<p>Volume of a Hopper lesson MG</p><p>Volume of a Farm Hopper lesson.</p><p>Intended learning objectives:</p><p> To design different nets</p><p> To calculate volume of simple shapes</p><p> To calculate volume of complex shapes</p><p> To use formula</p><p> To create formula</p><p> To solve complex geometrical problems </p><p> To use trial and error</p><p> To consider functionality and apply mathematics to real life problems. </p><p>Equipment needed:</p><p> Power point slides</p><p> Measuring jugs</p><p> Rice </p><p> Plain paper</p><p> Readymade nets</p><p> Copies of going into business as a hopper design questions to hand out</p><p>1) Prepare for learning: introductory video</p><p>Activity: Pupils enter the room as a video of corn be harvested is playing.</p><p>Why: To will allow the pupils to see that growing the crops is not that only thing that farmers need to consider, allowing them to think about the wider implications of farmer. </p><p>1 Volume of a Hopper lesson MG</p><p>2) Agree learning outcomes: How to store the grain</p><p>Activity: Class discussion or grouped mind map which is shared with the class.</p><p>Why: Pupils will consider how to store the grain hopefully coming to a conclusion of what do we need to know to tackle this problem. </p><p>Possible outcomes: pupils may consider,</p><p> The shape of storage containers, cuboids and cylinders. </p><p> They will realise they need to know about nets,</p><p> some may think about getting the grain from the container, doors, pulley systems to tip container, </p><p> where will the container be placed on the farm, </p><p> how to calculate the amount of grain the container can hold. </p><p>3) Construct: lets explore possible containers</p><p>Activity: In pairs pupils can either draw possible containers or start straight away folding paper into nets until they are happy with a design. Once they are happy with the design they can measure the amount of grain there container will hold.</p><p>Why: Pupils will consider different nets, how does folding the paper create a different shape. Allowing pupils to take ownership over their own design</p><p>Possible outcomes: pupils may consider,</p><p> How to the shape of storage containers, cuboids and cylinders. </p><p> Pupils may think about getting the grain out, measuring the volume will allow them to tip the shape, seeing how messy/how much spillage may occur. </p><p>2 Volume of a Hopper lesson MG</p><p>4) Apply and demonstrate: Share ideas: pros and cons</p><p>Activity: Pupils share their ideas with class, creating a discussion. </p><p>Why: To see pros and cons of each container. </p><p>Possible outcomes: pupils may consider,</p><p>– Effectiveness of containers. </p><p>– Ability to store container/stand</p><p>– Complexity of design</p><p>– Ability to get grain out</p><p>– The teacher should eventually lead the conversation down the route of suitability, saying that we want a container that does not need to be tipped, (e.g. No complicated pulley systems) Maybe a funnel would be good. </p><p>5-6) Present new information/Apply and demonstrate: Hoppers slide and what do you have?</p><p>Activity: comparing our designs to the hoppers. </p><p>– Level 1-4 pupils to measure their l,h,w of their cuboids. (which most will make) and compare it to their volume, eventually realising volume of a cuboids = lhw </p><p>–</p><p>– Level 5+ pupils to discuss compound shapes that we already know how to find the volume of cuboids, therefore how can we find the volume of a hopper.</p><p>Why: problem solving in real life situations. </p><p>3 Volume of a Hopper lesson MG</p><p>7) Construct: Generalising</p><p>1st Activity: Pupils will first be asked to write down what to they know about the shapes they have just been given seeking for similarities. </p><p>Why: to make pupils consider the different dimensions of shapes that need to be considered when calculating volumes.</p><p>Possible outcomes: (e.g, heights, bases ect) </p><p>– 2nd Activity: Pupils to measure how much more rice the cube can hold when compared to the pyramid. </p><p>– level 5+ pupils to discover the formula for calculating the volume of pyramids.</p><p>– Why: To apply old knowledge to new situations.</p><p>– Possible outcomes:</p><p>– Level 1-4 pupils: to realise that the cuboids can hold 3 times more rice than the pyramid. Some to realise that the pyramid is 1/3 of the volume of a cuboids..</p><p>– Level 5+ to discover the general formula for finding the volume of a pyramid (area of base)1/3h, or for a square based pyramid bwh1/3</p><p>2nd Activity: Pupils to measure how much more rice the cube can hold when compared to the pyramid. level 5+ pupils to discover the formula for calculating the volume of pyramids.</p><p>Why: To apply old knowledge to new situations.</p><p>Possible outcomes:</p><p>– Level 1-4 pupils: to realise that the cuboids can hold 3 times more rice than the pyramid. Some to realise that the pyramid is 1/3 of the volume of a cuboids..</p><p>– Level 5+ to discover the general formula for finding the volume of a pyramid (area of base)1/3h, or for a square based pyramid bwh1/3</p><p>4 Volume of a Hopper lesson MG</p><p>Discretion of Level 1-4 teachers to advance to plenary section.</p><p>8) Apply: Going into business as a hopper engineer. </p><p>Activity: Class effort at solving a hopper problem in a formal context </p><p>Why: Pupils need to see how to apply their new learning to different situations</p><p>Possible outcomes: Building confidence.</p><p>Solution: volume of pyramid= 5 x 5 x 5 x 0.3 = 41.7 (1dp)</p><p>Volume of cuboid = 125 (given)</p><p>Total volume = 125 + 41.7 = 166.7 (1dp) </p><p>9) Apply: Going into business as a hopper engineer.</p><p>Activity: Pupils to answer Qs independently. </p><p>Why: Pupils need to see how to apply their new learning to different situations</p><p>Possible outcomes: Building confidence.</p><p>Solution: </p><p>1a) Cuboid volume: 8 x 4 x 6 = 192m3</p><p> square based pyramid volume= 8 x 4 x 3 x 0.3 = 57.6m3</p><p> total volume = 192 + 57.6 = 249.6m3 b) 249.6 x 15 = £3744</p><p>5 Volume of a Hopper lesson MG</p><p>2a) 25 – 15 – 7 = 3m b) Square based pyramid volume= 12 x 10 x 7 x 0.3 = 252m3</p><p> cuboid volume given = 1800m3</p><p>Total volume = 1800 + 252 = 2052m3 </p><p>10) Apply: Going into business as a hopper engineer. Challenge Qs</p><p>Activity: Pupils to answer Qs independently, trial and error. </p><p>Why: testing understanding </p><p>11.12) Review: what where the learning objectives? </p><p>Activity: Pupils asked to discuss and think about the learning that has taken place.</p><p>Why: Allows pupils to reflect upon learning. </p><p>6 Volume of a Hopper lesson MG</p><p>Hopper Questions:</p><p>7</p>