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									                                                   KS3 Framework Materials: Year 7                          Tier: Main                    Spring Term : First Half
Class:                                                     Week:             Time: 3 hrs                   Maths Topic: Unit 8 / HD2

                                                                             Total of 5 hrs                 (Part 1 of 2):                                                     Data collection, Display &
L                                                            Key                                                                                                                                               Resourc
    Mental                    Learning                                          Introductory                                        Main Activity                                         Plenary
N   Starters                  Outcomes                     Vocabula             Ideas                                                                                                      (was hd3/1)           es
o                                                             ry                                                                     Suggested activities:
L OHS HD2/1:            given a problem that can be       survey            Pupils to suggest possible    1.      Discussion and interpretation in groups of range of data           OHS HD2/3:               pp 250 - 5
1 Shady                  addressed by statistical          questionnaire     answers to 3 - 5 everyday             displays. Record interpretations.                                  Misleading Charts        pp 262 - 273
  Statistics: for        methods, suggest possible         experiment        problems. Eg: 'Best way to                                                                               Highlight how data       OHS
  statement that         answers                           data              travel to school? (see        2. Share and compare results Discuss difference between groups.            displays can be          HD2/1:
1 'Men run                                                 grouped data      p248). Conduct straw poll.       Highlight ease of misinterpretation.                                    misleading.              Shady
  faster than                                              statistics        OHS HD2/2: Data                                                                                           Qs: When is this        Statistics
h women'.                                                  class interval    Display- Methods of                                                                                      sometimes done on
r Find reasons                                             tally             Transport                                                                                                purpose?                 OHS
  why Leanne                                               table             - how these were obtained ?                                                                              How could a soap         HD2/2:
  or Tariq may                                             frequency         - how or when might both                                                                                 powder co. use this to   Data
  be right                                                 data collection   be accurate?                                                                                             advantage?               Display-
L Interpret            decide which data is relevant to   sheet             Are boxes of Smarties all     1 Individually / Pairs: Ask pupils to record in their own way the          Ask for 1 statement or   Methods of
2 graph shapes,         an enquiry                         database          the same?                     colour frequencies for their box. (Suggest pupils count 30 sweets and      observation from each    Transport
  eg:                                                                        Hand out 1 box per pupil      discard excess!) Discuss data collection methods. Agree ground             pupil about whole
                     decide on data sources                Ma 1 words:      (or pair). Most popular       rules on frequency diagrams (tallies ...)                                  class results            OHS
1   OHS HD2/2:                                             any of -          colour? (mode).                                                                                          from table?              HD2/3:
                       plan how to collect & organise                                                     2 Pupils to: draw diagram / chart / graph of results; present data
    Data Display-       small sets of data                                    Predict results, count &                                                                                from display?            Misleading
h   Methods of                                             answer            compare results.              display & justify choice; Agree ground rules displays (labels,start at     Which is faster?         Charts
                                                                                                           0 ..)
r   Transport        design data collection sheet /       evidence                                                                                                                   Are whole class
                                                           explain           What other Qs could we                                                                                   results more or less
                      questionnaire                                                                 3      3 Pool class results in frequency table & graph (board / OHP). Use
                                                           explore           ask? Eg:                                                                                                 accurate than
                                                                                                           to consolidate ground rules. Interpret results; answer original Qs.
                     construct bar-line graphs &          investigate       How many colours? How                                                                                    individual results?
                      grouped frequency diagrams,          method            many sweets? All same                                                                                    Why?
                      using paper & ICT                    problem           frequency?                    4 Extension: Link with HD1 work on mode, median, mean, range.
                                                                                                                                                                                      (Highlight importance
                                                                             Order of frequency?...        (But note: Emphasis is on interpretation from graph shape in HD2.
                                                           reason                                          For Interpretation from 3 averages & range see HD3,)                       of sample size).
                     construct pie-charts using ICT
                                                           results           How would we collect the
                      (y8: on paper)                       solution, solve                                 For extensive weather data bank & educational activities, go to the        Discuss pupils'
                     interpret diagrams & graphs          true, false
                                                                                                                                                                                      answers to Smarties.
                      (including pie charts);draw                            Record decisions on which                     Birmingham Weather Station                                 Conclusion.
                      simple conclusions from graphs                         questions and which data
                      shapes                                                 collection method.
