| Lesson |
After the lesson, students should be able to... |
Areas and perimeters of simple and compound shapes
We’ll be exploring how using areas and perimeters of simple and compound shapes can help with planning out a stage or arena for your large-scale event.
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- convert between units of measure within one system, including time and metric units to metric units of length, area
- find the perimeter of rectangles; parallelograms and trapezia; compound shapes
- recall and use the formulae for the area of a rectangle
- find the area of a trapezium and recall the formula
- find the area of a parallelogram
- calculate areas and perimeters of compound shapes made from rectangles.
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Volume of cubes, cuboids and right prisms
We’ll be exploring how using volumes of cubes, cuboids and right prisms will help you to plan out a stage or arena for your large-scale event.
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- recall and use the formulae for the area of a triangle
- calculate volumes of right prisms and shapes made from cubes and cuboids.
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Surface areas of cuboids and prisms
We’ll be exploring how calculating surface areas and performance areas of cuboids and prisms can help you ensure that a stage or arena space can work best for your large-scale event.
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- sketch nets of cuboids and prisms
- find the surface area of a prism
- find surface area using rectangles and triangles.
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Circumferences and areas of circles and volumes and surface areas of cylinders
We’ll be exploring how using cylinders and other 3D shapes can help with creating spectacular stage sets for your large-scale event.
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- recall and use formulae for the circumference of a circle and the area enclosed by a circle circumference of a circle = 2πr = πd, area of a circle = πr^2
- use π ≈ 3.142 or use the π button on a calculator
- give an answer to a question involving the circumference or area of a circle in terms of π
- find the surface area and volume of a cylinder.
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Plans and elevations
We’ll be exploring how to interpret and make accurate drawings of triangles and other 2D shapes as well as front and side elevations and plans to help you construct the arena for your large-scale event quickly and accurately.
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- draw sketches of 3D solids
- understand and draw front and side elevations and plans of shapes made from simple solids
- given the front and side elevations and the plan of a solid, draw a sketch of the 3D solid.
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Forming and solving linear equations
We’ll be exploring how forming and solving linear equations can help you to plan the security for your large-scale event.
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- write expressions and set up simple equations including forming an equation from a word problem
- solve simple equations including those:
with integer coefficients, in which the unknown appears on either side or on both sides of the equation; with one unknown, with integer or fractional coefficients
- solve angle or perimeter problems using algebra.
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Forming and solving linear inequalities
We’ll be exploring how forming and solving linear inequalities will help you make sure your set is not too large for the arena at your large-scale event.
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- solve an inequality such as −3 < 2x +1 < 7 and show the solution set on a number line
- solve two inequalities in x, find the solution sets and compare them to see which value of x
- use the correct notation to show inclusive and exclusive inequalities
- construct inequalities to represent a set shown on a number line.
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Forming and solving quadratic equations
We’ll be exploring how forming and solving quadratic equations can help you design the best stage for your large-scale event.
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- multiply together two algebraic expressions with brackets
- square a linear expression, e.g. (x + 1)^2
- factorise quadratic expressions of the form
x^2 + bx + c
- solve quadratic equations by factorising. |
Pythagoras’ Theorem in 2D
We’ll be exploring how you can use Pythagoras’ Theorem to quickly, carefully and accurately find the shortest distance to help rescue a stranded vessel.
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- understand, recall and use Pythagoras’ Theorem in 2D, including leaving answers in surd form and being able to justify if a triangle is right-angled or not. |
Trigonometric ratios in 2D
We’ll be exploring how you can use the learning from the lesson above and trigonometric ratios to find the ship’s bearing and save the stranded vessel.
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- understand, use and recall the trigonometric ratios sine, cosine and tan, and apply them to find angles and lengths in general triangles in 2D figures
- use the trigonometric ratios to solve 2D problems including angles of elevation and depression.
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Substitution, forming and solving linear equations and simultaneous equations
We’ll be exploring how using substitution, forming linear equations and simultaneous equations and solving them can help you ensure there’s the right number of lifeboats for passengers on the stranded vessel.
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- write expressions and set up simple equations including forming an equation from a word problem
- solve simple equations including those:
with integer coefficients, in which the unknown appears on either side or on both sides of the equation; with one unknown, with integer or fractional coefficients;
- write simultaneous equations to represent a situation
- solve simultaneous equations (linear/linear) algebraically and graphically
- solve simultaneous equations. representing a real-life situation, graphically and algebraically, and interpret the solution in the context of the problem.
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Speed, distance and time and converting units
We’ll be exploring how you can use speed, distance and time calculations to work out how long it will take to rescue passengers on the stranded vessel.
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- Calculate average speed, distance, time – in miles per hour as well as metric measures
- Change d/t in m/s to a formula in km/h, i.e. d/t × (60 × 60)/1000 – with support.
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