zilongwang/ReadingBank huggingface dataset:
(c) Prove the above proposition can be generalised to . (4 marks) Marking key for Test 3 – Unit 3 Section One: Calculator-free (28 marks) Question 1 Define the set of vertices and a list of edges for Graph 1. Solution Behaviours Marks Item* (S/C) Defines the vertices of Graph 1 Defines the edges of Graph 1 1 1 simple simple Is Graph 1 planar? Explain Solution Yes the graph is planar since it can be drawn such that none of the edges intersect other than at the vertices. Behaviours Marks Item* (S/C) States that Graph 1 is planar States that Graph 1 can be drawn where no edges intersect. 1 1 complex complex Question 2
(b) Write a rule that will calculate the number of pictures in album type = Tn. Solution Behaviours Marks Item* (S/C) Applies the linear rule with correct common difference d Calculates a from the table of values States the rule in terms of n 1 1 1 simple simple simple (c) Write a rule that will calculate the cost of album type = Cn. Solution Behaviours Marks Item* (S/C) Applies the linear rule with correct common difference d Calculates a from the table of values States the rule in terms of n 1 1 1 simple simple simple Section Two: Calculator-assumed section (24 marks) Question 5 (a) Complete the table below for the first five terms of the sequence, defined by . Solution Behaviours Marks Item* (S/C) Calculates at least two terms correctly Calculates all terms correctly 1 1 simple simple (b) Evaluate. Solution Behaviours Marks Item* (S/C) Evaluates 1 simple
Behaviours Marks Item* (S/C) States the correct change in population 1 simple (e) Estimate, to the nearest whole number, the maximum number of fish that may be removed from the tank per month without the numbers of fish decreasing. Solution Behaviours Marks Item* (S/C) Uses recurrence formula to check values of k Shows that causes a decrease in Q Shows that causes an increase in Q States k=35 is the maximum value for which Q increases 1 1 1 1 complex complex complex complex Question 7 For the recurrence relation (a) Deduce the rule for the nth term of the relation. Solution Behaviours Marks Item* (S/C)
Uses a linear relation such as Defines a and d correctly Simplifies the expression 1 1 1 simple simple simple (b) Check the truth of the following proposition . Solution Behaviours Marks Item* (S/C) Substitutes the correct values into the equation Demonstrates the LHS of the equation = RHS 1 1 simple simple (c) Prove the above proposition can be generalised to . Solution Behaviours Marks Item* (S/C) Sets up equations (1) and (2) Eliminates the constant by subtraction Rearranges the equation to give the result 2 1 1 complex complex complex
A1 3 1 (0.3,1.9) M1 A1A1 for substitution or for rearrangement one mark each coordinate 2 ( M1 A1A1 for substitution or for rearrangement one mark each coordinate Note: award B2 if roiunded to 1dp or worse 3 ( or (-1,-2) or answer given as x=, y= M1 M1 A1A1 substituting linear into non-linear forming quadratic in x one mark for each set of solutions 4 1(i) 7 M1 A1 9-2 1(ii) + M1 M1 A1 multiplying top and bottom by 3 + if one (or none) error only 2(i) 30√2 M1 A1 for √8 = 2√2 or √50 = 5√2 2(ii) + M1 M1 A1 multiplying top and bottom by 6 + denominator = 11 (or 33) 5 1(i) 1 B1 1(ii) a8 B1 1(iii) B1 B1 B1 3b a3 inverse 2(i) ±5 M1 A1 for or seen 2(ii) 8x10y13z4 (or 23x10y13z4) B3 B2 for 3 elements correct B1 for 2 elements correct 6 1(i) Grad AB = 1 Grad BC = -1 product of gradients = -1 hence perp M1 M1 C1 1(ii) 10 M1 A1 Use of pythagoras 2 y = -4x + 19 cao Midpoint (4,3) verifying on line x + 2y = 10 M1 M1 A1 B1 C1 calculating m using (y -7) = m(x-3) 7 1 Cubic the correct way up -1, 2 and 5 indicated on x-axis 10 indicated on y-axis G1 G1 G1
2 Negative quadratic curve Intercept (0,9) Through (3,0) and (-3,0) G1 G1 G1 3 Any correct y value calculated (0,5), (1,1), (2,-1), (3,-1), (4,1) and (5,5) calculated Above points plotted Smooth parabola through the points B1 B1 G1 G1 8 1 y = (x – 2)2 - 4 B2 M1 if y omitted, or for y = (x + 2)2 - 4 2(i) Translation of () B1 B1 2(ii) y = f(x – 2) B2 B1 for y = f(x + 2) 3(i) Translation of () B1 B1 3(ii) sketch of parabola right way up min at (0,-4) and graph through (-2,0) and (2,0) B1 B1 9 1(i) 15.5 M1 A1 Use of Pythagoras 1(ii) x = 75.5° M1 A1 (cos x = ) correct ratio and substitution 2 √8 or 2√2 (but not ± √8) M1 M1 A1 Use iof pythagoras use of tan Ɵ = opp / adj 3 Smooth curve between y = 1 and y = -1 (90,0) and (270,0) (0,1), (180,-1), (360,1) G1 G1 G1 10 1(i) 9.0 or 8.96 or 8.960 M1 M1 A1 for use of cosine rule for square-rooting ‘their’ 80.2(8) 1(ii) 13.3 or better (13.2577..) M1 A1 A1 use of ‘their’ 0.5 x 4.1 x 6.6 x sin 108 correct values ans 2 BC = 384 (or better) Total length = 1034m (or better) M1 M1 A1 A1 recognisable attempt at cosine rule BC2 = 3482 + 3022 – 2x348x302xcos72 BC = 383.86….. Total length = BC + 650 ft
The Bridge to A level Diagnosis 1 Solving quadratic equations Question 1 Solve x2 + 6x + 8 = 0 (2) Question 2 Solve the equation y2 – 7y + 12 = 0 Hence solve the equation x4 – 7x2 + 12 = 0
Make c the subject of the formula P = (4) Total / 10 3 Simultaneous equations Question 1 Find the coordinates of the point of intersection of the lines y = 3x + 1 and x + 3y = 6 (3) Question 2 Find the coordinates of the point of intersection of the lines 5x + 2y = 20 and y = 5 – x (3) Question 3 Solve the simultaneous equations x2 + y2 = 5 y = 3x + 1
(4) Total / 10 4 Surds Question 1 Simplify (3 + )(3 - ) (2) (ii) Express in the form a + b where a and b are rational (3) Question 2 (i) Simplify 5 + . Express your answer in the form a where a and b are integers and b is as small as possible. (2) (ii) Express in the form p + q where p and q are rational
(5) Total / 10 7 Sketching curves Question 1 In the cubic polynomial f(x), the coefficient of x3 is 1. The roots of f(x) = 0 are -1, 2 and 5. Sketch the graph of y = f(x) (3) Question 2 Sketch the graph of y = 9 – x2 (3) Question 3 The graph below shows the graph of y = On the same axes plot the graph of y = x2 – 5x + 5 for 0 ≤ x ≤ 5 (4) Total / 10 8 Transformation of functions Question 1 The curve y = x2 – 4 is translated by ( ) Write down an equation for the translated curve. You need not simplify your answer. (2) Question 2 This diagram shows graphs A and B.
