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					                                                                   Five daily lessons

Unit 6
Division, decimals and problem solving

Year 6                                                                                                      This Unit Plan is designed to
Summer term                                                                                                 guide your teaching.
                                    Unit Objectives                                                         You will need to adapt it to
                                       Year 6                                                               meet the needs of your class.
        Derive quickly division facts corresponding to                    Page 59
         multiplication tables up to 10 x 10.
        Order a mixed set of numbers with up to three decimal             Page 29
                                                                                                        Resources needed to teach this unit:
        Solve a problem by extracting and interpreting                    Pages 115, 117
         information presented in tables, graphs and charts.                                                Resource sheet 6.1
                                                                                                            Resource sheet 6.2
                                                                                                            Resource sheet 6.3
                                       Link Objectives                                                      Resource sheet 6.4
                                                                                                            Resource sheet 6.5
                           Year 5                                   Year 7                                  OHT 6.1
                                                                                                            OHT 6.2
   Know by heart all multiplication facts up to            Consolidate the rapid recall of number         Self-assessment sheet 6.1
    10 x 10.                                                 facts, including multiplication facts to       Self-assessment sheet 6.2
   Order a set of numbers with the same number              10 x 10, and quickly derive associated
                                                                                                            Whiteboards
    of decimal places.                                       division facts.
                                                                                                            Calculators
   Solve a problem by representing and                     Compare and order decimals in different
    interpreting data in tables, charts, graphs and          contexts.
    diagrams.                                               Given a problem that can be addressed by
                                                             statistical methods, suggest possible
(Key objectives in bold)                                    Interpret diagrams and graphs.

                                                                      NNS Unit Plans
 Planning      Day One                                      Unit 6 Division, decimals, and problem solving                                       Term: Summer                                Year Group: 6
 Oral and Mental                                            Main Teaching                                                                                                                    Plenary
 Objectives and         Teaching Activities                 Objectives and                Teaching Activities                                                                                Teaching Activities/Focus
 Vocabulary                                                 Vocabulary                                                                                                                       Questions
Derive facts               Write 7 x 8 = 56 on the        Solve a problem by              On the board, present the table below:         Discuss strategies.                                Write on the board:
corresponding to            board. Ask the children to     extracting and
multiplication facts.       state facts which can be       interpreting information             Input                 Output              Q Is this a harder problem, why?                         Input             Output
                            derived from this fact.        presented in tables.                2 and 3                  4                                                                       1, 2 and 3             1
                            Record their suggestions,                                          7 and 4                  1                  Establish there are fewer pairs and no               2, 3 and 4             5
                            e.g.                                                               0 and 5                 10                  zeros.                                               1, 0 and 2             2
                                                                                               1 and 6                 11
                            56 ÷ 8 = 7                                                         4 and 8                 12                 Q If I tell you that 0 and 7 give an output          Ask the children to solve the
                            5.6 ÷ 8 = 0.7                                                                                                   of 21 does this help?                              problem.
                            56 ÷ 0.8 = 70                                                   Explain that the output number can be
                            5.6 ÷ 0.8 = 7                                                   made using the two input numbers.              Encourage the children to use this piece          Q What strategy did you use with a
                            70 x 8 = 560                                                    (Explain that the same operations have         of information to see that the second               three number input?
                            70 x 80 = 5600                                                  been used on each pair of numbers in           number is multiplied by 3.
                            7 x 16 = 112                                                    the table.)                                                                                        Collect responses and compare
                            14 x 4 = 56                                                                                                   Q What other pair of numbers would help              strategies. Confirm the rule is
                            28 x 2 = 56                                                   Q What operations have been carried out           you?                                               multiply the first number by the
                            0.7 x 80 = 56                                                   on the two input numbers to get the                                                                third number then subtract the
                            0.7 x 8 = 5.6                                                   output?                                        Agree that a pair with the second number            second number.
                            0.7 x 0.8 = 0.56                                                                                               zero would help.
                                                                                            Collect answers and discuss strategies.                                                      HOMEWORK – Ask the children to
                            Prompt the children to                                                                                        Q If 0 and 0 gives 0 does this help?           solve the two tables below:
                            identify, extend and explain                                  Q Which pairs of input numbers gave you
                            particular pattern of facts.                                    most help? Why?                                Agree it does not and invite the children              Input              Output
                                                                                                                                           to select another pair with a zero, e.g. 1              1, 3                6
                           Ask the children in pairs to                                    Encourage the children to explain which        and 0 gives 2. Confirm the rule is double              4, –1               11
                            use 6 x 9 = 54 and derive                                       pairs they used to establish a rule and        the first number and add triple the second             1, –2                1
                            as many related facts as                                        which they used to test it. Confirm rule       number. Highlight the strategies the                   2, –2                8
                            they can in two minutes.                                        is double second number and subtract           children used and draw out the
                            Collect examples to                                             first number.                                  usefulness of the zeros.                               Input              Output
                            identify patterns.
                                                                                                                                                                                                  2, 2, 2              6
                                                                                           Write:                                        Set the children to work in pairs producing            1, 5, 0              5
                           Repeat using another                                                                                           input/output tables of their own.                      2, 3, 1              5
                            multiplication fact with the                                        Input                 Output               Encourage them to have outputs that are                2, 0, 5             10
                            children recording only                                            2 and 5                 19                  negative numbers. Bring pairs together to
                            division facts.                                                    1 and 4                 14                  solve one another’s problems. Collect               (Answer: (3 x x) + (1 x y) = 6 and
                                                                                               4 and 3                 17                  examples and share with the whole class.
                                                                                                                                                                                               (0 x x) + (1 x y) + (2 x z) = 6)
                                                                                          Q What operations are used to get the
                                                                                            output?                                                                                            Where x is the first number, y the
                                                                                                                                                                                               second and z the third.
                                                                                            Allow the children a short time to work in
                                                           VOCABULARY                       pairs to find the rule.                                                                      ASSESSMENT – Explain to the
                                                           input                                                                                                                         children that during the week they will
                                                           output                                                                                                                        be completing ‘My Mathematics’ self-
                                                           operation                                                                                                                     assessment sheets they will take to
                                                                                                                                                                                         their secondary school.

