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Unit 5 - National Numeracy Strategy

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Unit 5 - National Numeracy Strategy Powered By Docstoc
					Unit 5
Fractions, decimals and percentages, ratio and proportion

Year 6
                                                                                                            National
Autumn term                                                                                                 Numeracy Strategy
                                                           Five daily lessons

                      UNIT OBJECTIVES

            Read a number with two decimal                                            Resources needed to teach this unit:
            places to the nearest tenth or to the
            nearest whole number.                                                     •   1-100 chart
                                                                                      •   0.1-1 chart
            Recognise the equivalence between                                         •   counting stick
            the decimal and fractions.                                                •   calculators

            Solve simple problems involving ratio
            and proportion.




Round a number with                     Recognise the
one or two decimal                      equivalence of
places to the nearest                   percentages, fractions
integer.                                and decimals.

Relate fractions to
their decimal
representations.




                                                      NNS Pilot Unit Plans – 9/2001
Planning Sheet     Day One                       Unit: 5 Fractions, decimals and              Term: Autumn                                               Year Group: 6
                                                 percentages, ratio and proportion
Oral and Mental                                              Main Teaching                                                                               Plenary
Objectives and     Teaching Activities                       Objectives and           Teaching Activities                                                Teaching Activities/focus
vocabulary                                                   Vocabulary                                                                                  questions
Know simple        •    Write a selection of fractions and   Find pairs with sum of   •   Explain that today’s work will focus on complements. Discuss   Repeat chanting exercise with
fractions as            percentages on the board e.g.        100, multiples of 50         the meaning of this.                                           individuals/ pairs of children for decimal
percentages.                                                 with sum of 1000,                                                                           complements to ten e.g.:
                    26%                   3                  decimals with sum of     Use 1 – 100 chart on OHP. Cover up 33. Ask for complement to       4.6 5.4
                                          5
Find simple                                                  1, 10.                   100.                                                               4.7 5.3
percentages.        70%                   0.8%                                                                                                           0.3 9.7
                    0.26%                 1
                                          4
                                                                                      •   Show / discuss how they can use the grid to help their
                   0.6                   74%                                              calculations of completion. Repeat with different numbers.
                   25%                    8
                                          4                                           Repeat process with 0.1 – 1 grid, recording examples.                 By the end of the lesson, the
                   0.25                   0.75                                                                                                              children should be able to:
                                                                                      •   Demonstrate, using the counting stick with questions like:
                       Q: Find a fraction greater                                         Range from 0 – 100, my finger marks 37, how much is left?        •   Mentally convert fractions to
                       than…                                                          •   Range 0 – 1, finger marks 0.6, how much is left?                     decimals and percentages to
                       Between…                                                           Increase speed to improve speed of pupils’ oral responses.           solve simple problems.
                       Less than …                                                        e.g.
                       Which fraction is equivalent to                                            36 64                                                    •   Find complements using
                       …                                                                          92 8                                                         decimals and percentages.
                       Which two fractions total a                                               0.1 0.9
                       whole? A half?                                                 •   Without the counting stick, practise multiples of 50 to give     (Supplement of examples, Section
                                                                                          totals of 1000, e.g.                                             6)

                   Ask questions like:                                                          350 and 650
                                                                                                150 and 850
                        Q: If I have £100 how much is                                 Discuss strategies used.
                        3 ? 0.25? three fifths?
                        4
                                                                                          Q: 60% of the class were girls, what percentage were
                                                                                          boys?

                                                                                          Q: A garment was 30% wool, 20% mohair and the rest
                                                                                          acrylic. What percentage was acrylic?


