# Maths Year 10 Foundation Tier Learning Map

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When?Content DomainTopicReferenceLearning ObjectivesHegarty Clip
Year 9 Half Term 1NumberIntegers and place value1a-1Use and order positive and negative numbers 14, 37
1a-2Add and subtract positive and negative numbers 39 - 41
1a-3Multiply and divide positive and negative numbers (integers)6, 15, 16
1a-4Multiply or divide any number by powers of 1042 - 44
1a-5Use brackets and the hierarchy of operations (not including powers)24, 44
1a-6Round numbers to a given power of 1017
1a-7Check answers by rounding and using inverse operations
NumberDecimals1b-1Identify the value of digits in a decimal or whole number45
1b-2Add and subtract with decimals47
1b-3Multiply with decimals48
1b-4Divide with decimals including decimal numbers49, 50
1b-5Perform calculations involving money743 - 754
1b-6Round to the nearest integer and a given number of decimal places56
1b-7Round to any given number of significant figures130
1b-8Estimate answers to calculations by rounding numbers to 1 significant figure131
1b-9Use one calculation to find the answer to another135, 136
NumberIndices, powers and roots1c-1Find squares and cubes99 - 101
1c-2Evaluate expressions involving squares, cubes and roots102, 103
1c-3Use index notation for powers of 10, including negative powers121
1c-4Use the laws of indices to multiply and divide numbers written in index notation105, 106
1c-5Use brackets and the hierarchy of operations with powers inside the brackets, or raising brackets to powers107
NumberFactors, multiples and primes1d-1List all three-digit numbers that can be made from three given integers670
1d-2Identify factors, multiples and prime numbers27, 28, 33
1d-3List all factors of a number and list multiples systematically31, 34
1d-4Find the HCF and LCM of integers29, 30
1d-5Find the prime factor decomposition of positive integers and write as a product using index notation29, 30
1d-6Find the LCM and HCF of two numbers, by listing, Venn diagrams and using prime factors: include finding LCM and HCF given the prime factorisation of two numbers32, 35
1d-7Solve simple problems using HCF, LCM and prime numbers36
Year 9 Half Term 2AlgebraAlgebra: the basics2a-1Write an expression151 - 153
2a-2Select an expression/equation/formula/identity from a list154
2a-3Simplify algebraic expressions involving addition/subtraction eg:Collecting like terms156, 157
2a-4Multiply together two simple algebraic expressions158
2a-5Divide two algebraic expressions eg: 28dpower 4 divide 7dsquared159
2a-6Use index laws in algebra173 - 175
AlgebraExpanding and factorising single brackets2b-1Simplify expressions involving brackets, i.e. expand the brackets160, 161
2b-2Simplify expressions involving brackets, i.e. expand the brackets, then add/subtract160, 161
2b-3Factorise algebraic expressions by taking out common factors168169
AlgebraExpressions and substitution into formulae2c-1Write expressions to solve problems representing a situation155
2c-2Substitute positive numbers in simple algebraic expressions780, 781
2c-3Substitute negative numbers into expressions784, 785
2c-4Substitute numbers into expressions involving brackets and powers782, 783
2c-5Substitute numbers into a formula279
Year 9 Half Term 3NumberFractions4a-1Write a fraction in its simplest form and find equivalent fractions59, 61
4a-2Order fractions, by using a common denominator60
4a-3Convert between mixed numbers and improper fractions63, 64
4a-4Add and subtract fractions, including mixed numbers65, 66
4a-5Understand and use unit fractions as multiplicative inverses67
4a-6Multiply a fraction by a fraction68,69
4a-7Understand and use unit fractions as multiplicative inverses70
4a-8Divide fractions by a whole number and fractions77 - 79
NumberFDP4b-1Find fraction of a quantity, including reverse fractions52, 73
4b-2Find reverse fractions73
4b-3Convert between fractions and decimals60, 46
4b-4Recognise recurring decimals and convert fractions75, 76
4b-5Compare and order fractions and decimal numbers149
4b-6Express a given number as a percentage of another number149
NumberPercentages4c-1Convert between fractions, decimals and percentages84, 85
4c-2Order fractions, decimals and percentages, including use of inequality signs88
4c-3Find a percentage of a quantity without a calculator93, 759, 760