L Informal           solve word problems;                                   Introduce investigation   5   Extend to enquiries into other everyday contexts involving discrete        Recap key steps in a     pp 24 - 25
3 survey for          investigate in a range of HD                           Profile of a Typical Y7       data, including grouped data.                                              DH enquiry: OHS
  Profile of a        contexts                                               Pupil. Discuss main steps 6   (Eg: Profile of a Typical Y7 Pupil ', using results of Starter survey.     HD2/4: Steps in
1 Typical Y7                                                                 and agree a plan.             Outcome will be statement such as He / she is a brown haired, 150          Handling Data
  Pupil                                                                      See OHS HD2/4: Steps in       cm tall, pizza-loving, Eastenders fan with a taste for hip hop music
h Record on                                                                  Handling Data                 & environment, plus back-up evidence in form of tables, diagrams
r OHS.                                                                                                     & charts). OR
                                                                                                       7   Conduct a Newspaper New Feature Survey
                                                    KS3 Framework Materials: Year 7                          Tier: Main                    Spring Term : First Half

Class:                                               Week:             Time: 2 hrs               Maths Topic: Unit 8 / HD2

                                                                       Total of 5 hrs            (Part 2 of 2):                                                            Data collection, Display & Interpretation
Les-      Mental             Learning                   Key     Introductory                                                      Main Activity                                              Plenary        Resour
son       Starters           Outcomes                Vocabulary Ideas                                                                                                                                        ces
No.                                                                                                                           Suggested activities:
L4       Write 2                decide which        survey            Which newspaper is        1). Brainstorm how we can find out and lead into activity where ...                        How readable    pp 250 -
         newspaper               data is relevant    questionnaire     easier to read, the                                                                                                  is your maths       255
         sentences on            to an enquiry;      experiment        'Times' or the 'Sun'?     2)... pupils are counting numbers of letters per word and                                  textbook?
1 hr     board. Which is         possible            data                                                                                                                                   (link to word   OHS
         easier to read?         sources             grouped data      Use photocopies of 2      3)... collecting results in a grouped frequency table,                                     length or       HD2/4:
         Why? (-see Qs            (pp 250 - 2)       statistics        articles of similar                                                                                                  sentence        Steps in
         below)                                      class interval    length, one from each     4) ... displaying results using appropriate display tools, and                             length)         Handling
         OR                     plan how to         tally             paper.                                                                                                               OR              Data
         Ask clozed              collect &           table                                       5)... interpreting their displays.                                                         OHS HD2/4:      (can use
         statistical Qs,         organise small      frequency                                                                                                                              Steps in        as hand-
         eg:                     sets of data        data collection   (Literacy link)           6)... drawing conclusions from graph shapes                                                Handling        out or
         Max word                (p254)              sheet                                                                                                                                  Data            enlarge &
         length? Min          design data           database                                    (7)...Extension into HD3: drawing conclusions from 3 averages & range)                     Review          use as
         word length?          collection sheet                                                                                                                                             processes of    poster)
         Sentence              / questionnaire                                                   For data collection and recording, try:                                                     data
         length? Mean?             (p254)                                                                                                                                                   collection >    Photocop-
         Mode? Median?                                                                                                Collecting and Recording Data                                         processing >    ies of the
                                construct bar-                                                                                         (level 1 or 2)                                      displaying >    'Times'
                                 line graphs &                                                                                                                                              interpreting    and the
                                 grouped                                                                                                                                                                    'Sun'
L5       Extract 3               frequency           Ma 1 words:       Introduce a third             Repeat processes of data collection, processing, displaying, interpretation from       Place these 3   pp 24 - 5
         sentences from          diagrams, using     any of -          newspaper, very close         graph shape & conclusion for 3rd newspaper.                                            papers in       The 'Mirror'
         1 of the papers.        paper & ICT                           to one of the other 2.                                                                                               order of        ,'Independ-
1 hr     Average length            (pp 262 - 4)      answer            Unlike the 'Times' and        OR                                                                                     readability.    ent' or
         of sentence?                                evidence          the 'Sun', can you tell       Produce a plan of how pupils would apply these processes, if time allowed, to                          similar
                             interpret              explain           by looking which is           3rd newspaper (in style of a coursework extension, referring to OHS HD2/4:             Give 3 main
         Which average?       diagrams &             explore           easier to read?               Steps in Handling Data in poster form or as a handout.                                 reasons why     OHS
                              graphs; draw           investigate       Why is the data                                                                                                      you decided     HD2/4:
         Range?               simple                 method            processing valuable           OR                                                                                     this.           Steps in
                              conclusions            problem           here?                         Focus mainly on collection and interpretation of grouped discrete data                                 Handling
         (Mention that        from graphs            reason                                                                                                                                                 Data
         we could use         shapes                 results           Predict & test if time.       For interpretation of data, try: Interpreting          Data
         average               (pp 268 - 270)        solution, solve                                                                                                                                        (can
         sentence length                             true, false                                                                                                                                            enlarge &
         or average word     solve word                                                                            'Your Nation' Geographical Data                                                         use as
         length to decide     problems;                                                                                (wide range of statistics on over 100 countries))                                    poster)
         on readability,      investigate in a                                                       OR
         but will focus       range of HD                                                                                     Data Handling Games
         on this more         contexts
         next term.)
