trying the resource. In this way the scheme will evolve...
21
This is intended as a starting point for lesson planning The main textbook resource will be “Maths Frameworking Book 3” supported by the use of “Teachers pack 3” Although the teachers pack does contain ideas for a starter, main activity and plenary for every lesson it is expected that staff will adapt these (and use their own ideas) as necessary to suit the needs of their students. The number of lessons listed is only intended as a guide and again staff can be flexible in their approach to ensure that their students make the best possible progress. It is expected that staff will use other resources such as - KS3 Boardworks software package - Vickers level 5 to 7 - SMP Booklets - Impact textbook 2R - Use of other ICT packages as appropriate Each module has sections “ICT” and “Other Resources”. If you use a different resource in your lessons and it proves successful please update the electronic version of this scheme (in maths shared area) so that other staff will have the option of also
Transcript of trying the resource. In this way the scheme will evolve...
This is intended as a starting point for lesson planning
The main textbook resource will be “Maths Frameworking Book 3” supported by the use of “Teachers pack 3”
Although the teachers pack does contain ideas for a starter, main activity and plenary for every lesson it is expected that staff will
adapt these (and use their own ideas) as necessary to suit the needs of their students.
The number of lessons listed is only intended as a guide and again staff can be flexible in their approach to ensure that their
students make the best possible progress.
It is expected that staff will use other resources such as
- KS3 Boardworks software package - Vickers level 5 to 7
- SMP Booklets - Impact textbook 2R
- Use of other ICT packages as appropriate
Each module has sections “ICT” and “Other Resources”. If you use a different resource in your lessons and it proves successful
please update the electronic version of this scheme (in maths shared area) so that other staff will have the option of also
trying the resource. In this way the scheme will evolve and we will also share good practice with each other.
Number and Algebra 1 CHAPTER 1
LESSON 1.1 Framework objectives – Multiplying and dividing negative numbers
Add, subtract, multiply and divide integers.
LESSON 1.2 Framework objectives – HCF and LCM
Recognise and use multiples, factors (divisors), common factor, highest common factor, lowest common multiple and primes.
LESSON 1.3 Framework objectives – Powers and roots
Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers.
LESSON 1.4 Framework objectives – Prime factors
Find the prime factor decomposition of a number.
LESSON 1.5 Framework objectives – Sequences 1
Generate and describe integer sequences. Generate terms of a linear sequence using termtoterm and positiontoterm definitions of the sequence.
LESSON 1.6 Framework objectives – Sequences 2
Begin to use linear expressions to describe the nth term of an arithmetic sequence, and justify its form by referring to the activity or practical context from which it was generated.
LESSON 1.7 Framework objectives – Solving problems
Solve more demanding problems and investigate in a range of contexts: algebra. Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techniques for calculation, algebraic manipulation and graphical representation.
Other resources Impact maths book 2R – see separate guides linking impact to units
ICT Boardworks
Shape, Space and Measures 1 CHAPTER 2
LESSON 2.1 Framework objectives – Alternate and corresponding angles
Solve problems using properties of angles, of parallel and intersecting lines, and of triangles
LESSON 2.2 Framework objectives – Interior and exterior angles of polygons
Explain how to find, calculate and use: the sum of the interior and exterior angles of quadrilaterals, pentagons and hexagons the interior and exterior angles of regular polygons. Solve problems using properties of polygons.
LESSON 2.3 Framework objectives – Geometric proof
Understand proofs that: The sum of the angles of a triangle is 180° and of a quadrilateral is 360°. The exterior angle of a triangle is equal to the sum of the two interior opposite angles.
LESSON 2.4 Framework objectives – The geometric properties of quadrilaterals
Solve geometrical problems using side and angle properties of special quadrilaterals, explaining reasoning with diagrams and text. Classify quadrilaterals by their geometric properties. Investigate in a range of contexts: shape and space.
LESSON 2.5 Framework objectives – Constructions
Use a straight edge and compasses to construct: the midpoint and perpendicular bisector of a line segment; the bisector of an angle; the perpendicular from a point to a line; the perpendicular from a point on a line. a triangle, given a right angle, the hypotenuse and a side (RHS)
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Handling Data 1 CHAPTER 3
LESSON 3.1 Framework objectives – Probability
Use the vocabulary of probability when interpreting the results of an experiment; appreciate that random processes are unpredictable.
LESSON 3.2 Framework objectives – Probability scales
Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 – p. Know that the sum of the probabilities of all mutually exclusive outcomes is 1, and use this when solving problems.
LESSON 3.3 Framework objectives – Mutually exclusive events
Find and record all mutually exclusive outcomes for single events and two successive events in a systematic way. Identify all the mutually exclusive outcomes of an experiment.
