Geology

Topic: Unit of Measurement (lesson 1)

Aims

Students will be familiarized with the different terms used to refer to the units of measurement and the international standard units used to identify units of measure. The class will also be introduced to quantities and units of measure. The following are the chief objectives the lesson intends to achieve:

• Students should be able to identify all symbols, operations, relation, and basic mathematical language relevant to units of measure


• Provide clear a concise definition of terms that will be used in the topic


• Students be able to identify several units of measure


• Students be in a position to clearly define units of measure and match them with their standard units


• Students will be able to predict the differences exhibited by two similar objects as presented by their differences in the measure of their quantity.

Learning Outcomes

• Each quantity whether derived or basic has a unit of measure


• Some basic mathematics operations are used to obtain quantity measures


• Measurements can be recorded using different units


• Units of measurement can be converted from one unit to another using mathematical methods

Teaching strategy

The strategy for teaching this class will take the following form:

Lecture: Each lecture session will take 45 minutes (3 lectures)   

To introduce the topic of units of measurements to the class, a lecturer will be necessary. This is important since at the introductory period of the unit a lecturer will be able to gather information on what students already know about measurements. Following are the main activities of the class:

• Welcome students and encourage them to develop positive attitude towards learning the unit


• Address any potential issue likely to arise during the lesson


• Try to explain the purpose of studying the topic to the students


• Introduce some symbols, basic operations, relations and some basic mathematics language that is necessary for student to understand units of measure

Guided practice: A single 45 minutes lesson

The strategy with focus on the whole class as a group and all the activities conducted during the practice will be guided by an instructor. In this session, the instructor will simply engage students to understand their skills and knowledge on the unit. The following main areas will be addressed in this activity:

• Start with lesson preparation: make all the materials required such as handouts with notes on the unit available for students.


• Analyze the topic of on unit conversion critically concentrating on areas of symbols, relations and mathematical language needed for understanding physical quantities, unit conversion, and classification of physical quantities to scalars and vectors.


• Actively engage the class using simple practice exercises on unit conversion.


• The session with also include a PowerPoint presentation to facilitate clear understanding of the methods of unit conversion.

Computer Activity

This will cover different online video tutorials aimed at giving the student a clear understanding of the units of measure topic. The activity tutorials will mainly aim at familiarizing students with symbols, operations, relations and other fundamental mathematical language significant in the understanding the units of measure. The tutorials will also provide information about definitions some important concepts used in the topic such as defining physical, scalar and vector quantities. Moreover, the tutorials will seek to provide students with adequate knowledge about the agreed units in the international system (SI units). The instructor in this activity will actively engage student using questions on the topic to advance their understanding of the units of measure. It is also important for the instructor to use random questions to assess the students understanding of what was covered in previous lessons. The following question will be used to evaluate students understanding of the topic.

• What are the different types of measurements?


• What is meant by SI units?


• What are the SI units of the basic units of measurements?

Interaction during learning

So as to promote a conducive learning environment, these levels of interaction will be employed:

Teacher-Whole Group:

This level will involve the instructor guiding the whole class on the calculations involved on converting units from one unit of measure to another. The interactive activities at this level will entail giving quick tests to students and checking the progress of each student.

Student individual:    

At this level of interaction, students will be expected to handle their own studies especially on anchor activities such as researching key terms used in the unit.

Students-students groups:

This level of interaction will involve students being paired into groups to carry out computer research on unit of measure.

 

