Planning Sheet by K6p19B

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									Unit 4                                                                 Five daily lessons
Fractions, decimals and percentages

Year 6
Autumn term
                                                                                                                  This Unit Plan is designed to
                                     Unit Objectives                                                              guide your teaching.
                                               Year 6
           Reduce a fraction to its simplest form by cancelling common factors.         Page 23                  You will need to adapt it to
                                                                                                                  meet the needs of your class.
           Recognise the equivalence between the decimal and fraction forms.            Page 31

           Use decimal notation for tenths and hundredths; extend to thousandths for    Page 29
            measurements.
                                                                                                              Resources needed to teach this unit:
           Know what each digit represents.                                             Page 29
                                                                                                                  Resource sheet 4.1
           Understand percentage as the number of parts in every 100.                   Page 33                  Resource sheet 4.2
                                                                                                                  Resource sheet 4.3
                                                                                         Page 33
           Find simple percentages of small whole number quantities.                                             Resource sheet 4.4
                                                                                                                  Resource sheet 4.5
                                                                                                                  Resource sheet 4.6
                                                                                                                  Resource sheet 4.7
                                         Link Objectives                                                          Resource sheet 4.8
                       Year 5                                                   Year 7
                                                                                                                  Resource sheet 4.9
    Use decimal notation for tenths and                       Simplify fractions by cancelling all common       Counting stick
     hundredths.                                                factors and identify equivalent fractions.        Related Key Stage 2 national test
                                                                                                                   questions
    Relate fractions to their decimal                         Recognise the equivalence of percentages,
     representations.                                           fractions and decimals.

    Use fraction notation, including mixed numbers,           Calculate simple percentages.
     and the vocabulary numerator and denominator.

    Begin to understand percentage as the number
     of parts in every 100, and find simple
     percentages of small whole number quantities.

 (Key objectives in bold)

                                                                         NNS Unit Plans
 Planning                       Day One                       Unit 4 Fractions, decimals and percentages                                               Term: Autumn                     Year Group: 6
 sheet
 Oral and Mental                                              Main Teaching                                                                                             Plenary
 Objectives and        Teaching Activities                    Objectives and                Teaching Activities                                                         Teaching Activities/ Focus Questions
 Vocabulary                                                   Vocabulary
Recognise equivalent        Using a fraction wall           Reduce a fraction to its        Cutting up Resource sheet 4.2, order fractions by converting them          Write the fraction 12/48 on the board; make sure
fractions.                   (Resource sheet 4.1) on the     simplest form by                 to fractions with a common denominator and position them on a               the fraction family extends in both directions.
                             OHP/wall chart to recap         cancelling common                number line. Lead on to questions such as:
                             equivalent fractions, record    factors in the numerator                                                                                   Q Can you tell me any other equivalent
                                                             and denominator.               Q How do you know that 2/5 is more than ¼?                                    fractions?
                             ½ = 2/4 = 4/8
                                                                                              Establish the need to change to a common denominator.                     Q Can you give me a fraction that is equivalent to
                             Ask children to continue the                                                                                                                 2
                                                                                                                                                                           /3 but has a denominator of 18. Invite
                                                                                                                                                   1            7
                             sequence, repeating with                                         Discuss other examples such as comparing ¼ and /3, ¾ and /10                individual children to explain their working.
                             thirds, sixths and twelfths.                                     etc.
                                                                                                                                                                        Q How do you know when you have the simplest
                           Q Can you write four more                                          Repeat with other examples if appropriate.                                  form of a fraction?
                             fractions equivalent to half?
                             Repeat with ½, 1/3, ¾.                                          Bring the class back together and discuss some of their examples.
                                                                                              Encourage children to explain their reasoning.
                            Revise the meanings of
                             numerator and denominator.                                       Show a fraction family such as:                                           By the end of the lesson children should
                                                                                                            3
                                                                                                             /10 = 30/100 = 300/1000                                    recognise that:
                                                                                                                                       300
                                                                                            Q How can we work backwards to reduce        /1000 to a family of            A fraction such as 5/20 can be reduced to an
                                                                                              fractions with smaller numbers?                                             equivalent fraction by dividing both
                                                                                                                                                                          numerator and denominator by a common
                                                                                              Introduce harder examples e.g. 600/800 where different factors are          factor;
                                                                                              required and cancelling can be introduced.                                 A fraction such as 3/10 can be changed to an
                                                                                                                                                                          equivalent fraction by multiplying both the
                                                                                            Q Can you continue the fraction family?                                       numerator and denominator by the same
                                                                                                                                                                          number;
                                                                                            Q What is happening to the numerator/denominator?                            If the numerator and denominator have no
                                                                                                                                                                          common factors, the fraction is expressed
                                                                                              Repeat with other fraction families.                                        in its lowest terms.

