Lesson 8

Applying mathematics to real-life problems

60 minute lesson

Syllabus indicators:

Students:

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

solve a variety of practical problems related to the volumes and capacities of prisms, cylinders and related composite solids

Working mathematically:

Find the volumes and capacities of various everyday containers, such as water tanks or cartons used by removalists (Problem Solving)
Dissect composite solids into two or more simpler solids to find their volumes (Reasoning)
Suggest strategies to go help solve the following questions (Reasoning, Problem solving)
Explain the relationship of a height--time chart (Fluency, Communicating)

Teaching and learning resources:

Pair tasks and group work (3 or 4 students)
A rectangular container and a cube
Butchers paper

Lesson goals:

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

Identify basic solids in more complicated composite solids
Solve for practical problems
Construct a height-time chart

Assumed knowledge:

Students can:

Draw on prior knowledge from lesson 1-5 in this unit of work
Calculate volume and find cross-sectional area (S4)

Lesson Sequence

INTRODUCTION

Revision

10:00 am

Description of the task:

The teacher collects students' designed questions at the beginning of the lesson for today's homework and revise the key learning from the previous lesson.

Introducing real-life related problems

10:05 am

Introduction: Introducing real-life related problems

Description of the task:

The teacher summaries the teaching program by introducing to students that today's lesson will be about real-life related problem.

BODY

Activity 1: Demonstration

Source: created by me

10:10 am

Description of the task:

This is an investigative tasks that teacher should demonstrate to the students in class. (Reasoning, Problem Solving, Fluency)

The teacher fills up a rectangular container and ask students the question below. The teacher can demonstrate to the students so they can see the water rises. However, the teacher should not tell students the dimension until later. OR the teacher can tell students the dimension of the rectangular container and the cube.

Regardless, each student must write their answer in a piece of paper with their name and guess it. Students will work in groups of 3 or 4 to figure out the answer and the student who gets the correct answer or is the closest wins.

NOTE: these numbers can and should be changed depending on students' ability.

Main question: How many cubes can I put in before the water flows out?

Activity 2: Investigation

10:20 am

Students are encouraged to work in pairs to solve these problems below. However, each student must have their own set of working out. Students can use these questions to show their thinking process and share this with other pairs if they are also experiencing difficulties. (Problem Solving, Reasoning, Communicating, Fluency)

What do we know? and What are the information that are given to us?
What is the question asking us to find?
What is it that we have to find to solve the question

Source: Links are embedded

Answer: 5 prisms can be made
Source: NRich Maths

Source: Alchemytuition

Activity 3: Group Task

10:35 am

Description of the task:

In this activity, students work in groups of 3 or 4 to solve this task. Students are expected to use the available butchers paper to brainstorm their ideas and graph the solutions according to the question given. (Understanding, Problem Solving)

Question(s) the teacher can ask the student:

What would go on the x axis? y axis?
Can you explain what each part of the chart corresponds to?

Source: NRich Maths

Conclusion

Consolidation

10:55 am

Description of the task:

The teacher asks students to do another PMI (this would help with the assessment task)

P: What are some of the positive things you have learnt from today's lesson? Which point in today's lesson that you enjoy the most and/or learn the most?

M: What are some things you are still unsure about? Was there anything you did not like from today's lesson? What is something you did not agree on today, whether it is from your peer or from your teacher?

I: What did you find in today's lesson that you did not know before? At any point in the lesson that your perspective changed - how and why?

Homework

Each student would get a different set of questions from which their peers have designed in lesson 7. This is to be handed in the next lesson.

Preparation for next lesson

Revise lesson 1 to lesson 8 materials

Lesson evaluation questions

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 ? (Check the PMI)

Google Sites

Report abuse