                                                                                                 NNS Unit Plans
 Planning      Day Two                               Unit 6 Division, decimals, and problem solving                                              Term: Summer                                 Year Group: 6
 Oral and Mental                                     Main Teaching                                                                                                                            Plenary
 Objectives and         Teaching Activities          Objectives and            Teaching Activities                                                                                            Teaching Activities/Focus
 Vocabulary                                          Vocabulary                                                                                                                               Questions
Derive quickly             Write 9 x 4 = 36 on     Solve a problem by          Show OHT 6.1.                                           Collect responses and write the predictions           Return to Table 5.
division facts              the board. Ask the      extracting and                                                                       on the board. Get the children to choose
corresponding to            children to state       interpreting                 Establish that it contains 36 numbers with one          six numbers and find their total from each           Q What is the largest number in the
multiplication facts.       division facts          information                  decimal place. Point to the last column.                of the two tables.                                     table?
                            derived from this       presented in tables.
                            fact. Record these                                 Q In order, which are the 2 smallest numbers            Q Was our prediction correct? Why?                       Collect the children’s responses.
                            facts, prompt the       Order a mixed set of         in this column?
                            use of patterns to      numbers with up to                                                                   Agree that the totals were 20 and that the           Q How did you scan the table to find your
                            extend the range of     three decimal                Agree they are 17.7 and 17.9 and write them             numbers on Tables 1 and 2 have been                    answer?
                            facts.                  places.                      on the board.                                           divided by 10 to give the numbers on
                                                                                                                                         Tables 3 and 4.                                        Discuss the different strategies the
                           Repeat, starting        Undertake column           Q What numbers lie between 17.7 and 17.9?                                                                        children used.
                            with other              addition of numbers                                                                 Ask the children to look at Tables 5 and 6.
                            multiplication facts.   involving decimals.          Collect answers and record the numbers, in                                                                   Q What is a systematic way of finding the
                            The children work                                    the correct order, between 17.7 and 17.9.             Q Can you predict the totals for these two               smallest number in the table?
                            in pairs and record                                                                                          tables?
                            answers on                                          Explain to the children that you are going to                                                                  Collect responses and agree that finding
                            whiteboards.                                         choose six numbers and sum them. Once                   Collect and record predictions encouraging             the smallest number in the first row and
                                                                                 you choose a number, you cannot choose                  the children to justify their predictions. Get         comparing this with numbers in
                           Identify some                                        any other number in that row or column.                 the children to test these predictions.                subsequent rows one at a time, is a
                            patterns used and                                    Choose 56.9 say, circle it, cross out the other         Agree that the totals are 2 and 2000                   systematic method.
                            ask the children to                                  numbers in the row and column containing                respectively. Explain to the children that
                            explain them.                                        56.9. Repeat, e.g. choose 24.4 from the                 they are going to try to find the answer to
                                                                                 remaining numbers. Continue crossing out                this question.                                   ASSESSMENT –
                                                                                 the relevant numbers until you have six                                                                   Give out ‘My Mathematics’ Self-
                                                                                 numbers left. Get children to add the six             Q What is it about the way the numbers are           assessment sheet 6.1. Explain that the
                                                                                 numbers up.                                             arranged that results in the same totals?          sheet is to help the children to identify
                                                                                                                                                                                            what mathematics they have been able
                                                                               Q What is the total of these six numbers?                Ask the children to identify any patterns in       to do during the week. There will be
                                                                                                                                         the tables.                                        some time each lesson for them to
                                                                                 Collect answers and agree the answer is 200.                                                               complete the sheet.
                                                                                                                                       Q Are there any connections between
                                                                                Give out Resource sheet 6.1. Tell the                   numbers in the different rows or                      Ask the children to work out the first
                                                                                 children to use Table 1 and choose six                  columns?                                               cloud question on the sheet. Say that
                                                                                 numbers of their own, using the same                                                                           you want them to write in the middle
                                                                                 process, and add these six numbers up.                  Encourage the children to use Table 6 and              loop, division facts corresponding to 3 x
                                                                                 Collect answers and confirm the answers are             to work from the numbers in the first row              8. When they have done this, they
                                                                                 all 200.                                                to see how the numbers in the other rows               should show their work to a friend.
                                                                                                                                         are connected. Collect the children’s                  Some of the children may need help.
                                                                                Get the children to repeat the exercise in              observations.
                                                                                 Table 2. Agree the total is still 200.                                                                        Tell the children that they should tick the
                                                                                                                                       Q If we add together the first row and adjust            box to say if they required any help.
                                                    RESOURCES                   Look at Tables 3 and 4.                                 the total in the same way that the rows
                                                    OHT 6.1                                                                              are connected, what number do we get?                 Give the children a few minutes to
                                                    Self-assessment            Q Can you predict the total for these tables?                                                                    complete this task and ask them to put
RESOURCES                                           sheet 6.1                                                                           Build on this to establish how the table was           this sheet away ready for their next
Whiteboards                                         Resource sheet 6.1                                                                   constructed.                                           mathematics lesson.