                                                                                         Children work independently on further examples.                              (Refer to supplement of examples, section 6,
                                                                                                                                                                        page 23.)


                                                             VOCABULARY
                                                             reduce to simplest form
VOCABULARY                                                   cancel
equivalent                                                   factors
numerator                                                    denominator
denominator                                                  numerator



RESOURCES                                                    RESOURCES
Resource sheet 4.1                                           Resource sheet 4.2



                                                                                               NNS Unit Plans
 Planning                         Day Two                  Unit 4 Fractions, decimals and percentages                                                    Term: Autumn                    Year Group: 6
 sheet
 Oral and Mental                                         Main Teaching                                                                                                               Plenary
 Objectives and       Teaching Activities                Objectives and                Teaching Activities                                                                           Teaching Activities/ Focus
 Vocabulary                                              Vocabulary                                                                                                                  Questions
Change an improper         Write 25/20 on the board.   Recognise the                   Write the following fractions on the board:                                                  Write on the board or use on OHT:
fraction to a mixed                                     equivalence between the
                                                                                                                      3          2     4
number and vice           Q Can you think of a          decimal and fraction                                           /10   ¼   /25   /5                                                          0.5 = ½
versa.                      different way to write      forms.                                                                                                                                     0.25 = □
                            this fraction?                                             Q Can you put these fractions in order?                                                                      □=¾
                            If necessary, suggest                                        Discuss how it can be done, leading to converting to hundredths.                                           □ = 1/10
                            writing a mixed number.                                                                                                                                                0.01 = □
                                                                                       Q Would it have been easier if the numbers had already been written in hundredths or                        □ = 1/1000
                           Practise converting from                                     as decimal fractions?
                            mixed numbers to                                                                                                                                           Discuss what goes in the boxes and
                            improper fractions and                                       Discuss how they can be converted to decimal form (i.e. 0.3, 0.25, 0.08, 0.8) and use         ask children to write out their own
                            back.                                                        the discussion to assess children’s previous knowledge of decimal notation in                 copy.
                                                                                         hundredths.
                                                                                                                                                                                 HOMEWORK – Learn the common
                                                                                         Repeat with other examples.                                                             fraction and decimal equivalences by
                                                                                                                                                                                 heart.
                                                                                        Draw a number line on the board.
                                                                                                                                                                                     Q What other equivalences can I work
                                                                                         Give out the cards on Resource sheets 4.3 and 4.4.                                            out?

                                                                                       Q Can you place your cards in the correct place on the number line?

                                                                                         Encourage children to justify why they choose a particular place on the number line.
                                                                                                                                                                                     By the end of the lesson the
                                                                                         Draw children’s attention to the fact that some children will want to put two or more       children should be able to:
                                                                                         cards in the same place. For example ¾, 75/100 and 0.75.
                                                                                                                                                                                      Convert an improper fraction to a
                                                                                        Provide differentiated examples for pupils to practise ordering fractions, decimals,          mixed number, such as 33/8 to 41/8
                                                                                         then a mixture of both on a number line.                                                      and 57/12 to 4¾;
                                                                                                                                                                                      Recognise the equivalence
                                                                                                                                                                                       between decimals and fractions.

                                                                                                                                                                                     (Refer to supplement of examples,
                                                                                                                                                                                     section 6, pages 23 and 31.)