A-Level Overview Year 2: Maths Term Teacher 1 Teacher 2 Key Skills / Coursework / PSAs / Deadlines 1 Binomial Theorem Formal Assignment Differentiation Formal Assignment Trigonometry Formal Assignment Parametric Equations Formal Assignment Make class notes Consolidate class learning with homework questions and reading text book Attend drop in help sessions on Tuesday afternoons after school when appropriate 2 Integration Formal Assignment Series and Sequences Formal Assignment Vectors Formal Assignment 3 Regression and Correlation Formal Assignment Probability Formal Assignment Moments and Forces Formal Assignment Application of kinematics and forces Formal Assignment 4 Normal Distribution Formal Assignment Further Kinematics Formal Assignment 5 Exam Preparation and Practice 6 A Level Exams
A-Level Overview Year 1: Maths (Further) Term Teacher 1 Teacher 2 Key Skills / Coursework / PSAs / Deadlines 1 Formal Assignments: Algebra and Coordinate Geometry Differentiaton and Integration Formal Assignments: Polynomials and Binomial expansion Algebra Trigonometry and Exponentials Make class notes Consolidate class learning with homework questions and reading text book Attend drop in help sessions on Tuesday afternoons after school when appropriate 2 Formal Assignments: Collecting, Representing and interpreting data Probability/Binomial and Hypothesis test Formal Assignments: Vectors and Units/Kinematics Forces and Newton’s laws 3 Formal Assignments: Proof and Algebra Binomial Theorem Integration Differentiation LARGE DATA SET work Formal Assignments: Numerical methods Trigonometry Parametric Equations Sequences and Series Vectors 4 Formal Assignments: Regression and Correlation Probability Normal Distribution Formal Assignments: Moments and Forces Application of kinematics and forces Further Kinematics 5 Past Paper Practice 6 A Level Exams Start Further Maths
3–4 Analysing time series data – examine and use concepts and techniques of time series analysis including smoothing data, calculating seasonal indices, deseasonalising a time series, modelling long-term trends and making predictions Task 6 (Week 4) 5 Loans, investments and annuities (4.2.1–4.2.7) Compound interest loans and investments – model, investigate and solve practical problems to compare compound interest loans, investments and depreciating assets 6–7 Reducing balance loans – model, investigate and solve practical problems involving loans with periodic repayments using a recurrence relation and with the aid of a financial calculator Task 7 (Week 7) 8–9 Annuities and perpetuities – investigate, model and solve practical problems associated with compound interest investments and loans with periodic payments made from the investment using a recurrence relation and with the aid of a financial calculator Task 8 (Week 9) 10 Networks and decision mathematics (4.3.1–4.3.1) Trees and minimum connector problems – identify minimal spanning trees and solve minimal connector problems using practical examples that can be represented by trees 11 Flow networks – solve small-scale network flow problems in practical situations including use of the ‘maximum flow-minimum cut’ theorem 12–13 Assignment problems – use graphs, tabular and/or matrix form to determine optimum assignment(s) by inspection or by using the Hungarian algorithm Task 9 (Week 13) 14 Project planning and scheduling using critical path analysis (CPA) – construct a network to represent a project and use a network to determine minimum time for completion, represent interdependencies and identify EST/LST and float times Task 10 (Week 14) 15 Semester 2 examination Task 11 (Examination week)
Year 2 2014 Mathematics Key Ideas in Number Class ______ Formative assessment Marking standard - Update as understanding develops Key idea not assessed Little understanding of key idea Some understanding of key idea Good understanding of key idea Whole Numbers Count forwards and backwards by twos, threes, fives and tens from any starting point Partition numbers of up to three digits using place value Read, write and order three-digit numbers Recognise, count and order Australian coins and notes according to their value Addition and Subtraction Make connections between addition and subtraction Use and record a range of mental strategies for addition and subtraction of two digit numbers Solve word problems involving addition and subtraction Multiplication and Division Model and use repeated addition as a strategy for multiplication Model and use arrays described in terms of ‘rows’ & ‘columns’ as a strategy for multiplication Model and use groups, arrays and repeated subtraction as strategies for division Record using drawings, words and numerals Fractions and Decimals Recognise, describe and represent halves, quarters and eighths of whole objects, shapes and collections Use fraction notation ¼ and ⅛
1.2 Three angles given:angle, angle, angle (: ΔABC with A = 80°, B = 60° and C = 40°. 1M per correct angle (3) 1A completion of triangle (1) 1.3 One side and two angles are given: side, angle, angle (S): ΔGHI with GH = 8 cm, G = 60° and H = 30°. 1M per correct angle (2) 1M per side with correct length (1) 1A completion of triangle (1) Answer Mark descriptor 1.4 If two sides and an inclusive angle are given: side, angle, side (SS): ΔJKL with JK = 9 cm, K = 130° and KL = 7 cm. 1M per angle with correct angle size (1) 1M per side with correct length
1A per correct ratio (6) 3.4 The corresponding sides are in the same relationship to each other. In this case the sides of Δ DEF are 1 as long as the sides of ΔBAC. 1A (1) 3.5 The sequence in which we write the letters in the notation of similar triangles indicate which sides correspond with the sides in the other triangle and which angles correspond with which angles in the other triangle. ΔBAC /// ΔDEF indicates thus: , A = E and C = F which are correct. 1A Mark descriptor (1) [15] SECTION B: ASSIGNMENT [30] QUESTION 1 Answer Mark descriptor 1 S,S,S SS S 90, Hypotenuse, S 1A per Answer (4) [4] QUESTION 2 2 Similar 1A (1) [1] QUESTION 3 3 3.1 Triangle ABC is congruent to triangle XYZ 1A naming of both triangles in correct order 1A term congruent (2)
A linear equation in two variables for example, and is an equation of the form , for example, . Matrices Addition of matrices If and are matrices of the same size (order) and the elements of are and the elements of are , then the elements of are For example, if SHORT ANSWER QUESTIONS Error! Bookmark not defined. SHORT ANSWER QUESTIONS Error! Bookmark not defined. and = SHORT ANSWER QUESTIONS Error! Bookmark not defined. SHORT ANSWER QUESTIONS Error! Bookmark not defined. then SHORT ANSWER QUESTIONS Error! Bookmark not defined. SHORT ANSWER QUESTIONS Error! Bookmark not defined. Elements (entries) of a matrix The symbol represents the () element occurring in the row and the column. For example, a general 3 2 matrix is: SHORT ANSWER QUESTIONS Error! Bookmark not defined. SHORT ANSWER QUESTIONS Error! Bookmark not defined. where is the element in the third row and the second column. Identity matrix A multiplicative identity matrix is a square matrix in which all of the elements in the leading diagonal are 1’s and the remaining elements are 0’s. Identity matrices are designated by the letter . For example, and are both identity matrices. There is an identity matrix for each size (or order) of a square matrix. When clarity is needed, the order is written with a subscript: Leading diagonal The leading diagonal of a square matrix is the diagonal that runs from the top left corner to the bottom right corner of the matrix. Matrix (matrices) A matrix is a rectangular array of elements or entities displayed in rows and columns. For example, = SHORT ANSWER QUESTIONS Error! Bookmark not defined. SHORT ANSWER QUESTIONS Error! Bookmark not defined.
