asking for new ways to use this new medium to
further extend interactivity and give variety to lessons.
This document is a response to that request.
By all means look at the activities first but please try and read the
document in its entirety since some key ideas on group work and further
stimulating resources are worth your attention.

Roger Ray KS3 Mathematics Consultant – The East Riding of Yorkshire.

Why use mini-whiteboards?
Have you ever observed or delivered a lesson where the pace seems good
and the question and answer sections really seem to flow? Did it then
become apparent later that only a small proportion of students were
responding to questions and that only they were really moving forward?
Did it become apparent when the students were then set a task after the
question and answer sections? Mini-whiteboards require all students to
respond to most questions in „show and tell‟ activities – particularly the
probing ones that assess real understanding. Asking students the
question „Do you all understand?‟ or even „Who doesn‟t understand?‟ is
often pointless with some groups of students (if not all groups of
students) – mini-white boards can give that instant insight into the
answers to those two questions without asking them.
Mini-whiteboards are great for brainstorming and quickly expressing
rough ideas. In mathematics we are really interested in thinking skills
and often recording questions in detail or formal setting out routines
reduce the pace of the lesson and the free flow of thinking. There is a
place for recording key ideas and consolidating our work in exercise books
but often after some exploration and clarification of ideas.
Types of mini-whiteboard, accessories and organising their use.

Many schools are using the commercially produced mini-whiteboards and
this is probably the ideal since they are durable and safe. However, as
teachers become more adventurous the standard commercial mini-
whiteboard can have their limitations. Other alternatives are:

Laminated card.
A word of caution here – make sure the edges are not too sharp since
they can cut fingers.
You can laminate cards of different colours and also write a code letter
or number on each card before laminating. This is useful for group work
etc.
 E.g.
Can the red cards get together and share their ideas.
Can the people with the letter „a‟ on their card sit together here.
I want an answer from a person with a green card.
Will the person in each group with a blue card feed back on the group‟s
ideas in 5 minutes time.

Sets of laminated cards can be cut into different shapes to help with
tessellation properties of shapes and yet still be used to write on.

Plastic see-through document wallets with card/paper inside.
This is a really cheap way of producing mini-white boards since the card
placed inside can be plain white or coloured or have diagrams, coordinate
grids, shapes, number lines etc. photocopied onto the paper/card. Some
photo-copiable masters for this are included in the resources at the end
of this document.

Whole schools approach.
In America some schools issue mini-white board to students to take to
each lesson. They also encourage students to carry an old white sock as a
wiper and to add a dry wipe marker to their „must have‟ list of equipment.
In the UK many schools issue hard backed planner/diaries, I feel sure
that with a little negotiation the companies producing these could make
the back cover a mini-white board which might eliminate some of the
graffiti problems!

Some teachers keep kits of whiteboard/pen/wiper in plastic zipper
wallets to ease the giving out and collecting in of the equipment and
keeping track of numbers.
            Activities and Ideas (standard mini-white boards)
Show and tell
This is the most obvious use of the mini-white board where students are
asked to respond to a question by writing a response on the whiteboard
and holding it up. This is sometimes followed by an oral expansion on the
response by the students. This sounds easy but, note the following.
It is stressful to be the only student still writing whilst others are waving
their boards in the air – give a time allowance for the response – ask
students to place their response face down on the desk until the time to
reveal – ask all to reveal at the same time.



True or False
Students write „true‟ on one side and „false‟ on the other side of their
board. They then respond to statements, hypotheses etc. This can be
very useful in plenary sessions in assessment of learning.
Caution – ask students to reveal their true or false side by holding them
in front of their body so as students behind can not work out their
response by reading the word on the back of the board.
Many answers to one question.
Someone once said that it is better to look at many answers to one
questions than to look at one answer to many questions. In maths we
often do the later in our attempt to generalise results. This often
reduces thinking and the bigger picture of the situation or problem under
discussion.
Having therefore asked an open question to students, e.g.
„The answer to a question is “Only positive numbers,” what was the
question?‟
Wait for responses and then collect mini-white boards from selected
students with interesting responses. E.g.
„Which numbers can only be square rooted?‟ or „What types of numbers
make the coordinates in the first quadrant?‟
Caution – you may want to highlight misconceptions and this could be
embarrassing for the student whose incorrect response has been
selected. To avoid this have a few spare clean boards and swap them for
students responses and then shuffle them before revealing them to the
class so they become almost anonymous.
Why not ask a question and invite half the class to give true responses
and the other responses that are misconceptions. Select some and then
go to the true/false activity etc. or simply discuss the responses.