                                                   KS3 Framework Materials: Year 7                        Tier: Main                Spring Term : First Half
Class:                                                               Week:             Time: 2 hrs                            Maths Topic: Unit 9a / N & M 3a / Calculations 2
                                                                                                                              (Part 1 of 2):            Mental, written & calculator methods
                                                                                       Total of 4 hrs                                                                                                  Place Value
son    Mental Starters                       Learning                   Key                   Introductory                             Main Activity                             Plenary               Resources
No                                           Outcomes                Vocabulary               Ideas                                     Suggested activities:
L1    Inverse Practice, eg:            understand the 4             operation         What is the cost of 28 Y7 workbooks    Calculations & simple word problems           Use Area calculation       pp 82 - 85
                                        operations as they apply     inverse           at £1.99 each?                         involving x and , including opportunities    for rectangles to
      I'm thinking of a number          to whole numbers &                             Use to compare 3 'levels' of           to:                                           review distributive        OHS
1     and when I ... I get ...,         decimals                     add, sum, total   efficiency from:                                                                     law, eg:                   NM3/1a:
hr    using 1-step calculations:                                     subtract,         1.99 + 1.99 +1.99 +1.99 + ....             relate division to fractions             L = 13cm                   Missing
      19 + ... = 40                       and                        difference        to                                         use commutative law                      W = 8cm                    Numbers
      45  ... = 5                                                   multiply          28 x 1.99                                  use distributive law                     A = 13 x 8
                                       understand the 4             product           to                                         use associative law                        =10 x 8 + 3 x 8 = ...
      and 2-step calculations:                                       divide            30 x 1.99 - 2 x 1.99
      7 + ... - 3 = 25
                                        operations as they apply                                                                  check answers by using inverse
                                        to whole numbers &           multiple          Check understanding of                      operations                               Use Volume
      ... x 4  5 = 8                   decimals                     factor            multiplication as repeated addition,                                                 calculation for
                                                                     quotient          but more efficient; 3rd method as an   For a review activity of place value for      cuboids to practise
      including ( ) if appropriate:
                                      and                            divisor           even more efficient strategy.          decimals, try:                                commutative law, eg:
      2(11 + ...) = 36
                                                                     remainder                                                                                              L = 12cm
      (36  4)  ... = 3                                                               Extend to division as repeated              Birmingham Grid for
                                           know how to use the                                                                                                             W = 6cm
                                                                     commutative       subtraction, eg: using                      Numbers from BGfL                        H = 2cm
      OR                                    laws of arithmetic &
                                                                                       How many dozen eggs is 156?                                                          V = 12 x 6 x 2 =...or
      OHS NM3/1a: Missing                   inverse operations
                                                                                       (show quotient can be expressed as                                                       6 x 12 x 2 =...or ..
      Numbers                                                                          a remainder, a fraction or a                                                         (Turn cuboid around to
                                                                                       decimal)                                                                             show 3 numbers are
L2              '24 Game':                 know & use the order     order of          Use a string of numbers on board to    1). Investigate ways of making different      I'm thinking of a          p 86
      Choose any 4 numbers,                 of operations,           operations        demonstrate different answers with     totals using same 3 numbers.                  number and when I...,
      use all 4 to make 24,                 including brackets       brackets          LTR and scientific calculators.        Eg: Starting with 2,4 and 5 can you make      then ... I get ...What     WS NM3/1b:
1     with any 4 arithmetical                                        calculate                                                numbers 1-10? Biggest number?                 number am I thinking       24 Game
hr    operations                           carry out calculations   calculation       Explain rules of BODMAS.               Smallest number? Number nearest to 0?         of?                        Score Sheet
      (whole class or in pairs)             with more than 1 step    calculator                                               10? ...
                                            using brackets & the     display           Use to write some solutions to 24                                                    Puzzles set by teacher
      Can use for jottings:                 memory, square root      key               Game as single expressions (or         2). Repeat with larger numbers.               (or individual pupils);
      WS NM3/1b: 24 Game                    and sign change keys     enter             equations), eg:                                                                      pupils to suggest how
      Score Sheet                                                    clear                                                    3). Collect results on board using rules of   to write this down.
                                                                     memory            4+ ( 4 X 5 X 1 ) from 1, 1, 4, 5       BODMAS.                                       (linking with later unit
                                                                                                                                                                            on equations A4)
                                                                                                                              4). Use WS NM3/1b: 24 Game Score
                                                                                                                              Sheet to allow pupils to play on pairs.
