Mathematics Key Learning Indicators of Performance: … · including making nets. Child F can...
Transcript of Mathematics Key Learning Indicators of Performance: … · including making nets. Child F can...
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
Number – number and place value Number – addition and subtraction Number – multiplication and division
Count forwards or backwards in steps of integers, decimals,
powers of 10.
Child F joins in with class counting. She is confident with
counting in decimal steps and uses her mental calculation
strategies to help her identify the next term, such as in the
sequence 3.242, 3.257, 3.272. She can also count forwards and
backwards through 0.
Read, write, order and compare numbers up to 10 000 000 and
determine the value of each digit.
Through all of her written work, Child F demonstrates the
ability to read and write both whole numbers with up to eight
digits, understanding the value of the digit according to its
place.
Identify the value of each digit to three decimal places.
Child F consistently identifies the value of decimal digits. She
understands tenths, hundredths and thousandths and knows
that ten thousandths has the same value as one hundredth etc.
Identify, represent and estimate numbers using the number line.
See Sample A
Order and compare numbers including integers, decimals and
negative numbers.
See Sample B
See Sample C
Find 0.001, 0.01, 0.1, 1, 10 and powers of 10 more/less than a
given number.
During starter sessions, Child F is able to identify numbers
which are 0.001, 0.01, 0.1, 1, 10, 100, 1000, 10 000 and 100 000
more or less than a given number, including where boundaries
are crossed. She uses her mental calculation skills to help her.
Round any whole number to a required degree of accuracy.
See Sample D
Round decimals with three decimal places to the nearest whole
number or one or two decimal places.
See Sample E
See Sample F
Multiply and divide numbers by 10, 100 and 1000 giving
answers up to three decimal places.
See Sample G
Choose an appropriate strategy to solve a calculation based
upon the numbers involved (recall a known fact, calculate
mentally, use a jotting, written method).
See Sample K
Select a mental strategy appropriate for the numbers in the
calculation.
See Sample L
Recall and use addition and subtraction facts for 1 (with
decimals to two decimal places).
See Sample M
Perform mental calculations including with mixed operations
and large numbers and decimals.
See Sample N
Add and subtract whole numbers and decimals using formal
written methods (columnar addition and subtraction).
See Sample O
Use estimation to check answers to calculations and determine,
in the context of a problem, an appropriate degree of accuracy.
Use knowledge of the order of operations to carry out
calculations.
See Sample P
Solve addition and subtraction multi-step problems in
contexts, deciding which operations and methods to use and
why.
See Sample Q
Solve problems involving all four operations, including those
with missing numbers.
See Sample H
See Sample I
See Sample M
See Sample P
See Sample Q
See Sample X
Choose an appropriate strategy to solve a calculation based
upon the numbers involved (recall a known fact, calculate
mentally, use a jotting, written method).
See Sample K
Identify common factors, common multiples and prime
numbers.
See Sample R
Use partitioning to double or halve any number.
During starter sessions, Child F uses partitioning strategies to
support her doubling and halving, for example, she was able to
halve 0.76 by partitioning it into 0.6 and 0.16 and halving each.
Perform mental calculations, including with mixed operations
and large numbers.
Child F uses her knowledge of tables, related facts, doubling,
halving and partitioning to help her to mentally multiply and
divide. When asked how she would solve 942 ÷ 6, she replied
‘I’d do it mentally. I can partition it into 600, 300 and 42
because they are all multiples of 6. 600 ÷ 6 is 100, 300 is half of
600 so 300 ÷ 6 is 50 and 42 ÷ 6 is 7 so the answer is 157.’
She was also asked to solve the problem ‘Three pens cost one
pound fifty pence altogether. How much would seven pens
cost? She knew the answer was £3.50 and when asked how she
knew, she replied ‘I have to find the cost of one pen first, so
that is 50p because it is £1.50 divided by 3. Then I timesed it by
7to make £3.50.’
See Sample N
Multiply multi-digit numbers up to 4 digits by a two-digit
whole number using the formal written method of long
multiplication.
See Sample S
Multiply one-digit numbers with up to two decimal places by
whole numbers.
See Sample T
Divide numbers up to 4 digits by a two-digit whole number
using the formal written methods of short or long division, and
interpret remainders as whole number remainders, fractions, or
by rounding, as appropriate for the context.
See Sample U
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
Number – number and place value (continued)
Number – multiplication and division (continued)
Use negative numbers in context, and calculate intervals across
zero.
See Sample I
Describe and extend number sequences including those with
multiplication and division steps, inconsistent steps, alternating
steps and those where the step size is a decimal.
See Sample H
Solve number and practical problems that involve all of the
above.
See Sample H
See Sample I
See Sample J
Use written division methods in cases where the answer has up
to two decimal places.
See Sample V
Use estimation and inverse to check answers to calculations
and determine, in the context of a problem, an appropriate
degree of accuracy.
Use knowledge of the order of operations to carry out
calculations.
See Sample P
Solve problems involving all four operations, including those
with missing numbers
See Sample W
See Sample X
See Sample Y
See Sample Z
Child F can confidently answer questions such as, “I’m thinking
of a number. I multiply it by 7 and then subtract 5. The answer
is 58. What is my number?” She understands the concept of
inverse and can solve these problems mentally.
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
Number – fractions Geometry – properties of shapes Measurement
Compare and order fractions, including fractions > 1 (including
on a number line).
See Sample AA
Use common factors to simplify fractions; use common multiples
to express fractions in the same denomination.
Child F effectively uses her knowledge of factors and multiples to
enable her to change the forms of fractions.
See Sample AA
See Sample AB
Recall and use equivalences between simple fractions, decimals
and percentages, including in different contexts.
