3D Trigonometry with Pyramid

3D Trigonometry with Pyramid

After completing worked example problems pairs (using silent teacher) the class worked on these worksheets. It was spread over 2 lessons with the homework sheet given at the end of the 2nd lesson. The idea was to have the student practice each step (type of question) in isolation before going onto the next type question, and gradually building and picking it all together.
karel
Isometric Alphabet

Isometric Alphabet

Each capital letter of the alphabet has been drawn on isometric paper. Students can use it to help them write their name or initials on isometric paper.
kirbybill
The Volume and Surface Area Of Cones and Spheres - Worksheets With Answers

The Volume and Surface Area Of Cones and Spheres - Worksheets With Answers

Three worksheets covering higher level GCSE questions on Cones and Spheres including Level 9 questions. Cones - A great worksheet which all higher level students will need to be able to cope with - 12 questions Spheres - 6 questions on volume and surface are of spheres and hemispheres. Cones and Spheres - 5 more difficult questions on the cone and spheres - these are level 8 and 9 ! Answers for each are provided separately.
happymathematician
Speed and density worksheets (with solutions)

Speed and density worksheets (with solutions)

A collection of three worksheets. Two worksheets on applying the formula of speed to calculate unknown speeds, distances and times and one worksheet on applying the formula of density to calculate unknown densities, volumes and masses. Detailed solutions are provided. From https://placeformath.blogspot.com/p/worksheet-shop.html
math_w
Density worksheet (with solutions)

Density worksheet (with solutions)

A worksheet on applying the formula of density to calculate unknown densities, volumes and masses. Detailed solutions are provided. From https://placeformath.blogspot.com/p/worksheet-shop.html
math_w
Volume of prisms

Volume of prisms

A presentation to support the teaching of volume with objectives, examples and differentiated task with answers.
wrighte
Volume of spheres

Volume of spheres

A complete lesson on the theme of volumes of spheres, best suited for more able students. Given that this can be a very dull, restricted topic if pupils just calculate volumes of spheres, hemispheres, etc given the volume formula, the focus is more on deriving a formula. I would teach this after pupils have met all other volume rules (cuboids, cylinders, cones, pyramids) - the derivations and activities require a knowledge of these other rules. Activities included: Starter: A question to get pupils thinking about the different volume rules they’ve already met (cube, pyramid, cylinder, cone). Main: Starting from an image of a square within a circle within a square, pupils are prompted to come up with an inequality for the area of the circle (ie use the inner square as a lower bound and outer square as an upper bound). This ‘leads’ to an estimate of pi=3, but the real purpose is to prepare pupils to do a similar process in 3D, to come with an estimate for the volume of a sphere… Starting from an image of a cone and a sphere within a cylinder (see cover image), pupils are prompted to come up with an inequality for the volume of the circle (using the cone as a lower bound and cylinder as an upper bound). This ‘leads’ to a conjecture for the volume rule of a sphere! Some simple examples using the rule. At this point, you could supplement with extra ‘basic’ questions if necessary. Some questions on the theme of the solar system, looking at volumes of planets and reverse problems (finding radius or diameter given the volume). This also involves standard form as the volumes involved are huge, and could be followed up with some questions about scale and volume factor. I’ve also thrown in a formal proof for the volume rule, that could be looked at with very able students. Plenary: A link to a short video showing a completely different (and fairly accessible) proof, that could be recreated using an orange, knife, and some messy cutting… Please review if you buy as any feedback is appreciated!
danwalker
Volume of cones and frustums

Volume of cones and frustums

A complete lesson on volume of cones. I would cover this after teaching volume of pyramids, so that the volume rules can be linked. See my other resources for a lesson on pyramids. Activities included: Starter: An animation showing pyramids with an increasing numbers of sides, followed by a prompt for pupils to consider what’s the same and different about prisms, pyramids and cones. Main: A slide showing the volume rules for prisms, pyramids and cones. The intention is that having done the starter, pupils will see the volume rule for a cone as a logical ‘extension’ of the rule for pyramids. Example problem pairs on calculating the volume of cones given first the radius and then the diameter, followed by a worksheet for pupils to consolidate. Plus a suggested extension task for those that finish quickly. Slides to define frustums, followed by two examples to calculate volume. Pupils are then presented with a challenge of splitting a cone into a smaller cone and frustum with equal volumes. This offers practice of volume calculations with a twist, and could be used to talk about scale and volume factors. I’ve also suggested a related extension task. Plenary: A prompt for pupils to consider different conic sections, by asking what would happen if you cut at an angle that wasn’t parallel to the base.
danwalker
Pyramids

