# Planning Sheet by lUTtoF

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```									Unit 10                                       Five daily lessons
Shape and space;
Position, movement and scales, and solve problems

Year 6                                                                                                                        This Unit Plan is designed to
Unit Objectives                                                                    You will need to adapt it to
Year 6                                                                    meet the needs of your class.

   Recognise where a shape will be after two translations.                                         Page 107
Resources needed to teach this unit:
   Identify and use appropriate operations (including combinations of operations) to solve         Page 83-89
word problems involving numbers and quantities based on ‘real life’ or measures
(including time), using one or more steps.
   Resource sheet 10.1/OHT 10.6
   OHT 10.1
   Choose and use appropriate number operations to solve problems and appropriate ways of          Page 75         OHT 10.2a
calculating (mental, mental with jottings, written methods, calculator). Explain methods                        OHT 10.2b
and reasoning.                                                                                                  OHT 10.3
Page 95         OHT 10.4
   Record estimates and readings from scales to a suitable degree of accuracy.
   OHT 10.5
   Know imperial units, know rough equivalents of lb and kg, oz and g, miles and km, litres and    Page 91         OHT 10.6
pints or gallons.                                                                                               OHT 10.7
   OHT 10.8
   OHT 10.9
   Counting stick
Year 5                                                        Year 7                                  Calculators
   Read and plot co-ordinates in the first quadrant.            Use conventions and notation for 2-D co-ordinates        Rulers with cm and mm
in all four quadrants; find co-ordinates of points        Tape measures with cm and inches
   Recognise where a shape will be after a                      determined by geometric information.                      Whiteboards
translation.                                                                                                           Related Key Stage 2 national test questions
   Recognise and visualise the transformation and
   Use all four operations to solve simple word                 symmetry of a 2-D shape translation.
problems involving numbers and quantities.
   Choose and justify the use of an appropriate
   Choose and use appropriate number operations                 and efficient method for solving problems.
to solve problems, and appropriate ways of
calculating (mental, mental with jottings, written          Solve problems and puzzles in a variety of contexts.
methods, calculator).
(Key objectives in bold)
NNS Unit Plans
Planning    Day One                        Unit 10 Shape and space:                                                                    Term: Autumn                                        Year Group: 6
sheet                                      Position, movement and scales, and solve problems
Oral and Mental                                       Main Teaching                                                                                                                        Plenary
Objectives and           Teaching Activities                  Objectives and             Teaching Activities                                                                               Teaching Activities/ Focus
Vocabulary                                                    Vocabulary                                                                                                                   Questions
Order a set of positive      Hold a counting stick           Read and plot co-            Show the first quadrant on OHT 10.1              Draw the diagram:                              Write (4, 2), (8, 2), (–2, 4), (–2, 8)
and negative integers.        horizontally and count from     ordinates in all four         (cover the other 3 quadrants).                                y-axis                              on the board. Explain that these
negative five through zero      quadrants.                    Remind children that both axes begin                                                              should be the vertices of a square.
to positive five in steps of                                  at zero and identify the x-axis and the                                                           Plot the points on OHT 10.1. Ask
one.                                                          y-axis. Say that if they forget, it might                       2    1                            the children to suggest where
help to remember that the x-axis goes                                        x-axis               mistakes have been made in the
Remind the children of the                                    across.                                                         3    4                            co-ordinate notation.
them to identify the biggest                                  Mark a point on the grid.                                                                       Q What must we remember
number on the stick and                                                                                                The Four Quadrants                       when we plot co-ordinates?
the smallest. Quickly point                                 Q What are the co-ordinates of this
to various divisions on the                                   point?                                            Ask the children to give you                    Establish that the first number in a
