Download Year 7 Maths AWL Number

1. Calculation: Knowledge
NUMBER
Structure and calculation
1. order positive and negative integers, decimals and fractions; use the symbols =, ≠, <, >, ≤, ≥
2. apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper
and improper), and mixed numbers – all both positive and negative; understand and use place value (e.g.
when working with very large or very small numbers, and when calculating with decimals)
3. recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify
calculations and expressions); use conventional notation for priority of operations, including brackets, powers,
roots and reciprocals
4. use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common
multiples, highest common factor, lowest common multiple, prime factorisation, including using product
notation and the unique factorisation theorem
5. use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4,
5; estimate powers and roots of any given positive number
6. calculate with roots, and with integer and fractional indices
7. calculate exactly with fractions, surds and multiples of π; simplify surd expressions involving squares (e.g.
) and rationalise denominators
8. calculate with and interpret standard form A x 10n, where 1 ≤ A < 10 and n is an integer.
Measures and accuracy
14. estimate answers; check calculations using approximation and estimation, including answers obtained using
technology
15. round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal
places or significant figures); use inequality notation to specify simple error intervals due to truncation or
rounding
16. apply and interpret limits of accuracy, including upper and lower bounds
Number Page 1
Place Value & Accuracy: Skills and Threshold
Threshold Grade
Skill: I can
Year
Foundation 1
1-3
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 estimate answers to calculations
 round positive and negative integers to nearest 10, 100, 1000
 order positive and negative integers
 place and indicate an integer on a number line
 write integers using place value e.g. ‘three thousand and forty seven’
 order decimals
 write the value of a given decimal digit
 use inequality and ≠ signs
 estimate answers to calculations (no division)
 round to decimal places
 round to 1 significant figure (integer)
 estimate answers in context (e.g. area)
 estimate answers to calculations (with division)
 round to 3 significant figures (integer)
 use place value in calculations (given 23 x 46 = 1058, calculate 2.3 x 4.6)
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Developing 4
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 estimate answers to calculations (complex)
 round to significant figures (decimal)
 round to significant figures (decimal leading zeroes)
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Key Words
place value integer
decimal
negative positive
digit
equal =
not equal ≠
round
decimal place significant figure accuracy inequality <,≤,>,≥ error interval lower bound upper bound
estimate
calculate
find
evaluate
Number Page 2
Operations: Skills and Threshold
Threshold Grade
Skill: I can
Year
Foundation 1
1-3
1
1
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 know and use multiplication tables to 10x10
 know and use the rules of BIDMAS
 understand and use inverse operations
 use multiplication tables for mental division (inverse)
 identify factors and multiples of a number
 know prime numbers to 100
 add and subtract positive and negative integers
 divide positive integers with integer results using written & mental methods
 multiply decimals by integers
 multiply positive integers using standard written methods
 interpret calculator display in context and round appropriately
 add and subtract decimals
 divide integers with decimal results
 multiply and divide negative integers with integer results
 multiply decimals by decimals
 multiply and divide decimals by powers of 10
 use BIDMAS correctly on a calculator
 know and use divisibility rules
 divide decimals by integers and decimals
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Developing 4
4-5
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 know not to use intermediate rounding
 multiply and divide by a number between 0 and 1
 find HCF using factors
 write an integer as the product of prime factors, including in index form
 find HCF using prime factor decomposition (PFD)
 find LCM using PFD
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Key Words
equal = not equal ≠
place value integer
decimal negative
positive
digit
add
sum
subtract difference
multiply
Gelosia divide
factor
multiple divisible prime number prime factor HCF
estimate
calculate find
LCM
inverse operation
BIDMAS
product of prime factors index form
evaluate
Number Page 3
Indices & Roots: Skills and Threshold
Threshold Grade
Skill: I can
Year
Foundation 1
1-3
1
1
2
2
2
2
2
 know square numbers to 144
 know cube numbers to 125
 calculate square and cube roots
 use a calculator to evaluate up to powers of 5
 use a calculator to evaluate square and cube roots
 write and understand index notation for positive indices
 use a calculator to evaluate indices
 use positive integer indices to evaluate expressions
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Developing 4
4-5
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 use positive integer indices to simplify expressions
 know and use power 0
 estimate the value of a power or root of any positive number
 write integers with negative indices; understand the relation to reciprocals
 use negative integer indices to simplify and evaluate expressions
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Key Words
integer
positive
negative
term
expression reciprocal
square
cube
index
power
square root cube root index form standard (index) form
surd
rationalise conjugate
evaluate simplify
expand
equivalent
Number Page 4
2. FDP & Ratio: Knowledge
NUMBER
Structure and calculation
1. order positive and negative integers, decimals and fractions; use the symbols =, ≠, <, >, ≤, ≥
2. apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper
and improper), and mixed numbers – all both positive and negative; understand and use place value (e.g.
