# Space, Shape and Position

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1 Series Student My name Space, Shape and Position

3 Series Contents Topic Lines, angles and shapes (pp. 9) parallel and perpendicular lines angles polygons and quadrilaterals types of quadrilaterals polygons and quadrilaterals symmetry symmetrical challenges create Date completed Topic Inves ga ng D figures (pp. 0 7) proper es of shapes drawing D figures different viewpoints cross sec ons nets dice puzzle solve painted cube solve Topic Posi on (pp. 8 4) Series Author: Nicola Herringer describing posi on following direc ons grids and coordinates using a map compass direc ons hit the points apply Copyright

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5 Lines, angles and shapes parallel and perpendicular lines Parallel lines are always the same distance away from each other at any point and can never meet. They can be any length and go in any direc on. Look at each group of lines. Trace over any parallel lines with a coloured pencil: a b c Perpendicular lines meet at right angles. Some mes they intersect (cross over), some mes they do not intersect. Trace each pair of perpendicular lines with a coloured pencil: a b c In this space, draw three pairs of parallel lines and three pairs of perpendicular lines:

6 Lines, angles and shapes angles An angle is the amount of turning between two lines that meet. There are three classifica ons of angles depending on their size. A right angle is 90 (degrees). An acute angle is smaller than a right angle. An obtuse angle is larger than a right angle. Classify each angle as right, acute or obtuse. a b c d e f Draw hands on each clock that show a me for each type of angle. a Right angle b Obtuse angle c Acute angle

7 Lines, angles and shapes angles Use your ruler to draw three more examples of each type of angle. a Right angles b Acute angles c Obtuse angles 4 Complete each closed shape according to the direc ons: Shape a has acute angles. Shape b has 5 right angles. Shape c has acute and obtuse angles. a b c

8 Lines, angles and shapes polygons and quadrilaterals Polygons are shapes with or more sides. Quadrilaterals are shapes with 4 sides. Check the polygons. Circle the quadrilaterals. Complete this table: Name Number of sides Number of angles a b c d e f g h rhombus pentagon trapezoid octagon hexagon square rectangle triangle Name one shape that is both a quadrilateral and a polygon: 4 Why is a circle not a polygon? 4

9 Lines, angles and shapes types of quadrilaterals A parallelogram is a quadrilateral with pairs of parallel sides. This is a parallelogram. Its opposite sides are an equal length and are parallel to each other. A square and a rectangle are also parallelograms. They have opposite sides that are equal lengths and are parallel to each other. A rhombus is a parallelogram. Its opposite sides are an equal length and are parallel to each other. It has 4 equal sides. How many pairs of parallel lines are there in these parallelograms? Count them: Write the number of shapes you can see in the box above. a b c d e Name rhombuses squares rectangles parallelograms quadrilaterals Number of shapes 5

10 Lines, angles and shapes types of quadrilaterals A trapezoid is a quadrilateral and has one pair of parallel sides. Check your understanding of types of parallelograms and trapezoids. a Draw a shape with two pairs of parallel sides and sides that are equal in length. b Draw a shape with one pair of parallel sides. This shape is a. This shape is a. c Draw a shape with two pairs of parallel sides and opposite sides that are equal. d Draw another parallelogram that is different to the others. This shape is a. This shape is a. 6

11 Lines, angles and shapes polygons and quadrilaterals Decide whether each shape in the table is a quadrilateral or a polygon or both. Write yes or no. a b c Name Quadrilateral Polygon square rectangle hexagon d octagon e pentagon f triangle Draw lines to connect the shapes to the labels. Then put a check in the shapes which are quadrilaterals and circle the parallelograms. The first one has been done for you. rhombus Some labels might have more than one connec ng line. square rectangle pentagon 4 sides hexagon 5 sides trapezoid 6 sides octagon 8 sides 7

12 Lines, angles and shapes symmetry A shape is symmetrical when you can fold it in half so that one half exactly covers the other half. The fold line is the axis of symmetry. Many D shapes have more than one line of symmetry. This shape has 4 lines of symmetry. Copy this page and cut out each copy shape. Find all the lines of symmetry. See how many different ways you can fold each shape in half. Then draw in all the lines of symmetry on the shapes on this page. a c b d Use the line of symmetry and a ruler to complete each shape. 8