stick asking which numbers                                                                                      instructions to plot (2, 5), (–2, 5),           pair of co-ordinates always refers
lie there. (It is helpful to                                  Discuss and remind children about                 (–2, –5) and (2, -5), start from (0, 0)         to the x-axis, the second to the y-
keep your thumb on zero.)                                     the notation, e.g. (3, 2).                        each time. Ensure that they are                 axis.
confident with this.
   Repeat holding the                                          Q If I move the cross 2 squares down                                                          HOMEWORK – Give the children
counting stick vertically so                                  what will the co-ordinates be?                   Tell the children to draw axes (each      squared paper on which to plot points
that negative five is at the                                                                                    from –10 to 10) on the squared paper      that make up 4 different shapes. For
bottom.                                                       Record the co-ordinates on the board.             and plot the following co-ordinates       each shape the children are to name
(–1, 1), (2, 5) and (5, 2). Tell the      the shape.
   Explain that the stick now                                  Q What if I move it 5 squares down?                 children that these are 3 of the 4
represents the range –25                                                                                        vertices of a square. Ask them to plot    Shape 1 - (–4, 6), (–3, 10), (5, 8), (4, 4)
to 25. Repeat the counting                                    Establish that the cross would be off             the fourth vertex and check this with a   Shape 2 - (–8, –4), (–8, 1), (–5, 4), (0, 4)
activity from –25 to 25 in                                    the grid.                                         partner.                                  Shape 3 - (–5, –5), (–2, 1), (–2, –8),
steps of 5, first with the                                                                                                                                          (–1, 0)
counting stick horizontally                                  Uncover the other 3 quadrants.                   Give the children other groups of co-     Shape 4 - (2, 4), (9, 1), (3, –3).
and then with the counting                                                                                      ordinates to plot which are vertices of
stick vertically.                                             Refer to the use of negative numbers              triangles and different quadrilaterals
on the stick in the oral/mental                   e.g. parallelogram. Get the children          By the end of the lesson children
   Remind the children that so                                   session. Explain that this is like two            to identify and plot the missing              should be able to:
far the zero has been in the                                  counting sticks crossing at zero which            vertices. Explain that there may be
middle. Ask them to                                           form four sections, or quarters. Say              more than one answer if only two               Read and plot points beyond
identify the zero on the                                      that these are called quadrants.                  vertices are given.                             the first quadrant;
stick for different ranges of   VOCABULARY                                                                                                                     Identify the co-ordinates of the
numbers, e.g. –10 to 40,        quadrant                                                                        Collect children’s results and correct
     Plot points in each quadrant of the                                                               4th vertex of a square.
–40 to 10, –20 to 30, –30       x-axis                                                                          any mistakes and misunderstandings.
grid, stress the (x, y) convention. Say
to 20, –15 to 35 etc. For       y-axis                                                                                                                        (Refer to supplement of examples,
that if they forget which comes first, it
each range get the children     origin                                                                        Q A square has vertices at (–1, 0) and          section 6, page 109.)
may help to remember that x comes
VOCABULARY                    to identify the step size for   vertex                                                                          (1, –2). What are the positions of
before y in the alphabet and so they
positive                      the divisions and as a          vertices                                                                        the other two vertices?
should read along the x-axis first.
negative                      whole class count forwards                                    Label each quadrant (first, second,
and backwards to confirm                                      third and fourth) pointing out that the           On the board or OHT show the 3
this and the position of                                      order is anti-clockwise around the                possible squares that have vertices at
zero.                           RESOURCES                                                                       (-1, 0) and (1, -2).
origin (0, 0).
RESOURCES                                                     OHT 10.1
Counting stick                                                Squared paper