WEEK 7 Numbers within 5 Say which number is 1 more or 1 less than a given number Estimate a number of objects and check by counting Count reliably within numbers 1-5 Place numbers 1-5 in order Say which number from 1-5 is 1 more or 1 less than a given number Recognise the numerals 1-5 Understand the conservation of number Week 8 Numbers within 5 Say which number is 1 more or 1 less than a given number Estimate a number of objects and check by counting Count reliably within numbers 1-5 Place numbers 1-5 in order Say which number from 1-5 is 1 more or 1 less than a given number Recognise the numerals 1-5 Understand the conservation of number EYFS PRINCIPLES Mathematics UNIQUE CHILD POSITIVE RELATIONSHIPS ENABLING ENVIRONMENT LEARNING AND DEVELOPMENT Recognising and praising effort so that every child develops positive attitudes to themselves as learners Consider each child’s: Unique development Individual interests Communication style Learning style Recognising and praising effort so that every child develops positive attitudes to themselves as learners Give children sufficient time, space and encouragement to discover new words, and mathematical ideas, concepts and ideas during activities Encourage children to explore real-life problems to make patterns, and to count and match together. Recognise the mathematical potential of the outdoor environment for children to discover things about shape, distance and measures through their physical activity. Exploit the mathematical potential of the indoor Develop mathematical understanding through all children’s early experiences including through stories, songs, games and imaginative play Provide a range of activities, some of which focus on mathematical learning and some which enable
Consider each child’s: Unique development Individual interests Communication style Learning style Support children who use a means of communication other than spoken English to develop and understanding specific mathematical language Value children’s own graphic and practical explorations of Problem solving, Reasoning and Numeracy. environment, enabling children to discover things about numbers, counting, and calculating Ensure that mathematical resources are readily available both indoors and outdoors mathematical learning to be drawn out., for example exploring shape, size and pattern during construction play. Use Mathematical terms during play and daily routines Outdoor maths opportunities: Snapshot focus in continuous provision Long focused obs
Maths Higher GCSE 2018 Topics after paper 1 Number Algebra Geometry Ratio and Proportion Statistics and Probability Rules of indices Estimate Fraction calculations Percentage profit Factorising difference of two squares Proof Expanding double brackets and simplifying Algebraic fractions Solving inequalities Perpendicular lines Plans and elevations Surface area Area triangle Transformations Geometric problems on axes Sharing by ratio Direct proportion Inverse proportion Speed Box Plot Best buys Currency LCM/HCF Product of primes Standard Form Error intervals Reciprocal Product rule for counting Conversion graphs Sequences (nth term) Changing the subject Graphing inequalities Simultaneous equations Quadratic / cubic graphs Iteration Completing the square Solve linear and quadratic equations Derive an equation Angles in parallel lines Bearings Angles in polygons Constructions and loci Circles, cones, spheres Pythagoras Trigonometry Similar shapes Area of triangle Vectors Density, pressure Fractions in ratio problems Convert between standard units (including area and volume) Reverse percentages Compound percentages Frequency trees Two-way tables Pie Charts Scatter Graphs Histograms Frequency polygons Stem and Leaf Cumulative Frequency Estimated mean Mean subset Estimate using probability Probability tree diagrams Conditional probability Capture Recapture Venn Diagrams
3.2.11 use first-order linear recurrence relations to model and analyse (numerically or graphically only) practical problems Topic 3.3: Graphs and networks (20 hours) The definition of a graph and associated terminology 3.3.1 demonstrate the meanings of, and use, the terms: graph, edge, vertex, loop, degree of a vertex, subgraph, simple graph, complete graph, bipartite graph, directed graph (digraph), arc, weighted graph, and network 3.3.2 identify practical situations that can be represented by a network, and construct such networks 3.3.3 construct an adjacency matrix from a given graph or digraph and use the matrix to solve associated problems Planar graphs demonstrate the meanings of, and use, the terms: planar graph and face 3.3.5 apply Euler’s formula, to solve problems relating to planar graphs Paths and cycles 3.3.6 demonstrate the meanings of, and use, the terms: walk, trail, path, closed walk, closed trail, cycle, connected graph, and bridge 3.3.7 investigate and solve practical problems to determine the shortest path between two vertices in a weighted graph (by trial-and-error methods only) 3.3.8 demonstrate the meanings of, and use, the terms: Eulerian graph, Eulerian trail, semi-Eulerian graph, semi-Eulerian trail and the conditions for their existence, and use these concepts to investigate and solve practical problems 3.3.9 demonstrate the meanings of, and use, the terms: Hamiltonian graph and semi-Hamiltonian graph, and use these concepts to investigate and solve practical problems Unit 4 Unit description This unit has three topics: ‘Time series analysis’, ‘Loans, investments and annuities’, and ‘Networks and decision mathematics’. ‘Time series analysis’ continues students’ study of statistics by introducing them to the concepts and techniques of time series analysis. The content is to be taught within the framework of the statistical investigation process. ‘Loans investments and annuities’ aims to provide students with sufficient knowledge of financial mathematics to solve practical problems associated with taking out or refinancing a mortgage and making investments. ‘Networks and decision mathematics’ uses networks to model and aid decision making in practical situations.
