Year 8 Review 1, Set 1 Number confidence (Four operations, place value, common indices and estimation)

Transcription

1 Year 8 Review 1, Set 1 Number confidence (Four operations, place value, common indices and estimation) Place value Digit Integer Negative number Difference, Minus, Less Operation Multiply, Multiplication, Times, Product Estimate Divide, Division, Divisible Divisor, Dividend Operation Estimate Approximate Round Decimal place Accuracy Read Roman numerals up to 1000 Read, write, order and compare numbers up to 1,000,000 Round any number up to 1,000, 000 Add and subtract numbers up to 4 digits showing a clear written method Multiply up to a 4 digit number by 1 digit or two digit numbers showing a clear method Divide up to a 4 digit number by a 1 digit number showing a clear method Find all the factors of a simple two digit number (eg. 20) Read, write, order and compare numbers up to 10,000,000 Add and subtract numbers with more than 4 digits Multiply a 3 digit by a 2 digit number Divide a 3 digit number by a 2 digit number Calculate using negative numbers, including finding intervals across 0. Recognise and use square and cube numbers up to 100 Calculate the square root of square numbers Perform mentally calculations, including with mixed operations and large numbers Solve addition and subtraction multi step problems deciding which operations and methods to use and why Use estimation to check answers to calculations to determine, in the context of a problem, and correct use of rounding (to two decimal places) Count forwards / backwards in powers of 10 Find the LCM of 9 and 12 Find the HCF of 24 and 30 Understand and use place value (eg when working with very large and small numbers and when calculating with decimals) Round numbers and measures to a specified number of decimal places Use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2,3,4,5. Find the square root of larger square numbers Use the 4 operations including formal written methods using down to 2 decimal places Use the =,, <, >,, symbols within simple problems. Solve problems using correct maths symbols (brackets) clearly showing the order to solve a problem Show a number as a product of its primes (eg 240) Interpret and use standard form correctly ( x 10 ) Calculate the cube root of cube numbers Apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers all both positive and negative Use the concepts and vocabulary of prime numbers, highest common factor, lowest common multiple, prime factorisation. Round numbers and measures to a specified number of significant figures Identify and interpret limits of accuracy (ideas of boundaries) Estimate using truncating in context Use inequality notation to specify simple error intervals due to truncation or rounding and explain through using examples Calculate with roots, and with integer indices using an understanding of index laws (including x & of indices and those with brackets) Calculate exactly with multiples of π

2 Place value Digit Negative number (Common) multiple (Common) factor Divisible Prime number, Composite number Pattern Year 8 Review 2, Set 1 Working with decimals, sequences, coordinates & algebraic graph functions Sequence Linear Term Ascending Descending X axes Y axes Add and subtract values to 2 decimal places Read, write, order and compare numbers up to 3 decimal places Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 Find a missing term in a linear sequence Generate a linear sequence from its description Find missing values within the sequence using the rule Show an understanding of the use of negatives values on a set of axes Show an understanding of plotting and reading coordinates in all four quadrants Count forwards / backwards in powers of 10 Round decimals up to two decimal places Calculate using negative numbers, including finding intervals across 0. Solve problems which require answers to be rounded to a specific degree of accuracy. Multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places Multiply numbers with up to one decimal place by one digit whole number Divide numbers with up to one decimal place by one digit whole number Show an understanding of Identifying the nth term within a numerical sequence and links to the times tables Generate a sequence from a nth term rule Read any points in all four quadrants Plot any points in all four quadrants Use coordinates in all four quadrants with missing vertex shape problems Understand and use place value (eg when working with very large and small numbers and when calculating with decimals) Round numbers and measures to a specified number of decimal places Use the 4 operations including formal written methods using down to 2 decimal place Identify the nth term within a numerical sequence Generate a sequence from a nth term rule involving squares Recognise square or cube number sequences and apply a rule Recognise triangular numbers within a sequence Work with coordinates confidently and fluently in all four quadrants Describe positions on the full coordinate grid (all four quadrants) Interpret and use standard form correctly ( x 10 ) Apply the four operations, including formal written methods, to integers, decimals all both positive and negative Round numbers and measures to a specified number of significant figures Identify the nth term for simple quadratic sequences Identify the nth term for sequences involving fractions Continue a quadratic sequence from a rule Plot equations as a graph Identify and interpret gradients and intercepts of linear functions (y = mx + c) Recognise, sketch and interpret graphs of linear functions and quadratic functions Identify and interpret limits of accuracy (ideas of boundaries) Find the nth term for more complex quadratic sequences Recognise and use Fibonacci type sequences Recognise and use quadratic sequences Use the form y = mx + c to identify parallel lines Find the equation of the line through two given points, or through one point with a given gradient Recognise, sketch and interpret graphs of simple cubic (x³) functions and the reciprocal function y = 1/x with x 0