NNS Unit Plans
Planning    Day Two                           Unit 10 Shape and space:                                                                      Term: Autumn                                      Year Group: 6
sheet                                         Position, movement and scales, and solve problems
Oral and Mental                                          Main Teaching                                                                                                                        Plenary
Objectives and         Teaching Activities                       Objectives and               Teaching Activities                                                                             Teaching Activities/ Focus
Vocabulary                                                       Vocabulary                                                                                                                   Questions
Read and plot co-            Ask the children to give you       Recognise where a              Collect names of shapes from                   Discuss with the children how to               Give the children the co-ordinates
ordinates in all four         quickly the pairs of numbers       shape will be after two         homework. Correct any errors and                describe the translation C to D.                of the trapezium after a two-step
quadrants.                    which total 5. As they give        translations.                   misunderstandings.                              Emphasise the 2 translations, C to A            translation. Ask children to
these to you, write them in                                                                                        then A to D and write on the board:             describe the translation of shape A
this order:                                                       Use OHT 10.2a with trapeziums A to                                                              to this new position.
G. Ask for the co-ordinates of                  C to D is translation +9 in x direction
5+0                                                                trapezium A. Using an overlay, OHT              and +5 in y direction. Ask children to          Compare answers, drawing
4+1                                                                10.2b, move shape A to shape B.                 describe G to B, C to E, F to C.                attention to the fact that the
3 + 2…                                                                                                                                                             movements could be described
Q How has the shape moved?                       Give the children squared paper. Get            differently.
so that they can see the                                                                                           them to draw axes (–10 to 10), and to
pattern.                                                           Discuss and establish that it has               draw the trapezium in the same                Q Why do we sometimes need two
moved 5 squares to the right.                   position as Shape A on OHT 10.2a.               instructions for moving a shape?
Ask what pair would come                                           Emphasise they must give direction              Tell them you are going to give them
next in the pattern after 0 + 5,                                   and distance and refer to the axes for          some translations of shape A, e.g. +4          Establish that a translation involves
e.g. -1 + 6, -2 + 7…                                               help. Emphasise it is the movement              in x direction and –2 in y direction.           a movement along a straight line in
of each corresponding vertex that               They are to draw the shapes after the           one direction. It is simplest to
     Using OHT 10.1 ask children                                        they are giving. Tell them this                 translations and identify the co-               describe a translation by
to come up and plot the                                            movement keeps the shape in the                 ordinates of the vertices. Give single          movements parallel to the graph
points represented by these                                        same upright position i.e. its                  and two-step translations and collect           axis we need two instructions for
pairs as co-ordinates, i.e.                                        orientation stays the same, and its             results. Check for errors and correct           moving a shape.
(5, 0), (4, 1)…                                                    area does not change.                           mistakes.
(–1, 6), (–2, 7)…
Q What do we call a movement in a
Q What do you notice about                                           straight line?                                                                                By the end of the lesson the
the position of the points?                                                                                                                                      children should be able to:
Establish that it is a translation.
Discuss and establish that                                                                                                                                        Sketch the position of a simple
they lie on a straight line.                                       Explain that in this case A is                                                                  shape after it has been
translated 5 places forward in the x                                                            translated.
Join the points up with a                                          direction. Write +5 in the x direction
straight line. Ask if the                                          on the board. Discuss how this                                                                (Refer to supplement of examples,
intermediate points on the                                         recording explains the translation.                                                           section 6, page 107.)
lines have meaning e.g. (3½,
1½).                                                              Ask the children to describe the
translations of A to C, A to D, A to E
     Ask what you think will                                            and write on the board:
happen if you started with
totals of 3 or 6? Repeat using     VOCABULARY                      A to C is translation –9 in x direction
3 and 6. Highlight the fact        trapezium                       A to D is translation +5 in y direction
VOCABULARY                    that the points are on parallel    translation                     A to E is translation –11 in y direction.
parallel                      lines and identify where they      orientation
intercept                     cut the axes.                                                      Get children to do the same for
translations B to C, B to F, D to E, G
to F etc.
RESOURCES
RESOURCES                                                        OHT 10.2a
OHT 10.1                                                         OHT 10.2b

