Shapes and Spaces Series: For Middle Primary

Ready-Ed Publications

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o e t The Shapes &r Spaces s B Series r e

oo p u Book 2-F or 8 to 10 Y eark Olds For Year S

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Shapes and Spaces for Middle Primary Students © ReadyEdPubl i cat i ons

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Written by Judy Gabrovec. Illustrated by Melinda Parker. © Ready-Ed Publications - 2000.

Published by Ready-Ed Publications (2000) P.O. Box 276 Greenwood W.A. 6024 COPYRIGHT NOTICE Permission is granted for the purchaser to photocopy sufficient copies for non-commercial educational purposes.

However, this permission is not transferable and applies only to the purchasing individual or institution.

ISBN 1 86397 338 9

Teacher Information “Shapes and Spaces for Middle Primary Students” is a comprehensive activity book suitable for 8 to 10 year old children, which explores the theme of spatial language and concepts. The activities are outcome based and provide children with the opportunity to develop spatial knowledge of:

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• pathways • mazes • spatial features of everyday objects • matching shapes • recognising the similarities and differences in shapes • arranging shapes according to size, shapes • symmetry • tessellations • classifying shapes using spatial features • mapping • ordered pairs • spatial features of 3-D shapes • enlarging and reducing • symmetrical patterns • traversable networks • model making • cross sections of 3-D shapes • manipulating 3-D shapes Included in the book are the templates for a variety of 3-D shapes that can be used to support the activities.

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Teacher Information .................................................................... 2 Pathways 1 ...................................................................................... 5 Pathways 2 ...................................................................................... 6 Mazes 1 ............................................................................................ 7 Mazes 2 ............................................................................................ 8 Ordered Pairs ................................................................................. 9 Amazing ........................................................................................ 10 School Map ................................................................................... 11 Enlarging a Picture ..................................................................... 12 Reducing a Picture ...................................................................... 13 Shapes ............................................................................................. 14 Similar Figures ............................................................................. 15 2-D Shapes..................................................................................... 16 Features of 2-D Shapes 1............................................................ 17 Features of 2-D Shapes 2............................................................ 18 Symmetry 1 .................................................................................. 19 Symmetry 2 .................................................................................. 20 Symmetry 3 .................................................................................. 21 Symmetrical Patterns ................................................................. 22 Moving Shapes ............................................................................. 23 Traversable Networks ............................................................... 24 Tessellations ................................................................................. 25 Tessellating Patterns ................................................................... 26 3-D Shapes..................................................................................... 27 Everyday 3-D Shapes .................................................................. 28 A 3-D Shape and its Faces ......................................................... 29 A 3-D Shape and its Many Faces ............................................. 30 Classifying 3-D Shapes ............................................................... 31 3-D Shapes..................................................................................... 32 Moving Models ............................................................................ 33 Make a 3-D Shape ........................................................................ 34 Model Making .............................................................................. 35 Cross Sections of 3-D Shapes ................................................... 36 Triangular Pyramid .................................................................... 37 Square Pyramid ........................................................................... 38 Triangular Prism ......................................................................... 39 Rectangular Prism ....................................................................... 40 Cube ............................................................................................... 41 Cylinder ........................................................................................ 42 Cone ............................................................................................... 43 Hexagonal Pyramid .................................................................... 44 Hexagonal Prism ......................................................................... 45 Rectangular Based Pyramid ...................................................... 46 Square Based Prism ..................................................................... 47 Octahedron ................................................................................... 48

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Contents

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Games and Activities Using Concrete Material It is vital that children’s early experiences with space and shape involve handling, arranging, building, stacking, packing, rolling, sorting, matching and investigating a variety of three dimensional objects that exist in their everyday environment.

The type of everyday objects that can be used to develop important mathematical spatial awareness are:

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blocks of all shapes and sizes; models of regular shapes (cubes, pyramids); building sets and construction kits; toys (marbles, buttons, balls, jigsaw puzzles); manipulative material (Plasticine, playdough, wire, string); playground equipment; school buildings; school grounds; classroom; furniture.

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Some suggestions on using these materials are:

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Compare the building blocks according to size, shape, colour and possible uses.

Classify blocks using properties like colour, shape, number of corners and number of faces.

Build structures from an assortment of blocks following a “brief” or a set of instructions, e.g. Build a tower using ten square blocks and ten rectangular blocks.

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Have discussions with children about which blocks would suit specific purposes, e.g. Which blocks would stack, roll or be more suitable for balancing on other blocks?

Investigate the ways in which the different blocks can move, e.g. Can they spin, roll, slide?