                                                             VOCABULARY
VOCABULARY                                                   Number pairs             Ask children to work on similar word problems in pairs (use both
Equivalent                                                   Complements              fractions and percentages).
Percentage                                                   Explain your reasoning
Decimal fraction                                                                      RESOURCES
                                                                                      1 – 100 chart
                                                                                      0.1 – 1 chart
                                                                                      Counting stick




                                                                                  NNS Pilot Unit Plans – 9/2001
Planning Sheet      Day Two                     Unit: 5 Fractions, decimals and               Term: Autumn                                                 Year Group: 6
                                                percentages, ratio and proportion
Oral and Mental                                             Main Teaching                                                                                  Plenary
Objectives and      Teaching Activities                     Objectives and            Teaching Activities                                                   Teaching Activities/focus
vocabulary                                                  Vocabulary                                                                                      questions
Round decimals to   •   Explain to the children that we     Round a number with       •   Tell the children we are going to work on rounding decimal       Write a set of statements on the board
the nearest whole       often round numbers to help         two decimal places to         numbers with more than one decimal place.                        where some are incorrect e.g.
number or nearest       mental calculation, for example     the nearest tenth or
tenth.                  when working out the area of        the nearest whole         Write 0.78 on the board.                                                       0.45       ≈ 0.4
                        carpet for a room. Show an          number.                   Establish that the number lies between 0.7 and 0.8. Which                      6.9        ≈ 7
                        example e.g. 3.8m x 4.1m will                                 number is it nearest to? We can record:                                        3.49       ≈3
                        give an area roughly 16 square      Give a decimal fraction                                                                                  32.01      ≈ 32.1
                        metres.                             lying between two         0.78 ≈ 0.8 (to the nearest tenth)                                              166.6      ≈ 16
                                                            others.                   Repeat for other examples                                                      644        ≈ 650
                    •   Discuss why we round one
                        number up and the other down.                                 •   Explain that another way of expressing this is to round to one   Ask children to find which are incorrect
                                                                                          decimal place.                                                   and to explain why.
                    •   Explain that 0.5 is rounded up to
                        the next whole number.                                        Consolidate with examples using both terms for the children to       Invite children to add more to the list –
                                                                                      work on.                                                             some correct and some incorrect.
                    •   Practise some examples from the
                        board, rounding to the nearest                                •   Extend to numbers with whole numbers and decimals e.g.:          Ask the class for comments.
                        whole number e.g.
                        9.7, 25.6, 148.3                                              Round 365.49 to
                                                                                             -   the nearest tenth
                                                                                                                                                               By the end of the lesson
                    •   Round to the nearest metre:                                          -   the nearest whole number
                                                                                                                                                               children should understand:
                        1.5m, 6.7m, 4.1m, 8.9m                                               -   nearest ten
                                                                                             -   nearest hundred
                                                                                                                                                               • How to round numbers with
                                                                                                                                                                 two or more decimal places
                                                                                                                                                                 to the nearest tenth.

                                                                                                                                                               (Supplement of examples Section
                                                                                                                                                               6, page 29)




                                                                                NNS Pilot Unit Plans – 9/2001
Planning Sheet          Day Three                             Unit: 5 Fractions, decimals and           Term: Autumn                                                       Year Group: 6
                                                              percentages, ratio and proportion
Oral and Mental                                                        Main Teaching                                                                                       Plenary
Objectives and          Teaching Activities                            Objectives and            Teaching Activities                                                       Teaching Activities/focus
vocabulary                                                             Vocabulary                                                                                          questions
Begin to convert a      Write a range of equivalent fractions          Recognise the             Ask the children in pairs to use a calculator to key in a set of
fraction to a decimal   on the board such as:                          equivalence between       fractions and record the results to 2 decimal places.                        Q: Which of these decimals is
using division.          3 , 4 , 1 , 5 , 6 , 7 , 10 , 100 .            decimals and                                                                                           equivalent to 193 ?
                        15 20 5 25 30 35 50 500                        fractions.                Gather results from the class. Record on the board.                                        100

                                                                                                 Choose 3 numbers and ask the children to order them from
                        Q: Use a calculator to find the                Develop calculator        smallest to largest.                                                         1.93, 10.193, 0.193, 19.13
                        decimal equivalents of these                   skills and use a
                        fractions. What do you notice?                 calculator effectively.   Extend to fractions with 3 decimal places