3 Year 8 Review 3, Set 1 Constructing expressions, solving equations, using formulae & angles proof Algebra, algebraic, algebraically Symbol Expression Variable Substitute Equation Unknown Enumerate Angle Degrees Right angle Acute angle Obtuse angle Reflex angle Protractor Vertically opposite Collect like terms within an expression Express missing number problems algebraically Solve simple one step equations from worded problems Use properties of rectangles to find missing angles Identify common 3D shapes based on their properties and sizes Describe the difference between a regular and irregular polygon Draw angles and measure them in Estimate and compare acute and obtuse angles Estimate and compare reflex angles Collect like terms within a problem (eg. perimeter) Solve one-step linear equations (not fractions) Express a missing number problem algebraically Find a pair of numbers which satisfy an equation with two unknowns List possibilities of combination of numbers with two variables Identify and explain perpendicular lines Identify and explain parallel lines Draw a 2D shapes based upon given angles and dimensions Recognise vertically opposite angles and solve missing angles problems using this idea Begin to prove why the angles in a triangle add up to 180 Find missing angles on a straight line and a triangle. Find angles sums of regular polygons Find interior angles of a regular polygon Solve an equation involving a fraction line Understand the vocabulary of expression, equation and formulae Understand and use standard mathematical formulae Solve two-step equations (Showing clear methods) Check the solution to an equation by substitution Simplify expressions by multiplying out a single bracket Know the meaning of the subject of an equation Use correct symbols for reading and labelling angles and sides of triangles (eg. showing equal or parallel sides) Identify properties of 3D shapes (vertices, edges etc) Identify, describe and construct congruent shapes including on a coordinate axes Identify fluently angles at a point, angles at a point on a line and vertically opposite angles Use and interpret algebraic notation, including: a²b in place of a a b Substitute numerical values into scientific formulae Understand and use the concepts and vocabulary of inequalities and factors Simplify and manipulate algebraic expressions by taking out common factors and simplifying expressions involving the laws of indices Rearrange formulae to change the subject Solve linear equations with the unknown on both sides of the equation Interpret plans and elevations on 3D shapes Use the fact that angles in a triangle total 180 to work out the total of the angles in any polygon Understand and use alternate and corresponding angles on parallel lines Identify, describe and construct similar shapes including the use on enlargement Construct all the equidistant points from two points Know the difference between an equation and an identity Simplify and manipulate an expression by expanding double brackets Simplify and manipulate algebraic expressions (including those involving surds) by factorising quadratic expressions of the form x² + bx + c, including the difference of two squares Argue mathematically that two expressions are equivalent (including perimeter contexts) Solve two linear simultaneous equations Solve quadratic equations by factorising Solve linear inequalities with one variable Represent an inequality on a number line Construct a perpendicular bisector using a ruler and compass Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) Construct plans and elevations of 3D shapes Construct an equidistant point from 3 points Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras Theorem

4 Year 8 Review 4, set 1 Confidence with fractions, decimals, percentages & showing chance (probability) Fraction Improper Proper fraction Top-heavy fraction Proportion Proportion Mixed number Equivalent Simplify Cancel Numerator, denominator Lowest terms Compare and order fractions whose denominators are all multiples of the same number Compare and order decimals up to 3 decimal places Read and write decimal numbers as fractions [for example, 0.71 = 71 / 100 ] Add and subtract fractions with the same denominator and denominators that are multiples of the same number Recognise and convert mixed numbers to improper fractions and vice versa (eg 2/5 + 4/5 = 6/5 = 1 1/5) Add and subtract fractions with denominators that are multiples of the same number) Multiply improper fractions by a whole number, supported by materials and diagrams Write percentages as a fraction out of 100 and as a decimal Solve problems which require knowing percentage and decimal equivalents of 1 / 5, 2 / 5, 4 / 5 and those with a denominator of a multiple of 10 or 25. Find percentages which are multiples of 10 Show the outcomes of a single event. Show the probability of these outcomes as a fraction Place common events correctly on the probability scale (from 0-1) Compare and order fractions, including fractions > 1 Use common factors to simplify fractions; use common multiples to express fractions in the same denomination Add and subtract fractions with different denominators, using the concept of equivalent fractions Multiply pairs of fractions and simplify ( 1 / 4 1 / 2 = 1 / 8 ) Divide proper fractions by whole numbers ( 1 / 3 2 = 1 / 6 ) Multiply fractions by a whole number Recall and use equivalences between simple fractions, decimals and percentages, including in different context Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3 / 8 ] Find any whole number percentage of an amount Show all the outcomes of two events. Find the probability of events using a fraction. Order positive & negative integers, decimals and fractions Calculate exactly with fractions (displaying a clear use of division) Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 Interpret percentages and percentage changes as a fraction or a decimal Compare two quantities using percentages Increase and decrease a quantity by a percentage Solve problems involving percentage change, including percentage increase/decrease Record, describe and analyse frequency of outcomes of probability experiments using tables and frequency trees Use simple relative frequency of probability to predict outcomes for future experiments Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or or 3/8) Multiply and divide improper fractions Work with percentages greater than 100% Solve problems involving percentage change, including original value problems, and simple interest including in financial mathematics Find the original amount following a % change Apply the property that all events sum to 1 Show all combinations of outcomes using tables, grids and venn diagrams and describe the probability Solve problems using compound interest and within the context of finances. Work with fractions, decimals and percentages in any context showing an exceptional understanding and working processes to support their knowledge Calculate the probability of independent and dependent combined events, using representations, and know the underlying assumptions Show an understanding that unbiased samples tend towards theoretical probability distributions, with increasing sample size Use relative frequency to predict future events