. te o c Identify things in their classroom, schoolyard, bedroom that are the same shape . c e as the blocks. her r o t sthem onto charts that Cut out appropriate pictures from s magazines andr glue upe represent different shapes.

Use blocks to play games to develop the concepts of repeated patterns and symmetry.

Develop children’s spatial language by encouraging them to describe their models and constructions to other children in the class.

Encourage children to evaluate their model making efforts by explaining how and why they constructed their model and if it was a success.

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Learning Outcome: Use instructions to follow a pathway where movements are in order.

Pathways 1

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R Follow the pathways to find out where Ben stopped on each different day.

Use the points of the compass to help you follow the pathways accurately.

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. te Ben stopped at the o c 1. Monday N4 E2 N4 W1 ................................................ . c e r 2. Tuesday S1 W5 N6h E4e ................................................ o t r s s per 3. Wednesday E4 N5 W5 N2 E5 u ................................................

Pathways

4. Thursday N7 W2 N1 W2 S3

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5. Friday W3 N5 E5 N2 W4

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6. Saturday N8 W4 S1 E8

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7. Sunday N2 E3 N2 W7 S2

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Learning Outcome: Give instructions for creating a pathway which requires movement to be done in order.

Pathways 2

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R Use the points of the compass to find out the pathways Ben took to visit the different places on the grid.

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o c Pathway Place visited Pathway . ch e r o N7 e E4 r Tunnel t s ......................... super ..........................

Bus stop .........................

Record the pathways here.

Place visited e.g. Skate park Horse Park

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Dog

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Bridge

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Learning Outcome: Find paths on informal maps and mazes.

Mazes

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R Help Ben find his way through the maze to visit Aaron, Scott and Kristie.

Find Ben a way home from Kristie’s house.

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o c . che e r o t r s super Explore Some Cyber Mazes!

Go to puzzlemaker.school.discovery.com/mazedthings/index.html on the Internet to find some fascinating mazes to print out.

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Learning Outcome: Attend to position and order when using a map or a maze.

Mazes 2 R Look at the maze below. Give a written description of the pathway that Ben has taken from: his house to school. ...........................................................................................

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............................................................................................................................ ............................................................................................................................ school to the park. ..............................................................................................

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the park to the ice cream shop. ......................................................................... ............................................................................................................................

the ice cream shop to home. ............................................................................. ............................................................................................................................

Ben

Ice cream shop

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Park

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Learning Outcome: Use ordered pairs to draw a picture.

Ordered Pairs When you use ordered pairs or co-ordinates the horizontal axis is always put first.

R Try tracing these (• starting point) •B1, D1, F3, G2, G1, I1, L4, M6, N9, N12, L8, J6, H8, H10, F12, F13, E13, E12, C12, C11, E11, E10, C10, D9, F9, D7, D5, F3 •E8, D8, C7, C6, D6

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•G8, F8, E7, E6, F6, F7, G7 •G2, H2, I3, H4, H5, I6, J6

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•B1, B2, C2, D3, C4, C5, D6 •B2, A1, B1 •G2, F1, G1 15 14 13 12 11

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Learning Outcome: Attend to position and order when using a map or a maze.

Amazing

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R Use co-ordinates or ordered pairs to show how Ben spent his afternoon.

Ben left school and went to visit the horse. ( ) He felt hungry so he went to the ice cream shop ( ). As he was walking along he dropped his ice cream on the ground ( ). He ran to the bus stop and caught the bus to the swimming pool ( ). Nobody was at the swimming pool so he decided to go to the basketball court instead. All his friends were there, so he decided to stay there until it was time to go home ( ).

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Extra: Write your own paragraph on the back and give it to a friend to put in the coordinates.

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Learning Outcome: Place important things in their environment on a map.

School Map R List all the different parts of the school you would use in a day, e.g. toilet, playground, drinking taps, etc. ..................................................................... ............................................................................................................................

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R Use the grid below to draw a map of your school.

Place all the important parts of the school from your list on the map.

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Learning Outcome: Reduce and enlarge images.

Enlarging a Picture

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R Enlarge the picture below using the larger grid.

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Learning Outcome: Reduce and enlarge images.

Reducing a Picture

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R Reduce the picture using the grid below.

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Learning Outcome: Understand that figures are exactly the same if one fits perfectly into another.

Shapes

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R Cut out the shapes in the left hand column. Find the perfect match in the right hand column and glue on.

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Learning Outcome: Distinguish rectangles, triangles and circles from similar figures.

Similar Figures R Look at all the figures below.

Identify all the circles. How many? ...............................

Colour them red.

Identify all the rectangles. How many? ........................

Colour them green.

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Identify all the triangles. How many? ............................

Colour them blue.

Identify all the squares. How many? ............................