LESSON 3.4 Framework objectives – Calculating probabilities
Find and record all the possible outcomes for single events and two successive events in a systematic way, using diagrams and tables.
LESSON 3.5 Framework objectives – Experimental probability
Estimate probabilities from experimental data. Understand that: if an experiment is repeated there may be, and usually will be, different outcomes increasing the number of times an experiment is repeated generally leads to better estimates of probability. Compare experimental and theoretical probabilities in a range of contexts; appreciate the difference between mathematical explanation and experimental evidence.
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Number 2 CHAPTER 4
LESSON 4.1 Framework objectives – Fractions and decimals
Know that a recurring decimal is a fraction; use division to convert a fraction to a decimal; order fractions by writing them with a common denominator or by converting them to decimals. Order decimals.
LESSON 4.2 Framework objectives – Adding and subtracting fractions
Add and subtract fractions by writing them with a common denominator; calculate fractions of quantities (fraction answers); multiply and divide an integer by a fraction.
LESSON 4.3 Framework objectives – Percentages
Interpret percentage as the operator ‘so many hundredths of’ and express one given number as a percentage of another.
LESSON 4.4 Framework objectives – Percentage increase and decrease
Use the equivalence of fractions, decimals and percentages to compare proportions; calculate percentages and find the outcome of a given percentage increase or decrease.
LESSON 4.5 Framework objectives – Reallife problems
Recall known facts, including fraction to decimal conversions; use known facts to derive unknown facts, including products such as 0.7 and 6, and 0.03 and 8.
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Algebra 2 CHAPTER 5
LESSON 5.1 Framework objectives – Algebraic shorthand
Begin to distinguish the different roles played by letter symbols in equations. Simplify algebraic expressions.
LESSON 5.2 Framework objectives – Like terms
Simplify or transform linear expressions by collecting like terms.
LESSON 5.3 Framework objectives – Expanding brackets
Know that algebraic operations follow the same conventions and order as arithmetical operations. Multiply a single term over a bracket. Simplify algebraic expressions by taking out singleterm common factors.
LESSON 5.4 Framework objectives – Using algebra with shapes
Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket.
LESSON 5.5 Framework Objectives – Index notation with algebra
Know that algebraic operations follow the same conventions and order as arithmetic operations; use index notation for small positive integer powers. Know simple instances of the index laws.
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Shape, Space and Measures 2 CHAPTER 6
LESSON 6.1 Framework objectives – The circle
Know the definition of a circle and the names of its parts.
LESSON 6.2 Framework objectives – Circumference of a circle
Know and use the formula for the circumference of a circle.
LESSON 6.3 Framework objectives – Area of a circle
Know and use the formula for the area of a circle.
LESSON 6.4 Framework objectives – Surface area and volume of prisms
Convert between area measures (mm2 to cm2, cm2 to m2, and vice versa) and between volume measures (mm3 to cm3, cm3 to m3, and vice versa). Calculate the surface area and volume of right prisms.
LESSON 6.5 Framework objectives – Imperial units
Use units of measurement to estimate, calculate and solve problems in everyday contexts involving length, capacity and mass; know rough metric equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons).
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Algebra 3 CHAPTER 7
LESSON 7.1 Framework objectives – Linear functions
Express simple functions in symbols; represent mappings expressed algebraically.
LESSON 7.2 Framework objectives – Finding a function from its inputs and outputs
Express simple functions in symbols; represent mappings expressed algebraically. Find the inverse of a linear function.
LESSON 7.3 Framework objectives – Graphs from functions
Plot the graphs of linear functions such as y = mx + c and ay + bx = c.
LESSON 7.4 Framework objectives – Gradient of a straight line
Recognise that equations of the form y = mx + c correspond to straightline graphs. Know the meaning of m and c in the graph of y = mx + c.
LESSON 7.5 Framework objectives – Reallife graphs
Construct linear functions arising from reallife problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations. Discuss and interpret distance–time graphs.
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Number 3 CHAPTER 8
LESSON 8.1 Framework objectives – Powers of 10
Read and write positive integer powers of 10; multiply and divide integers and decimals by 0.1, 0.01
LESSON 8.2 Framework objectives – Rounding
Round positive numbers to any given power of 10; round decimals to the nearest whole number or to one or two decimal places.
LESSON 8.3 Framework objectives – Estimations
Make and justify estimates and approximations of calculations. Check a result by considering whether it is of the right order of magnitude and by working the problem backwards.