13 Symmetrical challenges create Ge ng ready For these challenges, you will need a ruler and a pencil. What to do Here are four unfinished symmetrical designs on dot paper. You must must complete them. For each design, you must use a horizontal line, a ver cal line and two diagonal lines. When they are finished, they will each be symmetrical. For each design, decide where the line of symmetry will be. Pretend the line is a mirror what will the reflec on look like? 9

14 Investigating D figures properties of shapes In this topic, we are looking at the proper es of D figures. The pointy corner of a D figure is called a vertex. The plural is ver ces. Prisms have bases that are the same size and shape and are a type of polygon. Pyramids have only one base. All the faces are triangular and they meet at a common point also known as the apex. Complete the proper es of these prisms: a b c Name Faces Ver ces dges Complete the proper es of these pyramids: a b c Name Faces Ver ces dges Mahlia made a D figure using toothpicks and plas cine. She used nine toothpicks and six pieces of plas cine. Circle the shape she made. 0

15 Investigating D figures drawing D figures We can draw D figures easily by using dot paper. xample For a front view, use square dot paper. Step Step Step Draw these shapes on the dot paper below. You might like to try a few mes.

16 Investigating D figures drawing D figures xample For a corner view, use triangular dot paper. Step Step Step Draw these shapes below: a b c

17 Investigating D figures different viewpoints Here are some D models made from cubes. Shade in the squares on each grid to show the top, front and side view for each one. The top view of the first model has been done for you. Top View view Front view Side view a Top view Front view Side view b Top view Front view Side view c Top view Front view Side view d

18 Investigating D figures cross sections A cross sec on is what you see when you slice right through something. Draw the cross sec on next to each shape: a b c d e f Draw a line on each shape to show where you would cut to get the smallest possible circle. a b 4

19 Investigating D figures nets A net is the flat shape that a D figure can be constructed from. Draw a line to match these D figures with the nets below: copy Which of these nets will fold into a cube? You may like to ask your teacher to copy this page and enlarge the nets below so you can inves gate. Check the nets that work and cross the nets that don t. 5

20 Dice puzzle solve Ge ng ready In these two dice puzzles, you have to use the clues to imagine which face has which number. What to do Dice Puzzle Write the numbers to 6 on this net of the cube if: a is opposite 6. b is opposite 5. c is opposite 4. Dice Puzzle Chelsea made a die from a cardboard net of a cube. She puts s cker dots to represent the numbers on each side of the cube. Here is her cube shown in three different posi ons. ach me a different number is facing the front. Can you work out which number is on the opposite faces to these? a b c 6

21 Painted cube solve Ge ng ready Ma lda built a cube from 7 smaller cubes. She then dipped the large cube in blue paint. When it was completely dry, she broke it up into the smaller cubes. What to do Use the table below to predict the following: a How many small cubes have three faces covered with paint? b How many small cubes have two faces covered with paint? c How many small cubes have one face covered with paint? d How many small cubes have no faces covered with paint? Number of faces covered in paint a Number of small cubes b c d 0 Total 7

22 Position describing position When we use terms such as le and right, where we are in rela on to the object changes. Look carefully at each person s posi on and circle either le or right in each sentence: Lily Jo a The grapes are on the le / right of Roger. b The bo le is on the le / right of Jo. c The sandwiches are on Lily s le / right. d The jug is on Rachel s le / right. e Jo is si ng on the le / right Roger of Lily. f Roger is si ng on the le / right of Rachel. Rachel Solve this riddle: What is so fragile that even saying it out loud can break it? a b c d e f g A L F G C H M P I B O X J R W S Y N a Bo om row, third column from le. b Third row from bo om, second column from right. c Top row, second column from le. d Second row from bo om, first column. e Bo om row, column on far right. f Top row, column on far right. g Second row from bo om, first column. 8