                                                                                                                              Winning partner writes down their
                                                                                                                              solution using BODMAS rules.

                                                                                                                              Extend to larger numbers, squares and
                                                                                                                              square roots.
Class:                                                              Week:             Time: 2 hrs                                Maths Topic: Unit 9a / N & M 3a / Calculations 2
                                                                                                                                 (Part 2 of 2):             Mental, written & calculator methods
                                                                                      Total of 4 hrs                                                                                                                   Place Value
son        Mental                       Learning                      Key                     Introductory                                       Main Activity                                   Plenary                 Resour
No         Starters                     Outcomes                    Vocabula                  Ideas                                               Suggested activities:                                                   ces
L3    Mental + / -                   round whole + numbers         round             Rounding Introduction                      Activities involving rounding of whole numbers            Recap rules on                pp 42 - 45
      Strategies:                     to nearest 10, 100 or         nearest           Use newspaper headings such as 9000        and decimals in cross-curricular contexts, eg:            rounding, eg:                 pp 92 - 95
      Eg: If 24 + 67 = 91,            1000                          decimal place     Chelsea fans at Saturday's match to                                                                  What is 2945 to nearest
1     What is 2.4 + 6.7?                                            to 1 decimal      raise Qs such as: What might the                 Reading measuring instruments used in              10, 100, 1000?                OHS
hr    Other shortcuts?               round decimals to nearest        place (1       actual attendance have been?                      science, cookery, DT                               Pi is 3.14158 ...What is      NM3/2:
      (include                        whole number or 1d.p.         d.p.)             Smallest? Largest? Were they                     Food values on food packets                        it to nearest whole           Sum
      0.24 + 0.67 ...                                               approximate       rounded to nearest 10, 100, 1000 ...?            Geographical data                                  number? To 1d.p.?             Shortcuts
      2400 + 6700 ...
      and +/- relationship as
                                    consolidate & extend           nearly            Develop using other contexts and                 Diameters of atoms
                                     mental methods of + & -        rough             extend to decimals.                              Circumference of planets                           Recap 'Nearly Numbers'
      in:                                                                                                                                                                                                                Counting
      91 - 24 = ...                  to include FDP,                roughly                                                            Pollution levels in rivers, in ppm                 strategy:
                                                                    partition         +/ - Mental Arithmetic Introduction                                                                  If 1 CD tape is reduced       Stick
      91 - 67 =                      accompanied where
                                                                                      Use OHS from Starter to introduce                                                                    to £0.99, what is the         Newspape
      67 + 24 = ...)                 appropriate by suitable                                                                     For further practice, go to:
                                                                                      strategies involving:                                                                                cost of 2 tapes? … 3?         rs with
      OR                             jottings                                          Counting on & back                                Bitesize Approximations                          What if reduced               numerical
      OHS NM3/2: Sum                 and                                               +/- several small numbers                    For consolidation of reading scales and correct                                     headings
      Shortcuts                      solve simple word                                                                                                                                    to£0.98? … £ 0.90?
                                                                                       partition                                          metric units from scales Level 4:
      OR                             problems mentally                                                                                                                                     OR
                                                                                       nearly doubles                                                                                                                   Cross-
      Counting Stick: Count                                                            nearly numbers
                                                                                                                                                 Jack the Builder                           Review 'Nearly
      on or back in fractions                                                                                                    Or, for a mental maths skills workout against the         Numbers' strategy for         curricular
                                                                                       the +/- relationship
                                                                                                                                                                                           repeated addition of 9,       data
      & decimals from 0, 5,                                                            extending known sums to theirmultiples    clock, try: Mental Gym from BGfL
      & 10                                                                                                                                                                                 then 8; 90, then 80, etc.

