234 The National Strategies Secondary Mathematics exemplification: Y7

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1 234 Te National Strategies Secondary Matematics exemplification: Y7 Pupils sould learn to: Deduce and use formulae to calculate lengts, perimeters, areas and volumes in 2-D and 3-D sapes As outcomes, Year 7 pupils sould, for example: Use, read and write, spelling correctly: area, surface, surface area, perimeter, distance, edge and use te units: square centimetre (cm 2 ), square metre (m 2 ), square millimetre (mm 2 ) Deduce and use formulae for te perimeter and area of a rectangle. Derive and use a formula for te area of a rigt-angled triangle, tinking of it as alf a rectangle: area = 1 2 ase lengt eigt area = 1 2 alculate te perimeter and area of sapes made from rectangles. For example: Find te area of tis sape. 8 cm 6cm 5 cm 3 cm Find te saded area. 15 m 3m 10 m Find te area and outside perimeter of a pat 1 metre wide ordering a 5 metre square lawn. 3m Here is a flag. 60 cm alculate te area of te saded cross. 40 cm 10 cm 15 cm Find te area of tis quadrilateral: a. y completing te 3 y 3 square and sutracting te pieces outside te quadrilateral;. y dissecting te inside of te quadrilateral into rectangles and/or rigt-angled triangles PDF-EN-01 rown copyrigt 2008

2 Te National Strategies Secondary Matematics exemplification: Y8, As outcomes, Year 8 pupils sould, for example: Use vocaulary from previous year and extend to: volume, space, displacement and use te units: ectare (a), cuic centimetre (cm 3 ), cuic metre (m 3 ), cuic millimetre (mm 3 ) As outcomes, Year 9 pupils sould, for example: Use vocaulary from previous years and extend to: circumference, π and names of te parts of a circle. Link to circles (pages 194 to 4-197). Deduce formulae for te area of a parallelogram, triangle and trapezium. For example, explain wy: Te area of a triangle is given y A = 1 2, were is te ase and is te eigt of te triangle. A D V P A rectangle and parallelogram on te same ase and etween te same parallels ave te same area, A =, were is te ase and is te perpendicular distance etween te parallels. Te area of a trapezium, were is te perpendicular distance etween te parallel sides, is 1 2 (sum of parallel sides). D alculate areas of triangles, parallelograms and trapezia, and of sapes made from rectangles and triangles. For example: A rigt-angled triangle lies inside a circle. Te circle as a radius of 5 cm. alculate te area of te triangle. A B a B A D B 5cm V P Know and use te formula for te circumference of a circle. For example: Know tat te formula for te circumference of a circle is = πd, or = 2πr, and tat different approximations to π are 3, 22 7, or 3.14 correct to 2 d.p. Use te π key on a calculator. alculate te circumference of circles. For example: A circle as a circumference of 120 cm. Wat is te radius of te circle? Te diameter of King Artur s Round Tale is 5.5 m. A ook claims tat 50 people sat round te tale. Assume eac person needs 45 cm round te circumference of te tale. Is it possile for 50 people to sit around it? Te large weel on Wyn s weelcair as a diameter of 60 cm. Wyn puses te weel round exactly once. alculate ow far Wyn as moved. Te large weel on Jay s weelcair as a diameter of 52 cm. Jay moves er weelcair forward 950 cm. How many times does te large weel go round? A Ferris weel as a diameter of 40 metres. How far do you travel in one revolution of te weel? A touring cycle as weels of diameter 70 cm. How many rotations does eac weel make for every 10 km travelled? Te diagram sows a saded square inside a larger square. alculate te area of te saded square. 3cm 14 cm rown copyrigt PDF-EN-01