Transformations
In pairs one student draws a shape on their mini-white board. Another
student places their blank mini-white board next to it. Using the edge of
the board as a mirror line the students have to agree what the reflection
of the shape would look like and then sketch it. Similar activities could be
used for rotations and two students, if they drew congruent shapes, could
demonstrate translations to the class.
A group of four students could place their board together to make the 4
quadrants in the coordinate plane and explore ideas of transformations of
shapes.
Overlaps
In pairs ask the students to overlap their board to show 150% of the
area of a full board.
How else can it be done?
What fraction is this?
If this board‟s area represents the cost of an article – show me an area
with V.A.T. added on.
Overlap the board in a variety of ways and discuss fractions, areas,
perimeters.




Making Shapes

By overlapping or joining mini-white boards in a variety of ways in twos or
threes, shapes can be made and named.




 Concave hexagon          Concave octagon             Concave nonagon

With laminated mini-whiteboards of different shapes properties and
tessellations can be explored.
In groups, hollow prisms can be using several boards.




Why can‟t we make a complete cuboid?
Angles and Geometry
Obviously you can use „show and tell‟ to estimate the size of angles or
their names but in pairs two boards can be put together to form a
dihedral angle of a given size. Rotating one board reinforces the idea
that an angle is an amount of turn. Using the board in this way can be
useful for 3D geometry (angles between two planes could be discussed as
an extension). Parallel line work, similarity, enlargement etc. can all be
explored using the mini-whiteboard.



Number line
If 5 students come out with two board each and make a number line with
the 10 boards, you can use this as a giant or human counting stick.




Fraction, probabilities, decimals, percentages etc., can all be discussed.
Some teachers have successfully used mini-board laminated strips like
this,




Students can then write on the strip or point to positions in response to
questions. A paper clip added to the strip can be slid along by responsible
students again to show a response to questions like – „show me one fifth.‟
What about a board with a large decimal point drawn on it and other
students with digits written on their boards, moving to simulate
multiplication and division by multiples of 10?
Probability
10 pupils come to the front. Each holds up a white board with a number
from one to ten written on the back. The first number is revealed and
students have to calculate the probability of the next card being higher
or lower.

A number line from zero to one can be drawn on the board and students
have to position the probability of events described by the teacher or,
the teacher draws the line and in pairs students write down events that
match the indicated probability. Students can also write down events and
then be invited to replace a card on the human number line made up of
five students holding two boards each.



Algebra
Using the length of a mini-white board as „a‟ and the width as „b‟, you can
model expressions and equations and collect like terms.

      b       b       b
                                   a       a


How long is this?


      b                   b                b
                  a                    a



Is this the same length? Why?

                          10
          a                                a   a

                              22


What must „a‟ be? Why? Can we make an equation?

Students can then construct their own expressions or equations.
                                  Problems
The problems are few and (other than the pens running out to frequently)
can be overcome with a little practice. Try the following.
    Agree on a system of distribution and collection to minimise
      disruption and wasted lesson time.
    Decide when you will use them and how – remember they are not
      just for starter activities.
    Be firm with students on how they should not be used.
       No doodling, it wastes the ink
       No comments to be written on the back of the board to display
         to students behind when they are held up (perhaps insisting on
         the use of both sides to combat this).
       No wobbling the boards, Rolf Harris style, to make noises.




      Be clear on when you want a verbal response or a written mini-white
       board response- use „on your boards, or „tell me‟ as the beginnings
       of your questions.
      Decide what needs to be recorded in exercise books – remember in
       plenary sessions to ask “What have we learned - how did we learn it
       - what do we have to remember?”
      Ensure boards are thoroughly cleaned after use.
                         Working in Groups

The KS3 strategy promotes paired work and group work since students
learn much through discussing their ideas and misconceptions.
Here are a few ideas for working in this way if this territory is unfamiliar
to you.

Rainbowing
Students work in groups of 4 and discuss a problem or task. Each group
member has a colour or number (this could be the colour of a home made
mini-white board or a number on the board). Only four colours or
numbers are used. After discussion new groups are formed getting
together students with the same colour or number. This means that in a
class of 28, new groups of 7 members are formed and the findings or
ideas from each group of 4 can be shared. Pupils can then return to their
original groups of 4 armed with new ideas. You could of course begin
with 4 groups of 7, each with a colour of the rainbow and then form
smaller groups of 4 in the same way.