NNS Unit Plans
Planning    Day Three                 Unit 10 Shape and space:                                                                      Term: Autumn                                    Year Group: 6
sheet                                 Position, movement and scales, and solve problems
Oral and Mental                                  Main Teaching                                                                                                                  Plenary
Objectives and    Teaching Activities                   Objectives and                  Teaching Activities                                                             Teaching Activities/ Focus Questions
Vocabulary                                              Vocabulary
Convert between      Ask the children to give quick   Use all four operations to        Write on the board:                          Collect the results and discuss the          Collect answers to problems.
km, m, cm, mm.        responses to questions:          solve measurement word                                                           solutions. Correct any errors and             Emphasise steps and methods of
problems, including time.          A farmer buys 2.5 km of wire for              misunderstandings.                            recording. Remind children to
How many metres in 1 km?                                            fencing. He uses 850 m in one field                                                         decide whether to use a mental,
How many cm in 0.5 m? etc.       Choose appropriate                 and 1.25 km in another. How much             Write on the board:                           written or calculator method. They
operations and calculate           wire has he left? Ask the class to                                                          should always ask: ‘Can I do this in
Write calculations on the        methods. Explain                   identify the key information.                 Cars are about 1700 mm wide. The              my head?’
board such as the following:     working.                                                                         width of a parking space adds 25% to
Q What calculations are needed?                 the width of the car. How many              Q If 24 million people watch TV for
3.6 km + 550 m =                                                                                                 spaces could be made along a school           150 minutes each day, how many
7 m – 240 cm =                                                   Discuss the methods suggested and             playground 35 m long?                         minutes of watching TV does this
0.3 m + 45 cm =                                                   record, e.g.                                                                                total?
1 km – 725 m =                                                   2.5 km – (1.25 km + 850 m)                    Work out and record the calculations
or                                            needed and the conversions of units          Get the children to do the
Ask the children to work out                                        (2.5 km – 1.25 km) – 850 m.                   with the class. Estimate the answer,          calculation on the calculator,
the answers to these and                                                                                          then give out calculators and use             discuss what happens to the
then share their strategies                                        Emphasise that it is important to write       them to find the solution, recording          display. Then solve the problem
with a partner.                                                     down the calculations to help with            steps and interpreting the display.           mentally keeping the unit in
checking solutions. Ask children to           Highlight the need to round the               millions i.e. 24 x 150 million
children can convert between                                        through the calculation with the class,
units and deal with decimal                                         converting units and showing how to          Set other problems which the children
points correctly.                                                   set out the solution. Emphasise the           use the calculator to solve.
need to give the answer using the                                                         By the end of the lesson the
   Give five other calculations                                        units.                                                                                    children should be able to:
for children to do on their
own.                                                                Review the stages used to solve the                                                        Solve ‘story’ problems
problem. Show OHT 10.3 step-by-                                                             involving:
step guide. Emphasise that the                                                                      km, m, cm, mm, miles;
calculation can be done mentally or                                                                 seconds, minutes and
using a written method or with a                                                                    hours
calculator, but the calculations must                                                       and explain and record how
be recorded.                                                                                the problem was solved.

