KS3 Level

Number

Projected KS4 Grades

6

I can interpret a simple inequality on a number line and list of integers that satisfy it. I can write positive and negative powers of 10 I can find the prime factors of twodigit numbers. You know, use and explain the vocabulary of prime numbers, prime factors and composite (nonprime) numbers. I can recognise and use common multiples and lowest common multiple to solve problems. I can recognise and use common factors and highest common factors to solve problems. I can use mental methods for adding and subtracting any type of number I can use mental methods of addition and subtraction of simple fractions with common denominators. I can use efficient written methods to add and subtract decimals with up to two places I can solve addition and subtraction twostep problems in contexts, deciding which operations and methods to use and why.

I can use mental methods for multiplication of fractions accompanied where appropriate by suitable jottings e.g.. Multiplying by 1/2 or 1/4 or 1/10 is equivalent to dividing by 2, 4, 10 I can use mental methods for division of fractions accompanied where appropriate by suitable jottings e.g.. Dividing by 1/2 or 1/4 or 1/10 is equivalent to multiplying by 2, 4, 10 I can effectively use written methods of multiplication for numbers up to 4 digits in length. I can use long or short division to divide by 1 and 2 digit numbers. I can use a written method to divide numbers resulting in remainders and interpret these remainders as whole number remainders, fractions, or by rounding, as appropriate for the context. I can multiply and divide a decimal with 1 or 2 decimal places by a whole number

9

5

I can solve problems by applying the order of operations to more complex calculations involving positive and negative numbers including those with brackets. I can round numbers (including decimals) to a given number of significant figures. I can use numbers of any size rounded to 1sf to make a standardised estimation for calculations. I can use inverse operations in the context of decimals and fractions to check answers. I can use squares, square roots, cubes and cube roots for simple fractions and decimals. I understand the effect of multiplying the same integer to different powers. I can apply the index laws for multiplication and division of positive integer powers.

I can prove that any number to the power of 0 is 1 and have explored negative powers of I can use standard form notation in simple contexts. For example: 5000 = 5 x 10^3. I can explain the difference between an ordinary number and standard form. I can recognise the equivalency of fractions and ratio. I can recognise exploring equivalency of ratios, decimals and percentages. I can explain the multiplicative reasoning of ratios. For example: the ratio 1:3 means that one quantity is three times the size of the other. I can recognise the relationship between recurring decimals and their fractional equivalents. I can describe role of the denominator in recurring and terminating decimals.

8

4

I can multiply and divide integers and decimals by 1, 10, 100, 1000, and explain the effect. I can use efficient written methods to add and subtract any positive or negative whole number. I can add and subtract amounts of money to give change, using both pounds and pence in practical contexts. I can use your understanding of place value to reason out number calculations (e.g. the answer to 24 x 3 is ten times bigger than 2.4 x 3). I can complete two and three digit multiplication, using a proportional grid. I can divide by one or two digit number, using chunking (with remainders).

I can use an efficient written method to multiply and divide positive and negative numbers to solve problems. I can multiply and divide a decimal with one or two decimal places by a whole number. I can apply strategies to multiply together three, one or two digit numbers (e.g. 3x4x5, 23x4x5). I understand the associative law and how this applies to multiplication questions (e.g. 2 x 3 x 4 is the same as 3 x 2 x 4). I can use the order of operations, excluding brackets and indices, within a calculation. I am familiar with and can use the correct language for different types of numbers (e.g. natural numbers, integers, palindrome, happy numbers, directed numbers, rational numbers etc)

7

3

I recognise that prime numbers have only two factors and can recall prime numbers up to 19 and establish the prime numbers up to 100. • I understand and can apply knowledge of decimal notation for tenths, hundredths and thousandths. • I can round decimals to the nearest whole number. • I can round decimals to the nearest one decimal place and two decimal places. I can use the rules of arithmetic and inverse operations in the context of positive integers.