                        Move on to use an OHP calculator to                                      Ask the children to work in pairs to find and order decimals.
                        find the decimal equivalents of:                                                                                                                   Discuss without using a calculator and
                        1 , 3 , 5 , 7 , 3 , 1, 2
                                                                                                 Challenge some children by including     1   1, 2   in sets of numbers.   then use the calculator to check result.
                        4 4 8 10 5 3 3                                                                                                    3   6 3
                        Discuss results.                                                         Remind children of work on rounding in the previous lesson.               Repeat with other examples.




                                                                                                                                                                              By the end of the lesson the
                                                                                                                                                                              children should be able to:

                                                                                                 RESOURCES                                                                    •   Enter fractions into a
                                                                                                 Calculator                                                                       calculator
VOCABULARY
Divide                                                                                                                                                                        •   Use a calculator to compare
                                                                                                                                                                                  fractions.

                                                                                                                                                                              (Supplement of examples,
                                                                                                                                                                              Section 6)




                                                                                             NNS Pilot Unit Plans – 9/2001
Planning Sheet        Day Four                   Unit: 5 Fractions, decimals and              Term: Autumn                                                Year Group: 6
                                                 percentages, ratio and proportion
Oral and Mental                                               Main Teaching                                                                               Plenary
Objectives and        Teaching Activities                     Objectives and          Teaching Activities                                                  Teaching Activities/focus
vocabulary                                                    Vocabulary                                                                                   questions
Understand the        •   Assess (or recap) children’s        Solve simple problems   •   Use Framework examples from Y6 (Section 6 Page 27) to           •       Say there are 20 boys and 10 girls in
language associated       previous knowledge by asking        involving ratio and         assess children’s confidence in solving problems of the kind:           Class 6.
with ratio and            questions like:                     proportion.
proportion.                                                                           A mother seal is fed 5 fish for every 2 fish given to the baby.     Ask the children to:
                      John has one stamp for every two                                Alice fed the mother seal 15 fish. How many fish did its baby
                      that Mark has. Ask children what this                           get?                                                                    Q: Give me a sentence using the
                      means, recording results on the                                                                                                         word ‘ratio’ (or proportion). Ask for
                      board.                                                          •   Show the children a tower with 8 red and 2 yellow linking           alternatives.
                                                                                          cubes:
                      John has half as many stamps as
                      Mark

                      Mark has twice as many stamps as
                      Mark                                                                                                                                •       Repeat for other numbers. Take
                                                                                      Ask how many yellow cubes there are to each red.                            feedback and record results.
                      If Mark has 4 stamps, John has 2
                      stamps.                                                         Write on board ‘1 to every 4’ So what proportion of the strip is    •       Encourage children to use
                                                                                      yellow? ‘ 1 in every 5’.                                                    appropriate vocabulary.
                      •   Now extend the work by posing
                          questions like:                                             Explain that the first statement describes the ratio. Emphasise
                                                                                                                                                              By the end of the unit children
                                                                                      the language ‘to every’
                      If Mark has 400 stamps and John                                                                                                         should understand:
                      has 200.                                                        The second statement describes the proportion or fraction.
                                                                                                                                                              •      How to solve simple ration
                                                                                      Set children another problem                                                   and proportion problems
VOCABULARY                                                    VOCABULARY                                                                                             such as, at a gym club there
For every                                                     Ratio                   Julie has 20 sweets. She gives Jim one sweet for every 3 sweets                are 2 boys for every 3 girls.
To every                                                      Proportion              she eats. How many sweets does Jim get?                                        There are 30 children at the
In every                                                                                                                                                             club. How many boys are
As many as                                                                            Reinforce stages of problem solving and go through solution on                 there?
                                                                                      board. Check using real sweets.
                                                                                                                                                              (Supplement of examples Section
                                                                                                                                                              6, Page 27)
                                                                                      •   If children appear confident let them try 2 more questions in
                                                                                          pairs.




