Volume of a Farm Hopper Lesson

Volume of a Hopper lesson MG

Volume of a Farm Hopper lesson.

Intended learning objectives:

 To design different nets

 To calculate volume of simple shapes

 To calculate volume of complex shapes

 To use formula

 To create formula

 To solve complex geometrical problems

 To use trial and error

 To consider functionality and apply mathematics to real life problems.

Equipment needed:

 Power point slides

 Measuring jugs

 Rice

 Plain paper

 Readymade nets

 Copies of going into business as a hopper design questions to hand out

1) Prepare for learning: introductory video

Activity: Pupils enter the room as a video of corn be harvested is playing.

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.

1 Volume of a Hopper lesson MG

2) Agree learning outcomes: How to store the grain

Activity: Class discussion or grouped mind map which is shared with the class.

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.

Possible outcomes: pupils may consider,

 The shape of storage containers, cuboids and cylinders.

 They will realise they need to know about nets,

 some may think about getting the grain from the container, doors, pulley systems to tip container,

 where will the container be placed on the farm,

 how to calculate the amount of grain the container can hold.

3) Construct: lets explore possible containers

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.

Why: Pupils will consider different nets, how does folding the paper create a different shape. Allowing pupils to take ownership over their own design

 How to the shape of storage containers, cuboids and cylinders.

 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.

4) Apply and demonstrate: Share ideas: pros and cons

Activity: Pupils share their ideas with class, creating a discussion.

Why: To see pros and cons of each container.

– Effectiveness of containers.

– Ability to store container/stand

– Complexity of design

– Ability to get grain out

– 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.

5-6) Present new information/Apply and demonstrate: Hoppers slide and what do you have?

Activity: comparing our designs to the hoppers.

– 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

– 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.

Why: problem solving in real life situations.

7) Construct: Generalising

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.

Why: to make pupils consider the different dimensions of shapes that need to be considered when calculating volumes.

Possible outcomes: (e.g, heights, bases ect)

– 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.

– Why: To apply old knowledge to new situations.

– Possible outcomes:

– 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..

– 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

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.

Why: To apply old knowledge to new situations.

Possible outcomes:

– 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..

– 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

Discretion of Level 1-4 teachers to advance to plenary section.

8) Apply: Going into business as a hopper engineer.

Activity: Class effort at solving a hopper problem in a formal context

Why: Pupils need to see how to apply their new learning to different situations

Possible outcomes: Building confidence.

Solution: volume of pyramid= 5 x 5 x 5 x 0.3 = 41.7 (1dp)

Volume of cuboid = 125 (given)

Total volume = 125 + 41.7 = 166.7 (1dp)

9) Apply: Going into business as a hopper engineer.

Activity: Pupils to answer Qs independently.

Why: Pupils need to see how to apply their new learning to different situations

Possible outcomes: Building confidence.

Solution:

1a) Cuboid volume: 8 x 4 x 6 = 192m3

square based pyramid volume= 8 x 4 x 3 x 0.3 = 57.6m3

total volume = 192 + 57.6 = 249.6m3 b) 249.6 x 15 = £3744

2a) 25 – 15 – 7 = 3m b) Square based pyramid volume= 12 x 10 x 7 x 0.3 = 252m3

cuboid volume given = 1800m3

Total volume = 1800 + 252 = 2052m3

10) Apply: Going into business as a hopper engineer. Challenge Qs

Activity: Pupils to answer Qs independently, trial and error.

Why: testing understanding

11.12) Review: what where the learning objectives?

Activity: Pupils asked to discuss and think about the learning that has taken place.

Why: Allows pupils to reflect upon learning.

Hopper Questions: