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| 1. PLACE VALUE:
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Decimal notation
& PV; x & ÷ of integers & decimals
by 10, 100, 1000; explain effect |
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| 2. PLACE VALUE:
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Decimals- compare
& order; know measurements must be compared in same
units |
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| 3. PLACE VALUE:
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Negative numbers:
understand as positions on a no. line; order, + &
- in context |
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| 4. CALCULATIONS, MENTAL: |
Rapid recall of number facts,
including positive integer complements to 100 & X
facts to 10 x 10, & associated ÷ facts |
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| 5. CALCULATIONS, MENTAL: |
Estimations & approximations |
N&M3, N5 |
| 6. CALCULATIONS, WRITTEN: |
Use standard column procedures to + & - whole nos.
& decimals (1 or 2 dps)
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N5 |
| 7. CALCULATOR METHODS: |
Enter numbers & interpret
display (eg: decimals, money ...) |
N5 |
| 8. SOLVING
PROBLEMS: |
Solve
problems & investigate in a range of contexts:
Number |
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9. SOLVING PROBLEMS:
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Compare & evaluate solutions
to problems |
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| 1. PLACE VALUE: |
Rounding whole numbers & decimals |
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| 2. CALCULATIONS: |
All 4 operations for whole nos. & decimals; arithmetic
laws & BODMAS |
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| 3. CALCULATIONS: |
BODMAS |
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| 4. CALCULATIONS: |
Estimations & approximations |
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| 5. CALCULATIONS, MENTAL: |
Methods for whole nos &
FDP, plus jottings; solve simple word problems
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N5 |
| 6. CALCULATIONS, WRITTEN: |
Long multiplication &division -
whole nos & decimal nos |
N5 |
| 7. CALCULATOR METHODS: |
Check result using order of
magnitude & by working backwards |
N2, N4, N5 |
| 8. CALCULATOR METHODS: |
Calculations with > 1 step using: ( ), +/-, square
root and M keys |
N5 |
| 9. MEASURES: |
Names & abbreviations of units |
SSM1 |
| 10. MEASURES: |
Measure / estimate / calculate / solve problems in everyday
contexts
for: L, A, M, C, T |
SSM1 |
| 11. MEASURES: |
Convert 1 metric unit to another |
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| 12. MEASURES: |
Read & interpret measuring scales |
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| 13. SOLVING PROBLEMS: |
Break complex calculation
into simpler steps - appropriate & efficient operations,
methods and resources, including ICT |
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| 14. SOLVING PROBLEMS: |
Present & interpret solutions in context of original
problem |
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15. SOLVING PROBLEMS:
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Explain & justify methods
& conclusions, orally & in writing
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| 1. PLACE VALUE: |
Multiples, factors (divisors), CF, LCM, primes (<100);
simple divisibility tests |
A3 |
| 2. CALCULATIONS, MENTAL: |
Rapid recall of number facts, including + integer complements
to 100 |
N1 |
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& x facts to 10 x 10, & associated ÷
facts |
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| 3. CALCULATIONS, MENTAL: |
Methods for whole nos & FDP, plus
jottings; simple word problems |
N2, N&M3 |
| 4. CALCULATIONS, MENTAL: |
Estimations & approximations |
N1, N&M3 |
| 5. CALCULATIONS, WRITTEN: |
Use standard column procedures to + & - whole nos.
& decimals (1 or 2 dps) |
N1 |
| 6. CALCULATIONS, WRITTEN: |
Long multiplication &division
- whole nos & decimal nos |
N3 |
| 7. CALCULATOR METHODS: |
Check result using order of magnitude
& by working backwards |
N2, N4, N&M3 |
| 8. CALCULATOR METHODS: |
Calculations with more than 1 step using: ( ), +/-,
square root and M keys |
N1 |
| 9. CALCULATOR METHODS: |
Enter numbers & interpret display (eg:
decimals, %s ...) |
N1 |
| 10. SOLVING PROBLEMS: |
Break complex calculation into
simpler steps - appropriate
& efficient operations, methods and resources,
including ICT |
N&M3 |
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INTRODUCTION:
This strand contains the elements of place value, mental,
written and calculator-based calculations and the problem-solving
skills of comparing, evaluating, explaining & justifying
approaches & solutions whilst working toward more
complex calculations. These notes highlight some key features
you may wish to include in your delivery.