                                                                                 NNS Pilot Unit Plans – 9/2001
Planning Sheet         Day Five                     Unit: 5 Fractions, decimals and                Term: Autumn                                                Year Group: 6
                                                    percentages, ratio and proportion
Oral and Mental                                                Main Teaching                                                                                   Plenary
Objectives and         Teaching Activities                     Objectives and              Teaching Activities                                                  Teaching Activities/focus
vocabulary                                                     Vocabulary                                                                                       questions
Give a decimal lying   Draw a number line on the board         Extend knowledge of         •   Write the number 16 on the board and                            Ask a pair of children to record all their
between two others.    from 5 to 6. Ask questions such as:     decimals to several                                                                             stages on the board, explaining their
                                                               decimal places.                                       Target 100                                reasons for choosing each number.
                           Q: Give me a fraction that lies                                                                                                     Comment on strategies used.
                           between 5 and 6.                    Develop calculator skills
                                                               and use a calculator        at the side.                                                        Homework
                                                               effectively.                                                                                    Play target 100 starting with 96,
                                                                                           Ask the children to estimate what we must multiply 16 by to         36, 55.
                       Take feedback and extend the            Explain methods and         produce exactly 100. Discuss suggestions.
                       problem to’zoom in’ on the tenths       reasoning, orally and in                                                                        Ask children what they notice notice
                       divisions.                              writing.                    Children can try the suggestions on their own calculators.

                                                                                           Write children’s suggestions on the board e.g.                         By the end of the lesson the
                       •   Tell the children you now want      VOCABULARY                  8 x 16 = 128 (too large)                                               children should be able to :
                           them to find a number between 5     Ten thousandths             6 x 16 = 96 (almost there)
VOCABULARY                 and 5.5.                            Hundred thousandths         7 x 16 = 112 (too large)                                               •   Give a decimal lying between 2
Thousandths                Children respond using individual   Recurring                   What numbers come between 6 and 7?                                         others.
                           white boards.                       Decimal places
                                                                                           6.4 x 16 = 102.4 (too big)                                             •   Explain their reasoning to
                       •   Repeat for different numbers                                    6.3 x 16 = 100.8 (still too big)                                           others.
                           ‘zooming in’ each time to reach 2                               By trial and improvement reach the conclusion that the number
                           decimal places. For example:                                    lies between 6.2 and 6.3. Try 6.25.                                    •   Use a calculator and read the
                                                                                                                                                                      display in decimal notation.
                       Find me a number between                                            •   Repeat with a different start number, say 23.
                                                                                               Explain that we cannot always reach 100 exactly but we can         (Supplement of examples, Section
                             5.1 and 5.3                                                       getnearer and nearer.                                              6)
                             5.2 and 5.3
                             5.2 and 5.25
                                                                                           •   Stress the importance of recording each estimate to guide us
                             5.25 and 5.26 etc.                                                to the next move.
                                                                                               Discuss what each stage means using the language on
                           Q: Can I squeeze in another                                         tenths and hundredths and questions like ‘ how far off a
                           number? How do you know?                                            hundred is this?’ Continue until you reach an agreed level of
                                                                                               accuracy perhaps 4.349 x 23 = 100.027.

                                                                                           •   Children work in pairs using start numbers like 32, 48. Some
                                                                                               could be challenged with starting numbers like 11, 22, 45
                                                                                               which lead to recurring decimals. Others should be given
                       •   Emphasise the language of                                           numbers which only need to go to 1 or 2 decimal places, like
                           fractions when describing decimal                                   40, 80.
                           parts of a number. (i.e. 3.528 is
                           three and five tenths, two
                           hundredths and eight
                           thousandths.)




                                                                                      NNS Pilot Unit Plans – 9/2001

				
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