L4    Practice of simple             consolidate & extend          Ma 1 words:       X &  Mental Arithmetic Introduction             Further oral, written, practical activities that   Recap 'Nearly Numbers'        pp 96 - 101
      known FDP                       mental methods of x &         any of -          How many ways can you find to work                require use of strategies for X and               strategy:                     pp 28 - 31
      Equivalents                      to include F, D, %,                           out 2.4 x 50?                                                                                        Extend CD tapes
1                                     accompanied where             answer            Use this question & similar to                   FDP & word problems (or postpone until             question in L1 to             OHS
hr    If 1/2 = 50% = 0.5,             appropriate by suitable       evidence          introduce strategies (p.96) that use:             N5).                                               multiples: cost of 10         NM3/3:
      what is 1/4? 1/8?               jottings                      explain               factors                                                                                         tapes? 20? 25?                Equivale
      1/16? ...                      and                            explore               partitioning                          Conversion rules between metric units (formally                                         nce
                                     solve simple word             investigate           doubling / halving                    addressed in Unit 9 / N&Mc)
                                                                                                                                                                                           Recap range of                OHS
      OR                              problems mentally             method                x / relationship                     Eg: OHS NM3/4: Metric System
                                                                                                                                                                                           strategies used in
      Recap multiplication           break a complex               problem                                                                                                                                              NM3/4:
      tables                                                        reason                                                                                                                 lesson, eg:                   Metric
                                      calculation into simpler                        Repeat with  questions, such as:           For complex calculations set in a Theme park,
                                                                                                                                                                                           16 x 7.5
                                      steps, choosing & using       results                                                      explore 'Theme Park' at:                                                                System
      OR                                                            solution, solve                                                                                                        4.23 x 50
                                      appropriate & efficient                         How many ways can you find to work                    Roller Coaster Queues                          1/2 x 6
      OHS NM3/3:                      methods & resources,          true, false       out 504  14?
      Equivalence                                                                                                                                                                          246  12
                                      including ICT
                                                                                                                                 For an number investigation into newspaper                465  15
                                     present & interpret
                                                                                                                                 advertising costs, go to 'Newspapers' at:
                                      solutions in the context of                                                                                                                          OR
                                      the original problem;                                                                           Advertising: What's It Worth?                        Recap simple fraction -
                                         and                                                                                                                                               decimal equivalents
                                     explain & justify                                                                                                                                    using OHS NM3/3:
                                      methods & conclusions                                                                                                                                Equivalence
                                      orally & in writing
                                                       KS3 Framework Materials: Year 7                                Tier: Main               Spring Term : First Half
Class:                                                                             Week:                 Time: 3 hrs                          Maths Topic: Unit 10 / A 3 / Sequences 1
Note: A3 is an ambitious unit. If all learning outcomes in Lessons 3-5 cannot be                                                              (Part 1 of 2):                   Integers, Powers & Roots
achieved, they can be re-addressed in A5, Summer Term. The 2 Key Objectives
in A5 are1)Graphs & 2) Word problems & investigations                                                    Total of 6 hrs                                                                  Sequences, Functions & Graphs
son    Mental                              Learning                                   Key                      Introductory                             Main Activity                        Plenary             Resources
No     Starters                            Outcomes                                Vocabulary                  Ideas                                    Suggested activities:
L1    Find all the            recognise and use factors and primes (less          factor                OHS A3/1a:Factorpillars:         1). Activities to find prime, square, odd,      Factors of 64 or       pp 52 - 59
      factors pairs            than 100).                                          common factor         Discuss why Factorpillar 12 has 3and even numbers, factors & HCFs; be            72? - list in order,
      for numbers 1                                                                highest common                                         able to explain. Eg:
                                                                                                         pairs of legs); the other 2 factor                                               strategies for         OHS
1     - 20 and list           recognise multiples and find the lowest                factor, (HCF)      pillars? (1 prime & 1 square) -   - Investigate factorpillars with 1 leg (1),    ensuring a list is     A3/1a:Factor
hr    on board.                common multiple                                     prime                                                  2 legs (primes - babies!), 4 legs, 6 legs,      complete               -pillars
                                                                                   prime factor          Explain meaning of a prime       odd no. of legs (square numbers);               OR
      Note those              recognise first few triangular & square             factorise             number, square number; factor, - - Which factors do any 2 factorpillars          Is 1 a prime no?       OHS A3/1b
      with only 1              numbers to at least 12x12, &                        square number         common factor, odd, even.             have in common?                            Why?                   Mystery
      factor...2               corresponding roots                                 squared                                                2) Divisibility tests                           OR                     Factorpillars
      factors...even                                                               62 as 'six squared'    (DISPLAY WORK OPPORTUNITY)      OR Revise using:                                OHS A3/1b
      no. of factors          use the square root key                             65 as 'six 6 to the                                             Revising Special Numbers               Mystery
                                                                                   power 5' …                                                                                             Factorpillars
L2    Start at 0 &                                                                 triangular            WS A3/1:Multiplication Grid          1) Activities on multiples, eg:             Give 6 numbers         pp 52 - 59
      count up in                                                                     number             : ''Why do some answers occur        WS A3/2:Multiples on a 100-Grid             (2, 36, 1, 9, 32,)
      2's, 5's and                                                                 divisor               more than once? ...common            Use to reinforce multiples, prime           and ask Qs such        WS
1     10's. (Whole                                                                 divisible             multiples (CM) ... LCMs              numbers, factors. Extend to CMs, eg:        as:                    A3/1:Multipl-
hr    class)                                                                       divisibility test                                          find CMs eg: of 5 and 6 on grid; LCM?       Which ones are         ication Grid
      Extend to                                                                                          AND                                                                              square?