HOMEWORK - TERM TWO DEPARTMENT:Maths KS4 Year 9/10 WEEK DEADLINE LEVEL M1 M2/3 M4/5 M6 1 10th Nov GOLD Mymaths task Mathwatch Higher worksheets, pg 94, Q 2, 5, 6, 8, 9,10 & 11 Mymaths task Mathwatch Higher worksheets, pg 94, Q 2, 5, 6, 9 & 10 Mymaths task Mathwatch Higher worksheets, pg 94, Q 2, 5, 6, 7 & 9 Mymaths task Mathwatch Foundation worksheets, pg 94, Q 2, 5, 6 & 7 SILVER Mymaths task Mathwatch Higher worksheets, pg 94, Q 2, 5, 6, 8, 9 & 10 Mymaths task Mathwatch Higher worksheets, pg 94, Q 2, 5, 6, 7 & 9 Mymaths task Mathwatch Higher worksheets, pg 94, Q 2, 5, 6 & 7 Mymaths task Mathwatch Foundation worksheets, pg 94, Q 2, 5 & 6 BRONZE Mymaths task Mathwatch Higher worksheets, pg 94, Q 2, 5, 6, 9 & 10 Mymaths task Mathwatch Higher worksheets, pg 94, Q 2, 5, 6 & 7 Mymaths task Mathwatch Higher worksheets, pg 94, Q 2, 5 & 6 Mymaths task Mathwatch Foundation worksheets, pg 94, Q 2 & 5 2 17th Nov GOLD Mymaths task Mathwatch Higher worksheets, pg 96, Q 1, 2, 3 & 4 Mymaths task Mathwatch Higher worksheets, pg 96, Q 1, 2, 3 & 4b & 4d Mymaths task Mathwatch Higher worksheets, pg 96, Q 1, 2 & 3 Mymaths task Mathwatch Foundation worksheets, pg 96, Q 1 & 2 SILVER Mymaths task Mathwatch Higher worksheets, Mymaths task Mathwatch Higher worksheets, Mymaths task Mathwatch Higher worksheets, Mymaths task Mathwatch Foundation worksheets,
Session 1 10.30-11.15 1a 1b 1c 1d 1e 1f 1g 1h Julie Gallimore (NCP5 – St Edwards C of E, Leek) Matthew Stanlake and Hayley Coates (NCP2 – St Werburghs, Kingsley) Les Staves AQA Dave Bailey (St John Fisher Catholic College, Newcastle) Fiona Goddard (Independent Maths Consultant) Dave Miller (NCETM - PD Lead) Luke McNamara Ben McGarry (Outwood Grange Academies Trust, West Yorkshire) Phase focus Primary Primary P level / SEN Secondary Secondary Secondary Secondary Primary Workshop title Mastery lesson demonstration Singaporean Maths Mastery demonstration lesson. Very special maths – numeracy for pupils at P Levels Problem solving and transition of mastery to GCSE Singaporean style textbooks The Numicon approach motivating mathematicians and developing the use of C-P-A at Key Stage 3 Using manipulatives to develop mastery Same day intervention – learning from Shanghai Please indicate Preference 1 – 4 (1 = priority) Break 1 11.15-11.30 Session 2 11.30-12.15 2a 2b 2c 2d 2e 2f 2g 2h Repeat Repeat Repeat Repeat Repeat Repeat Repeat repeat
The Bridge to A level Test Yourself Mark Scheme Section Question Answer Marks Notes 1 1 x = ± 3 M2 M1 A1 Use of quadratic formula (M1) in x2 (M1) x2 = 9 cao 2(i) 4 (x – 3)2 - 9 B1 B1 M1A1 a = 4 b = 3 c = -9 2(ii) (3,-9) B2 B1 for each coordinate 2 1 B3 B2 for t omitted M1 for constructive first step M1 for finding square root of their ‘t2’ 2 M1 M1 A1 for 3x + mx = y + 5y oe for x(3 + m) or ft sign error 3 M1 M1 M1 for multiplying by x-2 for expanding brackets for cllecting x and ‘other’ terms
A1 7 1 Cubic the correct way up x-axis cuts at -1, 2, 4 shown y-axis cuts at 8 shown G1 G1 G1 2 Sketch of cubic correct way up Curve through (0,0) Curve touches x-axis at x=3 G1 G1 G1 3 Correct graph with clear asymptote at x = 2 (0, -0.5) shown G2 G1 (G1 for only one branch correct0 4 10 B1 8 1 y = x2 – 8x + 5 B1 2 f(x – 3) = (x – 3)3 –5(x – 3) + 2 (x2 – 6x + 9)(x – 3) f(x – x3 – 3x2 – 6x2 + 18x + 9x – 27 – 5x + 15 + 2 = x3 – 9x2 + 22x - 10 B1 B1 A1 B1 Substitution Partial expansion of cubic term All correct unsimplified Correct consolidation 3 f(x-4) = 2(x-4)3 + 7(x-4)2 – 7(x-4) – 12 2x3 – 17x2 + 33x M1 M1 M1 Substitution Correct expansion of one pair of brackets correct completion to given answer 4 (x + 1 – 3)(x – 2 – 3)(x – 4 – 3) ie (x -2)(x – 5)(x – 7) M1 A1 Allow one slip Oe 9 1 Tan 42° = 0.9004 = 13.5(06) m = height of pole M1 M1 A1 2 ± B3 B2 for either - or or ± oe or M1 for seen 3 (0, 0) ( 90, 1) (270, -1) (360, 0) B1 B1 B1 B1 10 1(i) C = 141.1….. Bearing = 038. 8 (accept 038.9) M1 M1 A1 A1 Correct attempt at cosine rule Correct full method for C C Bearing 1(ii) 3030 to 3050 acceptable M1 A1 Correct use of 0.5xaxbxsinC 2 AB = 7.80 (or better, 7.799…) Area = 52.2 to 52.3 M1 A1 M1 A1 Correct use of sine rule AB 2 x 0.5 x ’their AB’ x 11.4 x sin 36 Area
Use knowledge of number bonds and place value to subtract. Avoid counting on. Use questioning to help. How many tens in 40? What is one ten less? What is 10-2? 30 and 2 make? 40 – 2 =___ 30 – 4 =___ 20 - 1 =___ 30 – 5 =___ 40 – 3 =___ 20 - 6 =___ 40 - 7 = ___ 30 – 9 =___ 20 – 2 =___ 30 – 8 =___ 40 – 1 =___ 20 – 3 =___
b) Find the exact area by integration. {4 marks} c) Find the percentage error in the estimation made in (a) above. {2 marks} 23(a) Complete the table below for the function y = x3 – 4x. For -3 < x < 3 x -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 y -15 -5.625 1.875 -3 0 15 {2 marks} b) Draw the graph of y = x3 – 4x on the grid provided. {3 marks} c) Use your graph to solve i) x3 – 4x = 0 {1 mark} ii) x3 – 4x – 3 = 0 {2 marks}
Find the matrix and describe fully the transformation that maps A11B11C11D11 onto A111B111C111D111. (3 marks) Find the area of A111B111C111D111 (1 mark) The field book below gives measurement of a field. The distances are given in metres. AF= 100m. F 100 E40 80 60 D50 C40 40 20 B30 A Using a scale of 1cm represents 10m draw a map of the field with straight boundary edges. (4 marks) i) Find the area of the field in square metres. (5 marks)