4c-4Calculate percentage increase/decrease86
4c-5Use percentages in real-life situations
• Price after VAT (not price before VAT);
• Value of profit or loss;
• Simple interest;
• Income tax calculations
89
4c-6Use decimals to find quantities 90- 92
4c-7Use a multiplier to find a percentage of a quantity154
4c- 8Use a multiplier to increase or decrease by a percentage176
AlgebraEquations5a-1Select an expression/equation/formula/identity from a list
5a-2Write expressions and set up simple equations178, 179, 181, 182
5a-3Use function machines184, 185, 186
5a-4Solve simple linear equations183
5a-5Solve linear equations which contain brackets280-82
5a-6Solve linear equations in which the unknown appears on either side or on both sides of the equation180
5a-7Solve linear equations in one unknown, with integer or fractional coefficients287
5a-8Rearrange simple equations189
5a-9Substitute into a formula, and solve the resulting equation478, 813, 814, 552
5a-10Find an approximate solution to a linear equation using a graph188
5a -11Solve angle or perimeter problems using algebra265, 266
5a - 12Write an equation to solve a word problem267
Year 9 Half Term 4AlgebraInequalities5b-1Show inequalities on number lines268
5b-2Write down integer values that satisfy an inequality269 - 271
5b-3Construct inequalities to represent a set shown on a number line132
5b-4Solve simple linear inequalities134
5b-5Round answers to a given degree of accuracy774-777
5b -6Truncate numbers
5b - 7Use inequality notation to specify simple error intervals due to truncation or rounding197
AlgebraSequences5c-1Use function machines to find terms of a sequence198
5c-2Write the term-to-term definition of a sequence in words264
5c-3Find a specific term in the sequence using position-to-term or term-to-term rules261, 263
5c-4Generate arithmetic sequences of numbers196
5c-5Generate special sequences, such as triangular number, square and cube integers and sequences derived from diagrams198
5c-6Find the nth term of a linear sequence247
5c-7Find the nth term for a pattern sequence247
5c-8Answer questions using the sequence199
5c-9Continue a quadratic sequence and use the nth term to generate terms200
Year 9 Half Term 5AlgebraReal life graphs9a-1Draw, label and scale axes and identify points with given coordinates199
9a-2Find the coordinates of the midpoint of a line segment200
9a-3Draw and interpret straight-line graphs for real-life situations894, 895
9a-4Draw distance–time graphs 874 - 876
9a-5Interpret distance–time graphs877
9a-6Find the gradient of a straight line from real-life graphs201, 896
9a-7Interpret gradient as the rate of change in distance–time and speed–time graphs896
AlgebraStraight Line Graphs9b-1Use function machines to find coordinates
9b-2Plot and draw graphs of y = a, x = a, y = x and y = –x205
9b-3Plot and draw graphs of straight lines of the form y = mx + c using a table of values and recognise that equations of the form y = mx + c correspond to straight-line graphs206 - 209
9b-4Identify and interpret gradient from an equation y = mx + c. Sketch a graph of a linear function, using the gradient and y-intercept210
9b-5Identify parallel lines from their equations214
9b-6Plot and draw graphs of straight lines in the form ax + by = c280, 281
9b-7Find the equation of a straight line from a graph210 - 211
9b-8Find the equation of the line through one point with a given gradient212
9b-9Find approximate solutions to a linear equation from a graph
Ratio and ProportionRatio11a-1Write/interpret a ratio to describe a situation328
11a-2Write ratios in their simplest form329
11a-3Write a ratio as a fraction330
11a-4Write ratios in form of unit ratios331
11a-5Share a quantity in a given ratio including three-part ratios332
11a-6Use a ratio to find one quantity when the other is known333, 334
11a-7Use a ratio to convert between measures 707
Ratio and ProportionProportion11b-1Understand what is meant by direct proportion339, 340
11b-2Solve word problems involving direct proportion, including using the unitary method341
11b-3Understand inverse proportion and solve word problems involving inverse proportion342
11b-4Work out which product is the better buy763 - 770
11b-5Scale up recipes739 - 742
11b-6Convert between currencies707, 708
11b-7Recognise when values are in direct proportion by reference to the graph form and understand that for direct proportion y=kx343