      counting up in                                                               indices                                                    2)    Activities on square and square       prime? multiple of     WS
      9's (+10 -1                                                                  product               'where are the square numbers;            roots, eg:                             8?                     A3/2:Multiples
      strategy); then                                                              multiple              why?'                                 WS A3/1:Multiplication Grid                factor of 8?           on a 100-Grid
      in 6's, 7's &                                                                lowest common                                                - position of square nos on grid          both a square and
      8's.                                                                         multiple (LCM)                                               - diagrams of growing squares,            a multiple of 4?       WS A3/3:
                                                                                                                                                  mappings                                                       Matchstick
      OR                                                                           property                                                     - and table of coordinate pairs;          OR                     Patterns 1 ,
      Review                                                                       consecutive                                                  - link with graphs
      square                                                                       classify                                                   WS A3/3: Matchstick Patterns 1 for          see 6 Qs on p9
      numbers                                                                                                                                 growing patterns (inc. squares)
L3    'What Next          - generate terms of a simple sequence given a            sequence              Start with matchstick activity on    (See stopping point in Unit A1:)            Recap the method       pp 144-155
      and Why?               rule:                                                 term                  OHP or board;                                                                    of how to find the
      Activity: :          - term-to-term &                                        nth term              Sparks 8: Sequences 1: Q1 - next ?   1)    Introduce activity in WS A3/3:        10th term; any         Sparks 8:
1     Write on OHP         - position-to-term                                      consecutive           Q2 - Describe sequence (+3 each            Matchstick Patterns 1 and repeat      term.                  Sequences 1
hr    the 1st number                                                               rule,                 time)                                      Qs 1 - 6                              Review either use
      eg: 5, What is       generate sequence from practical contexts              relationship          Q3 - Why? (refer to 3 extra                                                      of nth term or         WS A3/3:
      the next              and describe the general term in simple cases          generate              matchsticks in context)                                                          formula as             Matchstick
      number? Eg:
                                                                                   predict               Q4 - 10th, 50th term?                                                            appropriate            Patterns 1
      1st is    5 yes      solve word problems & investigate in
      2nd is 10 no                                                                 continue              Q5 - General term? (nth term has
                            range of number & algebra contexts
      2 is 7 yes                                                                   increase,             3n+1, because ...)                                                               OR                     OHS A3/3 :
      3rd is 9 yes         identify information to solve a problem and            decrease              Q6 - Formula -words? Using                                                       OHS A3/3 : nth         nth Term
            WHY?           represent problems mathematically: symbols             finite, infinite      letters? (Link with A2)                                                          Term
                            / diagrams / tables / graphs
                                                       KS3 Framework Materials: Year 7                                Tier: Main               Spring Term : First Half
Class:       Note: A3 is an ambitious unit. If all learning      Week:           Time: 3 hrs                                 Maths Topic: Unit 10 / A 3 / Sequences 2
outcomes in Lessons 3-5 cannot be achieved, they can be re-                                                                  (Part 2 of 2):                        Sequences, Functions & Graphs
addressed in A5, Summer Term. The 2 Key Objectives in A5
are1)Graphs & 2) Word problems & investigations                                  Total of 6 hrs
Les-            Mental                    Learning                Key                     Introductory                                      Main Activity                                     Plenary                   Resour-
son             Starters                  Outcomes               Vocabu-                  Ideas                                                                                                                           ces
No.                                                               lary                                                                       Suggested activities:
L4        OHS A3/3 : nth                                         Previous list   Sparks 8: Sequences 1                       1)   Sequences requiring pupils to produce                Use mappings produced            pp160 - 163
          Term                           express simple         plus:           OR                                               mapping / inputs / outputs .                         to introduce term function       OHS A3/3 :
                                          functions in word,     input           Sparks 9: Sequences 2                                                                                 & notice some properties         nth Term
1 hr      Find next 2 terms               then using symbols;    output                                                      2)   Link to nth term, eg: nth term is 3n +1              of expressions:
          Find nth term                   represent in           function        Represent with mapping, function                                                                                                       Sparks 8:
                                          mappings               function        machine.                                    3)   Link to Equations (A2), eg: y = 3n + 1               Can write in > 1 way, eg:        Sequences
                                                                   machine       Mappings from other sequences:                                                                         (c-1)x2 or c x 2 - 2            1
                                                                 mapping         Given inputs & outputs, what is the          OR Review sequence patterns and general rules,           Can say more simply, eg;
                                                                                 rule?                                                         using:                                    d+1 +2 or d+3                  Sparks 9:
                                                                 and Ma 1        Inverse: Given output & rule, input?              Revising Patterns and Rules                                                          Sequences
                                                                 words: any      What is a mapping?                                                                                    Can invert it, eg:               2
                                                                 of -                                                                                                                   X + 4 = Y or X = Y - 4
L5        Use counting stick         generate terms of a                        Q: 'What is 4 x 8? How did you work it                       Activities that require                  Harry & Rajid start with         pp 148 - 153
