#### 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.

#### 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

#### 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

#### Perimeter area and volume of rectangles and cuboids- (spoons / matching game)

Spoons game: Look it up, there are loads out there but in a nutshell: in groups of four. need three spoons (any other item will do as well) try to make a set of four but passing one card to the left and receiving a card for the right. if you finish a set as secretively as you can grab a spoon when you do that everyone else tries to get a spoon too. person who misses out adds the next letter of SPOONS on their sheet. play continues till all but one have written spoons. they are the winner. can also be used as a simple matching activity.

#### Volume of prisms

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

#### 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!

#### 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.

#### Properties of 3D shapes

A presentation to help support the teaching of properties of 3D shapes with objectives and student tasks.

#### 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!

#### Primary & Junior Geometry Activities

10 different FUN &amp; 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!

#### Problem solving GCSE exam style practise

A lesson concentrating on the process of GCSE exam questions rather than just the calculations. Anwers given step by step. SMART Notebook and Powerpoint provided.

#### Year Six - Autumn, Spring and Sum 1 (Follows order of White Rose)

All teaching slides for Autumn and Spring and Sum 1. Influenced by recent maths hub CPD training and mastery/CPA approach to teaching mathematics. Includes reasoning and problem solving activities to explore, model and discuss in order to teach the underlying mathematical concepts. Follows ORDER of White Rose teaching guidance. Join the Facebook group ‘mastering primary maths’ for preview lessons in the files section :)

#### Perimeter, Area and Volume recap worksheet (Y5)

Just created these for my class. Can be used as an assessment after teaching shape. 3 levels of differentiation. For Year 5.

#### What's my shape game

cards that could be printed out or adapted. 3d shapes.

#### Sorting every day 3D Shapes

Activity to sort eery day 3d shapes in to their correct boxes by names. As an extension, children could begin to write down the properties of the shapes - verties, edges, faces etc..

#### Volume Consolidation Year 5 Summer Block 5 Reasoning and Problem Solving

This resource is aimed at Year 5 Expected and has been designed to give children the opportunity to consolidate the skills they have learned in the White Rose Maths Guidance and Examples Summer Block 5 – Volume The questions are based on the ‘small steps’ that are addressed in the block, but are presented in a different way so children can work through the pack independently and demonstrate their understanding and skills. This resource is themed around children taking part in a Design and Technology competition. You can find more Reasoning and Problem Solving resources designed to be used with the White Rose Maths Guidance here

#### 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!

#### 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!

#### 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.

#### Calculate volume of cylinders - Do It, Twist It, Deepen It

Another Do It (fluency), Twist It (reasoning) and Deepen It (problem solving) all about the volume of cylinders iIncluding three goal free problems. @howweteachit @mr_man_maths

#### Axes / Chart Generator (Plus all Worksheets)

Axes Generator plus Multiple worksheets

#### Volume Worksheets

Differentiated volume worksheet Great worksheet when calculating the volume of a prism Problem solving questions included

#### Year 6 – Measurement – Area, Perimeter and Volume – Block 5 (Weeks 8-9) - BUNDLE – Spring – White Rose

This bundle contains Pack 1 and 2 for the Year 6 - Measurement – Area, Perimeter and Volume - (Block 5). This bundle covers weeks 8 and 9. Pack 1 (Week 8) small steps include: • Shapes - Same area • Area and perimeter • Area of a triangle (1) • Area of a triangle (2) The resources in this pack listed below include worksheets and activities along with answers for each pack: • Worksheets - Shapes - Same area • Activity - Match cards - Shapes - Same area • Worksheets - Area and perimeter • Worksheets - Area of a triangle (1) • Worksheets -Area of a triangle (2) • Contextual planning sheet for guidance Pack 2 (Week 9) small steps include: • Area of a triangle (3) • Area of a parallelogram • Volume - Counting cubes • Volume of a cuboid The resources in this pack listed below include worksheets and activities along with answers for each pack: • Worksheets - Area of a triangle (3) • Activity - Ordering - Area of triangles (3) • Worksheets - Area of a parallelogram • Worksheets - Volume - Counting cubes • Activity - Challenge cards - Volume - Counting cubes • Worksheets - Volume of a cuboid • Template - Dotty paper • Contextual planning sheet for guidance The resources support a mastery approach to encourage a deeper understanding of the topics taught. It follows a CPA (Concrete, Pictorial, Abstract) approach to ensure all children can access learning. The pack provides pictorial and abstract representations, along with reasoning, problem solving and open-ended investigations. Details of this can be seen in the contextual overview provided. I hope you find them useful. If you have any questions, please email thedigitalstationer@gmail.com Thanks, The Digital Stationer