                                                                                                    NNS Unit Plans
 Planning                      Day Three            Unit 6 Division, decimals, and problem solving                                                   Term: Summer                                       Year Group: 6
 Oral and Mental                                    Main Teaching                                                                                                                                       Plenary
 Objectives and         Teaching Activities         Objectives and            Teaching Activities                                                                                                       Teaching Activities/
 Vocabulary                                         Vocabulary                                                                                                                                          Focus Questions
Derive division facts      Get the class to       Solve a problem by          Show the first table on OHT 6.2. Explain that it is                                                                      Return to the homework
corresponding to            recite the 8 and 9     extracting and               the results of a school sports day.                         Q How can we use this method to find the points for           set on day 1. Ask the
multiplication facts.       times tables.          interpreting                                                                               first place?                                                children to explain their
                            Repeat.                information                Q How many events took place?                                                                                               solutions to the two
                                                   presented in tables.                                                                      Collect responses and using the Yellow team’s               problems.
                           Recite the 8 times                                  Establish that there are 26 first, second and third           results work through;
                            table again but this   Explain methods              places.                                                       Yellow team; (10 x F) + (10 x 1) = 60 so                    Make links between the
                            time stop at a         and reasoning.                                                                             10 x F = 50 and F = 5.                                      homework and this lesson.
                            particular                                        Q How many points did each team collect?                                                                                    Emphasise that in each
                            multiplication fact.                                                                                             Give out Resource sheet 6.2. Discuss the three              case they are finding in the
                                                                                Agree that it depends on the points awarded for               tables. Explain that the school was trying out new          operation used in this
                           Ask a child to write                                first, second and third places. Say that there are 3          points systems. Tables 1 and 2 still result in the          lesson the points to
                            a related division                                  points for first place, 2 for second and 1 for third          same overall order of the four teams. However,              multiply the first, second
                            on the board. Ask                                   place.                                                        after some complaints, the Blue team was                    and third places by.
                            another child to                                                                                                  reinstated in two events as the winners, and                Emphasise that the
                            write another                                       Get the children to work out the points for each              another point system was used. This time the                number zero is particularly
                            related division and                                team and record these on the OHT.                             order of the teams has changed.                             helpful as multiplying zero
                            so on. Continue                                                                                                                                                               by anything still gives zero.
                            until six division                                 Show the second table on OHT 6.2. Compare the               Q Can you find the different three point systems
                            facts have been                                     total points in the two tables.                               used?
                            recorded. Get the                                                                                                                                                       ASSESSMENT –
                            rest of the class to                              Q Why are the totals different?                                Collect the answers to Table 1. Discuss the             Ask the children to
                            confirm the facts                                                                                                 strategies the children used.                            complete the next ‘cloud’
                            are correct and, in                                 Agree the awarding of points for places is different.                                                                  question on the ‘My
                            pairs, to use each                                  Say third place is still awarded 1 point.                   Q How do the positioned results of the Green and           Mathematics’ Self-
                            of the six facts to                                                                                               the Red teams differ?                                    assessment sheet 6.1.
                            derive another fact.                              Q What is the new point-awarding system?
                                                                                                                                              Agree that they only differ in their number of             Get each child to discuss it
                            Collect some                                        Ask the children to work in pairs to find the new             second places. Ask the children to explain how              with a friend as before and
                            responses quickly                                   point system. Collect answers and discuss the                 they might use this information, and to continue            tick the appropriate box.
                            and record these                                    children’s strategies. Remind the children that they          working on Tables 1 and 2.                                  Help those children who
                            on the board.                                       know third place was awarded one point.                                                                                   need it.
                                                                                                                                             Discuss how the children used the Green and Red
                           Repeat stopping at                                Q What information did you use to find the points               teams’ results to find the points for second place.        Give the children a few
                            other facts within                                  for second place?                                             Encourage the children to support their                     minutes to complete the
                            the 8 and 9 times                                                                                                 explanations and reasoning using the symbols                task and put the sheet
                            tables until the                                    Establish that the Blue team had no first places.             introduced earlier, e.g. Green team – Red team; 2           away carefully for the next
                            board is full of                                    On the board write down the statement;                        x S = 10 so S = 5.                                          lesson.
                            division facts.                                     Blue team; (10 x S) + (10 x 1) = 40.
                                                                                                                                             Collect responses to Tables 2 and 3. Remind the
                                                                              Q What does this statement mean?                                children of the importance of reading carefully the
                                                   RESOURCES                                                                                  information contained in the tables. Encourage
                                                   OHT 6.2                      Establish that S stands for the number of points for          them to invent and use their own symbolism.
                                                   Resource sheet 6.2           second place and the Blue team had 10 second                  Compare the different methods the children used.
                                                   Self-assessment              places and 10 third places. With the class deduce
                                                   sheet 6.1                    that this means; 10 x S = 30 so S = 3 points.