Yes/No groups (hot seat)
This is a good activity to make students use key language and to make
them think carefully about questioning. Students think of a shape and
the rest of a small group have to guess the name of the shape by asking
questions about it. The answers of course can only be „yes‟ or „ no‟.
Words can also be chosen for people to guess e.g, factor, expression,
denominator etc.
The person being asked questions is often said to be in the „hot seat‟.

Jigsawing
Groups of students work on different parts of a problem e.g. planning the
cost of a holiday or building a house. Groups then share information with
the rest of the class to complete the jigsaw. This can be done at a simple
level e.g. students exploring 2D shapes – which have line symmetry, which
have rotation symmetry, which can have obtuse internal angles, which for
a given perimeter give the biggest area etc.

Snowballing
Paired work combines, after initial discussion, to become work in groups
of 4. The groups of 4 then share ideas with other groups of 4.



Envoying/Experting
One person from a group of say 4 students moves to another group to
share their expertise or the group‟s ideas, with another group.
Listening Triangles
In groups of three, one student takes the role of speaker and explains a
key idea from the lesson, without interruption. Afterwards the listeners
can ask for clarification or correct misconceptions. Examples from a
session on fractions might be: How cancelling a fraction works; which
fractions are easy to add and which are not; the proper thing to do with
top heavy fractions!

Brainstorming/thought showering
This is an old idea for teachers but often new to some students. Mini-
whiteboards are great for getting ideas down for sharing.
An even better idea is to give each group an acetate sheet and OHT pen
and ask them to write down their best sentence or idea or general
statement about a concept. Each sheet can then be placed on the OHP to
give feedback. In fact if you overlay the acetate sheets, an idea from
each group can be displayed simultaneously.




Group work to give students opportunities to discuss at length is not
always possible in all lessons.
It is therefore well worth remembering that it takes time to come up
with good answers to open questions when a teacher is firing questions
from the front.
 “Turn to your partner for 30 seconds and together decide on an answer”
is a good phrase to use and can really improve progression for all the
students.
                     Plastic sleeve resources

The following may be photocopied and slipped into plastic sleeves to be
used as mini-whiteboard activities. Obviously standard graph paper and
spotty paper can be used as well. The beauty of this system is that time
is not wasted drawing grids axes etc. and it allows students to experiment
in rough first before say drawing a graph.

Blank 100 grid.
Useful for area fractions multiplication tables etc.

100 grid.
Useful for show me activities, multiples etc.

Clock Face
Obviously useful for time activities, but fractions and angles can also be
incorporated.
“Does ten to two give an acute or obtuse angle looking from above?

Circle and centre
Parts of a circle can be drawn – “Draw and show me a sector – now a
segment.”
Also useful for pie-chart work e.g. draw a simple bar chart and ask
students to sketch the pie chart to illustrate the same information.

Coordinate axes
Can be used to quickly check that students can plot coordinates
accurately.
Equations of lines can be quickly sketched. Simple vertical translations
can be done by sliding the paper inside upwards in the plastic sleeve.
Other translations can be done by removing the sheet from the sleeve
entirely and laying the sleeve on top of the axes sheet.

Probability Line
Students can place events on the line and relate the probability to
fractions.
Number Walls
Lots of ideas in the KS3 framework on using number walls particularly for
developing algebraic skills. Basically each lower brick is the sum of the
two above- the following should give you a few ideas.

    6            8         9         1     6       8          9     1
            14        17        10
                 31        27
                      58                                ?


        n        n+2       n+3       n-5       n       n+2              n-5
                                                             2n+5


                       58                                     58



Number lines
Good for supporting directed number work etc.

Fraction strips
These can be laminated and cut into individual strips for students and
then used for fractions or probability activities etc. Otherwise
photocopy the sheets and slip them into plastic sleeves as before. The
sixths strip is useful for probability and dice throwing.

Web Diagrams
Start in the centre with something known e.g 6 x 7 = 42 or 3y + 2m = p
And then write other things you can deduce in the surrounding bubbles.
Good for creating discussion in starter activities.
          0.6 x 0.7 =0.42                         42 ÷ 7 = 6


                                                                         60 x 7 = 420


                                6 x 7 = 42




My grateful thanks go to the maths consultants at Education Leeds for sharing their plastic sleeve
ideas.




100 grid blank
Fraction strips (tenths)
Fraction strips (sixths)

				
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Description: Interactive teaching using mini-white boards in secondary mathematics