Lesson 1 Plan Template

week	lesson	Topic	Content	Activity	duration
1	1	Unit of measurement	Symbols, operations, relations, and the basic language of mathematics	Presents the students with several mathematics symbols and ask them to identify them The symbols to be presented include: t, m, +, =, > among others Explain to students the symbols used to represent numbers, those used to represent physical quantities and the symbols used to indicate mathematical operations or relationships such as the greater than sign Teach students about the typographical conventions required in representation of numbers used in measurement and symbols indicating physical quantities In algebraic expressions, the letters in the expressions are typed in italic if they represent a number value of if they represent a physical quantity Plain roman type is on the other hand used to indicate units or labels of a measurement Ask students to convert English sentences to algebraic expression employing the typographical  conventions learned and the mathematical symbols and relations introduced For instance, “Mark is two meters taller than John.” For this sentence, the students are expected to come up with the following equation M = J + 2m where M stands for height of Mark, = is the equal sign, J is the height of John, + addition sign and m is the label of measure representing units in meters Sources Cohen, E.R., 2007. Quantities, units and symbols in physical chemistry. Royal Society of Chemistry. Redish, E.F., 2006. Problem solving and the use of math in physics courses. Xiv preprint physics/0608268.	45mins
			Conversion of unit	Clearly explain to student the easiest way of unit conversion based on the algebraic rule of multiplying anything by 1 without causing value change Illustrate this using a simple example of conversion of kilograms to grams 1kg = 1000g, 1 = 1000g/1kg Consider conversion of 1.2 kg to grams 1.2kg = 1.2kg × 1000g/1kg = 1200g Sources Cardarelli, F., 2012. Scientific unit conversion: a practical guide to metrication. Springer Science & Business Media.	45 mins
			Scalar and vector physical quantities and  SI units	Clearly explain the meaning of scalar and vector physical quantities to the class. Make sure that student understands the difference between the two Scalar quantities are characterized by a single numerical value and a specified unit while vector quantities are described using both magnitude and direction Ask students to give examples of scalar and vector physical quantities Scalar quantities should include: distance, temperature, and mass. Vector quantities on the other hand consists of: velocity, acceleration, and force Introduce the concept of international system of units (SI units) Ask students to obtain the names of SI units given to all the base quantities The following website link will assist students in obtaining the names http://physics.nist.gov/cuu/Units/units.html Ensure that students are aware of the seven basic units that can be used to express all physical quantities They include: length, mass, time, electric current, temperature, amount of substance and luminous intensity Sources Aris, R., 2012. Vectors, tensors and the basic equations of fluid mechanics. Courier Corporation.

 

 

 

Assessment

Individual students will be required to answer exercise questions to show their understanding of the topic. The questions will focus on the three areas covered on units of measure. The test will be arranged systematically starting from the section on symbols, operations, relations and the basic mathematical language to conversion of units and end with the section on scalar and vector quantities and SI units.

The test will focus on the following key questions:

1. List several symbols, operations and relations used in combining measurements and indicate their meaning


2. What are the typographical conventions of writing symbols denoting physical quantities?


3. Give several physical quantities with different units and give the students instruction to convert the units


4. Define scalar and vector quantities giving several examples in each case


5. What is meant by the term SI units?


6. What are the seven base units in the international system?

 

Topic: Volume, Mass, Density (lesson 2)

Aims

This lesson aims at introducing students to the measurement of volume, mass, and density of substances. By the end of this lesson;

• Students should be able to define volume, mass and density clearly


• Students should draw the relationship between volume, mass, and density


• Students should be in a position to identify the units used to indicate volume, mass, and density


• Students should also be in a position to use different methods to obtain accurate measure of mass, density and volume

Learning outcomes

• The measure of density, volume and mass can be obtained using mathematical methods


• There is a relationship between volume and density


• Density, volume, and mass are all derived scalar quantities

Teaching strategy

Teaching this lesson will involve the following activities

Sponge Activity

Before getting started on the lesson, individual students will be instructed to use resources in the library to review and extend their knowledge of the units of measurements. Students should particularly focus on familiarizing themselves with types of derived scalar quantities. Students should also review their knowledge the basic operations and relations used in measurements.

Lecture: Three lectures each 45 minutes

Utilizing lecturers in this lesson is important. The lecturer will be significant especially in introducing the three quantity measures in class. The lecture will be used to connect with students and actively engage them to understand their know-how on the topic of derived measures. The main activities during the lecture include:

• Welcoming the students


• Actively engaging students to designate any problem they might have experienced in the previous lesson


• Address any potential challenge that may emerge


• Inform the class on the significance studying the topic


• Use PowerPoint to introduce the definitions of mass, density, and volume

Educational video

The educational video will help students to learn the various method of obtaining mass, volume, and density of different objects. The video will specifically focus on the many experiments carried out by instructors to show students how to measure mass and how to derive volume and density of substances. The video will also educate students about the instruments involved measuring the three quantities. During the video, the students are encouraged to fill KWL charts which the instructor can later use to evaluate their understanding of the topic.