Year 9 Half Term 6Geometry and MeasurePerimeter and area8a-1Convert between metric units 691
8a-2Measure shapes to find perimeters and areas using a range of scales553
8a-3Find the perimeter of triangles, rectangles, parallelograms and trapezia, including compound shapes548 - 552
8a-4Find the area of a rectangle and triangle554, 557
8a-5Find the area of a trapezium and recall the formula559
8a-6Find the area of a parallelogram556
8a-7Calculate areas and perimeters of compound shapes made from triangles and rectangles555, 558
8a-8Find the surface area of a prism using rectangles and triangles584, 585
8a-9Convert between metric area measures700, 701
Geometry and Measure3D forms and volume8b-1Identify and name common solids: cube, cuboid, cylinder, prism, pyramid, sphere and cone829, 830
8b-2Sketch nets of cuboids and prisms833- 836
8b-3Recall and use the formula for the volume of a cuboid568, 569
8b-4Find the volume of a prism, including a triangular prism, cube and cuboid570, 571
8b-5Estimate volumes etc by rounding measurements to 1 significant figure131
8b-6Convert between metric volume measures702, 703
8b-7Convert between metric measures of volume and capacity698, 699
Statistics and ProbabilityProbability 113a-1Use the language of chance to describe events (impossible, unlikely, even chance, likely and certain)349
13a-2Mark events and/or probabilities on a probability scale of 0 to 1350
13a-3Find the probability of an event happening using theoretical probability. Write the probabilities in fractions, decimals and percentages350 - 352
13a-4Find the probability of an event not happening353
13a-5Identify different mutually exclusive outcomes and know that the sum of the probabilities of all outcomes is 1354
13a-6List all outcomes for single events systematically670
13a-7Work out probabilities from frequency tables
13a-8Work out probabilities from two-way tables422, 423
Year 10 Half Term 1Statistics and ProbabilityProbability 213b-1Find the probability of an event happening using relative frequency356
13b-2Calculate expected frequency355
13b-3Use and draw sample space diagrams358, 359
13b-4Use tree diagrams to calculate the probability of two independent events360 - 363
13b-5Use tree diagrams to calculate the probability of two dependent events364 - 366
13b-6Use set notation, including union and intersection370 - 378
13b-7Work out probabilities from Venn diagrams to represent real-life situations379, 380
Geometry and MeasureProperties of shapes6a-1Know that there are 360° in a full turn, 180° in a half turn and 90° in a quarter turn455
6a-2Estimate sizes of angles457
6a-3Measure angles using a protractor458 - 460
6a-4Identify parallel lines821
6a-5Recall the properties and definitions of special types of quadrilaterals824 - 826
6a-6Use the fact that angle sum of a quadrilateral is 360°560
6a-7Recall and use properties of angles at a point, angles on a straight line, right angles, and vertically opposite angles477 - 480, 812 - 815
6a-8Distinguish between scalene, equilateral, isosceles and right-angled triangles823
6a-9Find missing angles in a triangle using the angle sum in a triangle and the properties of an special triangles485 - 487
6a-10Understand and use the angle properties of parallel lines481 - 483
Geometry and MeasurePolygons6b-1Recognise and name pentagons, hexagons, heptagons, octagons and decagons822
6b-2Understand ‘regular’ and ‘irregular’ as applied to polygons 822
6b-3Use the sum of angles of polygons561
6b-4Calculate and use the sums of the interior angles of polygons562
6b-5Use the sum of the exterior angles of any polygon is 360°563
6b-6Use the sum of the interior angle and the exterior angle is 180°564, 565
Year 10 Half Term 2Statistics and ProbabilityTables3a-1Sort, classify and tabulate data, both discrete and continuous, quantitative data, and qualitative data401 - 403, 392, 393
3a-2Use correct notation for time, 12- and 24-hour clock
3a-3Work out time taken for a journey from a timetable
3a-4Construct tables for time–series data450
3a-5Design and use two-way tables for discrete and grouped data422 - 424
3a-6Identify the mode from a frequency table and modal class from a grouped frequency table415
Statistics and ProbabilityCharts and graphsProduce and interpret:
3b-1• pictograms426
3b-2• composite bar charts425