                                                        VOCABULARY
                                                        decimal fractions

VOCABULARY
proper fraction
improper fraction                                       RESOURCES
mixed number                                            Resource sheets 4.3, 4.4



                                                                                                  NNS Unit Plans
 Planning                       Day Three                     Unit 4 Fractions, decimals and percentages                                                       Term: Autumn                     Year Group: 6
 sheet
 Oral and Mental                                               Main Teaching                                                                                                       Plenary
 Objectives and           Teaching Activities                  Objectives and                 Teaching Activities                                                           Teaching Activities/ Focus Questions
 Vocabulary                                                    Vocabulary
Consolidate knowing          Play a ‘loop’ or ‘follow me’    Use decimal notation for     Ask questions like:                                                              Write on the board and discuss:
by heart up to 10 x 10.       card game (Resource sheets      tenths and hundredths;
                              4.5 and 4.6). Set a time. Try   extend to thousandths for       Q When do we meet decimals in real life?                                      Q If the running track is 500m how many laps
Derive quickly division       to beat your own record.        measurements.                                                                                                   are needed to run 2.5km?
facts corresponding to                                                                        Q What in this room would measure 0.5m, 0.08m, 15.7cm etc?
tables up to 10 x 10.                                         Know what each digit                                                                                            Establish that conversion to the same unit of
                                                              represents.                     Q What in this room holds 0.27 litres?                                          measurement is necessary to solve the
                                                                                                                                                                              problem.
                                                                                               Explore metric units and the relationship between them.
                                                                                                                                                                            Q There are 2.54cm to 1 inch. 1 yard is 36
                                                                                                Pupils begin to convert larger metric units to smaller and convert            inches. About how many centimetres are
                                                                                                halves, quarters, tenths and hundredths to larger units.                      there in a yard?

                                                                                                e.g.           ¾ kg       = ? grams                                           (Other problems from supplement of
                                                                                                               3.5m       = ? cm                                              examples, section 6, page 87.)
                                                                                                               1.25km     = ? metres
                                                                                                               2 litres   = ? ml
                                                                                                               500ml      = ? litres
                                                                                                               6000cm     =?m                                               By the end of the lesson children should
                                                                                                               100mm      = ? cm                                            be able to:

                                                                                                Some children might be limited to one decimal place whilst others can        Convert, for example, 3.125km to metres;
                                                                                                be introduced to thousandths and associated word problems.                    300ml to 0.3 litres.

                                                                                                                                                                            (Refer to supplement of examples, section 6,
                                                                                                                                                                            page 29.)




VOCABULARY
multiple



                                                              VOCABULARY
RESOURCES                                                     double
Resource sheets 4.5,                                          factors
4.6                                                           multiple



                                                                                                 NNS Unit Plans
 Planning                     Day Four                    Unit 4 Fractions, decimals and percentages                                                         Term: Autumn                   Year Group: 6
 sheet
 Oral and Mental                                                  Main Teaching                                                                                               Plenary
 Objectives and       Teaching Activities                         Objectives and              Teaching Activities                                                      Teaching Activities/ Focus Questions
 Vocabulary                                                       Vocabulary
Recognise the              Use questions to recall the          Understand percentage        Using a 100 square, shade all the even numbers. (Teacher                 Allow children to report back their findings.
equivalence between         homework from day 2.                 as the number of parts in     could do this using an OHT of Resource sheet 4.7, or children
the decimal and                                                  every 100.                    could do this on their own copy).                                         Draw out the connections between fraction,
fraction forms.           Q What other equivalences can you                                                                                                              decimal and percentage notation.
                            work out?                            Find simple percentages      Q What percentage of the square is shaded?
                                                                 of small whole number                                                                                   For example: 15/100 = 15% = 0.15
                           Extend children’s understanding by   quantities.                  Q What percentage of the square is not shaded?
                            asking questions about other                                                                                                               Q Which would you rather have?
                            fractions and decimals using an                                     Now shade all the multiples of 5.                                        a) 50% of £90
                            equivalence table for example:                                                                                                               b) 25% of £200
                                                                                              Q What percentage of the square is/is not shaded?
                                 0.1   =□                                                                                                                                Children work in pairs and feed back their
                                                                                                                                                                         answers and methods. Repeat with other
                                 0.2   =□                                                       Repeat with other examples.
                                                                                                                                                                         examples if appropriate.
                                 0.7   =□
                                                                                              Stressing appropriate vocabulary, remind the children that
                                 0.04  =□                                                      percentage means the number of parts in every 100.
                                 0.09  =□
                                 □     = 3/100                                                  Using the multiples of 5 example, point out that: 20/100 = 20% =
                                                                                                0.2.                                                                   By the end of the lesson children should
                                 0.006 = □                                                                                                                             be able to:
                                 □     = 9/1000                                                 Repeat with other examples.
                                                                                                                                                                        Answer questions such as which of
                                                                                              Children work in pairs to make up some of their own.                      these percentages is equivalent to 0.26?
                                                                                                                                                                         0.26%, 2.6%, 26%, 260%;
                                                                                                Make sure that they can make connections between the fraction           Know that
                                                                                                                                                                         13
                                                                                                and percentage notation.                                                   /100 = 13% = 0.13