          to generate                 simple sequence, given     answer          out if you didn't know it by heart?'        - term-to-term approach, eg:                              £1 pocket money in week
          sequences from a            a rule:                    evidence                                                          1st term is 100, each term is 10 times              1 of the new year. Which         Counting
1 hr      rule:                       - term-to-term &           explain         Compare term-to-term approach -                   the one before; 1st 5 terms?                        pocket money rule is             sticks
          Eg: start with 3.           - position-to-term)        explore          (Start No is 8, keep adding 8: 8, 16,            describe sequence in words                          better? - Why? -
          Keep doubling and                                      investigate     24, 32)                                     - position-to-term approach, eg:                          Harry: 2 x week no. + 1          Graphical
          adding 1; finishing        solve word problems        method          with position-to-term approach -                  nth term of a sequence is 2n - 1, 1st 5 terms?      Rajid: 2 x (week no. + 1)        calculators
          number (end of              & investigate in range     problem         (1st. term is 1 x 8, 2nd is 2x 8,                 Describe sequence (eg: odd nos)
          stick)?                     of number & algebra        reason           3rd is 3 x 8, 4th is 4 x 8)                OR                                                        What do they each get in
          (Review / extend            contexts                   results                                                     Graphical Calculator Investigation: p 148                 Week 100? (position-
          sequences used in                                      solution,       Highlight difference, which is easier for   OR                                                        term).
                                     identify information       solve
          A1).                                                                   early terms, late terms...?                 (Spreadsheets to explore both approaches, see page
                                      necessary to solve a       true, false                                                 148)
                                      problem and
                                                                                 Link to mappings                            Extend to word problems, eg:
                                     represent problems
                                      mathematically:                                                                             Crossing the River from BGfL
                                      symbols / diagrams /
                                      tables / graphs
L6        Review plotting &          generate coordinate        coordinates     Introduce co-ordinate pairs, eg :           Activities to include:                                    OHS A3/2: Co-ordinate            pp 164 - 171
          reading coordinates         pairs that satisfy a       coordinate                                                  1) generating coordinate pairs from equation              Grid
          in 1st quadrant (> 4th      simple linear rule; plot      pair/point   "Give rule such as                          2) generating table of x, y values from equation          Oral work with whole             OHS A4/2:
1 hr      quadrant).                  graphs of simple           x-coordinate    C = 3D+ 4, tell me a pair of co-            3) plotting points, drawing a line through                class: generate family of        Car Hire
                                      linear functions, (in      y-coordinate    ordinates that C and D could be".               points & extending line                               graphs for y=x, y=2x,
          Eg:                         form y = ..x...) using     grid, origin    Plot on a coordinate grid.                  4) read off intermediate points; check they fit rule      y=3x, y=4x                       OHS A3/2:
                                      paper & ICT                axis, axes                                                  5) extend this to fractions & negative nos                Use to recap correct methods     Co-
          OHS A4/2: Car               and                        graph           OHS A3/2: Co-ordinate Grid                  6)  begin to notice key graph features (of form y = mx)   for plotting and line drawing.   ordinate
                                                                                                                                                                                       Use to highlight that;
          Hire                       recognise straight-line    variable        Link with secure learning of previous       OR plot given shapes, using:                                                               Grid
                                                                                                                                                                                       all go through origin
                                      graphs parallel to x-      straight-line   A3 lessons, eg; sequences, mappings,         Coordinate Shapes from BGfL OR                           all are straight lines
                                      axis or y-axis                  graph      nth term & formulae                                                                                   vary in steepness
                                                                 equation (of                                                The Coordinate Game from BGfL
                                                                 a graph)
                                                      KS3 Framework Materials: Year 7                                Tier: Main               Spring Term : First Half
Class:                                                      Week:             Time: 2 hrs               Maths Topic: Unit 9b / N & M 3b / Calculations 2
                                                                                                        (Part 1 of 1):                           Mental, written & calculator methods
                                                                              Total of 2 hrs                                                                                                                      Place Value
Les-      Mental                  Learning                     Key     Introductory                                                      Main Activity                                          Plenary             Resour
son       Starters                Outcomes                  Vocabulary Ideas                                                                                                                                         -ces
No.                                                                                                                                   Suggested activities:
L1       OHS N1/1:            multiply 3-digit by 2-       multiply          Introduce problem                             Activities involving long multiplication.                          What is 239 x        p 104
         Place Value           digit numbers; extend        multiplication    leading up to X of two           Focus on grid method for a number of problems. (Eg: see p 104)                 41? Grid
         chart                 to multiplying decimals      divide            nos with at least 2-              (Rough estimate by approximating before each calculation.)                     method? Other        OHS
1 hr     - an activity (to     (1d.p. & 2 d.p.) by 1-       division          digit; ask pupils to                                                                                             methods?             N1/1:
         practice x facts      digit whole numbers          subtract          explain how they                 Explain distributive law and link to grid method                                                    Place
         to 10 x 10).                  (p 104)              subtraction       solved it.                        Eg: 26 x 19? Estimate: 25 x 20 = 500                                                                Value
                              make and justify             add, addition     Eg: 5 minibuses with               Calculation: 26 x 19 = 20 x 19 + 6 x 19 OR 26 x 20 - 26 x 1 = 494                                  chart
                               estimates &                                    19 pupils in each one.
