Foundation Tier Order of Topics ( )

Transcription

1 oundation Tier Order of Topics ( ) The order is an approximate guide to the order of topics taught in Years 10 and 11 by term and will depend on teaching group. This order and timings can change over the course of the year. Time will also be left over for revision of topics over the course of the two years and for completion of past exam papers. Written homework will be set along with some online homework. Assessments take place throughout the year and dates will be placed on the S onnect pages during the term prior to these. Year 10: Autumn Term Topic Objectives rade N1. Integers (Whole Numbers) Write a number in words Write a number in figures (e.g. write one hundred and ten in figures) Understand place value in integers (e.g. what s the value of 6 in 562?) Understand and order integers (whole numbers) Add, subtract, multiply and divide integers Add, subtract, multiply and divide negative integers Understand simple instances of BIMAS, e.g. work out Multiply and divide whole numbers by a given multiple of 10 e.g. 6 x 100 Understand odd and even numbers, and prime numbers ind the H and the LM of numbers Write a number as a product of its prime factors, e.g.108 = / A1. Use of Symbols Simplify algebraic expressions by collecting like terms e.g. 7p + 2p = 9p Simplify algebraic expressions by collecting like terms (two terms and with powers) e.g. x 2 + 4x 2 = 5x 2 Multiply and divide with letters and numbers xpand single brackets e.g. 3(x+5) = 3x + 15 xpand two single brackets and collect like terms e.g. 5(x+1)+2(x+3) = 7x + 11 actorise an expression (put in to brackets) e.g. x 2 3x = x (x 3) N2. Rounding Round whole numbers to the nearest, 10, 100, 1000, Approximate decimals to a given number of decimal places or significant figures Approximations, e.g heck answers by reverse calculation, e.g. if 9 23 = 207 then = 23 Use estimation e.g. stimate: 6.91 x SSM1. Angles istinguish between acute, obtuse, reflex and right angles stimate the size of an angle in degrees Measure and draw angle to the nearest degree Use angle properties on a line and at a point to calculate unknown angles Measure a bearing (acute and obtuse) Measure a bearing (reflex) alculate bearings Mark parallel lines in a diagram / /

2 Use angle properties of triangles and quadrilaterals to find missing angles ind missing angles using properties of corresponding angles and alternate angles, giving reasons ind the three missing angles in a parallelogram when one of them is given Identify and list the properties of quadrilaterals (including kites) Name all quadrilaterals that have a pair of opposite sides that are equal SSM2. Properties of Triangles SSM3. Properties of Polygons Show that the angles of a triangle add up to 180 and use this to find angles Show that an exterior angle of a triangle is equal to the sum of the interior opposite angles Identify isosceles, equilateral and right-angled triangles Use the word congruent when triangles are identical Use angle properties of isosceles, equilateral and right-angled triangles ind missing angles in triangles by forming and solving an equation Use angle properties on a line and at a point to calculate unknown angles. Measure a bearing alculate bearings Mark parallel lines in a diagram Use angle properties of triangles and quadrilaterals to find missing angles (including in algebraic form) ind missing angles using properties of corresponding angles and alternate angles, giving reasons ind the three missing angles in a parallelogram when one of them is given Identify and list the properties of quadrilaterals (including kites) Name all quadrilaterals that have a pair of opposite sides that are equal alculate and use the sums of the interior angles of polygons of sides 3, 4, 5, 6, 8, 10 Know, or work out, the relationship between the number of sides of a polygon and the sum of its interior angles Know that the sum of the exterior angles of any polygon is 360 degrees ind the size of each exterior/interior angle of a regular polygon Autumn Assessment: Non-alculator test (1 lesson) testing the topics covered so far. ate will be announced during the term and placed on the S oundation tier onnect page. / - N3. Powers and Indices SSM4. Perimeter and Area alculate squares and square roots (with and without the use of a calculator) alculate cubes and cube roots (with and without the use of a calculator) Use function keys on a calculator for powers and roots Use the terms square, positive square root, negative square root, cube and cube root Recall integer squares from 2 2 to and the corresponding square roots Recall the cubes of 2, 3, 4, 5 and 10 Use index notation and index laws for positive and negative powers e.g. 4 2 x 4 8 = 4 10 and ind the perimeter of a shape by counting sides of squares and area of a shape by counting squares. Work out the area of a simple rectangle/square. Work out the area of a triangle, parallelogram, kite and trapezium. ind the area and perimeter of compound shapes ind the area and perimeter by forming and solving an equation first. (algebraic method) Name the parts of a circle (centre, radius, chord, diameter, / /

