English

not defined

no text concepts found

Alcester Academy Curriculum Planning: Key Stage 3 Department: Maths Year Group: Year 8 Term Topic/ subject Assessment Objectives Skills Include detail of any differentiation Literacy, numeracy and SMSC opportunities Autumn 1 Ratio and Scale Interpret scales on a range of measuring instruments including mm, cm, m, km, ml, cl, l, mg, g, kg, tonnes. Draw and measure line segments and angles in geometric figures, including interpreting scale drawings. Use scale factors, scale diagrams and maps. Give a bearing between the points on a map or scaled plan, interpret bearing and scaled drawings. Convert between different metric measures and know their imperial equivalence. Draw angles using a protractor. Interpret scales on a drawing. Draw plans using a scale. Draw and measure bearings. Use fractional scale factors. Calculate reverse bearings using angle rules. Key words: Ratio, metric, imperial, scale and bearings. Able to recall the names of quadrilaterals and 3D shapes and identify their properties. Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetrical. Able to label correctly and use correct notation i.e. “A” and “a” are used in different contexts on a shape. Know the names of different quadrilaterals and their properties. Recognise parallel and perpendicular lines. Use the correct angle notation. Describe a shape in terms of its rotational symmetry. Solve problems using the properties of different polygons. Collecting like terms. Solve linear Equations. Substitute integer values into expressions and formulae. Be able to change the subject of a formula; not including powers, brackets, fractions or the subject appearing twice. Standard algebraic techniques including collecting like terms, substitution of numbers into simple formulae, expanding a single bracket, solving linear equations Solve an equation with unknowns on both sides. Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids. Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures. Enlargement of 2-D shapes, including given a centre of enlargement and a positive integer scale factor. Record, describe and analyse the frequency of outcomes of simple probability experiments Construct triangles SAS, ASA and SSS. Enlarge shapes with integer and fractional scale factors. Enlarge shapes from a centre on a coordinate grid. Rotate, translate and reflect shapes. Use a column vectors to describe and draw translations. Written instructions for the different transformations. Place events on a probability scale using the appropriate language. Creating events to place a probability scale. Students will Shape Properties Autumn 2 Algebra 3 Transformations Spring 1 Probability Final assessment task and title Being able to estimate using different measures, helps students understand the world around them. Use of real life maps to understand scales and drawings. Using the correct spelling for key words: Isosceles, perpendicular, parallel etc. Problem solving skills and teamwork are fundamental to Mathematics, through creative thinking, discussion, explaining and presenting ideas. Students are always encouraged to develop their Mathematical reasoning skills, communicating with others and explaining concepts to each other. Create expressions from worded problems and vice versa. Examples of where algebra is useful in the real world. Links to different cultural patterns and art work. Improves students’ spatial awareness. . Alcester Academy Curriculum Planning: Key Stage 3 Construction and Loci Spring 2 Summer 1 Interpreting Data Circles involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale. Understand that the probabilities of all possible outcomes sum to 1. Create sample spaces and be able to calculate the probability of an event from this list. Complete a probability tree. Calculate probability of an event as a fraction. Know that all probabilities add up to one. Calculate the probability of an event NOT occurring. Know the difference between theoretical and experimental probability and carry out an experiment. Complete probability trees and use them to calculate the probability of two independent events. need to able to reason why they have placed different events. Derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line. Apply standard ruler and compass constructions in problems involving loci. Be able to recall and apply Pythagoras' theorem. Find a long or short side (2 sides given). Understand and recall common Pythagorean triples. Use a compass to construct triangles, perpendicular bisector and angle bisector in a range of ways. Apply constructions to loci. Find missing sides of right angled triangles by understanding Pythagoras. Create instructions for the different constructions. Describe simple mathematical relationships between two variables in observational and experimental contexts and illustrate using scatter graphs. Identify and describe the correlation and relationship between two variables and draw on a line of best fit, use this line of best fit to estimate values. Draw and interpret stem and leaf diagrams. Calculate