23 Position describing position Write the names of each student according to Miss Flenley s sea ng plan: a Josh is in front of Rachel. b mily is in front row second from the right. Rachel c Karl is behind mily. d Liam is in middle row on the far right. e Bec is on mily s le. f Gina is behind Karl. g Megan is between Josh and Karl. h Lyn is on Gina s le. i Jo is in front of Megan. j Simon is next to Gina. k Andrew is in front of Josh. Front 4 Here is a map showing the best secret hiding spots in a backyard. A D B C A = Behind the clothes line B = Behind the garage C = Up the tree D = Around the side of the house = Next to the recycling bins Where are these kids hiding? Write the le er. a llie is row, column. Hint: Row is the bo om row. b George is row, column 6. c Akhil is row 5, column. d Bri is row 4, column 4. e Taylor is row 5, column 5. 9

24 Position following directions up On this page, you will prac se following the direc ons up, down, le and right. le right down Three kids are playing a computer game where they have to move through as many stars as possible to get the most points. Colour each player s paths according to the direc ons below: a Gemma s path is: Start in the bo om row; 6th square from the le ; up; squares le ; 6 squares up; and squares le. b Azumi s path is: c Tyler s path is: Start in the nd row from the bo om on the right; squares up; squares le ; squares up; squares right; and squares up. Start in the bo om row; st square on the right; squares le ; squares up; squares le ; 5 squares up; and square right. d A star is worth 0 points, what was each player s score? Gemma Azumi Tyler 0

25 Position grids and coordinates Maps are o en set up in a grid with le ers and numbers down the sides. We use these le ers and numbers to pinpoint a par cular part of the map. A B C D A B C D Some mes, it is the rows and columns that are labelled. 4 Other mes it is the lines that are labelled. 4 Answer the ques ons about what is in each part of the grid. a Name the shape at C4. b Mul ply the number at A by. c Name the shape at B. d Add the numbers at D and A. 9 À 6 6 Â 5 T 4 4 Ä 8 A B C D e What is different about the shape at B compared with the other shapes in this grid? Plot and join the following points. What picture have you made? a D to A, A to C, C to C7, C7 to 7, 7 to, to G, G to D A B C D F G H b to D4, D4 to A4, A4 to C6, C6 to B9, B9 to 7, 7 to H9, H9 to G6, G6 to 4, 4 to F4, F4 to A B C D F G H Picture: Picture:

26 Position using a map Here is a map from a street directory. When you learn to drive, you will some mes use a street directory to find out how to get somewhere. Look carefully at this map and answer the ques ons below: Denison Ln Alt St Alt Ln Cuthbert St Cuthbert St Denison Ln Alt St Alt Ln Birrell St Birrell St Keiran Ln Denison St Lawson Ln Lawson St Kieran St Walter St Clemenston Park Newland St Newland St Newland St Newland Ln Newland Ln Stanley St Stanley Ln Fitzgerald St Newland Ln Mackenzie St Lawson Ln Gardiner St bley St bley St A B C D F G H I J K L M N a Which street is at 4? b What is parallel to Denison Lane at 8? c Which street is at J9? d What are the coordinates that best pinpoint the intersec on of Birrell St and Newland St? e Draw one way to get from the corner of Lawson St and bley St to the corner of Cuthbert and Fitzgerald St. f Describe how to get to Clemenston Park from B8.

27 Position compass directions We can use a compass to help us with direc on. There are four main points on a compass: N north S south east W west NW N N The points in between the four main points help us describe posi on more accurately. NW north west N north east S south east SW south west W SW S S On each compass, some direc ons are missing. Fill in the missing ones: a b c N N N Here are four clowns that must find their way to class at circus school. Write the direc on that each clown needs to go to get to their class in the spaces below. Take note of where north is. Pogo Fire twirling Face pain ng Magic tricks Dimples a Pogo is going to the acroba cs class. b Dimples is going to the juggling class. Juggling Acroba cs c Bozo is heading to the face pain ng class. Bozo Flying trapeze Hint: Use the points between the four main points. d Twinkles is heading to the magic tricks class. e Once Twinkles is at the magic tricks class, which direc on will he go to get to the flying trapeze class? N Twinkles

28 Hit the points apply Ge ng ready This is a game for two players. You will need four copies of this page (two grids for each player) and 0 counters. copy What to do ach player places all 0 counters in different posi ons on their grid without the other player seeing. Take turns to find each other s counters by calling out coordinates. The aim of the game is to find out where all the counters are before the other player does. Don t waste your guesses. Keep track of your guesses by marking them on the second grid. A B C D F G H I J

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