3 A2. quations and Inequalities circumference, tangent, arc, sector and segment) raw a circle given the radius or diameter alculate the area and circumference of a circle. alculate the area and perimeter of a semi-circle. x Solve equations such as = 10, 2x= 30, x+ 5= 15 5 Solve equations such as 2x+ 3= 11, 5x 4= 26, 2( x+ 1) = 6 Solve equations with the unknown on both sides e.g. 7x+ 5= 5x+ 11 Solve inequalities such as 3x < 9 and 12 3n < 20 Solve linear inequalities such as 4x 3 < 10 and 4x < 2x + 7 Represent sets of solutions on the number line Year 10: Spring Term A3. ormulae Use a formula written in words, such as cost = 20 distance travelled. istinguish between a formula, equation and expression. Write an expression from a problem. Substitute numbers in to simple formulae e.g. P= 2q + 5 Substitute numbers into more complicated formulae such as ( A + 1) = 9 Rearrange linear formulae such as p = 2q + 5 SSM5. oordinates Plot coordinates in the first quadrant e.g. plot (2, 5) Plot coordinates in all four quadrants e.g. plot (-2, 3) raw lines such as x = 3, y = x + 1 ind the midpoint of a line segment e.g. find the midpoint of (2,3) and (4, 8) A4. raphs of Plot the graphs of simple functions such a x = 3 and y = -2 linear functions omplete a table of values for graphs such as y = 2x + 5 (Straight Line Solve problems such as finding the coordinates of intersection graphs) between y = 3x + 5 and y = 6 Sketch straight line graphs such as y = -3x + 6 without a table ind the gradient of straight line graphs A5. Quadratic 2 raw graphs of simple quadratic functions such as y= x and raphs y = x ind the points of intersection of quadratic graphs with lines Use graphs to find the approximate solutions of quadratic equations N4. ractions ind the fraction of a shape shaded ind equivalent fractions e.g. 1 3 = 2 6 Simplify fractions (cancelling down) Order fractions by size ind fractions of quantities such as ¼ of 20 ind one fraction of another Add/subtract fractions (with same denominator) Add/subtract fractions (with different denominators) Add/Subtract fractions in mixed form with different denominators Multiply and divide fractions e.g. 1 1 N5. ecimals Write down the place value of a digit, for example, what is the value of the 4 in 0.24? Order decimals e.g. 0.24, 0.3 Add and subtract decimals Multiply two decimals e.g. 0.2 x 0.08 ivide two decimals e.g onvert decimals to fractions and percentages 2 3 / /

4 Spring Assessment: alculator test (1 lesson) testing the topics covered so far. ate will be announced during the term and placed on the S oundation tier onnect page. N6. Percentages Understand that a percentage is a fraction in hundredths Write a percentage as a decimal; or as a fraction in its simplest terms Write one number as a percentage of another number alculate the percentage of a given amount Increase/decrease an amount by a given percentage (with and without a percentage) Use multipliers to increase/decrease by a given percentage Work out a percentage increase or decrease. or example, find the percentage increase from 50 to 65 N7. Ratio and Understand what is meant by ratio Proportion Write a ratio in its simplest form; and find an equivalent ratio Share a quantity in a given ratio (e.g. ivide 10 in to the ratio 2: 3) Understand and use examples in direct proportion Interpret map/model scales as a ratio H1. ollecting Understand the data handling cycle ata esign a suitable question for a questionnaire Understand the difference between: primary and secondary data; discrete and continuous data esign suitable data capture sheets for surveys and experiments Understand about bias in sampling esign and use two-way tables for discrete and grouped data H2. Statistical ind the mode for a set of numbers. Measures ind the median for an odd/even set of numbers. ind the mean and range for a set of numbers. ind the mean from an ungrouped frequency table. ind the mean from a grouped frequency table. ind the modal and median class interval from a grouped table. / / Year 10: Summer Term H3. raphical Represent data as: Representation Bar charts (including dual bar charts) Pictograms Line graphs Histograms (intervals with equal width) requency polygons hoose an appropriate way to display discrete, continuous and categorical data Represent categorical data in a pie chart Interpret categorical data in a pie chart H4. Scatter Plot points to produce a scatter graph raphs Appreciate that correlation is a measure of the strength of association between two variables istinguish between positive, negative and zero correlation using a line of best fit Appreciate that zero correlation does not necessarily imply no correlation but merely no linear relationship raw lines of best fit by eye and understand what it represents H5. Probability Use probability in words e.g. likely, certain, impossible Write down the theoretical probability for an equally likely event stimate a probability by relative frequency Know that a better estimate for a probability is achieved by increasing the number of trials omplete two-way tables and find probabilities SSM6. Reflections Rotate a shape anywhere and from a point and Rotations Reflect shapes in a given mirror line. Initially line parallel to the /