When asked to calculate the cost of a £20 item in a 5% off sale,
Child F explained ‘To find 5%, you can find 10% and then halve
it. 10% is the same as 10100
, or 110
. So I divide 20 by 10 which is 2
and then halve it to get 1. £20 take away £1 is £19.’
See Sample AC
Associate a fraction with division and calculate decimal fraction
equivalents (e.g. 0.375 and 3
8).
Add and subtract fractions with different denominators and
mixed numbers, using the concept of equivalent fractions.
Child F knows that fractions have to have the same denominator
to enable them to be added or subtracted. She effectively uses
her knowledge of multiples to do this.
See Sample AD
Multiply simple pairs of proper fractions, writing the answer in its
simplest form (e.g. 1
4 x
1
2 =
1
8).
See Sample AE
See Sample AF
Divide proper fractions by whole numbers (e.g. 1
3 ÷ 2 =
1
6).
Find simple percentages of amounts.
See Sample AG
See Sample AH
Solve problems involving fractions.
See Sample AI
Solve problems which require answers to be rounded to
specified degrees of accuracy.
Solve problems involving the calculation of percentages (e.g. of
measures and such as 15% of 260) and the use of percentages
for comparison.
See Sample AJ
Compare/classify geometric shapes based on the
properties and sizes.
See Sample AK
Draw 2-D shapes using given dimensions and angles.
See Sample AL
Illustrate and name parts of circles, including radius,
diameter and circumference and know that the diameter
is twice the radius.
Child F can name the parts of a circle correctly. Through
investigation she identified the relationship between
radius and diameter.
See Sample AM
Recognise, describe and build simple 3-D shapes,
including making nets.
Child F can recognise, name and describe the properties
of cube, cuboid, pyramid (variety of different shaped
bases), sphere, hemisphere, cone, cylinder, prism (variety
of different shaped end faces), tetrahedron, octahedron
and dodecahedron. She identifies faces and curved
surfaces on shapes. She can identify where faces are
parallel or perpendicular to one another.
See Sample AN
Recognise angles where they meet at a point, are on a
straight line, or are vertically opposite, and find missing
angles.
See Sample AO
See Sample AP
See Sample AQ
Find unknown angles in any triangles, quadrilaterals,
regular polygons,
See Sample AP
See Sample AQ
Use, read and write standard units of length, mass, volume and
time using decimal notation to three decimal places.
Child F understands what the abbreviations mm, cm, m, km, g, kg
and cm3 stand for and uses them in her work. She can also record
time to two decimal places.
Convert between standard units of length, mass, volume and time
using decimal notation to three decimal places.
Child F uses her knowledge of place value and multiplying and
dividing by 10, 100 and 1000 to convert between metric
measures. She knows the relationship between seconds, minutes,
hours and days, and uses her mental multiplication and division
strategies and knowledge of related facts to convert these.
See Sample G
Convert between miles and kilometres.
See Sample AR
Recognise that shapes with the same areas can have different
perimeters and vice versa.
See Sample AS
Calculate the area of parallelograms and triangles.
See Sample AT
See Sample AU
Recognise when it is possible to use formulae for area and
volume of shapes.
See Sample AT
See Sample AU
See Sample AV
Calculate, estimate and compare volume of cubes and cuboids
using standard units, including cubic centimetres (cm3) and cubic
metres (m3), and extending to other units (e.g. mm3 and km3).
See Sample AV
See Sample AW
Calculate differences in temperature, including those that involved
a positive and negative temperature.
Child F uses a number line to calculate differences in
temperature. When calculating between negative and positive
temperatures, she uses two jumps, one from the negative to the
0, and one from the positive to the 0.
Solve problems involving the calculation and conversion of units
of measure, using decimal notation up to three decimal places
where appropriate.
See Sample AX
Geometry – position and direction
Describe positions on the full coordinate grid (all four
quadrants).
See Sample AY
Draw and translate simple shapes on the coordinate
plane, and reflect them in the axes.
See Sample AY
See Sample AZ
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
Ratio and Proportion Algebra Statistics
Solve problems involving the relative sizes of two quantities
where missing values can be found using integer
multiplication/division facts.
See Sample BA
Solve problems involving unequal sharing and grouping using
knowledge of fractions and multiples.
See Sample BB
Solve problems involving similar shapes where the scale factor is
known or can be found.
See Sample BC
Use simple formulae.
See Sample AT
See Sample AU
See Sample AV
See Sample BD
Generate and describe linear number sequences.
See Sample H
See Sample BE
Express missing number problems algebraically.
See Sample BF
Find pairs of numbers that satisfy an equation with two
unknowns.
See Sample BD
Enumerate possibilities of combinations of two variables.
Continue to complete and interpret information in a variety of
sorting diagrams (including sorting properties of numbers and
shapes).
Child F uses her knowledge of properties of numbers and
shapes to sort them in both Carroll and Venn diagrams.
See Sample AK
Interpret and construct pie charts and line graphs and use these
to solve problems.
See Sample BG
See Sample BH
Solve comparison, sum and difference problems using information
presented in all types of graph.
See Sample BG
See Sample BH
Calculate and interpret the mean as an average.
See Sample BI
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
A B
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
C D
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
E F
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
G H
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
I
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
J K
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
L M
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
N O
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
P Q
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
R S
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
T U
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
V W
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
X Y
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
Z AA
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AB AC
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AD AE
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AF AG
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AH AI
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AJ AK
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AL AM
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AN AO
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AP AQ
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AR AS
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AT AU
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AV AW
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AX AY
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
AZ
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
BA
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
BB
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
BC BD
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
BE BF
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
BG BH
Mathematics
Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)
© Lancashire County Council (2016)
BI