LESSON 8.4 Framework objectives – Adding and subtracting decimals
Consolidate standard column procedures for addition and subtraction of integers and decimals with up to two places; round numbers to three decimal places.
LESSON 8.5 Framework objectives – Efficient calculations
Carry out more difficult calculations effectively and efficiently using the calculator function keys for sign change, powers, roots and fractions; use brackets and the memory.
LESSON 8.6 Framework objectives – Multiplying and dividing decimals
Use standard column procedures for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations.
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Shape, Space and Measures 3 CHAPTER 9
LESSON 9.1 Framework objectives – Congruent shapes
Know that if two 2D shapes are congruent, corresponding sides and angles are equal.
LESSON 9.2 Framework objectives – Combinations of transformations
Transform 2D shapes by simple combinations of rotations, reflections and translations, on paper and using ICT. Know that translations, rotations and reflections preserve length and angle and map objects on to congruent images.
LESSON 9.3 Framework objectives – Enlargements
Recognise that enlargements preserve angle but not length, and understand the implications of enlargement for perimeter. Identify the scale factor of an enlargement as the ratio of the lengths of any two corresponding line segments. Enlarge 2–D shapes, given a centre of enlargement and a negative whole number scale factor, on paper.
LESSON 9.4 Framework objectives – Planes of symmetry
Identify reflection symmetry in 3D shapes.
LESSON 9.5 Framework objectives – Shape and ratio
Consolidate understanding of the relationship between ratio and proportion; reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation. Interpret and use ratio in a range of contexts.
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Algebra 4 CHAPTER 10
LESSON 10.1 Framework Objectives – Solving equations
Solve linear equations with integer coefficients, with and without brackets.
LESSON 10.2 Framework Objectives – Equations involving negative numbers
Solve linear equations with integer coefficients, with and without brackets, and with negative signs anywhere in the equation.
LESSON 10.3 Framework Objectives – Equations with unknowns on both sides
Solve linear equations with integer coefficients, (unknown on both sides), with and without brackets.
LESSON 10.4 Framework Objectives – Substituting into expressions
Substitute integers into simple expressions and formulae.
LESSON 10.5 Framework Objectives – Substituting into formulae
Substitute integers into simple expressions and formulae.
LESSON 10.6 Framework objectives – Creating your own expressions and formulae
Derive simple formulae.
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Handling Data 2 CHAPTER 11
LESSON 11.1 Framework objectives – Statistical surveys
Discuss a problem that can be addressed by statistical methods and identify related questions to explore. Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources. Plan how to collect the data, including sample size; design and use twoway tables for discrete data. Collect data using a suitable method, such as observation, controlled experiment, including datalogging using ICT, or questionnaire Communicate orally and on paper the results of a statistical enquiry and the methods used, using ICT as appropriate, justify the choice of what is presented.
LESSON 11.2 Framework objectives – Stemandleaf diagrams
Calculate statistics, including with a calculator; recognise when it is appropriate to use the range, mean, median and mode; construct and use stemandleaf diagrams.
LESSON 11.3 Framework objectives – Interpreting graphs and diagrams
Gather data from specified secondary sources, including printed tables and lists from ICT based sources. Discuss how data relate to a problem. Interpret graphs and diagrams, and draw inferences to support or cast doubt on initial conjectures.
LESSON 11.4 Framework objectives – Scatter graphs
Construct, on paper and using ICT: pie charts for categorical data; bar charts and frequency diagrams for discrete data; simple scatter graphs. Identify which are most useful in the context of the problem. Interpret tables, graphs and diagrams for discrete data and draw inferences that relate to the problem being discussed; relate summarised data to the questions being explored.
LESSON 11.5 Framework objectives – Analysing data
Discuss a problem that can be addressed by statistical methods and identify related questions to explore. Decide which data to collect to answer a question, and the degree of accuracy
needed; identify possible sources. Plan how to collect the data, including sample size; design and use twoway tables for discrete data. Collect data using a suitable method, such as observation, controlled experiment, using ICT, or questionnaire. Communicate orally and on paper the results of a statistical enquiry and the methods used, using ICT as appropriate; justify the choice of what is presented
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Number 4 CHAPTER 12
LESSON 12.1 Framework objectives – Fractions
Understand addition and subtraction of fractions; use the laws of arithmetic and inverse operations.
LESSON 12.2 Framework objectives – Adding and subtracting fractions
Understand addition and subtraction of fractions; use the laws of arithmetic and inverse operations.
LESSON 12.3 Framework objectives – BODMAS
Use the order of operations, including brackets with more complex calculations.
LESSON 12.4 Framework objectives – Multiplying decimals
Use standard column procedures for multiplication of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations.
