# Maths Scheme of Work. Class: Year 10. Term: autumn 1: 32 lessons (24 hours) Number of lessons

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1 Maths Scheme of Work Class: Year 10 Term: autumn 1: 32 lessons (24 hours) Number of lessons Topic and Learning objectives Work to be covered Method of differentiation and SMSC 11 OCR 1 Number Operations and Integers 1.01 Calculations with integers 1.01a Four rules GCSE book F1: a Use non-calculator methods to calculate the sum, difference, product and F2: 6-48 quotient of positive and negative whole numbers. H1: Whole number theory 1.02a Definitions and terms 1.02a Understand and use the terms odd, even, prime, factor (divisor), multiple, common factor (divisor), common multiple, square, cube, root. 1.02a Understand and use place value. 1.02b Prime numbers 1.02b Identify prime numbers less than b Express a whole number as a product of its prime factors. e.g. $$\displaystyle 24 = 2\times 2\times 2 \times 3$$ 1.02b Understand that each number can be expressed as a product of prime factors in only one way. 1.02b Identify prime numbers. 1.02b Use power notation in expressing a whole number as a product of its prime factors. e.g. $$\displaystyle 600 = 2^3 \times 3 \times 5^2$$ 1.02c Highest Common Factor (HCF) and Lowest Common Multiple

2 (LCM) 1.02c Find the HCF and LCM of two whole numbers by listing. 1.02c Find the HCF and LCM of two whole numbers from their prime factorisations Combining arithmetic operations 1.03a Priority of operations 1.03a Know the conventional order for performing calculations involving brackets, four rules and powers, roots and reciprocals 1.04 Inverse operations 1.04a Inverse operations 1.04a Know that addition and subtraction, multiplication and division, and powers and roots, are inverse operations and use this to simplify and check calculations, for example, in reversing arithmetic in I m thinking of a number or missing digit problems. e.g = = = 50 6 = = a [see also Calculation and estimation of powers and roots, 3.01b] 10 OCR 2 Fractions, Decimals and Percentages 2.01 Fractions 2.01a Equivalent fractions 2.01a Recognise and use equivalence between simple fractions and mixed numbers. e.g. 26 = = b Calculations with fractions 2.01b Add, subtract, multiply and divide simple fractions (proper and improper), including mixed numbers and negative fractions. Gcse book F1: F2 : H1:38-64

3 e.g b Carry out more complex calculations, including the use of improper fractions. e.g b [see also Algebraic fractions, 6.01g] 2.01c Fractions of a quantity 2.01c Calculate a fraction of a quantity. e.g. 25 of c Express one quantity as a fraction of another. 2.01c [see also Ratios and fractions, 5.01c] 2.01c Calculate with fractions greater than Decimal fractions 2.02a Decimals and fractions 2.02a Express a simple fraction as a terminating decimal or vice versa, without a calculator. e.g. 0.4= a Understand and use place value in decimals. 2.02a Use division to convert a simple fraction to a decimal. e.g. 16 = a Convert a recurring decimal to an exact fraction or vice versa.

4 e.g = b Addition, subtraction and multiplication of decimals 2.02b Add, subtract and multiply decimals including negative decimals, without a calculator. 2.02c Division of decimals 2.02c Divide a decimal by a whole number, including negative decimals, without a calculator. e.g c Without a calculator, divide a decimal by a decimal. e.g Percentages 2.03a Percentage conversions 2.03a Convert between fractions, decimals and percentages. e.g. 14 =0.25=25% 112 =150% 2.03b Percentage calculations 2.03b Understand percentage is number of parts per hundred. 2.03b Calculate a percentage of a quantity, and express one quantity as a percentage of another, with or without a calculator. 2.03c Percentage change 2.03c Increase or decrease a quantity by a simple percentage, including simple decimal or fractional multipliers. Apply this to simple original value problems and simple interest. e.g. Add 10% to 2.50 by either finding 10% and adding, or by multiplying by 1.1 or

5 Calculate original price of an item costing 10 after a 50% discount. 2.03c Express percentage change as a decimal or fractional multiplier. Apply this to percentage change problems (including original value problems). 2.03c [see also Growth and decay, 5.03a] 2.04 Ordering fractions, decimals and percentages 2.04a Ordinality 2.04a Order integers, fractions, decimals and percentages. e.g. 45,34, 0.72, b Symbols 2.04b Use <,>,,,=, 7 OCR 3 Indices and Surds 3.01 Powers and roots 3.01a Index notation 3.01a Use positive integer indices to write, for example, = a Use negative integer indices to represent reciprocals. 3.01a Use fractional indices to represent roots and combinations of powers and roots. 3.01b Calculation and estimation of powers and roots 3.01b Calculate positive integer powers and exact roots. e.g. 2 4 =16 9 =3 8 3 =2 3.01b Recognise simple powers of 2, 3, 4 and 5. e.g. 27=3 3 Gcse book F1: F2: 32, 279, 282 H1: H2: , 206

6 3.01b [see also Inverse operations, 1.04a] 3.01b Calculate with integer powers. e.g. 2 3 = b Calculate with roots. 3.01b Calculate fractional powers. e.g =1(1 4 6) 3 = b Estimate powers and roots. e.g. 51 to the nearest whole number 3.01c Laws of indices 3.01c [see also Simplifying products and quotients, 6.01c] 3.01c Know and apply: a m a n =a m+n a m a n =a m n (a m ) n =a mn 3.01c [see also Calculations with numbers in standard form, 3.02b, Simplifying products and quotients, 6.01c] 3.02 Standard form 3.02a Standard form 3.02a Interpret and order numbers expressed in standard form. 3.02a Convert numbers to and from standard form. e.g. 1320= , =

7 3.02b Calculations with numbers in standard form 3.02b Use a calculator to perform calculations with numbers in standard form. 3.02b Add, subtract, multiply and divide numbers in standard form, without a calculator. 3.02b [see also Laws of indices, 3.01c] 3.03 Exact calculations 3.03a Exact calculations 3.03a Use fractions in exact calculations without a calculator. 3.03a Use multiples of π in exact calculations without a calculator 3.03a Use surds in exact calculations without a calculator. 3.03b Manipulating surds 3.03b Simplify expressions with surds, including rationalising denominators. e.g. 12 =23 13 = = OCR 4 Approximation and Estimation 4.01 Approximation and estimation 4.01a Rounding 4.01b Estimation 4.01c Upper and lower bounds Gcse book F1: H1:13-19 H2:

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