3b-3• dual/comparative bar charts for categorical and ungrouped discrete data425
3b-4• bar charts and line charts425
3b-5• line graphs for time–series data450
3b-6• stem and leaf (including back-to-back)430 - 432, 434
Statistics and ProbabilityPie Charts3c-1Measure and draw angles, to the nearest degree461
3c-3Construct pie charts for categorical data and discrete/continuous numerical data427, 428
3c-4Find the mode and the total frequency from a pie chart429
Statistics and ProbabilityScatter Graphs3d-1Understand and identify the types of correlation. Draw and interpret scatter graphs453
3d-2Distinguish between positive, negative and no correlation using lines of best fit453, 454
3d-3Identify outliers and ignore them on scatter graphs453
3d-4Draw the line of best fit on a scatter diagram by eye and use the line of best fit to make predictions454
3d-5Use a line of best fit to predict values of a variable given values of the other variable453, 454
Year 10 Half Term 3Statistics and ProbabilityStatistics and Sampling7a-1Recognise types of data: primary, secondary, quantitative and qualitative392, 393
7a-2Identify which primary data they need to collect and in what format, including grouped data393
7a-3Understand how sources of data may be biased394
7a-4Explain why a sample may not be representative of a whole population394
7a-5Understand sample and population395
Statistics and ProbabilityAverages7b-1Calculate the mean, mode, median and range for discrete data404 - 410
7b-2Interpret and find the median, mean, mode and range from a (discrete) frequency table414 - 417
7b-3Interpret and find the range, modal class, interval containing the median, and estimate of the mean from a grouped data frequency table418
7b-4Interpret and find averages and the range from a bar chart 425
7b-5Interpret and find the median, mode, mean and range from stem and leaf diagrams430 - 433
7b-6Compare the mean, median, mode and range (as appropriate) of two distributions using bar charts, dual bar charts, pictograms and back-to-back stem and leaf
7b-7Recognise the advantages and disadvantages between measures of average413
Geometry and MeasureTransformations - Rotations and Translations10a-1Identify congruent shapes by eye680
10a-2Rotate a shape about the origin or any other point on a coordinate grid648, 649
10a-3Describe a rotation fully using the angle, direction of turn, and centre653, 654
10a-4Translate a given shape by a vector637, 638
10a-5Use column vectors to describe translations650
Year 10 Half Term 4Geometry and MeasureTransformations - Enlargements and Reflections10b-1Transform 2D shapes using single reflections 639 - 641
10b-2Describe reflections on a coordinate grid652
10b-3Enlarge a shape using a positive or fractional scale factor only
10b-4Enlarge a given shape using positive and fractional scale factors and a centre of enlargement642, 643
10b-5Describe an enlargement using the scale factor and centre of enlargement651
10b-6Combining transformations656, 657
Geometry and MeasurePythagoras and Trigonometry12-1Understand, recall and use Pythagoras’ Theorem in 2D to find the hypotenuse or a shorter side in a right angled triangle497 - 499
12-2Given 3 sides of a triangle, justify if it is right-angled or not497
12-3Apply Pythagoras’ Theorem to solve various problems, including area problems500 - 504
12-4Apply Pythagoras’ Theorem with a triangle drawn on a coordinate grid including calculating the length of a line segment AB given pairs of points
12-5Understand and recall the trigonometric ratios sine, cosine and tan and the trig values for 0, 30, 45, 60 and 90508
12-6Use trigonometry to find missing sides of a right angled triangle509, 510
12-7Use trigonometry to find missing angles in a right angled triangle511, 512
12-8Use the trigonometric ratios to solve 2D problems513, 514
12-9Find angles of elevation and depression515
Year 10 Half Term 5NumberIndices and Standard Form18-1Use index laws to simplify and calculate the value of numerical expressions105 - 107
18-2Use numbers raised to the power zero121
18-3Convert large and small numbers into standard form and vice versa122 - 124
18-4Add and subtract numbers in standard form127
18-5Multiply and divide numbers in standard form125, 126
18-6Use a calculator with standard form128
AlgebraQuadratic equations: expanding and factorising 16a-1Define a ‘quadratic’ expression222