I can recognise and use cubes and cube roots for positive and negative integers and the notation for cubed, including on a calculator. I can write positive and negatives powers of 10. I can work interchangeably with fractions, decimals and percentages. I can recognise where converting between fractions, decimals and percentages can make a calculation easier. I can use division to convert a fraction to a decimal and distinguish between recurring and terminating decimals.

6

2

I can recognise and show families of common equivalent fractions. • I can compare and order unit fractions and fractions with the same denominators. • I can find fractions of simple whole numbers (e.g. one quarter of 8 kg equals 8 divided by 4). • I can add and subtract fractions with the same denominator. • I can multiply proper fractions by whole numbers writing the answer in its simplest form. • I can identify the effect of dividing proper fractions by whole numbers (e.g. 1/3 ÷ 2 = 1/60). I can complete percentage calculation to find any percentages (e.g. 17.5% by finding 10%, 5% and 2.5%).

I can express one quantity as a percentage of another (e.g. finding percentages from test results and using these to make comparisons). • I can divide an amount into a given ratio. • I can solve simple problems involving ratio and direct proportion (e.g. recipe quantities, cheapest option, simple exchange rates I can simplify a ratio and be able and use this to solve problems. Explore and use equivalent ratios to compare ratios.

5

1

I can multiply and divide integers and decimals by 1, 10, 100, 1000, and explain the effect. I can read and write numbers up to four digits and show understanding of place value up to four digits. I can understand and use the concepts of greater than and less than. I can read, write and compare decimal numbers with up to 2.d.p, and apply this to different situations e.g. using pounds and pence, reading temperatures etc. I can show understanding of place value of decimals using notation for tenths and hundredths. I can identify the position of decimal numbers on a number line. I can recognise and interpret negative numbers in contexts such as temperature and money. I can identify positive and negative numbers on a number line and use this to order positive and negative numbers. I understand and can find multiples, factors, factor pairs, proper factors and common factors for most numbers.

I can use mental strategies to add and subtract numbers with up to two digit numbers. You understand how the commutative law applies to addition and subtraction. I can recall and use positive integer complements to 100. You understand how to subtract larger 1 digit positive integers from smaller 1 digit positive integers producing negative numbers. I can add and subtract 1 digit positive integers from 1 digit negative numbers and know how to subtract a 1 digit negative integer from a 1 digit negative or positive integer. I can use efficient written methods to add up to 2 digit positive integers and subtract up to 1 or 2 digit positive integers. I understand and can use the vocabulary associated with multiplication and division.

4

WT+

You understand that division is the inverse of multiplication. You can develop mental strategies for multiplication by doubling and halving and you understand that halving is the inverse of doubling. You can use a written method to multiply or divide any positive integers to solve problems. You understand how to solve onestep problems involving one and two digit numbers and all four operations using a calculator. You can explore rounding for convenience when multiplying and dividing. For example: round 54 to 55 when dividing by 5. You can apply knowledge of place value, and number facts to check calculations. You can explore a range of methods to use rounding to help estimate the solutions to calculations. You understand the importance of checking the 'soundness' of answers, thinking 'does that make sense?' You can use knowledge of multiplication facts to quickly derive squares of numbers to 12 x 12. You can investigate triangular numbers visually and numerically and thus be able to derive them. You can introduce square roots as the inverse of square numbers and define square root notation. You can recognise and use squares and square roots with positive and negative integers and the notation for squared. You can recognise and use the notation for squared and square root on a calculator.

You can develop mental strategies to know the 2, 4, and 8 multiplication tables and derive associated divisibility facts. You can develop mental strategies to know the 3, 5, 6, 9 and 10 multiplication tables and derive associated divisibility facts. You understand the distributive and associative laws and how they apply to multiplication and division. You understand how to solve onestep problems involving whole numbers and decimals and all four operations using a calculator. You can explore the relationship between approximation and rounding and investigate how this can help with calculations. You understand how to approximate before carrying out an addition or subtraction and explain why this may be useful.

3

WT

2

WT

1