                                                            guess, estimate                                    Discuss other informal methods of multiplication as appropriate.
                               approximations of                              Total? 15 buses? 26
                                                                              buses? 243 buses?                Check results from order of magnitude & by working backwards
                              check a result by            not enough        Review understanding
                               considering whether it       approximately     that X is repeated        For practice in speed multiplication of two 2-digit numbers, play:
                               is of the correct order of       equal to      addition and highlight                                 Batter's Up Baseball
                               magnitude and by                 (& symbol)    one efficient method,
                               working the problem          roughly           eg: grid method.
                               backwards                    nearly
                                        (p110)              too many
L2       OHS N1/3:            divide 3-digit by 2-digit    too few           Introduce problem for     Activities involving long division                                                     1) Return to         pp 102,
         Growing/Shrin         numbers; extend to           enough             of two 2-digit                                                                                                 Minibus              106, 110
         king Snakes to        dividing decimals (1d.p.                       numbers.                  1) Focus on chunking method using a range of problems.                                 problem :
1 hr     practise powers                                                                                       Carry out rough estimate by approximating first.
                               & 2 d.p.) by 1-digit                           Share different pupils'                                                                                          50019=26            OHS N1/3:
                                                                                                               (Chunking links division to repeated subtraction, in this method, in chunks)
         of 10                 whole numbers                                  methods.                                                                                                         Remainder 6.         Growing/S
                                                                                                                Eg: 494  19 ?
                                       (p106)                                 Review understanding                                                                                             Is this 26 or 27     hrinking
         OR                                                                   that division is          19      I 494          Estimate: 494  19 is approximately 500  20 = 50  2 = 25      minibuses?           Snakes
                              make and justify                               repeated subtraction          -    380            (19 x 10 = 190, so 19 x 20 = 380, subtract 20 x19)             Should you
         Counting stick:       estimates &                                    and highlight one             =    114                                                                           always round         Counting
         subtracting 2-        approximations of                              efficient method, eg:            - 114            ( 6 x 19 = 114, so subtract 6 x 19)                            up? Why?             stick
         digit numbers         calculations                                   chunking method.               =     0            Ans: 20+6 =26
         such as 19, 26                  (p102)                                                                                                                                                OR
         eg: from 100;                                                        Eg: 19 pupils per         2) Focus on Listing method to solve a range of problems.
         (to practise for     check a result by                              minibus, how many                (Listing links division to repeated subtraction).                              2) Discuss
         division)             considering whether it                         buses for all of Y7 (95                                                                                          informal
                                                                              pupils)?                       Eg: 28519? 19, 38, 57, 76, 95, 114, 133, 152, 171, 190, ...List too              methods of
                               is of the correct order of
                                                                              Lower School (285)?       long so…                                                                               division for
                               magnitude and by
                               working the problem                            Whole school (500)?                   015        19's in 2? 0                                                    decimals, eg:
                                                                                                             19 I 2 8 5
                               backwards                                      (last one has a                                                                                                  2.4 x 1.2.
                                                                                                                               19's in 28? Look at list: 1x19=19 Rem 9
                                        (p110)                                Remainder
                                                                                                              - 19            bring down 5
                                                                                                                 0 9 5.       19's in 95? Look at list: 5x19=95
                                                                              Discuss rounding                 - 95
                                                                              up/down issue.                      00         no Rem: stop. Ans: 15
                                                                                                               Discuss other informal methods of division s appropriate.
                                                                                                               Check results from order of magnitude & by working backwards.

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