16a-2Expand double brackets including the difference of two squares162 - 165
16a-3Factorise quadratic expressions of the form x² + bx + c221, 223
16a-4Factorise a quadratic expression x² – a² using the difference of two squares224
16a-5Solve quadratic equations by factorising230
16a-6Find the roots of a quadratic function253
AlgebraQuadratic equations: Graphs16b-1Generate points and plot graphs of simple quadratic functions251
16b-2Identify the line of symmetry of a quadratic graph254
16b-3Find approximate solutions to quadratic equations using a graph 253, 323
16b-4Identify and interpret roots, intercepts and turning points of quadratic graphs252 - 255
Year 10 Half Term 6Geometry and MeasurePerimeter, area and volume: circles, cylinders, cones and spheres17-1Identify, name and draw parts of a circle including tangent, chord and segment592
17-2Find the circumference of a circle, semi-circle and quarter circles, including giving your answers in terms of π534 - 538
17-3Find the area of a circle, semi-circle and quarter circles, including giving your answers in terms of π539 - 543
17-7Find the volume of a cylinder 572 - 574
17-8Find the surface area of a cylinder586
Ratio and ProportionMultiplicative Reasoning14-1Perform calculations involving speed716 - 724
14-2Perform calculations involving density725 - 731
14-3Calculate percentage profit or loss759, 760
14-4Find the original amount given the final amount after a percentage increase or decrease96
14-5Solve simple interest problems93
14-6Work out the multiplier for repeated proportional change as a single decimal number91, 92
14-7Solve problems involving repeated percentage change. Including compound percentage problems94, 95
14-8Solve proportion problems involving currency conversions707, 708
14-9Solve proportion problems involving rates of pay755, 756
14-10Solve proportion problems involving best buys763 - 772
Geometry and MeasurePlans and Elevations15a-1Draw circles and arcs to a given radius or given the diameter659
15a-2Measure and draw angles, to the nearest degree461
15a-3Draw sketches of 3D solids832
15a-4Know the terms face, edge and vertex830
15a-5Identify and sketch planes of symmetry of 3D solids827
15a-6Understand and draw front and side elevations and plans of shapes made from simple solids837 - 840
15a-7Given the front and side elevations and the plan of a solid, draw a sketch of the 3D solid841 - 844
Year 11Geometry and MeasureConstructions, loci and bearings 15b-1Construct the perpendicular bisector of a given line660
15b-2Construct the perpendicular from a point to a line662, 663
15b-3Construct the bisector of a given angle661
15b-4construct angles of 90°, 45°664
15b-5Solve problems involving loci674 - 678
15b-6Estimate lengths using a scale diagram864 - 866
15b-7Make an accurate scale drawing from a diagram867, 868
15b-8Use three-figure bearings to specify direction492 - 496
15b-9Mark on a diagram the position of point B given its bearing from point A869
Geometry and MeasureSimilarity and Congruence in 2D19a-1Understand congruence and solve angle problems involving congruence680, 681
19a-2Use the basic congruence criteria for triangles (SSS, SAS, ASA and RHS)682
19a-3Understand similarity of triangles and of other plane shapes608
19a-4Identify the scale factor of an enlargement of a shape609
19a-5Solve problems to find missing lengths in similar shapes610 - 614
Geometry and MeasureVectors19b-1Understand and use column notation in relation to vectors 622
19b-2Be able to represent information graphically given column vectors623, 624
19b-3Calculate using column vectors, and represent graphically, the sum of two vectors, the difference of two vectors and a scalar multiple of a vector625 - 628
AlgebraRearranging equations, graphs of cubic functions and simulataneous eqautions20-1Know the difference between an equation and an identity and use and understand the ≠ symbol 154
20-2Change the subject of a formula including the use of square roots and squares280 - 286
20-3Simple algebraic proofs325, 326
20-4Find the equation of the line through two given points213
20-5Recognise, sketch and interpret graphs of simple cubic functions298, 299
20-6Recognise, sketch and interpret graphs of the reciprocal function300, 301
20-7Solve simultaneous equations algebraically including in context191 - 195
20-8Solve simultaneous equations graphically218, 219