     Work through another problem                                                              (Refer to supplement of examples,
following the step-by-step guide,                                                         section 6, pages 87 and 89.)
discussing each stage with the
children, and showing them how to
record the solution.

     Set the class problems to do. Ensure
these include mixed units, the four
operations and time; no calculators at
this stage.
RESOURCES
Calculators
OHT 10.3

NNS Unit Plans
Planning    Day Four                        Unit 10 Shape and space:                                                                       Term: Autumn                                       Year Group: 6
sheet                                       Position, movement and scales, and solve problems
Oral and Mental                                         Main Teaching                                                                                                                      Plenary
Objectives and        Teaching Activities                       Objectives and               Teaching Activities                                                                  Teaching Activities/ Focus Questions
Vocabulary                                                      Vocabulary
Count on in steps of        Hold the counting stick            Record estimates and           Ensure that each child has a ruler          Write on the board:                           Collect children’s responses.
0.1, 0.2, 0.25, 0.5…         horizontally and say that one      readings from scales to         with cm and mm scales. Ask each
and then back.               end represents 1 kg and the        a suitable degree of            child to measure their hand span,            1 litre is about 1¾ pints                     Write the following on the board:
other 2 kg. Point to various       accuracy.                       the length of their middle finger
points asking what                                                 and the width of he nail on their            Get the class to say ‘A litre of water         Measuring your waist for a new pair of
measurement lies there.            Know imperial units             little finger. Check that everyone           is about a pint and three quarters’.           jeans.
and rough metric                measured from 0. Ask for the                 Use this to calculate that:                    Measuring out a dose of medicine.
Q What does each division            equivalents.                    measurements in cm and mm.                                                                  Putting petrol in the car.
represent in kg?                                                   Ask if their measurements are                2 litres is about 3½ pints                     Weighing flour to make a cake.
likely to be accurate to the nearest         5 litres is about 8¾ pints.                    Measuring the bedroom floor before
Establish that each tenth is                                       cm, the nearest mm. Ask how                                                                 ordering a carpet.
0.1 kg.                                                            many times longer their finger is           Remind the class that there are 8              Telling someone the distance from
than their nail, and their hand span         pints in 1 gallon or 5 litres is just          where you live to the nearest
Q What do they represent in                                          than their finger. Agree a                   over 1 gallon. Show the class OHT              supermarket.
grams?                                                             representative set of values for the         10.6 the litre/gallons scale. Give             Measuring the amount of tread on a
class and explain that this is an            out copies (Resource sheet 10.1)               tyre.
Establish the answer as 100 g.                                     estimate rather than an accurate             for pairs to refer to. Ask:
measure.                                                                                  Q These are all situations where we use
Q What does half a division                                                                                     Q How many litres in 3 gallons?                  some form of measurement. Can you
represent?                                                        Give pairs of children measuring             How many gallons and pints in 15               suggest some others?
tapes which have both metric and             litres?
Establish 0.05kg or 50 g.                                          imperial units (cm and inches).                                                           Q How accurate do we need to be in
Discuss the two scales and ask              Write on the board:                            each case? Can you think of any
Count from 1 kg in steps of                                        children to convert from one to the                                                         situations where we need to be really
0.1 kg. Then use grams                                             other. Ask:                                  1 litre of water weighs 1 kg.                  accurate?
counting from 1000 g in steps of
100 g.                                                           Q 4 inches is about how many mm?               Reshow OHT 10.5.                               Suggest that in many cases,
approximate measurements are
Repeat with one end                                                Ask the children to measure their          Q If the watering can was full could             sufficient. Accuracy could be critical in:
representing 0.1 kg and the                                        hand spans in inches. Ask for this           you lift it up to water the plants?            – dispensing powerful drugs,
other 0.2 kg, and 0 g to 500 g,    VOCABULARY                      length to the nearest inch, the                                                             – measuring engine parts for
inches                          nearest ¼ inch, 1/8 inch etc.
etc.                                                                                                           Discuss how to use the litre/gallon              aircraft,
feet                            Discuss other imperial units for                                                            – adjustments to car engines,
yards                                                                                                                       – measuring accurate temperatures in
     Show the class the OHT 10.4 of                                     length and establish that there are          and to check the values on the
pints                           12 inches in 1 foot and 3 feet in 1                                                           certain manufacturing processes like
the scales with the central                                                                                     board. Use calculators to convert
gallons                         yard. Discuss metric equivalents                                                              brewing beer.
needle/pointer missing. Ask the                                                                                 and discuss the degree of
scale                           and establish that 1 metre is about
class what this might be used to                                                                                accuracy.
degree of accuracy              3 feet and 3 inches, or one yard                                                          By the end of the lesson the children
measure and in what units.
Point to 0.4 and ask for this in                                   and 3 inches, or 39 inches.                 Set litres to gallons questions for          should be able to:
kg and g. Repeat with different                                                                                 pairs to answer.
measurements including                                                                                                                                        Read measuring scales, converting
RESOURCES
between indicated values.                                                                                                                                      the unit to an equivalent metric unit;
OHT 10.6
Emphasise the accuracy that                                                                                                                                   Read both metric and imperial units
RESOURCES                                                       Resource sheet 10.1
can be obtained.                                                                                                                                               from measuring scales that show
Counting stick                                                  Rulers with cm and
both units.
OHT 10.4                                                        mm
     Show OHT 10.5 of the can for
OHT 10.5                                                        Measuring tapes with
measuring litres and repeat the                                                                                                                              (Refer to supplement of examples,
cm and inches
exercise.                                                                                                                                                    section 6, pages 91 and 95.)