5 SSM7. nlargements and Translations SSM8. Area and Volume coordinate axes and then y = x or y = x escribe a single transformation fully e.g. rotation, 90 o clockwise, centre (0, 1) Identify congruent shapes Understand translation as a combination of a horizontal and vertical shift (including vector notation) nlarge a shape from anywhere nlarge shapes by a given scale factor from a given point; using positive whole number scale factors escribe a single transformation fully e.g. enlargement, scale factor 3, centre (0, 1) ind volumes of shapes by counting cubes Use formulae for the volume of cuboids Solve a range of problems involving volume (volumes of prisms e.g. triangular prisms, cylinders) alculate surface areas of prisms and cylinders onvert between units of area e.g. cm 2 to m 2 nd of Year Assessment: Non-alculator and alculator tests (2 lessons in total) testing the topics covered so far. ate will be announced during the term and placed on the S oundation tier onnect page. A6. Sequences ind the missing numbers in a number pattern or sequence ind the nth term of a number sequence ind whether a number is part of a given sequence Use a calculator to produce a sequence of numbers A7. Trial and Solve cubic functions by successive substitution of values of x Improvement e.g. / - SSM9. Pythagoras Theorem Value of x x 3 + 3x = 20 omment 2 14 Too small 3 36 Too big ind missing sides (hypotenuse or shorter side) using Pythagoras Theorem in right-angled triangles. Apply Pythagoras Theorem to find the length of line segments. Year 11 Autumn Term SSM10. Measures Use the relationship between distance, speed and time to solve problems onvert between metric units of speed e.g. km/h to m/h Use the correct notation for time, 12- and 24-hour clock (including in bus/train timetables) Use and interpret mileage charts Recognise accuracy in measurements given to the nearest whole unit Plan a schedule/day using a timetable SSM11. Real-Life Plot points of a conversion graph and read off positive values. raphs Read from a conversion graph for negative values onvert between different currencies using a given conversion Interpret simple distance-time graphs alculate simple/complex speeds from distance-time graphs - / SSM12. onstructions ount the vertices, faces and edges of 3- shapes raw nets of solids and recognise solids from their nets raw and interpret plans and elevations raw planes of symmetry in 3- shapes Recognise and name examples of solids, including prisms Use a ruler and compass to draw accurate triangles, and other 2- shapes, given information about their side lengths and angles. Use straight edge and compass to construct: an equilateral triangle; the midpoint and perpendicular bisector of a line segment; the /

6 bisector of an angle onstruct triangles using a compass given all three sides (SSS), two sides and an angle (SAS), two angles and a side (ASA). Recall and use angle properties of equilateral, isosceles and rightangled triangles Recall and use the properties of squares, rectangles, parallelograms, trapeziums and rhombuses Recall and use properties of circles Appreciate why some shapes tessellate and why some shapes do not tessellate. SSM13. Loci ind the locus of points e.g. the locus of points equidistant to two given points Solve loci problems, such as identifying points less than 3 cm from a point P A8. Algebraic Proof ecide with a reason whether a simple/harder statement is true or false Year 11 Mock xam: Non-alculator and alculator tests testing the entire S oundation tier course. ach paper is 1 hour and 45 minutes. ate will be announced during the term and placed on the S oundation tier onnect page. Time is left over for revision of topics and completion of exam papers. The pace of lessons will vary on teaching group. /