Colour them black.

Identify all the ovals. How many? .................................

Colour them yellow.

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How many shapes left over? .............................

Explain why they do not fit into the shapes categories above. ......................... ............................................................................................................................ ............................................................................................................................ ............................................................................................................................ ............................................................................................................................

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© ReadyEdFig.P3ubl i cat i ons Fig. 5 Fig. 4 Fig. •1f orr eFig. vi e ur pose sonl y• 2 wp

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Learning Outcome: Explore the features of 2-D shapes.

2-D Shapes R Use the table to record the features of the 2-D shapes.

No. of sides

No. of vertices

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Name

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Learning Outcome: Explore features of a 2-D model.

Features of 2-D Shapes 1

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R Discuss the features of the 2-D shapes below.

Use the table on the next page to classify the 2-D shapes.

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Learning Outcome: Explore features of a 2-D model.

Features of 2-D Shapes 2 R Use the 2-D shapes from page 17 and classify them into the correct group. Draw a sketch of the shape in the correct box. Some 2-D shapes will fit into more than one group. Can you think of other ways to classify the shapes?

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Shapes without corners.

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Shapes with corners.

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Shapes with no straight lines.

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Shapes with rounder corners.

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Learning Outcome: Explore symmetry using cut-out figures.

Symmetry 1 A shape has symmetry if both its parts match when it is folded along a line.

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R Cut and fold the shapes along the fold line to see if they are symmetrical.

Experiment with folding the shapes in different ways to discover which shapes have more than one line of symmetry.

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Learning Outcome: Explore symmetry using cut-out figures.

Symmetry 2

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R Use a mira to discover which fold line is the line of symmetry. Tick it.

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Learning Outcome: Explore symmetry using cut-out figures.

Symmetry 3

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R Complete these figures so they are symmetrical.

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Learning Outcome: Explore symmetry in patterns.

Symmetrical Patterns The following patterns are symmetrical. Discuss why.

VB 3(

VB 3(

VB BV

(33(

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3 VB 3 VB

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Which of the following patterns are symmetrical?

BV 3(

(3VB

V3(B

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( 33 (

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Complete these symmetrical patterns.

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3 (

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VB BV

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Learning Outcome: Using spatial language, describe how a figure has been altered.

Moving Shapes R Make a list of words to describe how a shape can be altered, e.g. flipped, rotated. ............................................................................................................................

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R Look at the set of shapes below. Describe how they have been altered.

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Fig. 1

Figure 2 ...............................................................................................................

Figure 3 ...............................................................................................................

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Figure 4 ...............................................................................................................

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Figure 2 ...............................................................................................................

Figure 3 ...............................................................................................................

Figure 4 ...............................................................................................................

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Learning Outcome: Trace over shapes.

Traversable Networks

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A network is traversable if you can trace over it without retracing any line of the network.

These networks are traversable.

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R Experiment with the following shapes to discover which ones are traversable.

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o c . c e r R Using a geoboard, h make your own traversable o networks.

Record your e t r s s up networks on the back of this sheet.

Challenge eryour classmates to find the correct path around the networks. Can you find a rule that will help you work out whether a network is traversable?

Hint: The rule applies to the number of odd and even points or vertices in a network.

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Learning Outcome: Explore tessellating patterns.

Tessellations A tessellation is formed when one or more shapes fit together without leaving any gaps or overlapping.

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The following patterns are tessellations.

R Look around your school environment. List the things you see that have a tessellating pattern. How many shapes are there in each tessellation? e.g. brickwork (1 shape).

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© ReadyEdPubl i cat i ons R Use firm card to make a template of the shapes below. Use the template to •f or ev i ew p powill se sao nl y• experiment on r blank paper to see ifu ther shape form tessellating pattern.

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Tessellations in Cyberspace Visit forum.swarthmore.edu/alejandre/students.tess.html to see some wonderful tessellations that children from all over the world have published on the net.

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Learning Outcome: Explore tessellating patterns.

Tessellating Patterns

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R The patterns below are semi-regular tessellations because they have two shapes in them. Colour in the tessellations.

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For a selection of tessellations to print and colour visit the following site: library.thinkquest.org/16661/templates/ Page 26

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Learning Outcome: Identify cubes, rectangular boxes, cylinders, cones and spheres.

3-D Shapes Some common 3-D shapes are cubes, rectangular boxes, cylinders, cones and spheres. All 3-D shapes have faces (sides), vertices (corners) and edges.

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vertices

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1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123

R Use the descriptions to label each of the shapes below.

A rectangular box has 8 vertices and 6 faces.

A cube has 8 vertices and 6 identical faces.

A cylinder has circular ends and a curved surface.

