KS3 Level

Number

Projected KS4 Grades

5

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).

9

4

• 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

8

3

• 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.

7

2

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 understand and can find multiples, factors, factor pairs, proper factors and common factors for most 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. 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 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.

6

1

I understand that division is the inverse of multiplication. I can develop mental strategies for multiplication by doubling and halving and you understand that halving is the inverse of doubling. I can develop mental strategies to know the 2, 4, and 8 multiplication tables and derive associated divisibility facts. I 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. I can use a written method to multiply or divide any positive integers to solve problems. I understand how to solve onestep problems involving one and two digit numbers and all four operations using a calculator. I understand how to solve onestep problems involving whole numbers and decimals and all four operations using a calculator. I can explore the relationship between approximation and rounding and investigate how this can help with calculations. I understand how to approximate before carrying out an addition or subtraction and explain why this may be useful.

I can explore rounding for convenience when multiplying and dividing. For example: round 54 to 55 when dividing by 5. I can apply knowledge of place value, and number facts to check calculations. I 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?' I can use knowledge of multiplication facts to quickly derive squares of numbers to 12 x 12. I can investigate triangular numbers visually and numerically and thus be able to derive them. I can introduce square roots as the inverse of square numbers and define square root notation. I can recognise and use squares and square roots with positive and negative integers and the notation for squared. I can recognise and use the notation for squared and square root on a calculator.

5

WT+

• I know the percentage and decimal equivalents of fractions where the denominator is a factor of 100 • I can discover and use the relationship between decimals and terminating fractions, e.g. 0.23=23/100. • I can recognise and express a larger whole number as a fraction of a smaller one (e.g. recognise that 8 slices of a 5slice pizza represents eight fifths or 1 and three fifths pizzas). • I can use diagrams to compare two or more simple fractions (e.g. is it bigger or smaller than a 1/2) and are able to position fractions on a number line • I can find fractions of simple whole numbers (e.g. one quarter of 8 kg equals 8 divided by 4). • I understand how to add and subtract fractions with the same denominator using diagrams. • I can find simple percentages of diagrams (25% and 50%) extending to finding other percentages of diagrams.

• I can develop strategies to calculate simple percentages of amounts. • I can solve problems involving the calculation of percentages [e.g. of measures, such as 15% of £360]. • I understand what is the same and what is different between ratio and proportion e.g. ratio of black beads to white beads and what is the fraction of black beads • I understand ratio notation and the importance of ratio conventions. I can find a ratio which represents a worded problem and interpret and write ratios to describe a situation. I appreciate that direct proportion is equality of ratio and can determine direct proportionality from a table of values/graphs.

4

WT

I know and am able to explain the properties of special numbers such odd, even, zero. I understand and can use the vocabulary associated with addition and subtraction e.g. take away, finding difference and counting on, combining etc. I understand the meaning of the equals sign and use the symbol = ; the concept of 'does not equal' ≠; and these symbols <,>,≤, ≥ I can use the inequality symbols to describe the difference and relationships between integers (positive or negative) = ≠, <,>,≤, ≥ I can develop and apply strategies involving multiplication of 2 digit and 1 digit integers and division of 3 digit by 2 or 1 digit integers. I understand how to round positive whole numbers to the nearest 10, 100 and 1000. I can explore percentages and decimal equivalents to simple fractions e.g. 1/4, 1/2, 3/4 I understand and can use fraction notation e.g. 5 slices out of an 8 slice pizza is five eighths.

I can express one number as a fraction of another e.g. 4 is a quarter of 16. I understand the connection between division and fractions. I can recognise the percent symbol (%) and understand that per cent relates to ‘number of parts per hundred’ I can covert a percentage to fraction of hundredths. I can solve simple problems involving direct proportion by scaling quantities up or down (e.g. 1 orange costs 30p, how much do 3 cost?).

3

WT

1/2