Pyramids

A range of resources on the theme of pyramids, but touching on topics including the definition of a pyramid and consideration of their properties, representations (3D sketches, nets, pan views) and volume. Probably a couple of lessons worth of activities. Activities included: Prompts to consider a definition of a pyramid, and a closer look at the definitions of base, apex and height. Introductory slides and a worksheet on different representations of pyramids, plus a link to a geogebra file to look at pyramids dynamically. A venn diagram activity for pupils to consolidate their understanding of the above. A link to a video of someone using three pyramids of water to fill a cuboid (ie to demonstrate the volume rule) A nicely animated related question to calculate volume of a pyramid. A physical ‘puzzle’ where pupils cut out 3 nets of identical pyramids, fold and glue them to create 3D pyramids, then try to arrange them to make a single cuboid, thus demonstrating the volume rule. A mini-investigation into step pyramids, that ultimately shows something similar to the physical puzzle above, but in a much more abstract way, and could even be used with a further maths class to look at summations! Some images of regular and irregular pyramids, to get pupils discussing the measurements they would need in order to calculate volume, followed by a prompt for pupils to create their own examples of pyramids with a given volume. A few examples of pyramids in architecture to finish. Please review if you buy as any feedback is appreciated!
danwalker
Primary & Junior Geometry Activities

Primary & Junior Geometry Activities

10 different FUN & ENGAGING geometry activities! Focussing on 2-D and 3-D shapes, symmetry, characteristics of shapes, and creative worksheets for students! Can easily be used for extra practice, early finishers, and added components to your lessons!
VanessaHM11
Volume of prisms

Volume of prisms

A complete lesson on calculating volumes of prisms, probably best aimed at a higher ability group. One activity is designed to be used with multilink cubes and isometric paper. I’ve decided I don’t want to present a formal ‘rule’ for this topic any more, so there is no direct reference to V=A x L and in fact most examples look at multiple ways of calculating the volume. Activities included: Starter: Some basic area questions. Main: Animations to define or remind pupils what a prism is, followed by a prompt for pupils to explore what prisms they can make using 12 multilink cubes. Followed by a prompt for pupils to reflect on the distinctions between the possible answers. This could be extended further, with pupils trying to justify finding or having found all possible answers. A prompt for pupils to work out the volume of a prism made up of smaller cubes, followed by a prompt to ensure that all pupils consider four particular ways of finding the volume (see cover slide). The four methods are then nicely animated. A prompt for looking at a triangular prism, followed by a closer look at two methods for finding the volume. A final example/prompt, looking at a cylinder (only one method). After this, pupils could reflect on the methods seen, and possibly look at what’s the same, what’s different. Pupils are then given four related ‘challenges’ to do; one on cuboids, two on cylinders and one that’s entirely open-ended. I’d use this last task as a basis for a final discussion or showcase of pupils’ efforts. Possible key questions and follow-up tasks are given in the comments boxes at the bottom of slides. Please review if you buy as any feedback is appreciated!
danwalker
Volume of cuboids

Volume of cuboids

A complete lesson on volumes of cuboids whose sides are whole numbers of centimetres, although I’ve thrown in elements of listing combinations systematically and forming algebraic expressions to make the topic more challenging and stimulating. I would personally do a lesson on volume as a concept before this lesson (focusing on one shape type). Activities included: Starter: A simple prompt for pupils to think about properties of a cuboid. Main: A slide giving an initial definition of a cubic centimetre as a cube with sides of 1cm. This is obviously a specific case of a cubic centimetre, but it helps pupils understand conceptually the rule for calculating volumes of cuboids with sides that are integer numbers of centimetres! Then a couple of related examples of volumes of cuboids. A prompt for pupils to try to work out the volume of a 4 by 3 by 2 cm cuboid, followed by a further prompt for them to see three different ways of doing it (see cover slide) A prompt for pupils to investigate what other cuboids can be made with a volume of 24 cubic centimetres, possibly using multilink cubes. Plus a few suggested follow-up questions that give pupils a chance to make conjectures and test them. The set of integer solutions are then presented as a systematic list, at which point you could explain how this list has been made, or let pupils think about that. Pupils are then given a similar but bigger problem - of listing all the cuboids with integer sides and a volume of 216 cubic centimetres. For pupils that finish this quickly, there is a related set of problems to do, with an algebra element (but no solving of equations), and the potential for pupils to create their own similar questions. Plenary: A quick look at other units of volume (litre and cubic metre), that also give a chance to check pupils are clear on the basic method. No printing really needed, although the final extension task could be given out separately as a worksheet. Please review if you buy as any feedback is appreciated!
danwalker
Volume of robots - volume problem solving!

Volume of robots - volume problem solving!