A cone has a circular base and only one vertex.

A sphere is a perfectly rounded shape that has no vertices or edges.

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Learning Outcome: Identify cubes, rectangular boxes, cylinders, cones and spheres in everyday items.

Everyday 3-D Shapes R Identify which 3-D shape (cube, rectangular box, cylinder, cone or sphere) is shown in the pictures below.

Give three examples of something in your environment that is the same shape.

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Three examples of each shape .................................................... ....................................................

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Learning Outcome: Select 2-D shape figures to match the faces of a 3-D shape.

A 3-D Shape and its Faces R Use the models of 3-D shapes on pages 39, 43 and 44 to help you do this activity.

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Draw lines to show which 2-D shapes match the faces of the 3-D shapes.

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Learning Outcome: Distinguish between a 3-D shape and its faces.

A 3-D Shape and its Many Faces R Look at the 3-D shapes below. What shape are the numbered faces?

Face 1 ................................................

1

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Face 2 ................................................

Face 3 ................................................

6

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Face 1 ................................................

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Face 4 ................................................

Face 5 ................................................

Face 6 ................................................

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Face 4 ................................................

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Learning Outcome: Classify objects by how many faces they have and the shape of the faces.

Classifying 3-D Shapes R Use the nets from pages 37 to 48 to make up some 3-D shapes.

Use the models to complete the table.

faces

faces faces $ faces & faces

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Model

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Learning Outcome: Explore the features of 3-D shapes.

3-D Shapes R Use the templates on pages 37, 38, 39, 40, 41, 42 and 45 to make some 3-D models. Fill in the table below using the models to help.

Vertices

Name

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No. of faces No. of edges

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Learning Outcome: Make constructions which meet given criteria.

Moving Models R Look at the diagrams of 3-D models in the table below. Using a tick, predict how each model could move or be arranged.

Name

Rolls

Stacks

Slides

Balances

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Diagram

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Use the nets on pages 37- 44 to make the 3-D models in the table.

Experiment with the models to test your predictions.

Indicate which predictions are correct by circling the tick.

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Learning Outcome: Construct a 3-D shape.

Make a 3-D Shape

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R Using straws, pipe-cleaners or a construction kit, copy the 3-D model below. Fill in the information for each model you have copied.

Name ......................

Name .......................

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A triangular pyramid has ..... vertices, ..... faces and ..... edges.

A cube has ..... vertices, ..... faces and ..... edges.

A rectangular prism has ..... vertices, ..... faces and ..... edges.

A square pyramid has ..... vertices, ..... faces and ..... edges.

A triangular prism has ..... vertices, ..... faces and ..... edges.

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Learning Outcome: Make constructions that meet given criteria.

Model Making Make a collection of 3-D shapes (e.g. tissue boxes, toilet rolls, cereal boxes) or use the nets on page 37- 44 to make some 3-D shapes.

R Using glue, pipe-cleaners, string etc. construct a model from the boxes or 3-D shapes that consists of at least five different 3-D shapes and is able to be rolled along the ground.

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Draw and label your model.

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How could you improve your model? ............................................................... ............................................................................................................................ ............................................................................................................................

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Page 35

Learning Outcome: Explore the properties of 3-D shapes.

Cross Sections of 3-D Shapes If you cut through a 3-D model, the shape that is made on the surface of that model is called a cross section.

R Look at the cross section of the 3-D models below.

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Draw the shape that would be made if the following 3-D models were cut into two at the dotted line. e.g. This cross section is a circle.

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e.g. This cross section is a triangle.

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Construct 3-D shapes.

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Triangular Pyramid

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Page 37

Construct 3-D shapes.

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Square Pyramid

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R eady-Ed Publications

Construct 3-D shapes.

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Triangular Prism

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Page 39

Construct 3-D shapes.

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Rectangular Prism

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R eady-Ed Publications

Construct 3-D shapes.

r o e t s Bo r e p ok u S

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Teac he r

Cube

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Page 41

Construct 3-D shapes.

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Cylinder

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R eady-Ed Publications

Construct 3-D shapes.

r o e t s Bo r e p ok u S

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Teac he r

Cone

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Page 43

Construct 3-D shapes.

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Hexagonal Pyramid

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R eady-Ed Publications

Construct 3-D shapes.

r o e t s Bo r e p ok u S

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Teac he r

Hexagonal Prism

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Page 45

Construct 3-D shapes.

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Rectangular Based Pyramid

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o t r s super

R eady-Ed Publications

Construct 3-D shapes.

r o e t s Bo r e p ok u S

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Teac he r

Square Based Prism

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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Page 47

Construct 3-D shapes.

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Octahedron

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