ii) QRP (3 marks) Find the area of the land in hectares. (4 marks) a) Complete the table below for the function y = x3 + 2x2 – 3x – 4, to 1 d.p. (2 marks) x -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 y -4.0 0.4 1.6 0.0 -4.0 -4.9 6 b) On the axes provided, draw the graph of y = x3 + 2x2 – 3x – 4, using the values in the completed table. (2 marks)
Recap / focus on gaps in learning Recap / focus on gaps in learning Recap / focus on gaps in learning Key stage 3 Number systems Exploring time Exploring data Calculating Mathematical movement September year tests Measures Problem solving Money Shape and construction Time (recap) ASSESSMENT STAGE Got it? sheets Number systems including fractions Exploring time Exploring data and probability Calculating Mathematical movement Fill in the gaps Problem solving Money Shape and construction Time (recap) ASSESSMENT STAGE Got it? sheets Number systems including algebra Exploring time Calculating including fractions Mathematical movement Fill in the gaps Exploring data and probability Measures Problem solving Money Shape and construction Time (recap) July year tests Key stage 4 Number systems including fractions, decimals and percentages Data and statistics Problems and puzzles Time Assessment tests Shape and construction Calculating Finance Measures Fill in the gaps Number systems including fractions, decimals and percentages Data and statistics Problems and puzzles Time Entry level tests for year 11 Shape and construction Calculating Finance Fill in the gaps Number systems including fractions, decimals and percentages Data and statistics Problems and puzzles Time Assessment tests Shape and construction Calculating Finance Measures Fill in the gaps Sixth Form EL1 Number 0-20 Addition and Subtraction EL2 Properties of number Addition, multiplication and division EL1 Ratio EL2 Addition, multiplication and division Ratio EL1 Money Days of the week and time EL2 Money Calendar and time EL1 Measure Geometry EL2 Measure EL1 Geometry EL2 Geometry Charts and Graphs EL1 Statistics Revision EL2 Double and Halving
Level 3 Homework Exercise 3 Show all of your working! 1. The population of Aylesbury is 48700 and the population of Bracknell is 57500. (a) Find the total population for both towns. (b) How many more people live in Bracknell? 2. Calculate: (a) (85) 4+6 (b) 68 273 (c) 9 13 9 (d) 5773 3. The band “Josie Pussy Cats” came on stage at pm and performed for 2 hours 27 minutes. At what time did their performance end? 4. Round these numbers to 2 significant figures: (a) 3082 (b) 48·55 (c) 0·006249 (d) 1·7932 5. Make a neat sketch and find the missing angles (a) (b)
4 6.1 Year 1 Representatives to relay the message to Year 1 group, and ask that students arrive on time. Year 1 Rep 5 6.2 Year 3 Representatives to relay the message to the group that steady work throughout the semester is the route to success. Please attend the final lectures of the year. Year 3 Rep
5 4.4 Let itd know if specific help is needed and he will ask demonstrators in the workshops to assist. He will also investigate availability of model solutions. Year 2 reps, itd Done. Model solutions now available. 6 4.4 rsd to ask Edwin Flikkema if more help from PG’s could be made available at the next helpdesk session. rsd Done 7 4.9 MathSoc to email yus10 details and he will advertise within the department. thp18 Done 8 4.9 MathSoc to send information about these sessions to the Admin Team to circulate to all staff and students. thp18 Ongoing 9 6.0 Year Reps to advertise Careers Fair to all students. All Year reps Done 10 6.0 mrj11 to circulate more information about AberGrad to students. mrj11 Ongoing 11 6.0 MathSoc to advertise yus10’s employability emails on their FaceBook page. thp18 Ongoing 12 7.0 rsd to circulate details of IMPACS rep to Maths SSCC members. rsd Done 13 7.0 sif4 to raise again the problem of more plugs for laptops to be provided in PS Library sif4 Done. Now with Estates. 14 7.0 sif4 to raise request of 24 hour PS Library opening at a higher level meeting sif4 Done. Issue here is authorisation of access to the building. Matter arising: MA30110 Group Theory and MA38410 Control Theory deadlines have been moved to Fridays to help ease workload congestion, and aid module twinning arrangements. 3. Student Matters 3.1 TUN – There had been several complaints from Year 3 students about the exam timetable. Having decided to not use Saturdays, Timetabling had to fit 10 level 3 examinations into 10
Stage 0 PROMPT sheet 0/1 Recognise numerals 1 to 5 0/2 Counting objects Say and touch the number as you count 0/3 Counting up to 10 0/4 Count from a large group Say the number as you count each object To select 6 from this group of children 0/5 Select the numeral Check!! 3 9 1 7 2 6 5 10 4 8 0/6 Count a number of objects Say and count to find how many balls here 0/7 Estimate and check by counting I estimate there are 6 apples here. Check by counting! 0/8 More and fewer 1 2 3 4 5 6 1 2 3 0/9 Total number in two groups
