Learn what triangular numbers are by looking at the appropriate number of counters arranged as triangles, then starting to learn the sequence of numbers, looking at how to work out the next number numerically, without using pictures. Hide

Look at the Fibonacci sequence of numbers, learning how to work out what the next number is. Relate the Fibonacci sequence to aspects of nature, first looking at a pictorial version of the sequence, Fibonacci squares. Hide

Learn to add and subtract using negative numbers, first by starting with a single digit number and adding or subtracting a two digit number, then starting with a two digit number and adding or subtracting a two digit number. For example: 5 – 19 = -14, then 25 – 39 = -14. Learn to use a 2-step approach of adding or subtracting to zero first, then carry out the second part of the calculation. Hide

Learn about square roots: what they are and how they are written and link to times table and particularly square number knowledge. For example, knowing 4 x 4 = 16 relates to √16 = 4. Work on instant knowledge of the first 12 square roots through practice. Hide

Learn what cube numbers are, encouraging an understanding of starting with square numbers to reach cube numbers. Learn the sequence of the first 12 cube numbers and be able to put in any missing cube numbers. Hide

Multiply 3 digit x 3 digit numbers in columns, without carry digits, next carrying tens and then with any carry digits. Briefly review grid multiplication and also look at estimating multiplications as a form of checking answers. Practise both without and with carry digits. Hide

Learn to divide by 2 digit numbers, emphasising the use of times table facts, starting with whole number answers and then moving on to answers with remainders. Practise on a mixture of division questions. Hide

Learn to divide 3 digit numbers by 2 digit numbers, using the long division draw-down method, starting with whole number answers and then moving on to answers with remainders. Also look at chunking as a division method and how to check division answers with multiplication. Practise on a mixture of division questions. Hide

Learn to divide 4 digit numbers by 2 digit numbers, using the long division draw-down method, starting with whole number answers and then moving on to answers with remainders. Also look at chunking as a division method and how to check division answers with multiplication. Practise on a mixture of division questions. Hide

Learn to divide 2 digit numbers, working into decimal places to get exact answers, rather than whole numbers with remainders. Develop understanding of the remainder also being divided out, encouraging quick identification of easy decimal answers. For example: 18 ÷ 4 = 4 R 2 or 4.5, because of knowledge that 0.5 = 2/4. Work initially with answers that have 1 decimal place, then answers with 2 decimal places. Hide

Learn to divide 3 digit numbers, working into decimal places to get exact answers, rather than whole numbers with remainders. Develop understanding of the remainder also being divided out, encouraging quick identification of easy decimal answers. Work initially with answers that have 1 decimal place, then 2 decimal places and finally 3 decimal places, practising a mixture of these. Hide

Learn to divide by 3 digit numbers, using long division draw-down method, starting with dividing 4 digit numbers, such as 9984 ÷ 416 = 24, then moving onto dividing 5 digit numbers, such as 61116 ÷ 132 = 463.Hide

Learn about cancelling fractions to their lowest or simplest form, by finding the Highest Common Factor for the numerator and denominator. Practise finding the lowest form of fractions. Hide

Learn to add and subtract fractions with different denominators, by first finding the Lowest Common Denominator (LCD) and converting fractions to these, before carrying out the addition or subtraction. Finally, learn to put answers into their lowest form. Hide

Learn to add and subtract mixed numbers (numbers with a whole number part and a fraction part), using pictures of pizzas to help understanding and finding the Lowest Common Denominator (LCD) in order to convert fractions. Progress to working numerically, ensuring that answers are fully converted to mixed numbers, with no improper fractions included, exchanging for whole numbers wherever necessary. Hide

Use fractions, with numerators bigger than the denominators, as 'operators' of both multiplication and division, reducing to lowest forms if necessary, with mixed number answers where appropriate. Hide

Learn to multiply 2 proper fractions, multiplying the numerators, then the denominators and cancelling to the simplest form if necessary. Look at a fraction multiplication in pictorial form to help understanding of why the answer is smaller than the fractions started with. Hide

Learn to use a calculator to find more difficult percentages of amounts. Work through using the equivalent fraction to the percentage to multiply by, as well as learning to use the % button on a calculator. For example: 71.59% x 382.4 = 273.76016 Hide

Extend finding percentages to finding percentage increases in relation to money. Work through finding percentages of money and then adding to the original amount, to reach the total price after the increase. For example: £35 with a price increase of 5% will give £36.75 as the new price. Hide

Extend finding percentages to finding percentage decreases in relation to money. Work through finding percentages of money and then subtracting from the original amount, to reach the new, reduced price. For example: £460 with 30% off will give £322 as the new price. Hide