mean, median, mode and range from a list, frequency table or grouped frequency table. Draw pie charts. Derive and illustrate properties of a circle, and be able to identify and label the parts of a circle. Use constructions to draw circles, given the radius or diameter. Calculate and solve problems involving: perimeters and areas of 2-D shapes (including circles), areas of circles and composite shapes. Be able to split up a composite shape into 2 or more shapes to find its area and perimeter. Draw and interpret information from tables and graphs. Draw and interpret scatter graphs. Calculate mean, median, mode and range from a list. Calculate mean, median, mode and range from frequency table or grouped frequency table Read information from table and graphs and write conclusions. Find the area and perimeter of different 2D shapes including compound shapes. Label the parts of a circle. Know how to find the area and circumference of a circle. Solve functional problems involving area of compound shapes. Find the area and perimeter of shapes that involve circles. Key words: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment. The teaching of probability introduces the idea of gambling and will address issues related with this. Use of Loci in situations such as town planning. Students to understand how the media could use different graphs and averages to influence our decisions. Solving functional problems involving area and perimeter. Pupils will calculate how much paint would be needed to decorate a room. Alcester Academy Curriculum Planning: Key Stage 3 Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment. Proportion 2 Summer 2 Solving Equations and Inequalities Plotting and Sketching Graphs Solve problems involving direct and inverse proportion, including graphical and algebraic representations. Be able to solve a direct or inverse proportion problem when the information is given as a formula. Know how to solve numerical problems which are direct or inverse proportion. Use percentage change for growth and decay problems. Solve linear equations in one unknown algebraically including those with two stages of calculation and/or with brackets. Translate simple situations or procedures into algebraic expressions or formulae; derive an equation and solve the equation and interpret the solution. Solve equations with multisteps including those with unknown on both sides. Solve linear inequalities in one variable and represent the solution set on a number line and using set notation. Solve quadratic equations. Find approximate solutions using a graph. Use the unitary method to solve proportion problems. Represent proportion problems graphically, Calculate the best buy. Use algebraic methods to solve proportion problems. Understand compound interest and decay problems. Give definitions for the key words ratio, proportion, and share and simplify. Solve linear equations. Form equations from a range of situations to solve problems e.g. perimeter problems. Understand inequalities and represent on a number line. Solve multistep equations that include unknowns on both sides. Solve inequalities and represent on a number line. Solve quadratic equations. Key words: Equation, Formula and Identity. Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane. Use plots in all four quadrants and substitution skills for 2 variables. Plot and recognise graphs of the form x=a and y=b and the equation of a line y=mx+c, including the use of tables of values, gradient and intercept. Plot quadratic graphs and recognise that this will result in a parabola. Plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify parallel and perpendicular lines; find the equation of the line through two given points, or through one point with a given gradient. Calculate the gradient of a given straight line. Calculate the gradient of a Plot coordinates in all four quadrants. Substitute into formulas with 2 variables. Plot and recognise lines in the form x = a and y = b. Plot quadratic graphs and recognise that they will always result in a parabola. Use conversion and other similar graphs. Understand difference between a negative and positive gradient. Give definitions for the key words sequence, term and position. Solve problems involving y=mx+c. Being able to reason proportionally provide useful life skills. Pupils learn to cope with new concepts through perseverance. . Mathematics applied in different cultures and historical aspects of mathematical development are developed through investigating the Fibonacci sequence. Students are encouraged to discuss the use of mathematics in cultural symbols and patters. Alcester Academy Curriculum Planning: Key Stage 3 straight line given 2 coordinates. Identify and interpret roots, intercepts, turning points of quadratic functions graphically. Reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically. Be able to draw graphs of quadratic functions using a table of values and find the turning points and the roots graphically and be able to find the line of symmetry. Know that when mm' = -1 two lines are perpendicular.