                                                                                                   NNS Unit Plans
 Planning    Day Four                                                           Unit 6 Division, decimals, and problem                                       Term: Summer                      Year Group: 6
 sheet                                                                          solving
 Oral and Mental                                                                Main Teaching                                                                                                  Plenary
 Objectives and      Teaching Activities                                        Objectives and              Teaching Activities                                                                Teaching Activities/Focus
 Vocabulary                                                                     Vocabulary                                                                                                     Questions
Order a mixed set           Write on the board: 2.407.                        To solve a problem           Give out Resource sheet 6.3. Explain that the first half of the sheet sets         Stop the class.
of numbers with up                                                             by extracting and             out costs of holidays. Give the children time to read the sheet and
to three decimal     Q How do we decide whether 2.217 is bigger or             interpreting                  discuss the information contained in the table.                                   Q How are you recording your
places.                smaller than 2.407?                                     information                                                                                                       costings?
                                                                               presented in tables.      Q What does it cost to fly to Villa Dream from the East Midlands?
Explain methods              Collect reasons and discuss the values of the                                                                                                                       Discuss alternatives and share
and reasoning.               different digits. Write the two numbers on the                                  Confirm the children can read the information and interpret the                     strategies. Tell the children to put
                             board with a large gap between the numbers.                                     supplements.                                                                        their work away carefully as they will
                                                                                                                                                                                                 continue with the task in the next
                     Q Where should I write 2 and 2.5?                                                   Q What will it cost for a ten-year-old child to stay 7 nights in the Grand              lesson.
                             Establish where these numbers should be
                             recorded and write on the board as:                                             Confirm the children understand the reductions that apply for children        ASSESSMENT –
                                                                                                             under 15. Continue to probe the children’s use and understanding of             Ask the children to complete the last
                         2     A 2.217 B 2.407 C          2.5   D   2.8   E                                  the table.                                                                       two ‘cloud’ questions on the ‘My
                                                                                                                                                                                              Mathematics’ Self-assessment sheet
                             Where A, B, C, D and E are the intervals                                       Explain that the second table on the sheet identifies the local facilities.      6.1, discuss them with a friend and
                             between the numbers. The children might                                                                                                                          tick the appropriate box. Help any
                             find it helpful if all the numbers had three                                Q Which accommodation has access to a swimming pool?                                 children who need it. Give the
                             decimal places, e.g. 2 = 2.000; 2.3 = 2.300.                                                                                                                     children a few minutes to complete
                                                                                                             Ensure the children can interpret the table correctly.                           the table.
                     Q Where should I record 2.3?
                                                                                                            Give out Resource sheet 6.4. Explain that the sheet sets out the                   Discuss the work with the children
                             The children show their answers using                                           holiday requirements of four families. Give the children time to read the           then ask them to put their sheets
                             whiteboards. Discuss why 2.3 is in the                                          set of four requirements.                                                           away for next lesson.
                             interval B between 2.217 and 2.407. Repeat
                             using numbers with one, two and three                                       Q Which families enjoy shopping?
                             decimal places.
                                                                                                              Ensure the children can identify the different holiday requirements of
                            Write the digits 3, 7, 2, 5 on the board.                                        each family.