Materials and Equipment

• Relevant text books


• Blank KWL charts


• Videotape and player


• Pencils/ rubber/ ruler


• Lecturer's whiteboard and markers


• Calculators


• PowerPoint presentation

Lesson 2 Plan Template

week	lesson	Topic	Content	Activity	duration
	2	Density, mass, and volume	Introduction to mass and volume	Ask the students to define mass The simple definition expected should indicate that mass is the amount of matter in an object and remains constant no matter the force exerted on the object by gravity How to differentiate mass and weight Clearly explain to the class that weight differs from mass in that it depends on gravity How to obtain mass of different objects using scale balance in grams Instruct every student to be possession of a notebook and a pen to be adequately prepared for the educational video activity Every student should submit a precise definition of the experiment performed in the video for the measurement of mass at the end of the video Ask students to name instruments that can be used to measure mass of objects Introduce the concept of volume to the class Defining volume as the amount of space occupied by an object Unit of measurement of volume is liters in liquid and cubic centimeters in solids After the video session, require that student in groups if two people to submit not clearly describing small experiments used to obtain volume of objects Clearly explain to the class the existing mathematical relationship between mass, density, and volume Ensure that every student can be able to use the following relation in obtaining the value of one quantity having the value of the other two Mass = Density × volume For further studies on measuring mass and volume, students should use computers to access the following video link. http://www.teachertube.com/video/measuring-mass-volume-and-density-167069?utm_source=video-google&utm_medium=video-view&utm_term=video&utm_content=video-page&utm_campaign=video-view-page Sources Chao, A.W., Mess, K.H., Tigner, M. and Zimmermann, F. eds., 2013. Handbook of accelerator physics and engineering. World scientific. Halloun, I.A. and Hestenes, D., 1985. The initial knowledge state of college physics students. American journal of Physics, 53(11), pp.1043-1055.	45 mins
			Concept of density	The density of an object is said to be the mass per unit volume of an object. Measurement of density is understood as the measure of how matter is closely packed together Explain to the class how the relationship between volume, density, and mass explained earlier is used to obtain density of objects Density = Mass/Volume Explain why density is classified as an intrinsic physical property Density of an object is constant no matter the change in total amount of the substance whose density I being considered Explain to class the principle of buoyancy as associated with density. For an object to float on a given liquid, it has to have lower density as compared to the liquid Sources Hawkes, S.J., 2004. The concept of density. J. Chem. Educ, 81(1), p.14.	45 mins
			Density of liquids	Referencing the experiments illustrated in the video, ask students to mention methods that can be used to measure density of liquids One of the methods of density measurements in liquids illustrated in the video is the use of a hydrometer. The hydrometer is observed to float at a high level in liquids with higher density  while it floats at a lower level in lower density liquids Sources Tritton, D.J., 2012. Physical fluid dynamics. Springer Science & Business Media.	45 mins

 

Assessment

Students will be required to answer questions on mass and volume to understand the relationship between the two and also carry out a practical activity on density to test their understanding of the concept of density. The questions will focus on the areas taught in the lecture and also evaluate the knowledge of students obtained from watching the educational video. The density functional activity, on the other hand, will focus on measurement of the density of liquids to test the understanding of students on the experiments illustrated in the video.

The following are the key questions on mass and volume

1. Define mass and volume


2. Differentiate between weight and mass


3. Set some questions to test the student's knowledge on the relationship between density, mass, and volume especially on the use of equation Mass = Density × Volume


4. For the practical activity on measuring the density of liquids, the students are required to be in manageable groups. The activity will aim at promoting further understanding of the concept of density.

Apparatus and materials required

• Two clean and dry measuring cylinders


• Water and olive oil


• A chemical balance

Method

1. Measure the mass of the measuring cylinder in grams using the balance


2. Remove the measuring cylinder from the balance and carefully add some water and get its new mass with water in grams.


3. Repeat the step above adding 10ml of water each time and recording the measure of total mass and volume until the cylinder is full. For each recording of volume, get the reading of the mass of liquid alone.


4. Repeat the steps 1 to 3 using the olive oil.


5. Finally, use the readings obtained to plot a graph of mass of liquid against volume to get the density of olive oil from the gradient of the graph.