#### Measurement Problem Solving KS2 Romans

This activity combined our History topic of Romans, with our Maths focus of measurement, plus a little bit of shapes and fractions thrown as an assessment of the previous units taught. Students receive a letter from Emperor Hadrian, with the command to rebuild sections of Hadrian`s Wall. They then worked in differientiated groups for calculate the correct measurements for the wall. Once the correct measurements had been calculated they then used their knowledge of 3-D shapes to build the wall. I have included the activity and instructions in pdf and word format for editing. My class loved it, but I have to be honest - it took them all morning! Learning Objectives covered: Geometry: Property of Shapes: • Draw 2-D shapes and make 3-D shapes using modelling materials. Measurement: • Measure, compare, and add lengths (m/cm/mm) • Continue to measure using the appropriate tools and units, progressing to using a wider range of measures, including comparing and using mixed units and simple equivalents of mixed units (for example, 5m = 500cm). Fractions: • Recognise, find and write fractions of a discrete set of objects. • Recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10

#### Volume of a Prism revision mat (Great for independant revision or homework!)

This revision mat allows pupils memory to be jogged about the topic with out giving them all the details, which they will have to fill in for themselves enabling students to become more independent about their revision . please review :)

#### Inquiry: n cube sponge.

A 15-minute Mathematical Inquiry Assessment Item for Junior and Middle Secondary.

#### Inquiry: Cutting Corners.

A 15-minute Mathematical Inquiry Assessment Item for Junior and Middle Secondary.

#### End of Year 5 Maths Test Assessment

This resource is to support teachers with end of year progress assessments by assessing against the Year 5 mathematics objectives from the National Curriculum. It also includes a tracker sheet to help identify gaps in knowledge. For more Assessment resources, visit our website here.

#### 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.

#### Volume of Cubes and Cuboids Activity Cards

This is a collection of 30 colorful activity cards to use as a starter activity or plenary. These starter activity cards can be used for your class team games, a quick activity to kick off your lessons,  to end your lessons, or to provide a nice distraction in the middle. The cards will help your pupils to calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³]. They can be printed, laminated and reuse with your class as many times as you want. Can also be used as worksheet for home and class use.

#### Volume problem solving - missing numbers Year 5

We’d been doing volume of cuboids and then I made up this sheet to see if they could calculate missing measurements. For LA mainly stuck to them calculating total volume to secure. MA/HA varied which measurement was missing. (1st sheet is answer sheet)

#### 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.

#### Shapes Notebook

This SMART Notebook file explains how to categorise 2D and 3D shapes as well as how to calculate the area and perimeter of shapes. Finding lines of symmetry and drawing reflections is also included in this file. ClassLab activities help pupils to consolidate their understanding about how to sort 2D and 3D shapes as well as drag and drop activity.

#### 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.

#### 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.

#### Investigation: Don't Rubbish the Bin

A Mathematical Investigation Assessment Item for Year 9 &amp; 10 students.

#### 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.

#### Year 3 Compare Capacities Summer Block 4 Step 7 Lesson Pack

This Year 3 Compare Capacities lesson pack includes a teaching PowerPoint and differentiated varied fluency, and reasoning problem solving questions. The varied fluency resource is differentiated in three ways and includes a selection of different questions types. The reasoning and problem solving resource is differentiated in three ways and includes two reasoning and one problem solving question types. You can find more resources which follow the same small steps White Rose Maths Guidance here.

#### Year 3 Add and Subtract Capacities Summer Block 4 Step 8 Lesson Pack

This Year 3 Add and Subtract Capacities lesson pack includes a teaching PowerPoint and differentiated varied fluency, and reasoning problem solving questions. The varied fluency resource is differentiated in three ways and includes a selection of different questions types. The reasoning and problem solving resource is differentiated in three ways and includes two reasoning and one problem solving question types. You can find more resources which follow the same small steps White Rose Maths Guidance here.

#### Year 5 Estimte Volume Summer Block 5 Step 3 Lesson Pack

This Year 5 Estimate Volume lesson pack includes a teaching PowerPoint and differentiated varied fluency, and reasoning problem solving questions. The varied fluency resource is differentiated in three ways and includes a selection of different questions types. The reasoning and problem solving resource is differentiated in three ways and includes two reasoning and one problem solving question types. You can find more resources which follow the same small steps White Rose Maths Guidance here.

#### Year 5 Compare Volume Summer Block 5 Step 2 Lesson Pack

This Year 5 Compare Volume lesson pack includes a teaching PowerPoint and differentiated varied fluency, and reasoning problem solving questions. The varied fluency resource is differentiated in three ways and includes a selection of different questions types. The reasoning and problem solving resource is differentiated in three ways and includes two reasoning and one problem solving question types. You can find more resources which follow the same small steps White Rose Maths Guidance here.

#### FREE Year 5 What is Volume? Summer Block 5 Step 1 Lesson Pack

This Year 5 What is Volume? lesson pack includes a teaching PowerPoint and differentiated varied fluency, and reasoning problem solving questions. The varied fluency resource is differentiated in three ways and includes a selection of different questions types. The reasoning and problem solving resource is differentiated in three ways and includes two reasoning and one problem solving question types. You can find more resources which follow the same small steps White Rose Maths Guidance here.