Find the lightest – put it at the beginning Find the heaviest – put it at the end Lightest Heaviest 0/17 Order capacity (continued) Find the smallest capacity – put it at the beginning Find the largest capacity – put it at the end Smallest capacity Largest capacity 0/18 Everyday language related to time The months and seasons The days of the week Parts of a day 0/19 Everday language related to money Our coins 1p 2p 5p 10p 20p 50p £1 £2 0/20 Sequence familiar events A B C D A – Get out of bed C – Clean teeth D – Go to school B – Go to bed
2/27 Sequence of shapes Make these shapes into a pattern 2/28 Describe position, direction & movement LEFT RIGHT ANTICLOCKWISE CLOCKWISE Clockwise (1 right angle) or ¼ turn Anticlockwise(1 right angle) or ¼ turn Half turn (2 right angles) 2/29 Tables and graphs Tally chart showing animals in the zoo Animal Tally Number of animals Penguin llll 4 Lion lll 3 Snake llll l 6 Giraffe ll 2 Monkey llll ll 7 Block graph to show animals in the zoo 7 6 5 4 3 2 1 2/30 Questions about tables and graphs Example: Questions about ‘Animals in the zoo’
3/8 Estimate answers to calculations Round off each number Then do the calculation Check using the inverse Example: Estimate 83 – 28 80 – 30 = 50 Inverse: 50 + 30 = 80 3/9 Missing number problems Fact family for +/- 34 + 23 = 57 57 - 23 = 34 23 + 34 = 57 57 – 34 = 23 3/10 Know the 3, 4 and 8 times tables 1 x 3 = 3 2 x 3 = 6 3 x 3 = 9 4 x 3 = 12 5 x 3 = 15 6 x 3 = 18 7 x 3 = 21 8 x 3 = 24 9 x 3 = 27 10 x 3 = 30 11 x 3 = 33 12 x 3 = 36 1 x 4 = 4 2 x 4 = 8 3 x 4 = 12 4 x 4 = 16 5 x 4 = 20 6 x 4 = 24 7 x 4 = 28 8 x 4 = 32 9 x 4 = 36 10 x 4 = 40 11 x 4 = 44 12 x 4 = 48 1 x 8 = 8 2 x 8 = 16 3 x 8 = 24 4 x 8 = 32 5 x 8 = 40 6 x 8 = 48 7 x 8 = 56 8 x 8 = 64 9 x 8 = 72 10 x 8 = 80 11 x 8 = 88 12 x 8 = 96 Fact family for x/÷ 9 x 8 = 72 72 ÷ 9 = 8 8 x 9 = 72 72 ÷ 8 = 9 3/11 Multiply & divide A 2-digit number by a single digit Column method 3 8 3 x 1 1 4 2 Grid method 30 8 3 90 24 90 + 24 = 114 Partitioning method 38 x 3 = 30 x3 + 8 x 3 = 90 + 24 = 114 3/12 Multiply & divide Look for connections between two sums Remember the fact family for x/÷ Example: 6 x 4 = 24 So 60 x 4 = 240 So 240 ÷ 4 = 60 Example: 9 x 8 = 72 So 18 x 8 = 144 So 144 ÷ 8 = 18 3/13 Tenths tens units . tenths 8 2 6 This represents 6 tenths = Counting in tenths (continued)
The bigger the denominator, the smaller the fraction 3/19 Add & subtract measures The units must be the same Length – Example 3cm + 7mm = 30mm + 7mm = 37mm or 3cm 7mm or 3.7cm 3cm 0.7cm Mass – Example 3kg – 450g = 3000g – 450g = 2550g or 2kg 550g or 2.55kg 3/19 Add & subtract measures (continued) Volume – Example 800ml + 720ml = 1520ml = 1 litre and 520ml = 1.52 litres 3/20 Perimeter PERIMETER is the distance round the outside of a shape On a centimetre square grid – count round Perimeter of this shape = 12cm Measurements given - add up all round 6cm 4cm 4cm 6cm Perimeter of this shape = 6 + 4 + 6 + 4 = 20cm 3/21 Bills and change To work out a bill 1 chocolate bar - £1.10 1 pen – 10p 1 pencil – 8p Total = £1.28 To find change by the ‘add-on’ method +2p +20p +50p = 72p £1.28 £1.30 £1.50 £2.00 3/22 Time Analogue clock Roman Hindu-Arabic 12- and 24-hour clock
5/10 Multiplication using a formal method By a ONE-DIGIT number e.g. 3561 x 7 COLUMN METHOD 3561 7x 24927 3 4 e.g. 3561 x 7 GRID METHOD 3000 500 60 7 7 21000 3500 420 49 21000 + 3500 + 420 + 49 = 24927 By a TWO-DIGIT number e.g. 152 x 34 COLUMN METHOD 152 34x 608 (x4) 4560 (x30) 5168 e.g. 152 x 34 GRID METHOD 100 50 2 30 3000 1500 60 4 400 200 8 152 x 34 = 3400 + 1700 + 68 = 5168 5/10 Division using a formal method By a ONE-DIGIT number e.g. 9138 ÷ 6 1 5 2 6 6 )9311318 By a TWO-DIGIT number e.g. 4928 ÷ 32 SAME METHOD (Except write down some of your tables down first) 32 64 0 1 5 4 96 32 449172 128 128 160 4928 ÷ 32 = 154 e.g. 4928 ÷ 32 ALTERNATE METHOD Divide Multiply Subtract Bring down - Make a new number Divide ... 0 1 5 4 32 4 9 2 8 -3 2 1 7 2 -1 6 0 1 2 8 -1 2 8 0 0 0 4928 ÷ 32 = 154
can be shown in a diagram 1 ½ = 1½ Improper fraction Mixed number A mixed number can be changed back into an improper fraction 1½ = 2¾ = 5/16 Multiply fractions Multiply is the same as repeated addition + + x 3 = + + = = 2 OR x = = 2 5/17 Round decimals Rules for rounding Find the ‘round off’ digit Move one digit to its right Is this digit 5 or more Yes – add one to the round off digit No – don’t change the round off digit To the nearest whole number e.g. 1 – To round 5.62 to the nearest whole ‘round off’ digit this digit is 5 or more 5.62 rounded to nearest whole = 6 e.g. 2 – To round 5.32 to the nearest whole ‘round off’ digit this digit is NOT 5 or more 5.32 rounded to nearest whole = 5 To one decimal place e.g. 1 – To round 12.37 to 1 decimal place ‘round off’ digit this digit is 5 or more 12.37 rounded to 1dp = 12.4 e.g. 2 – To round 12.32 to the nearest whole ‘round off’ digit this digit is NOT 5or more 12.37 rounded to 1dp = 12.3
Know factors and factor pairs Prime numbers to 20. Know square and cube numbers. Common factors, common multiples, prime factors and composite numbers. Write simple fraction(e.g. ½ of 6 = 3) and recognise equivalence of ½ and 2/4. Know half of 1, 3, 5, 7, 9 and apply this to tens and hundreds AND to evens e.g. half of 27. Fractions equal to decimals Fractions = Decimals = Percentages Find percentages of quantities. Read time to O’ Clock and half past Read time to the quarter to and quarter past. Read a.m. and p.m. on a digital clock. Read time on analogue and 24 hour clock.