when working with very large or very small numbers, and when calculating with decimals)
3. recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify
calculations and expressions); use conventional notation for priority of operations, including brackets, powers,
roots and reciprocals
Fractions, decimals and percentages
10. work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and or 0.375
or ); change recurring decimals into their corresponding fractions and vice versa
11. identify and work with fractions in ratio problems
12. interpret fractions and percentages as operators.
Measures and accuracy
13. use standard units of mass, length, time, money and other measures (including standard compound
measures) using decimal quantities where appropriate
RATIO, PROPORTION and RATES of CHANGE
2. use scale factors, scale diagrams and maps
3. express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
4. use ratio notation, including reduction to simplest form
5. divide a given quantity into two parts in a given part : part or part : whole ratio; express the division of a
quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving
conversion, comparison, scaling, mixing, concentrations)
6. express a multiplicative relationship between two quantities as a ratio or a fraction
7. understand and use proportion as equality of ratios
8. relate ratios to fractions and to linear functions
9. define percentage as ‘number of parts per hundred’; interpret percentages and percentage changes as a
fraction or a decimal, and interpret these multiplicatively; express one quantity as a percentage of another;
compare two quantities using percentages; work with percentages greater than 100%; solve problems
involving percentage change, including percentage increase/decrease and original value problems, and simple
interest including in financial mathematics
10. solve problems involving direct and inverse proportion, including graphical and algebraic representations
11. use compound units such as speed, rates of pay, unit pricing, density and pressure
12. compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric
ratios) and scale factors
16. set up, solve and interpret the answers in growth and decay problems, including compound interest and work
with general iterative processes.
Number Page 5
Fraction: Skills and Threshold
Threshold Grade
Skill: I can
Year
Foundation 1
1-3
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 find equivalent fractions
 understand fraction as division
 visualise a fraction diagrammatically
 order fractions
 simplify proper and improper fractions
 convert between mixed number & improper fraction
 convert between fractions and decimals
 calculate fraction of a quantity
 understand fraction as an operator
 add fractions
 multiply fractions
 subtract fractions
 use a calculator efficiently with fractions
 express one quantity as a fraction of another
 know the meaning of reciprocals and the relation to division
 understand and use unit fractions as multiplicative inverse of division
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Developing 4
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 understand that terminating and recurring decimals represent fractions
 recognise common recurring decimals and their fraction equivalents
 divide fractions
 operations with mixed numbers
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Key Words
fraction
numerator
denominator
fraction bar proper
equivalent
simplify
cancel
convert
improper mixed number reciprocal
common denominator recurring decimal terminating decimal
calculate
find
evaluate
of
multiply divide
Number Page 6
fraction of
Percentage: Skills and Threshold
Threshold Grade
Skill: I can
1st year
Foundation 1
1-3
2
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3
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3
 understand % as 'out of 100'
 calculate percentage of a quantity
 compare and order fractions, decimals and percentage
 convert between percent, fractions and decimals
 express one quantity as a percentage of another
 compare two quantities using percentages
 understand and use percentages >100%
 calculate percentage increase and decrease
 calculate simple interest and VAT
 write and evaluate simple iterative relations
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Developing 4
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 understand % as a multiplier
 calculate percentage change given original & final quantity
 calculate percentage profit and loss
 calculate compound interest
 calculate successive percentage change, not using a power
 solve reverse percentage problems
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Key Words
percent
percentage
denominator
percentage of
increase
decrease
simple interest compound interest growth
VAT
original
multiplier
decay
depreciation profit
loss
Number Page 7
Ratio & Proportion: Skills and Threshold
Threshold Grade
Skill: I can
Year
Foundation 2
1-3
2
3
3
3
3
3
3
3
 understand and write a ratio
 calculate equivalent ratios
 convert exchange rates
 solve exchange rate problems
 solve problems of ‘best buy’
 construct and interpret scale drawings and maps
 share a quantity in a given ratio
 solve simple ratio and proportion word problems
 convert between fractions and ratios
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Developing 4
4-5
 solve ratio and proportion problems using the unitary method 7+
Key Words
ratio
part : part proportion
equivalent cancel
simplify
best value scale
exchange rate
convert
calculate
find
fraction
multiplier
Number Page 8