Download Number and calculation (NC)

Number and calculation
(NC)
Level 1:
 To understand addition as finding the total of two or more sets of objects, relate addition to counting on, that addition can
be done in any order
 To understand subtraction as ‘taking away’ objects from a set and finding how many are left, be able to find a ‘difference’
by counting up
 To be able to solve addition/subtraction problems involving up to 10 objects e.g.
o given a number work out ‘how many more to make...’
o choose which of given pairs of numbers add to a given total
o solve measuring problems such as how many balance with... (M)
o recognise coin values to 10p, solve money problems
o begin to use the vocabulary related to addition and subtraction and symbols to describe and record addition and
subtraction number sentences
 To be able to record their work e.g.
o begin to use the symbols ‘+’ and ‘=’ to record additions
o use practical and informal written methods to support the addition of a one-digit number or a multiple of 10 to a
one-digit or two-digit number
o use practical and informal written methods to support the subtraction of a one-digit number from a one-digit or
two-digit number and a multiple of 10 from a two-digit
Level 2:
 To be able to recognise sequences of numbers, including odd and even numbers e.g.
o continue a sequence that increases or decreases in regular steps
o recognise numbers from counting in tens or twos
 To be able to use the knowledge that subtraction is the inverse of addition and vice versa e.g.
o given 14, 6 and 8, make related number sentences: 6 + 8 = 14, 14 – 8 = 6, 8 + 6 = 14, 14 – 6 = 8
 To understand halving is the inverse of (‘undoing’) doubling and vice versa
 To be able to choose the appropriate operation when solving addition and subtraction problems e.g.
o use repeated addition to solve multiplication problems
o begin to use repeated subtraction or sharing equally to solve division problems
 To be able to solve number problems involving money and measures e.g. (M)
o add/subtract two-digit and one-digit numbers, bridging tens where necessary in context using units such as pence,
pounds, centimetres
 To be able to record written methods e.g.
o record their mental calculations as number sentences
o use practical and informal written methods to add and subtract two digit numbers
Level 3:
 To be able to use understanding of place value in numbers e.g.
o recognize that some numbers can be represented as different arrays
o use understanding of place value to multiply/divide whole number by 10 (whole number answers) (PV)
o use understanding of place value to multiply whole numbers by 100 (PV)
o combine with knowledge of addition and subtraction to derive sums and differences of pairs of multiples of 10, 100
or 1000
 To be able to use place value to make approximations (PV)
 To understand negative numbers e.g.
o in context such as temperature (M)
o positioned on a number line
 To be able to recognise a wider range of sequences e.g.
o recognise sequences of multiples of 2, 5 and 10
o recognise and continue number sequences formed by counting on or back in steps of constant size
 To understand that division is the inverse of multiplication and vice verse and be able to derive associated division facts
from known multiplication facts e.g.
o given a number sentence, use understanding of operations to create related sentences (e.g. given 14 x 5 = 70,
create 5 x 14 = 70, 70 ÷ 5 = 14, 70 ÷ 14 = 5, 14 x 5 = 10 x 5 add 4 x 5
o use inverses to find missing whole numbers in problems such as ‘I think of a number, double it and add 5. The
answer is 35. What was my number?’
 To begin to understand the role of ‘=’ the ‘equals’ sign e.g.
o solve ‘balancing’ problems such as 7 x 10 = 82 - ⃝
 To be able to use mental recall of addition and subtraction facts to 20 in solving problems involving larger numbers e.g.
o choose to calculate mentally on paper or with apparatus
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o solve one-step whole number problems appropriately
o solve two-step problems that involve addition and subtraction
To be able to solve whole number problems including those involving multiplication or division that may give rise to
remainders e.g.
o identify appropriate operations to use
o round up or down after simple division depending on context
To be able to add and subtract three digit numbers using written method e.g.
o use written methods that involve bridging 10 or 100
o add and subtract decimals in the context of money, where bridging is not required (FDPR)
To be able to use knowledge of number operations and corresponding inverses to estimate and check calculations
To be able to multiply and divide two digit numbers by 2, 3, 4, or 5 and 10 with whole number answers and remainders e.g.
calculate 49 ÷ 3….. moving on to….