3 236 Te National Strategies Secondary Matematics exemplification: Y7 Pupils sould learn to: Deduce and use formulae to calculate lengts, perimeters, areas and volumes in 2-D and 3-D sapes (continued) As outcomes, Year 7 pupils sould, for example: Using a pinoard, make different sapes wit an area of 2 square units. Investigate relationsips etween perimeters and areas of different rectangles. For example: Sketc and lael some sapes wic ave an area of 1 m2. Find te perimeter of eac sape. A rectangle as a fixed area of 36 cm2. Wat could its perimeter e? Wat sape gives te smallest perimeter? A rectangle as a fixed perimeter of 20 cm. Wat could its area e? Wat sape encloses te most area? Do tese sapes ave: a. te same area?. te same perimeter? PDF-EN-01 rown copyrigt 2008

4 Te National Strategies Secondary Matematics exemplification: Y8, As outcomes, Year 8 pupils sould, for example: On a 1 cm grid, draw a triangle wit an area of 7.5 cm 2 and an otuse angle. Use metods suc as dissection or oxing of sapes to calculate areas. For example: Draw tese sapes on a 1 cm spotty grid and use te dased lines to elp find teir areas. Make quadrilaterals on a 3 y 3 pinoard. Find te area of eac quadrilateral. Te area of te parallelogram is 10 cm2. alculate te eigt of te parallelogram. 4cm eigt Te area of te trapezium is 10 cm2. Wat migt e te values of, a and (a > )? As outcomes, Year 9 pupils sould, for example: Know and use te formula for te area of a circle: A = π d 2 /4 or A = πr 2 For example: A circle as a radius of 15 cm. Wat is its area? alculate te area of te saded sape. A curc door is in te sape of a rectangle wit a semicircular arc. Te rectangular part is 2 m ig and te door is 90 cm wide. Wat is te area of te door? 1.5 m 90 cm 2.75 m Napoli Pizzas make two sizes of pizza. a. A small pizza as a diameter of 25 cm. Wat is te surface area of te top of te pizza?. A large pizza as twice te surface area of te small one. Wat is te diameter of te large pizza? c. A small oy reckons e could just aout manage to eat a 120 wedge (sector) of te large pizza. Wat is te area covered y topping on tis piece? Te inside lane of a running track is 400 m long, 100 m on eac straigt and 100 m on eac semicircular end. Wat area in te middle is free for field sports? 2m a Use a pinoard and spotty paper to investigate simple transformations of te vertices of triangles and parallelograms, and ow tey affect te area of te sapes. For example: A 2 A A 1 A 2 B B 1 B 2 A 1 A D B Find te area of eac parallelogram or triangle and explain wat is appening. rown copyrigt PDF-EN-01

5 238 Te National Strategies Secondary Matematics exemplification: Y7 Pupils sould learn to: Deduce and use formulae to calculate lengts, perimeters, areas and volumes in 2-D and 3-D sapes (continued) As outcomes, Year 7 pupils sould, for example: Find te surface area of cuoids and sapes made from cuoids. eck y measurement and calculation. Unfold packets in te sape of cuoids and oter 3-D sapes to form a net. Relate te surface area to te sape of te net. Estimate te surface area of everyday ojects. For example: Estimate te surface area of a ouse rick, a large cereal packet, a matcox eck estimates y measurement and calculation. Derive and use a formula for te surface area S of a cuoid wit lengt l, widt w and eigt : S = 2(lengt widt) + 2(lengt eigt) + 2(eigt widt) S = 2lw + 2l + 2w PDF-EN-01 rown copyrigt 2008