                     Q Using these four digits, what numbers can                                            Explain to the children that they are to use the information on Resource
                       you make that fit in the interval B?                                                  sheet 6.3 to select and cost appropriate holidays for the families. They
                                                                                                             are to present their findings as short portfolios for each family.
                             Collect answers and establish that 2.375 and
                             2.357 fit in the intervals.                                                 Q What should go in these portfolios?

                     Q Using these four digits, can you make                                                  Discuss the children’s ideas and record these on the board. Ensure the
                       numbers that fit in any other intervals?                                               costings include travel and accommodation costs. Ensure that the
                                                                                                              facilities are also included. Remind children that two of the families
                             Discuss possibilities and establish numbers in                                   have identified budgets and would not be likely to exceed these by
                             interval D only are possible. Give the children                                  much. Explain to the children that they are acting as travel agents who
                             another four digits, e.g. 9, 2, 1, 2 to use.      RESOURCES                      want to sell their holidays so they might want to emphasise key points.
                                                                               Resource sheet 6.3             Discuss how the children might do this.
                            Repeat using another starting decimal             Resource sheet 6.4
RESOURCES                    number, e.g. 7.016.                               Self-assessment                Set the children to work in pairs constructing their holiday portfolios.
Whiteboards                                                                    sheet 6.1