5 Year 8 Review 5, set 1 The relevance of ratio & proportion, formula for area, perimeter and volume & confidence with circles Proportion Quantity Integer Share Multiples Ratio Compare, comparison Part Simplify Common factor Cancel Lowest terms Unit Volume Capacity Perimeter, area, Square, rectangle, parallelogram, triangle Composite rectilinear Polygon Cube, cuboid Square centimetre, square metre, Cubic centimetre, Formula, formulae Correctly share out a quantity into a ratio Simplify simple ratios Use proportion within a problem using multiplication or division Measure and calculate the perimeter of composite rectangular shapes in cm and m Calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm²) and square metres(m²) Estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes) Identify the radius and diameter of a circle Solving problems involving unequal sharing or grouping using fractions and multiples Solve problems involving similar shapes where the scale factor is shown or can be found Show an understanding of proportion given as times bigger or smaller Solve problems involving the relative sizes of two quantities multiply or divide to find the missing value Solve problems involving a calculation of percentages (eg. 15% of 360) Recognise that shapes with the same areas can have different perimeters and vice versa Calculate the area of a triangle Calculate the area of a parallelogram Calculate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³) Identify and explain what a circumference is Express one quantity as a fraction of the other Divide a given quantity into two parts in a given part:part or part:whole ratio Compare two quantities using percentages Solve problems using percentage change using percentage increase and decrease Calculate perimeters of 2D shapes Know and apply formulae to calculate the area of parallelograms & trapezia Know and apply formulae to calculate volume of cuboids Measure line segments in geometric figures Know the formulae: circumference of a circle = 2πr = πd Know the formulae: area of a circle = πr² Show an understanding of how the circumference links with the diameter Use ratio freely within other contexts (eg speed, prices) Use compound units such as speed, rates of pay and prices Express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations) Identify and work with fractions in ratio problems Understand and use proportion as equality of ratios (strong link to the parts of the ratio) Use scale factors, scale diagrams and maps Compare lengths, areas and volumes using ratio notation Solve problems involving direct and inverse proportion, including graphical and algebraic representations Solve problems using percentages change Work with percentages greater than 100% Calculate the circumference of a circle Calculate the area of a circle showing in units² Find the area of composite shapes (some using circles) Know and apply formulae to calculate volume of right prisms (including cylinders) Change freely between compound units (e.g. density and pressure) in numerical contexts Use compound units such as density and pressure Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y Interpret the gradient of a straight line graph as a rate of change Calculate arc lengths, angles and areas of sectors of circles Calculate surface area and volume of spheres, pyramids, cones Know the formulae for: Pythagoras theorem, a² + b² = c², and apply it to find lengths in right-angled triangles in two dimensional figures Apply the concepts of congruence and similarity including the relationships between lengths in similar figures

6 Year 8 Review 6, set 1 Presenting a variety of data and measuring information (including averages) Data, Categorical data, Discrete data Pictogram, Symbol, Key Frequency Table, Frequency table Tally Time graph, Time series Scale, Graph Axis, axes Maximum, minimum Average Spread Consistency Mean Median Mode Range Measure Data Statistics Approximate Find the mode from a set of numerical data Show the range of a set of data Solve comparison, sum and difference problems using information presented in a line graph Complete, read and interpret information in tables, including timetables Find the mean of a set of data Find the median of a set of data Use an understanding of mean, median and mode to find missing values in average problems Interpret and construct pie charts and use these to solve problems Interpret and construct line graphs and use these to solve problems Interpret, analyse and compare the distributions of data sets from cumulative frequency diagrams through appropriate measures of central tendency (median, mean, mode and modal class) and spread (range) Find the averages of grouped data sets using midpoints within a table Construct a stem and lead diagram to compare sets of data using appropriate averages Interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data and know their appropriate use Interpret, analyse and compare the distributions of data sets using mean, median, mode and the importance of the range. Have a basic understanding of data sets from cumulative frequency graphs, using the median and range of the data to make reasonable comments about the findings. Find the averages of grouped data sets using midpoints within a table Apply statistics to describe a population Interpret, analyse and compare the distributions of grouped data sets using mean, median, mode and the importance of the range. Use and interpret scatter graphs using correct language Recognise and describe reasonable explanations of the correlation of the data Find and use the central tendency (average) of frequency polygons Make comparisons using the estimated mean of frequency polygons Interpret and construct tables, charts and diagrams, including tables and line graphs for time series data and know their appropriate use (time/distance and real life graphs) Draw an accurate line of best fit on a scatter graph Use the line of best fit to make predictions or solve problems Describe an understanding that correlation does not indicate that it will cause something to happen Show an understanding of using apparent trends of data (scatter graphs) and know the dangers of doing so with examples