- WHY MEASURES in NUMBER? The
numerical measurement LO's are arguably well placed
in N&M3 because they include estimating, calculating
(including metric conversion) and problem-solving
skills. The inclusion of estimation of everyday measurements
infers a practical approach. Although the unit suggests
a teaching focus on the Measures content for 2/3 of
the 8 hours teaching time, there is an equally valid
argument for a much more integrated approach. For
example:
'When will you be 1 million
seconds old?' or
'What is 1000 (100000, etc)
seconds in days, hours, minutes and seconds?'
There are also several opportunities
listed within the 8-hour time allocation for use of
measuring contexts as part of the Calculations content.
Clearly, enormous scope for imaginative planning in
this 8-hour unit.
- PROBLEM SOLVING & PUPIL
CONFIDENCE: Because there is a problem-solving key
objective in each unit, attainment of the place value
and calculation objectives needs to be secure. Hence,
a notable feature in the focus of each unit is the
inclusion of approaches that are likely to increase
pupils' confidence & independence in using and
applying their knowledge, skills & understanding
within a variety of contexts. These include rapid
recall of number facts & tables, estimation and
approximation of answers & calculator handling
efficiency. There is also a clear progression from
the N1 skill of merely comparing a& evaluating
solutions - an ideal opportunity for oral discussion
re different methods - to the N&M3 skill of explaining
& justifying methods & conclusions. Because
the latter relies upon use by pupils of more efficient
& appropriate methods & of an ability to justify
those methods, attainment of this L.O. is a clear
indicator of pupils' confidence in Level 5 Calculations.
- The basic pattern for each unit
is as follows:
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N1
6h Autumn Term Key L.O's: Word problems & investigations
- number, compare & evaluate solutions
The N1 L.O.s are pre-requisites to both the N&M3 and
A2 units. It builds directly upon Y5/6 Programmes relating
to Place Value (including decimal notation)and Calculation
methods (mental, written & calculator). Its overall
aim is to consolidate pupils' understanding of whole nos,
decimals and negative numbers so that further skills in
rounding, ordering, adding & subtracting are well
understood & clearly established. These include rapid
recall of positive integer complements to 100 and multiplication
facts to 10 x 10. Ability to derive associated division
facts from multiplication facts is also included and extended
in Y8 programme to decimals.
Key L.O. is a problem-solving one and therefore content-based
learning needs to be secure. Efficient calculation methods
are also developed here and again in N5. N1 L.O.s are
also pre-requisites to A2. |
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N&M3
8h Spring Term Key L.O's: 1. BODMAS 2. Mental methods
for FDP 3. Long X & ÷ whole nos & decimals
4. Checking answers from order of magnitude 5. Metric
conversion 6. Reading scales 7. Breaking down complex
calculations 8. Explaining & justifying
Whereas N1 Calculation methods concentrate on + &
- , N&M3 encompasses all 4 operations. The emphasis
here is on a broad-based but in-depth understanding of
the laws of arithmetic and of BODMAS. Although a variety
of written methods can be explored and evaluated in all
3 units, column addition is targeted in N1 and long X
and ÷ in N&M3 (extending to decimals). Also
included here, and in N5, are mental arithmetic strategies
for whole numbers, decimals & fractions (see N2).
Measures L.O.s are included here as noted above. N&M3
L.O.s are also pre-requisites to N4. |
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N5
8h Summer Term Key L.O's: 1. Mental methods for FDP 2.
Long X & ÷ for whole numbers & decimals
3. Checking from magnitude 4. Equivalence of FDP 5. Complex
calculations
As expected, the main aim of this unit is to consolidate
and extend the N1>N3 strand (Calculations) and the
N2>N4 strand (FDPRP), in a more integrated manner.
Here, secure skills & understanding of mental, written
& calculator-based methods of calculation are applied
to FDPRP, with the ultimate goal of using & applying
them in complex problem-solving situations. (See key L.O).
As noted for other Summer Term units, ICT methods are
proposed primarily to consolidate & extend. Use of
factors as divisors (also CFs), multiples (and LCMs) and
prime numbers are formally included here, and extend the
Y5/6 Programme (where simple multiples and factors were
introduced) and unit A3. Divisibility tests, also introduced
in Years 5 and 6, are linked more formally here to factors
and multiples. |
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