Lesson 6

Exploring other possibilities with Cylinders

60 minute lesson

Syllabus indicators:

Students:

Solve problems involving volume for a range of prisms, cylinders and composite solids (ACMMG242)
- find the volumes of solids that have uniform cross-sections that are sectors, including semicircles and quadrants
- find the volumes of composite solids involving prisms and cylinders, e.g. a cylinder on top of a rectangular prism

Working mathematically:

Apply strategies to solve for volume of cylinders with no end, half open/half close, open at both ends (Reasoning, Problem Solving, Understanding)

Teaching and learning resources:

A cylinder net worksheet
scissors, tape or glue
students' workbook
Individual
All these questions have a link embedded in them - not created by me
ICT learning - SketchUp

Lesson goals:

By the end of the lesson, students should be able to:

Solve for volumes of cylinders with different alterations done to it
Use SketchUp to generate some examples of composite solids with these uniform cross sections

Assumed knowledge:

Students can:

Dissect a composite solids into one or two solids (lesson 5)
use SketchUp

Lesson Sequence

INTRODUCTION

Hand in homework task (AOL)

10:00 am

The teacher collects students' homework and their definition for sectors and quadrilaterals. The homework task would get distribute throughout the lesson. The teacher calls each student up and go through the marking criteria with students. (Fluency, Reasoning, Problem Solving)

To ensure students did the work, the teacher will have a BLANK question paper and ask the student to walk through the steps to get the answers. (Communicating)

Question(s) the teacher can ask the student:

Can you walk me through your steps to get the answer to this question?
What is another approach to answer this question?

Revision

10:05 am

Introduction: Practising harder problems

Description of the task:

The teacher begins by revising with students on previous lessons on how to calculate volumes of composite solids with right prisms and cylinders. The teacher puts one question on the board and each student will do them and hand the book to the teacher for marking. (AOL) (Problem Solving)

The teacher defines sector and quadrilaterals for students.

Source: Big Idea maths (link is embedded)

BODY

Activity 1: Exploring Other Possibilities

10:15 am

Activity: Exploring other possibilities

Description of the task:

The teacher writes these on the board:

closed cylinder
cylinder with one open end
closed half-cylinder
half-cylinder with open top
half-cylinder with open top, one end open
cylinder open at both ends

The teacher asks each students to make 6 of these based on the words written on the board. This is an investigative task to see if students can see other alternatives. (Understanding)

Source: © mathsmentality.com.au 2014

Nets_for_making_solids_U-7.pdf

Activity 2: Exploring and Calculating

10:35 am

Activity 2: Exploring and Calculating

Description of the task:

PART I:

From activity 1, each student work on these exercise individually in their workbook. (Reasoning, Problem Solving,, Understanding

Question(s) the teacher can ask students:

What are your strategies to solve question e.g. e?
Why do you think learning about these different possibilities useful to you?

Source: Alchemytuition (link is embedded)

PART II: ICT learning

Description of the task:

Students go onto Google SketchUp and generate their own sets of composite solids using sectors and/or quadrilaterals. The teacher can show this example to students.

Source: Oup (link is embedded)

CONCLUSION

Consolidation

10:50 am

EXIT CARD

The teacher gives general feedback on the homework and reiterate key learning ideas of this lesson.

Before students leave the classroom, the teacher asks students to leave the room one by one and ask the student one of these questions:

What shape is a swimming pool? What shape is a pipe?

answer: a rectangular prism with open top & a cylinder with both open ends

Homework

For homework, students have to come up with at least one real-life example where these specific types of cylinders are used (from activity 2) and ask them to add these terminologies into their key vocabulary worksheet.

Preparation for next lesson

In preparation for next lesson, the teacher asks each students to bring in one bottle or one container from home for a revision lesson on Volume and Capacity next lesson. Further, letting students know that the next lesson is going to challenge them is a good way to ensure they are revising and preparing for it.

Lesson evaluation questions

How did the students perform in the homework task?
Were the use of ICT effective? Were students able to draw their own composite solids using sectors/quadrilaterals?
Were the students able to achieve the learning goals?
What considerations should I take into account so the next lesson can be improved ?

Lesson 5

Lesson 7

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