Say days of the week and months of the year Know the order of days of the week and months of the year. Know there are 7 days in a week, 52 weeks in a year and 365 days in a year. Know how many days in each month and leap years. Apply all date facts to simple problems. Name simple 2D shapes. Identify right angles within shapes in various orientations. Use a ruler accurately with mm Use a protractor
T1 T2 T3 T4 T5 T6 Calculations Geometry Fractions & Ratio Algebra Sequences & Graphs Equations Probability Statistics Trigonometry Revision Mocks in all 3 papers PPE’s in all 3 papers Exam Dates 24th May 2018 Exam Dates 7th June 2018 12th June 2018 Assessment English Language
Graphs Real World Graphs C Formulae C Angles 1 F 2D Shapes D Angles 2 D Measure C Area & Perimeter C 3D Shapes C Questionnaires E Collection and Bias D Pie charts E Comparing data sets D Pie charts to Bar charts D Averages & Range D Stem and Leaf D Class interval data C Scatter Graphs C
Probability 1 F Probability 2 E Probability 3 D Probability 4 C Calculator skills E Best buy D Percentages D Percentages C Equations D Equations C Inequalities C Quadratic Graphs C Formulae E Tessellation E Angles D Bearings D Circles C Nets E 3D elevations E 3D dimensions D
6% Semester 1 Week 7 Task 5: Determine cost and change when shopping from catalogues 8% Semester 1 Week 14 Task 8: Measure and mark the placement of plants for a hedge 7% Semester 1 Week 15 Task 9: Plan a journey between home and a concert using public transport: use timetables, addition and subtraction to calculate elapsed time 4% Semester 2 Week 2 Task 11: Prepare the ingredients for a recipe involving amounts expressed in fractions: fractions applied to mass and capacity 7% Semester 2 Week 12 Task 15: Prepare and determine the total cost of a shopping list to cater for a barbecue for a group of friends 6% Semester 2 Week 15 Task 18: Plan how to store 60 heavy cartons within a room 8% Semester2 Week 16 Task 19: How much fertiliser do you need to purchase to cover the garden and lawn? Total 100% 100%
Mathematics Curriculum Area Plan Measurement and Geometry Sample Program – Years 7 to 10 Approximate hours of teaching 3 6 9 12 15 18 21 24 27 Year 7 Semester 1 Angles, lines and shapes - 7.1.3 Length and area - 7.1.4 Sub-strand: Geometric reasoning Sub-strand: Using units of measurement Semester 2 Coordinates, graphs and transformations 7.2.5 Time and money - 7.2.6 Solids, volume, capacity and mass - 7.2.7 Sub-strand: Location and transformation Sub-strand: Using units of measurement Sub-strand: Using units of measurement; Shape (See number and algebra) (See number and algebra) Year 8 Semester 1 Properties of plane shapes - 8.1.3 Measurement: time and shapes - 8.1.4 Sub-strand: Geometric Sub-strand: Using units of measurement Semester 2 Angles, polygons and solids - 8.2.3 Volume and surface area 8.2.5 Sub-strand: Geometric reasoning Sub-strand: Using units of measurement Year 9 Semester 1 Pythagoras’ theorem - 9.1.2 Similarity and trigonometric ratios - 9.1.7 Sub-strand: Pythagoras and trigonometry Sub-strand: Geometric reasoning; Pythagoras and trigonometry Semester 2 Applications of trigonometry - 9.2.1 Shapes, prisms and cylinders - 9.2.4 Sub-strand: Pythagoras and trigonometry Sub-strand: Using units of measurement Year 10 Semester 1 Measurement - 10.1.1 Sub-strand: Using units of measurement Semester 2 Trigonometry - 10.2.2 Geometry - 10.2.3 Sub-strand: Pythagoras and trigonometry Sub-strand: Geometric reasoning Approximate hours of teaching 3 6 9 12 15 18 21 24 9 Key Measurement and Geometry sub-strand Topic, level, semester and sequence
Higher Key Topics Still To Come Up Algebra I can do this Title Iteration. Equation of a circle Gradients and area under a graph Factorising and Solving Quadratic equations (completing the square) Functions Expand 2 or 3 brackets Sequences Graphs and transformations of graphs Quadratic formula Simultaneous equations (linear and quadratic) Inequalities Algebraic fractions Forming and solving equations Equation of a line Changing the subject Geometry and Measures I can do this Title Vector arguments and proof Trigonometry inc Sine and Cosine rule Pythagoras and trig 2D and 3D Transformations Congruence and Similarity Arc lengths and sectors Loci Volume and area Alternate and corresponding angles Areas of triangles, trapezia and parallelograms Bearings Polygons Statistics I can do this Title Cumulative frequency Histograms with unequal class widths Scatter graphs Probability I can do this Title Conditional and Theoretical Probability Tree Diagrams Venn Diagrams Number I can do this Title Index Laws (negative and fractional) Recurring Decimals Upper and lower bounds Error intervals and accuracy Index Laws Checking calculations Compound measures Converting metric units Estimation Interpret calculator displays LCM and HCF and Prime Factorisation Standard Form Ratio, Proportion and rates of change I can do this Title Gradients and the rate of change Compound Units eg D, M, V Percentage change and reverse percentages Scale factors and similarity Simple and Compound Interest and depreciation
Math and Science Center Tutor Hours and Subjects Syeda Enayet Tuesday: 2 – 5 p.m. Wednesday: 2 – 5 p.m. Sunday: 4 – 7 p.m. Subject: MAT 100, 104, 143 ECN 131, 141 MGT 101 CJ Smith Monday: 2 – 4 & 6 – 9 p.m. Tuesday: Noon – 2 p.m. Sunday: 6 – 9 p.m. Subjects: MAT 100, 104, 151, 201, 202 CHE 103, 105, 211, 212, 331, 332 Anastasia Fitzpatrick Wednesday: 5 – 9 p.m. Sunday: 1– 4 p.m. Subjects: MAT 100, 104 BIO 101, 102 Kelsey Dowdall Monday: 3 – 6 p.m. Tuesday: 5 – 9 p.m. Thursday: 5 – 9 p.m. Subjects: MAT 100, 104, 112, 151, 201, 202, 301, 303, 305, 313 Hnin Phyo Friday: 12:30 – 5 p.m. Sunday: 12:30 – 2 p.m. Subjects: MAT 100, 124, 143 ACC 201 Tony Nguyen Thursday: 12:30 – 2 & 4 – 6 p.m. Friday: 12:30 – 3 p.m. Subjects: MAT 100, 124 ACC 201 ECN 131
Set Theory (Introductory) Video (about 25 mins) Introduction to Set Concepts and Venn Diagrams Venn Diagrams Video (about 25 mins) Practical Video Tutorial on Venn Diagram – demonstrates solutions to given problems. Boolean Logic Website This site is dedicated to growing awareness and interest among students about the broader impact of maths, exemplified by the unique contribution of George Boole Contains Teacher Lesson Plans and Worksheets that show a different approach to teaching STEM skills through real world puzzles and fun activities. University College Cork (UCC) Downloads include Number Tricks, Geometrical Approach to Counting, Teacher Workshop and Handbook Website circles allow students the space to develop their problem solving skills in an environment that isn't driven by any goal other than the enjoyment of investigation and discovery.circles allow students the space to develop their problem solving skills in an environment that isn't driven by any goal other than the enjoyment of investigation and discovery Maths Circles Binary Arithmetic Game Cisco Binary Game Cisco Binary Arithmetic Game Binary Number Game Number Systems Worksheet Website A website for generating ‘free to use’ worksheets in PDF format.
