Transition Unit: Kensuke’s Kingdom
Year 7 Mathematics
Overview for mathematics teachers What you need to know about the book – although this brief summary does not beat reading the book for yourself! Michael, his parents and his dog Stella Artois undertake a round the world trip on their yacht, Peggy Sue. Shortly after leaving Australia Michael and Stella get swept overboard. He is washed up on a tropical island. Eventually he discovers that the island has one other inhabitant – an old Japanese man, Kensuke.
In their maths lessons at the end of year 6 the pupils will have looked at different aspects of preparing for the voyage, the voyage itself and Michael’s explorations of the island. At the end of the year the pupils were given a gap task. They were given a message to decode. The message asks them to draw a picture of what they would like to find in a treasure chest hidden on the island and explain why they have chosen that item. A copy of this task is attached (Appendix …) The Year 7 mathematics unit is in two parts: Desert Island Mathematics: This is based on the theme of Desert Island Discs and will further develop the idea in the gap task that the pupils where given at the end of Year 6. This activity will probably take three lessons. Kensuke’s World: Here we will use paper folding to develop work on geometric reasoning. It replaces the Shape, Space and Measures 2 unit from the Sample Medium Term Plans for the Autumn Term – and can be taught as the first unit since it is not dependant on any earlier unit.
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Desert Island Mathematics:
This group activity follows on from the gap task. It is likely to take up to three hours. It is based on the idea of Desert Island Discs.
The Challenge: What three pieces of mathematics do you think you would find most useful if you were marooned on an island? And in the true spirit of Desert Island Discs, one luxury is also allowed – but this luxury has to have some mathematical significance.
The outcome is a presentation which can take a variety of different forms, for example posters, poems, models, songs, PowerPoint presentations to name a few. It should describe the mathematical ideas and luxury item the group has selected, together with their reasons.
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Main Activity: Phase One: Setting the scene and brainstorming The pupils have been asked to bring their gap task to the first maths lesson. Ask individual pupils to share with the class which item they wanted to find in the treasure chest and why. Wherever possible draw out any mathematical connections: e.g. a box of matches would not only be extremely useful for lighting a fire but can also be used to create and solve all those matchstick problems with which that maths teachers are so obsessed! Make a wall display of the pupil sheets under the heading “Brainstorming” Ask the pupils to describe to you the sort of maths they were doing at the end of last term and how it related to the book “Kensuke’s Kingdom” Record these suggestions on the board or a flipchart. Discuss with the pupils which of these ideas they might have found particularly useful if they had been in Michael’s position on the island and why. Phase Two: The Challenge Organise the class into groups of 3 or 4 pupils. Ask the pupils to imagine themselves in Michael’s position on a desert island. What mathematics do they think that they would find most useful on the island? (Refer them back to phase one). Also what piece of mathematical equipment would they like to have found in the treasure chest? Ask each group to agree on three pieces of useful mathematics and one piece of mathematics luxury or equipment. Phase Three: Planning the presentations Once the groups have agreed their lists, there needs to be some teacher input on the type of different presentations they consider using. Phase Four: The presentations Each group is allowed some time to present their ideas to the rest of the class.
Notes and comments
The groups need to be mixed in terms of feeder school and in terms of ability (in the context of the class)
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Kensuke’s World: Paper Folding
Background: Kensuke tells Michael that he grew up in Nagasaki. During the war he was a naval doctor and he was the only survivor on a warship which is bombed. Before the ship sank he heard on the radio that the Americans had bombed Nagasaki and that many people are dead. He assumed that he had lost all of his family. If he had a supply of paper, we can imagine Kensuke sitting in his cave and folding squares of paper to make elaborate models of the birds and animals around him – the ancient Japanese art of origami. (There is no evidence in the book that he did – but then there is no evidence that he didn’t!)