6 Te National Strategies Secondary Matematics exemplification: Y8, As outcomes, Year 8 pupils sould, for example: Know te formula for te volume of a cuoid and use it to solve prolems involving cuoids. As outcomes, Year 9 pupils sould, for example: alculate te surface area and volume of a rigt prism. Understand te formula for te volume of a cuoid y considering ow to count unit cues. Suppose te cuoid is l units long, w units wide and units ig. Know tat a prism is a polyedron of uniform crosssection trougout its lengt. A cuoid is a common example. Use knowledge of prisms made up of cuoids to write an expression for te total volume of suc a prism. For example: A prism as cross-section areas A 1, A 2, A 3,, all of lengt. Ten: area of ase = lw square units volume = area of ase numer of layers = lw cuic units A 2 A 3 A 1 Estimate volumes. For example: Estimate te volume of everyday ojects suc as a rectangular copping oard, a ar of soap, a soe ox eck estimates y measurement and calculation. Suggest volumes to e measured in cm 3, m 3. V = A 1 + A 2 + A 3 + = (A 1 + A 2 + A 3 + ) = total area of cross-section lengt Volume and displacement In science, start to appreciate te connection etween volume and displacement. For example, Make some cues or cuoids wit different numers of enticues. Put tem into a measuring cylinder alf filled wit water. How many millilitres does te water rise? Wat is te connection etween te volume of te cue or cuoid and te volume of water displaced? (1 ml of water as a volume of 1cm 3.) rown copyrigt PDF-EN-01

7 240 Te National Strategies Secondary Matematics exemplification: Y7 Pupils sould learn to: Deduce and use formulae to calculate lengts, perimeters, areas and volumes in 2-D and 3-D sapes (continued) As outcomes, Year 7 pupils sould, for example: Solve simple prolems suc as: How many unit cues are tere in tese sapes? Wat is te surface area of eac sape? Investigate te different cuoids you can make wit 24 cues. Do tey all ave te same surface area? Tis solid cue is made from alternate lue and wite centimetre cues. Wat is its surface area? How muc of its surface area is lue? Tis sape is made from tree identical cues. Te top cue is placed centrally over te oter two. Te faces of te sape are to e covered in sticky paper. Sketc te different sapes of te pieces of paper required. Say ow many of eac sape are needed. If eac cue as an edge of 5 cm, wat is te surface area of te wole sape? ompare different metods of working tis out. alculate te surface area in cm 2 of tis girder. 3cm 15cm 9cm 4cm 12 cues wit 1 cm edges are eac covered in sticky paper. How muc paper is needed? Te 12 cues are wrapped in a single parcel. Wat arrangement of te cues would need te least paper? 3cm Link to lines, angles and sapes (pages ) PDF-EN-01 rown copyrigt 2008

8 Te National Strategies Secondary Matematics exemplification: Y8, As outcomes, Year 8 pupils sould, for example: As outcomes, Year 9 pupils sould, for example: Solve prolems suc as: Find te volume of a 3 cm y 4 cm y 5 cm ox. Find te volume in cm3 of tis H-saped girder y splitting it into cuoids. 12cm 40 cm 12cm 2m Solve prolems suc as: A ox for coffee is in te sape of a exagonal prism. Eac of te six triangles in te exagon as te same dimensions. alculate te total area of te exagon. 4cm 10 cm 8cm 12cm 12cm ontainers come in tree lengts: 12 m, 9 m and 6 m. Eac is 2.3 m wide and 2.3 m tall. How many crates measuring 1.1 m y 1.1 m y 2.9 m will fit in eac of te tree containers? Boxes measure 2.5 cm y 4.5 cm y 6.2 cm. Te ox is 12 cm long. After packing, te coffee fills 80% of te ox. How many grams of coffee are in te ox? (Te mass of 1 cm 3 of coffee is 0.5 grams.) Tis door wedge is in te sape of a prism. 6.0 cm 2.5 cm 2.5cm 3.5cm Te saded face is a trapezium. alculate its area. alculate te volume of te door wedge. 2.5 cm 4.5 cm 6.2 cm A sopkeeper puts tem in a tray. 2.5 cm 31 cm 9cm Work out te largest numer of oxes tat can lie flat in te tray. Wat is te total surface area of tis ox? Find te lengt of eac edge. Tis lock of ceese is in te sape of a cue. Eac edge is 8 cm long. It is cut into two pieces wit one vertical cut. 1cm alculate te volume and surface area of te saded piece. 120 cm 2 96 cm 2 80 cm 2 10 cm 1cm 8cm Link to lines, angles and sapes (pages ). Link to lines, angles and sapes (pages ). rown copyrigt PDF-EN-01

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