To develop and use written methods to record, support and explain multiplication and division of two-digit numbers by a
one-digit number, including division with remainders
To be able to use a calculator e.g.
o carry out one-step and two-step calculations involving all four operations
o recognise negative numbers in the display
o correct mistaken entries and interpret the display correctly in the context of money
Level 4:
 To be able to recognise, describe and use number relationships including multiple, factor and square e.g.
o identify pairs of factors of two-digit whole numbers and find common multiples (e.g. for 6 and 9)
 To be able to use place value to multiply and divide whole numbers by 10, 100 and 1000 (PV)
 To be able to use inverse operations e.g.
o use a calculator and inverse operations to find missing numbers, including decimals (FDPR)
o ‘undo’ 2-step problems
o understand ‘balancing sums’ including those using division, such as 20 + ⃝ = 100 ÷ 4
 To understand the use of brackets in simple calculations
 To be able to state inequalities using the symbols < and > with negative numbers (e.g. -3 > -5, -1 < +1)
 To be able to identify the doubles of two-digit numbers, use these to calculate doubles of multiples of 10 and 100 and
derive the corresponding halves
 To be able to solve problems with or without a calculator e.g.
o solve two-step problems choosing appropriate operations
o deal with two constraints simultaneously
o interpret a calculator display of 4.5 as £4.50 in context of money
o carry out simple calculations involving negative numbers in context
o solve problems using decimals or fractions
 To be able to check the reasonableness of results with reference to the context or size of numbers
 To begin to be able to use simple formulae expressed in words
 To be able to use efficient written methods of addition and subtraction and of short multiplication and division e.g.
o calculate 1202 + 45 + 367 or 1025 – 336
o calculate HTU x U
o calculate TU x TU
o calculate HTU ÷ U
 To be able to add and subtract decimals to two places (FDPR)
 To be able to use knowledge of rounding, place value, number facts and inverse operations to estimate and check
calculations
 Find fractions using division (e.g. 1/100 of 5kg), and percentages of numbers and quantities (e.g. 10%, 5% and 15% of £80)
(FDPR)
 To be able to multiply a simple decimal by a single digit, e.g. (FDPR)
o calculate 36.2 x 8
Level 5:
 To be able to use understanding of place value to multiply and divide whole number and decimals by 10, 100 and 1000 and
explain the effect (FDPR) (PV)
 To be able to order negative numbers in context
 To be able to find the difference between a positive and a negative integer, or two negative integers, in context
 To be able to recognize and use number patterns and relationships e.g.
o understand and find two-digit prime numbers (including finding the prime factors of two-digit numbers)
o make generalisations about sequences saying whether much larger numbers will be in the sequence or not
 To be able to use known facts, place value and knowledge of operations to calculate e.g.
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o calculate decimal complements to 10 or 100, such as 100 – 63.8 (FDPR)
o multiply a two-digit number by a single digit (e.g. 39 x 7)
To be able to apply inverse operations
To be able to use brackets appropriately e.g.
o know and use the order of operations including brackets
To be able to understand and use an appropriate non-calculator method for solving problems that involve multiplying and
dividing any three-digit number by any two-digit number
To be able to solve simple problems involving ordering, adding, subtracting negative numbers in context
To be able to approximate to check answers to problems are of the correct magnitude
To be able to check solutions by applying inverse operations or estimating using approximations
To be able to construct, express in symbolic form, and use simple formulae involving one or two operations e.g.
o understand simple expressions using symbols (e.g. ‘2 less than n’ can be written as ‘n – 2’)
o evaluate expressions by substituting numbers into them
o use symbols to represent an unknown number or a variable