Themes addressed include Popular Math Insights, Arithmetic & Number, Algebra and Counting, Geometry, Trigonometry, Statistics and Calculus. license. General Website mathstutor.ie – free for teachers – collection of maths videos but targeted to project maths. Some of the resources may be of use at level 5. Eamon Toland – founder and managing director. General Website studyclix.ie – free for teachers – collection of resources for a variety of subjects including maths. Maths section is focussed on project maths but linking to certain videos suitable for level 5 is probably the best solution. Studyclix is an innovative education company based at the Innovation Centre at Sligo Institute of technology. Created by Luke Saunders and Keith Wright. General Website A series of resources covering Arithmetic, Algebra, Functions/Graphs, Geometry, Vectors, Trigonometry, Differentiation and Integration Each topic contains a video tutorial, support text, diagnostic test and an exercise to do. Some topics also have an extension film mathtutor.ac.uk is developed by a group of teachers, mathematicians and new media producers from the Universities of Leeds, Lougborough
Mathematics Curriculum Area Plan Incorporating Statistics and Probability Sample Program – Year Prep to Year 6 Approximate hours of teaching 3 6 9 12 15 18 Prep Semester 1 0.1.3 Collecting Data Sub-strand: Data and Representation Semester 2 0.2.3 Interpreting Data Sub-strand: Data Representation and Interpretation Year 1 Semester 1 1.1.3 Represent Data and Use to Predict Future Outcomes 1.1.12 Will it Happen Sub-strand: Data and Representation Sub-strand: Data Representation and Interpretation Semester 2 1.2.3 Represent Data and Developing Questions 1.2.5 Recognise and Classify 3D Shapes Sub-strand: Data Representation and Interpretation Sub-strand: Shape Year 2 Semester 1 2.1.3 Language of Chance Sub-strand: Chance Semester 2 2.2.3 Asking Questions, and Collecting, Showing and Interpreting Data Sub-strand: Data Representation and Interpretation Year 3 Semester 1 3.1.5 Data Representation and Interpretation Sub-strand: Data Representation and Interpretation Semester 2 3.2.5 Chance and Probability Sub-strand: Chance Year 4 Semester 1 4.1.5 Data Representation and Interpretation Sub-strand: Data Representation and Interpretation Semester 2 4.2.5 Chance and Probability Sub-strand: Chance Year 5 Semester 1 5.1.6 Representing and Interpreting Data Sub-strand: Data Representation and Interpretation Semester 2 5.2.6 Qualifying Chance as a Fraction Sub-strand: Chance Year 6 Semester 1 6.1.6 Comparing Representations of Data Sub-strand: Data Representation and Interpretation Semester 2 6.2.6 Quantifying Chance as a Fraction, Decimal and Percent Sub-strand: Chance Approximate hours of teaching 3 6 9 12 15 18 Key Statistics and Probability Strand
ANSWER SHEET NAME:__________________________ Q 2.1 Hours (h) 0 1 2 4 5 10 Kilometers covered (km) 0 2,59 10,36 23,31 31,08 Q 2.4 Q 6.2
Lesson Observation Grid 2017/18: Mathematics (parts 1,2 &3 to be completed) Part 1: General Observation: attach to eRPD Grade 1 2 3 4 Stds 1, 7 Pupils’ attitudes to learning are exemplary. Approach is enthusiastic and motivational. There is a systematic, consistently and confidently applied approach to behaviour management. Lesson proceeds without unnecessary interruption in a purposeful environment. Sets high expectations and generates high commitment to learning in most pupils. Children must use skills of independence to succeed, with support mechanisms in place. Pupils are typically considerate, respectful and courteous. Consistently enthusiastic. Pupils respond very well to the teacher’s behaviour systems and work cooperatively with each other. Low level disruption is uncommon and children only need occasional reminders to stay on task. Gives regular opportunities to work independently and sets high expectations. Promotes resilience and confidence in pupils so they can tackle challenging tasks independently. Has some rapport with the class and shows some enthusiasm for the role Can use school behaviour policy consistently and fairly but pupils do not always respond promptly to teacher’s direction. Major disruption to learning is uncommon, but occasional low-level disruption may occur. The children have opportunities to demonstrate independence during lesson. Beginning to set appropriately high expectations for behaviour and learning. Rapport with class not yet established. Enthusiasm for the teacher’s role is not always apparent. School behaviour policy used but with inconsistencies. Pupils’ lack of engagement and persistent low-level disruption contribute more than occasionally to reduced learning and/or a disorderly classroom environment. Classroom practice does little to promote independence. Expectations for learning and behaviour not established consistently. Trainee name: Yr Gp. Date: Observer name: No. Pupils