                                                                                                      NNS Unit Plans
 Planning    Day Five                               Unit 6 Division, decimals, and problem solving                                                 Term:                  Year Group: 6
 sheet                                                                                                                                             Summer
 Oral and Mental                                                     Main Teaching                                                                  Plenary
 Objectives and   Teaching Activities                                Objectives and           Teaching Activities                                      Teaching Activities/Focus Questions
 Vocabulary                                                          Vocabulary
Consolidate            Write the following grid on the board:      To solve a problem         Remind the children about the holiday                   Collect in the calculators and give out Resource sheet 6.5. Say that this
mental skills.                                                      by extracting and           requirements they were costing and the                   represents some of the items the families bought before they went on
                                 First        Second                interpreting                portfolios they were preparing in the                    holiday.
                      Number                              Result
                               Operation     Operation              information                 previous lesson. Set the children to
                                                                    presented in tables         continue to work in pairs on their planning            Q The Ahmeds bought two pairs of sunglasses and a bottle of suntan
                        4                                   60      and charts.                 and costing portfolios.                                  lotion; how much did they spend?

                                                                                               As the children complete their portfolios,               Collect answers and pose a question about each family.
                       Explain that the children are to identify                               organise them into groups of four to read
                        two operations that convert 4 into 60.                                  one another’s portfolios and to compare                 Ask the children to compare the way the information is set out on Resource
                        Say that one operation must be x or ÷,                                  the costings etc. Ask them to decide                     sheet 6.5 with the tables on the other Resource sheets 6.3 and 6.4.
                        the other + or –. Write three examples                                  whether the portfolios they are reading:
                        on the board:                                                                                                                  Q When does a table help you; when is a table unnecessary?
                                                                                                –    give detailed costings for travel and
                        – 1, x 20; x 50, – 120; + 116, ÷ 2.                                          accommodation;                                      Collect responses and discuss the relative merits of the tables and the
                                                                                                –    identify the facilities that are available;         chart.
                      Q Do these three examples work?                                           –    are accurate;
                                                                                                –    meet the budgets of the two families;
                        Collect answers and establish that                                      –    sell the holidays to the families.            ASSESSMENT –
                        x 50, – 120 gives 80 not 60.                                                                                                Give out ‘My Mathematics’ Self-assessment sheet 6.2.
                                                                                               After the children have read one another’s
                       Ask the children for other examples for                                 portfolios, discuss with the class the                   Allow time for the children to read and complete the three input–output
                        class to check. Change the rules about                                  different holidays that have been offered to             tables on the sheet and describe their strategies.
                        the operations and change the                                           the families and the costings involved. As
                        numbers. Use decimals, make the                                         a class, agree on which holidays they think              Discuss the solutions to the problems with the class.
                        result negative, have a result smaller                                  meet the requirements of the different
                        than the start number.                                                  families and confirm the costs of the                   Explain that the table on the bottom half of the sheet is for the children to
                                                                                                holidays.                                                summarise how well they have been able to answer each question.

                                                                                                                                                         Ask the children to look at the statements in the left-hand column. The
                                                                                                                                                         questions alongside each statement are intended to remind the children
                                                                                                                                                         what each statement means. Ask the children to look back on their work to
                                                                                                                                                         help them fill in the table.

                                                                                                                                                         Encourage the children to complete each statement by putting a tick in one

                                                                                                                                                         Ask the children to complete the target statement by choosing one of the
                                                                                                                                                         three areas of mathematics where they think they need to improve.

                                                                                                                                                         For those children who where able to answer all the questions without
                                                                                                                                                         help, discuss the learning objectives for Year 7 shown on the front page of
                                                                                                                                                         the unit.
                                                                    Resource sheet
                                                                                                                                                        Get the children to stick ‘My Mathematics’ Self-assessment sheets 1 and 2
                                                                                                                                                         in their books under their work.
                                                                    sheet 6.2

                                                                                                NNS Unit Plans