This Unit:
The unit covers the same objectives as Shape, Space and Measures 2 unit from the Sample Medium Term plans with the exception of the work on coordinates. This will have been covered in the year 6 part of this transition unit. Although two lesson plans have been produced, these should be seen as suggested starting points and will need to be adapted to suit the ability and context of the group being taught. After the lesson plans there are some suggested additional activities that are linked to the teaching objectives for this unit. Teaching Objectives: Core: Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes Identify parallel and perpendicular lines, know the sum of the angles at a point, on a straight line and in a triangle and recognise vertically opposite angles Begin to identify and use angle, side and symmetry properties of triangles and quadrilaterals. Use angle measure; distinguish between and estimate the size of acute, obtuse and reflex angles. Extension: Identify alternate and corresponding angles; understand a proof that: -sum of the angles of a triangle is 180˚ and of a quadrilateral is 360˚. Classify quadrilaterals by their geometric properties
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Key lesson plan: Classifying Quadrilaterals
Learning objectives To be able to label the equal angles and equal sides in the same quadrilaterals To be able to find the number of lines of symmetry and order of rotational symmetry for different quadrilaterals To be able to classify quadrilaterals by their geometric properties (Extension)
Starter Vocabulary Quadrilateral Square Rectangle Kite Rhombus Parallelogram Trapezium Resources Kite, parallelogram, square, trapezium and a kite with a right angle included, cut out from bright card. A board to hide the shapes Class set of whiteboards There is an interactive version of this activity on the ATM Interactive CD rom.
Reviewing Key Stage 2 work Hide and reveal: The pupils are asked to identify the shapes as they emerge from behind the board. The square emerges to reveal one right angle and two equal sides. Q: What shape could this be? Q: What other shape could it be? Possible answers: square, rectangle, kite. Reveal a second angle. Q: Now what shape is it going to be? (A: Square) The kite is revealed with the right angle first, giving possible alternative answers of square and rectangle. A second angle is revealed. Q: How do we know that the shape is not a square? These questions are then repeated for the other shapes. As each of the key words is introduced write the word on the board and reinforce the correct spelling
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.Main Activity
Vocabulary – new for year 7 Delta Arrowhead Supplement of examples: Introduce this unit to the pupils by explaining that the work on Shape and Space is based on paper folding – linking it with origami. Model the folding of a piece of A4 or A5 paper into a square Discuss the properties of the square; draw one on the board, modelling the correct labelling conventions for equal sides and for right angles. Ask the pupils how we could make a parallelogram and trapezium by folding paper. Draw a parallelogram on the board, modelling the labelling conventions for parallel lines and equal angles Model the method for folding a kite. In pairs/groups ask the pupils to make as many different quadrilaterals as possible by folding. They need to record their results, to correctly label their diagrams and name the quadrilaterals. Allow creativity here – a delta is best made from two triangles!
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This table needs to be copied onto a large piece of paper. The group/pairs need to draw and name quadrilaterals in the appropriate spaces. Q: Will any of the spaces stay empty? If so, why? Number of pairs of parallel sides 1 2 3 Number of pairs of equal sides 1 2 3
Extension work: True, False and Iffy sheet The pupils need to work in pairs and are given an A3 sheet of paper and the sheet of True, False and Iffy statements. They need to decide which category each of the statements fit into and give the reason why. Plenary Draw a Venn Diagram on the board with three overlapping sets each set is used for a different attribute, for example: rotational symmetry greater than one, at least one line of symmetry and at least one pair of equal sides. The pupils then need to suggest shapes that could fit into the different regions.
Notes: The classifying activity can be adapted using many different criteria: e.g. order of rotational symmetry and lines of symmetry.
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Number of pairs of parallel sides
1
Number of pairs of equal sides
2
3
1 2 3
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Resource sheet: Ma1.1: Square
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Resource sheet: Ma1.2:Kite
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Resource sheet: Ma1.3:Folding a Rhombus
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Resource sheet Ma1.4a: True, False and Iffy Statements