NNS Unit Plans
Planning    Day Five                    Unit 10 Shape and space:                                                                     Term: Autumn                                    Year Group: 6
sheet                                   Position, movement and scales, and solve problems
Oral and Mental                                Main Teaching                                                                                                                      Plenary
Objectives and       Teaching Activities          Objectives and            Teaching Activities                                                                 Teaching Activities/ Focus Questions
Vocabulary                                        Vocabulary
Solve problems          Write on the board:     Record estimates            Remind children that miles are         Write on the board:                        Remind the children that they have been plotting points
based on measures.                               and readings from            imperial units. Discuss the other                                                   and drawing shapes and graphs on different axes, using
Bath           44       scales to a suitable         imperial units used in the last         1 litre = 1¾ pints                          different scales. Emphasise that it is important to plan
Bristol        28       degree of accuracy.          lesson and record on the board.         1 m = 40 inches                             carefully how the scales on the axes are to be arranged
Exeter        150                                                                                                                        and to draw them carefully.
Taunton        84       Know imperial units        Q What are the imperial units             Explain that these are
Gloucester     64       and rough metric             used for weight?                        approximations. Give out squared            Hold up the counting stick. Explain to the class that the
Plymouth      230       equivalents.                                                         or graph paper and say that you             divisions on the stick are like the divisions on the scales.
Write on the board; pounds,             want to be able to use the graphs           The size of each division depends on the numbers at the
Explain this                                         ounces. Discuss these units.            to convert up to 10 l, 10 kg and            start and end of the stick. There are 10 divisions so
represents the return                                                                        10 m to imperial units.                     each is worth one tenth of the length. Remind the
journeys in miles                                    Get the class to say:                                                               children some scales are wrapped around a circle; some
made by a salesman.                                                                          Give the children time to work out          span negative and positive numbers. The important
He gets 12p per mile                                 ’Two and a quarter pounds of            how the axes are to be arranged.            thing is to look at the first and last numbers, count the
from his firm.                                       jam is round about one                  Discuss these with the class and            divisions and work out what each division is worth.
kilogram.’                              ensure they know how the axes
Ask children to                                                                              are to be scaled and which points          Draw on the board:
choose a journey and                                 Explain that a better conversion        to plot to make the graphs.
work out the amount                                  is: 1 kg = 2.2 pounds. Write this                                                          A
he should receive.                                   on the board.                           Ask children to draw their graphs.                     10                               20

Collect methods and                                 Explain that children are going        When children have completed
solutions. Compare                                   to construct their own                  their graphs, display OHT 10.7.                    B
methods and the                                      conversion graphs. They can             Remind the class that the                              20                              40
recordings made.                                     choose whether to construct a           equivalents are approximate and
graph for converting between:           discuss the statement 10 litres ≈           Ask:
17.5 pints.
litres and pints                                                             Q How many divisions are there on each scale? What is
VOCABULARY                        metres and inches                  Ask the children to give one or two         each division worth? Where are the arrows pointing?
approximately equal               kg and pounds                      further approximate equivalents
to (≈ )                                                              and demonstrate how to use the             Collect responses and discuss methods used. Correct
imperial                                                             graph to find them.                         any misunderstandings.
pounds
ounces                                                              Repeat with OHT 10.8, then OHT
pints                                                                10.9.                                     By the end of the lesson the children should be able
inches                                                                                                         to:
divisions                                                            Ask children to use their own
scales                                                               graphs to find other approximate           Read measuring scales, converting the unit to an
equivalents, recording them using           equivalent metric unit;
the ≈ sign.                                Know the approximate equivalence between
VOCABULARY
commonly used imperial units and metric units;
miles                                            RESOURCES
 Read metric and imperial units from measuring
per mile                                         Counting stick
scales that show both units.
Squared or graph
paper
(Refer to supplement of examples, section 6, pages 91
OHT 10.7
and 95.)
RESOURCES                                        OHT 10.8
Whiteboards                                      OHT 10.9

NNS Unit Plans

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