                                                                                                For example: digits whose sum is 10 is: 9/100 = 9% = 0.09.             (Refer to supplement of examples, section 6,
                                                                                                                                                                       page 33.)




                                                                 VOCABULARY
                                                                 percentage
                                                                 per cent
                                                                 %
                                                                 in every


VOCABULARY
equivalent                                                       RESOURCES
equivalence                                                      Resource sheet 4.7


                                                                                             NNS Unit Plans
 Planning                       Day Five                          Unit 4 Fractions, decimals and percentages                                                  Term: Autumn               Year Group: 6
 sheet
 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        Using a counting stick, count on        Find simple percentages    Remind children of the previous lesson’s question:
0.1, 0.2, 0.25, 0.5…         and back in steps of 01, 0.2, 0.25,     of small whole number
                                                                                                                                                                     Q What is wrong with this statement?
and then back.               0.5 from different start points.        quantities.                   Q Which is bigger:
                                                                                                     50% of £90 or
                                                                                                                                                                       To calculate 10% of a quantity you divide it
                             Pointing to various places, ask                                         25% of £200?                                                      by 10. So to find 20% you must divide it by
                                                                                                                                                                       20.
                           Q If this is 0.2, what will this be?                                      Encourage children to discuss their methods of finding these
                                                                                                     percentages.
                                                                                                                                                                       Take feedback on responses.
                           Q Will 0.35 (for example) be in this
                             sequence?                                                              Use two sets of cards                                             Emphasise that in some cases, calculations
                                                                                                     – three cards selected from Resource sheet 4.8 (to suit the       can be done in a single step. Often two or
                                                                                                       ability range of the pupils)                                    more steps may be more appropriate. Show
                                                                                                                                                                       examples.
                                                                                                     – all the cards from Resource sheet 4.9 placed face down on a
                                                                                                       table.
                                                                                                                                                                     By the end of the lesson children should
                                                                                                     Ask a child to choose at random one card from each set to       understand:
                                                                                                     create a problem such as 20% of 240m.
                                                                                                                                                                      How to find simple percentages of small
                                                                                                     Ask everyone to calculate the percentage of the measurements
                                                                                                                                                                       whole number quantities, without a
                                                                                                     and discuss methods used. Repeat with different combinations.
                                                                                                                                                                       calculator e.g. find 60% of £40, 40% of
                                                                                                                                                                       3m.
                                                                                                    Ask questions like:
                                                                                                                                                                     (Refer to supplement of examples, section 6,
                                                                                                   Q If I know 10% of £40 is £4 what other percentages do I know?    page 33.)
                                                                                                   Q What are the most useful percentages to find?

                                                                                                    Children work in pairs to calculate other percentages.




                                                                     VOCABULARY
                                                                     percentage
                                                                     per cent
                                                                     %
VOCABULARY
tenth
twentieth
hundredth
                                                                     RESOURCES
                                                                     Percentage cards
                                                                     Measurement cards
RESOURCES                                                            Resource sheet 4.8
Counting stick                                                       Resource sheet 4.9


                                                                                               NNS Unit Plans

								
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