A. A rectangle is a parallelogram
B. If the opposite corners of a quadrilateral are right angles, then the shape must be a rectangle.
C. A rhombus is a parallelogram with all sides equal
D. All squares are rectangles.
E. The diagonals of a rectangle cross at right angles
F. The diagonals of a rhombus cross at right angles
G. A quadrilateral has four sides of the equal length
H. A kite is a quadrilateral with exactly two equal, adjacent sides
I. A concave quadrilateral is called a delta.
J. The exterior angles of a quadrilateral add up to 360
K. A kite has two lines of symmetry
L. A trapezium only has one line of symmetry and rotational symmetry of order 1.
M. An oblong is a rectangle where the adjacent sides are not equal
N. A parallelogram has rotational symmetry of order 4.
O. All four sides of a trapezium have to be of different lengths
P. A regular quadrilateral is a square
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Resource Sheet Ma1.4b Solutions to True, False and Iffy Statements. A B C D E F G H I J K L M N O P True False True True Iffy – only if the rectangle is a square True False False – it has two pairs of equal, adjacent sides True True Iffy – only true if it also a rhombus Iffy – true if it an isosceles trapezium True Iffy – only if it is a square Iffy – not true if it is an isosceles trapezium True
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Key lesson plan: Folding Triangles
Learning objectives Starter
Vocabulary Triangle Equilateral Isosceles Scalene Parallel Perpendicular Acute Obtuse Reflex Perpendicular Parallel Resources: Resource sheet Ma2.1(a and b)
To be able to recognise the vertically opposite angles. Extension: to be able to recognise Reviewing Key Stage 2 work: Definitions: Each group of four pupils needs a copy of resource sheet Ma2.1 cut into cards. They then need to agree a definition of the term at the top, using as many as possible of the words given below. They need to complete as many as possible in the time allowed and so should be encouraged to share out the task. The groups then swap definitions for checking and marking – points are allocated according to the number of the listed words they have correctly used in the definition. (The group marking will need access to a maths dictionary or the QCA glossary.)
Main Activity
Vocabulary: In addition to the above list: Intersect Opposite (angles) Resources: Resources sheets Ma 2.2 and 2.3
Model folding a piece of A4 (or A5) paper into an equilateral triangle. Reinforce from the starter the properties of the triangle. Q: What do you notice about the angles? Q: What do you notice about the sides? Q: How many lines of symmetry does it have? Q: What is the rotational symmetry? Pupils fold their own triangles, using the resource sheet 2.2 as a prompt. Ask the pupils to open out the piece of paper and to look at the fold lines. (Some pupils may need to draw over these lines.) Q: What shapes do you have? Q: Work out the sizes of the angles made by the fold lines. Q: What do you notice about the angles which are the same? Repeat all the above for the isosceles triangle. See resource sheet Ma2.3 for folding instructions. Support Group working with a support assistant: Whale (See attached sheet) For the different polygons formed (quadrilateral, isosceles triangle, scalene triangle, kite) ask the pupils the following questions: Q: What do you notice about the angles? Q: What do you notice about the sides? Q: How many lines of symmetry does it have? Q: What is the rotational symmetry Feedback from the different groups about the properties of the different quadrilaterals.
Plenary
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Resource sheet: Ma2.1: Equilateral Triangle
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Resource sheet: Ma2.2: Isosceles Triangle
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Resource sheet: Ma2.3 Whale
www.mathinmotion.com/whalefld2.html
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Resource sheet: Ma2.4a
Equilateral triangle equal three vertices sixty side
Isosceles Triangle two same angles lengths
Scalene Triangle different degrees 180 obtuse
Obtuse greater than acute 180 degree
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Resource sheet: Ma2.4b
Acute right angle 0 (zero) vertex lines
Reflex less than big(ger) acute 360
Right angle quarter turn ninety straight line
Parallel railway meet distance two
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Additional Suggested Activities:
There is a list of different visualisation activities on page 184 of the supplement of examples from the Framework for teaching mathematics: Years 7,8 and 9. These make excellent starters. Again from the supplement of examples page 14: Two overlapping squares Two squares can be overlapped to make different shapes. The squares can be the same size or different sizes. Which of these shapes can be made by overlapping two squares: rhombus, isosceles triangle, pentagon, hexagon, octagon, decagon, kite, trapezium. If you think that a shape cannot be made, explain why. Another visualisation activity: Imagine an equilateral triangle.Imagine another identical equilateral triangle. Place it alongside the original so that the edges match exactly. What is the name of the shape you have made? Is there one than one possibility Explain how you know. Tangrams Unfold a folded isosceles triangle and cut along the creases to make three triangles. Use the three triangles to make these shapes: kite, a parallelogram, a trapezium and a rhombus (not done). What other shapes can be made with the three tangram pieces. A paper folding investigation: Take a piece of A4 paper and fold it in half, in half again, and again. Ask the pupils to predict the number of regions created by each folding. How many folds will there be on the piece of paper? How many of the folds with be up and how many down? e.g. I fold gives 1 down 2 folds give 2 up and 1 down 3 folds gives 7 creases – 4 down and 3 up (This takes some thinking about here – what is counted as a crease) What quadrilaterals can you make by fitting together two isosceles triangles?
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