LESSON 12.5 Framework objectives – Dividing decimals
Use standard column procedures for division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations.
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Algebra 5 CHAPTER 13
LESSON 13.1 Framework objectives – Expand and simplify
Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket.
LESSON 13.2 Framework objectives – Solving equations by trial and Improvement
Solve equations by trial and improvement.
LESSON 13.3 Framework objectives – Constructing equations to solve
Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g., inverse operations, transforming both sides in same way).
LESSON 13.4 Framework objectives – Problems with graphs
Plot the graphs of linear functions, where y is given explicitly in terms of x.
LESSON 13.5 Framework objectives – Reallife graphs
Plot graphs arising from reallife problems; discuss and interpret graphs arising from real situations.
LESSON 13.6 Framework objectives – Change of subject
Simplify or transform linear expressions by collecting like terms.
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Solving Problems CHAPTER 14
LESSON 14.1 Framework objectives – Number and measures
Solve more demanding problems and investigate in a range of contexts: number and measures. Solve increasingly demanding problems and evaluate solutions; explore connections in mathematics across a range of contexts.
LESSON 14.2 Framework objectives – Using algebra, graphs and diagrams to solve problems
Identify the necessary information to solve a problem; represent problems and interpret solutions in algebraic or graphical form, using correct notation. Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techniques for calculation. Begin to use graphs and set up equations to solve simple problems involving direct proportion.
LESSON 14.3 Framework objectives – Logic and proof
Use logical arguments to establish the truth of a statement; give solutions to an appropriate degree of accuracy in the context of the problem. Suggest extensions to problems, conjecture and generalise; identify exceptional cases or counterexamples. Present a concise, reasoned argument, using symbols, diagrams and graphs, and related explanatory text.
LESSON 14.4 Framework objectives – Proportion
Consolidate understanding of the relationship between ratio and proportion. Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100% or as a whole.
LESSON 14.5 Framework objectives – Ratio
Reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation; divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion. Compare two ratios; interpret and use ratio in a range of contexts, including solving word problems.
Other resources Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Shape, Space and Measures 4 CHAPTER 15
LESSON 15.1 15.2 Framework objectives – Plans and elevations
Visualise and use 2D representations of 3D objects; analyse 3D shapes through 2D projections, including plans and elevations.
LESSON 15.3 Framework objectives – Scale drawings
Use and interpret scale drawings.
LESSONS 15.4 Framework objectives – Finding the midpoint of a line segment
Given the coordinates of points A and B, find the midpoint of the line segment AB.
LESSON 15.5 Framework objectives – Map scales
Use and interpret maps.
LESSON 15.6 Framework objectives – Loci
Find simple loci, both by reasoning and by using ICT, to produce shapes and paths.
LESSON 15.7 Framework objectives – Bearings
Use bearings to specify direction.
LESSON 15.8 Framework objectives – A cube investigation
Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shapes made from cuboids.
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
Handling Data 3 CHAPTER 16
LESSON 16.1 Framework objectives – Collecting data and frequency tables
Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources. Plan how to collect data, including sample size; construct frequency tables with equal class intervals for sets of continuous data. Discuss how data relate to a problem; identify possible sources, including primary and secondary sources. Design a survey or experiment to capture the necessary data from one or more sources; determine the sample size and degree of accuracy needed; design, trial and if necessary refine data collection sheets.
LESSON 16.2 Framework objectives – Assumed mean and working with Statistics
Calculate statistics, including with a calculator; calculate a mean using an assumed mean.
LESSON 16.3 Framework objectives – Drawing frequency diagrams
Construct, on paper and using ICT: bar charts and frequency diagrams for continuous data; simple line graphs for time series. Identify which are most useful in the context of the problem.
LESSON 16.4 Framework objectives – Comparing data
Interpret tables, graphs and diagrams for continuous data and draw inferences that relate to the problem being discussed; relate summarised data to the questions being explored. Compare two distributions using the range and one or more of the mode, median and mean.
LESSON 16.5 Framework objectives – Comparing sets of data
Compare two or more distributions or make inferences, using the shape of the distributions, the range of data and appropriate statistics.
LESSON 16.6 Framework objectives – Experimental and theoretical probability
Communicate orally and on paper the results of a statistical enquiry and the methods used, using ICT as appropriate; justify the choice of what is presented. Compare experimental and theoretical probabilities in different contexts.
Solve more complex problems by breaking them into smaller steps or tasks, choosing and using graphical representation, and also resources, including ICT. Appreciate the difference between mathematical explanation and experimental evidence.
Other resources
Impact maths book 2R – see separate guides linking impact to units
ICT
Boardworks
