Lesson 7

Challenging and miscellaneous problems

60 minute lesson

Syllabus indicators:

Students:

Solve problems involving the volumes of right prisms (ACMMG218)
Solve problems involving volume for a range of prisms, cylinders and composite solids (ACMMG242)

Working mathematically:

Dissect composite solids into two or more simpler solids to find their volumes (Reasoning)
Communicate key vocabulary in a coherent and appropriate context (communicating, Fluency)
Apply strategies to solve for volume of composite solids (Reasoning, Problem Solving)

Teaching and learning resources:

Small strips of paper
Classroom whiteboard
A small box or hat
Individual and whole class
LIT activity
Worksheets created by me
Green and red slip from lesson 5

Lesson goals:

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

Calculate volume of a composite solids by using Pythagoras Theorem to find the perpendicular height
Use available information to find missing dimensions
Represent volume with algebraic expressions
Define and differentiate between 'volume' and 'capacity'

Assumed knowledge:

Students can:

Lesson 1-6 of this unit teaching program
All the content from Volume S4

Lesson Sequence

INTRODUCTION

Revision

10:00 am

Description of the task:

The teacher asks students for their homework and check if they have added in the new key terms from lesson 6 into the glossary worksheet. The teacher also revisits key idea from yesterday's lesson.

Introduction: Q & A's (LIT)

10:05 am

Description of the task: (LIT)

The teacher introduces today's lesson is solely based on working with challenging and harder problems. The teacher allows students time to write down questions that they have up until this point and the whole class will engage in a Q & A's question. Students write on a slip of paper, fold it, put it into a box and the teacher reads out loud each one. (Communicating)

BODY

Challenging Problems.docx

Source: NRich Maths

Activity 1: Miscellaneous

10:15 am

Description of the task: Building on and applying from previous knowledge and understanding

These questions are categorized into three groups. The teacher allows students to choose one out of the three groups to work on. This task is designed for 2 -3 students per group. (AFL) (Problem Solving, Understanding, Reasoning, Communicating)

Group 1: Missing measurements
Group 2: Volume and algebraic expressions
Group 3: Calculating volume of composite prisms

If the students have a hard time, ask the students to use the green and red card slip capture the teachers' attention. Further, the teacher must check students' work before allowing them to move onto the next group.

Question(s) the teacher can ask students:

What are some of the strategies you have discussed as a group?
What are the key components to solve any volume of a composite solid?

Activity 2: Challenging problems

10:30 am

Activity 1: Challenging problems

Description of task:

The teacher and students work together to solve the first one.

Question 2 of this worksheet gives the slanted height, the teacher makes sure students are aware of this and let students apply their own understanding to see if they could find the perpendicular height. (Problem Solving, Reasoning)

Volume1.pdf

Source: Matrix Education https://www.matrix.edu.au/beginners-guide-year-9-maths/part-6-maths-volume/

Activity 3: Revision - Volume and Capacity

10:40 am

Description of the task:

The teacher asks students to take out the materials that were asked from the previous lesson for this task. In Part 1, students use the red and green slip (False and true respectively) and ask students at random to answer 'why'? For Part 2, students work in pairs to come with these statements and swap it with another group. (Understanding, Reasoning, Communicating)

Question(s) the teacher can ask students:

What is the difference between volume and capacity?
How could you explain this concept so that your peer could understand it? (for struggling learners)

Part 1: Individual task

Part 2: Pair task

Volume and Capacity.pdf

Source: TESS India

CONCLUSION

Consolidation

10:55 am

The teacher reiterates key learning concept for today's lesson and ask students do to the three W's. This time, it will be an individual task activity. Students are to answer these three questions in their book and the teacher asks each student to share their answers (one out three) to the class and hand in the book to the teacher. (AFL)

What did we learn today?
What is the relevancy, importance and usefulness of this lesson?
What are we going to do with this new knowledge?

Homework

Students are to design a question similar to Question 9 in activity 1, using two letters present in their name. These will get randomly distributed in class so they must also have an answer sheet available for other peers to check the answer.

Preparation for next lesson

Revise lesson 1 to lesson 7 materials

Lesson evaluation questions

How did students perform in these challenging tasks?
How much detail did students include in their responses?
Were students engaged in the activities today?
Were the students able to achieve the lesson outcomes for this lesson?
What considerations should I take into account so the next lesson can be improved ?

Lesson 6

Lesson 8

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