Work out the volume of the three robots (one fairly easy, one medium, one quite tricky). The robots are made of cubes, cuboids and cylinders. The students will need to know that the volume of a cylinder can be calculated as the area of the cross-section multiplied by the length/height. This worked really well with both my KS3 and KS4 classes and is a fun way to practice finding volumes of compound solids. The last robot has some tricky metric conversions of length and area also. Tables are provided for each robot to scaffold the calculation of the total volume, and answers are provided. Worksheet provided in both PDF and Publisher versions.
grw100
Volume Worksheets

Volume Worksheets

Differentiated volume worksheet Great worksheet when calculating the volume of a prism Problem solving questions included
Stemorris
Nets of 3D Solids (KS3)

Nets of 3D Solids (KS3)

Whole lesson for nets of 3D solids. Includes presentation, lesson plan and activity. Get learners to walk around and identify the 8 different nets of the 3D shapes. Also includes Kagan Activities, making solids from nets activity and individual work based on properties of 3D solids.
jasper_1895palae
Volume Investigation

Volume Investigation

A practical volume investigation for KS2/KS3 pupils This lesson was used for an observation after the children had spent a week learning about volume. The children construct boxes and investigate volume by cutting different sized squares from the corner of a grid to find out which dimensions give the greatest volume. Lots of opportunity for discussion and reasoning. I delivered this lesson the day before Eid so linked it to party boxes, but it could be easily adapted! Differentiated 5 ways and includes IWB flipchart, activity sheets and worksheets.
aliceeliza
Outside With Perimeter Area And Volume

Outside With Perimeter Area And Volume

During this lesson students investigate, measure and use formulas outdoors in preparation for furthering their understanding in the topic of geometry. They apply their understanding of perimeter, area and volume to real world situations by looking for and recording a range of shapes around their school. Students will develop communication skills as they justify answers and reflect on the topic. This lesson is designed to be taught outside. By spending time outdoors and connecting to nature, students are more likely to care for and conserve nature as adults.
TheTeachersFriend
Angles In Trees

Angles In Trees

During this lesson students investigate, estimate, identify and classify angles in the outdoors in preparation for furthering their understanding of geometry. They apply their understanding of angles to the real world by identifying a range of angles in their local environment. Students will develop communication skills as they write instructions and provide feedback. This lesson is designed to be taught outside. By spending time outdoors and connecting to nature, students are more likely to care for and conserve nature as adults.
TheTeachersFriend
Design a bedroom project

Design a bedroom project

Pupils are required to design and decorate a bedroom completing a scale drawing, researching and costing furniture and decorative items and calculating the cost of decorating the room.
drooke
Metric and Imperial Equivalents

Metric and Imperial Equivalents

Students can practice converting metric to imperial units and vice versa in a range of questions. This will help them develop the skills needed for GCSE Maths or Functional Skills Maths (Level 2) There are conversions in the boxes for reference if they wish to use them. Teachers can use practical resources alongside such as metre sticks, rulers, weighing scales and measuring jugs. Can be used for revision or as a worksheet.
kajal_intwala92
Huge Bank of KS3 Shape Starters

Huge Bank of KS3 Shape Starters

A set of 11 lesson starters I’ve compiled which I have used in lessons on Shape topics with my KS3 Maths students. Topics covered are: 2-D and 3-D Shapes, Perimeter, Angles, Nets of 3-D Shapes, Units of Measurement and Plans/Elevations. As well as being useful for lesson starters, these resources are also useful to check pupils’ prior understanding of a topic and as plenary activities.
jcoulter62
Identify 3D polygons (name, edges, faces, vertices - answers included)

Identify 3D polygons (name, edges, faces, vertices - answers included)

Designed to easily fit into an exercise book without folding, this activity sheet focuses on the national expectations for children with regards to 3D polygons. An editable version has been included for you to adapt the activity to your class, if required. Additionally, a robust answer sheet is included. Children will need to: -Name each 3D polygon Identify the number of faces Identify the number of vertices Identify the number of edges
GalvaniseEDU
Geometry: Volume Exam Questions (with Answers)

Geometry: Volume Exam Questions (with Answers)

These are exam questions on volume. I predominantly use these for either homework or revision. Do view my excellent lesson on the topic. https://www.tes.com/teaching-resource/geometry-volume-1-volume-of-prisms-worksheet-11265223 NOTE: Feel free to browse my shop for more excellent free and premium resources, and as always please rate and feedback, thank you.
ajf43
Geometry: Volume of Prisms Exam Questions

Geometry: Volume of Prisms Exam Questions

These are exam questions on volume of prisms. I predominantly use these for either homework or revision. Do view my excellent lesson on the topic. https://www.tes.com/teaching-resource/geometry-volume-1-volume-of-prisms-worksheet-11265223 NOTE: Feel free to browse my shop for more excellent free and premium resources, and as always please rate and feedback, thank you.
ajf43
World Cup football 2018 - Truncated Icosahedron

World Cup football 2018 - Truncated Icosahedron

3d truncated icosahedron nets with each face representing one of the 32 countries in the world cup. Works well in groups and should take 1 to 2 lessons. Ideal for post exam / end of term. Print on card. You need glue, scissors and colour pens.
kateauld
GCSE Calculator Bundle

GCSE Calculator Bundle

GCSE Calculator Bundle All answers are included. If bought independently, these 3 resources would cost £9.50, but I am offering them in this bundle for £7.50, a saving of 21%. To view items individually, please go to Maths Shop
Elsie99
Volume of Prisms Codebreaker

Volume of Prisms Codebreaker

I needed further mixed practice for a low ability Year 8 group to practice volume of prisms. The first is where they need to find the volume - the second, they make up their own 3D shapes with those volumes as an extension.
missblilley