As I??™m working towards the end of my second year as a Bachelor of Education student (P-12) at Victoria University, Melbourne, we were given an innovative assessment to research widely to find three terrific lesson plans for teaching year 5 or 6 mathematics. I was required to select a lesson plan from 3 different sources and at least one of those lessons must use ICT and no lessons were to be used that were based on pen and paper worksheets! My first pitstop for finding terrific lesson plans was in Miss Amanda Sullivans grade 5/6 class at West Meadows Primary School. I thought what better way to find terrific and credible sources than in a grade 5/6 classroom itself The following review includes my critique of each lesson along with it??™s features that can be linked to the curriculum for teaching and learning mathematics.
Lesson plan 1: ???Teacher??™s Resource, Nelson Maths for Victoria ( Numeracy for the Middle years, working towards CSF II, Level 4) by Jenny Feely.
The first resource that I found I wanted it to be from a book and a teacher??™s resource and Miss Sullivan described it as ???my bible??? because she draws activities from the various lessons to help her plan activities and lessons for teacher-focus groups, students working in groups, whole class focus and whole- class share time. The complete reference of the book is Feely, J 2003, ???Teacher??™s Resource, Nelson Maths for Victoria, Thomson Learning, Victoria. The lesson I chose from the resource was ???Lines and Angles??™, unit 6, pages 39-41, CSP II, learning outcomes level 4 ???Shape and Space??™. According to the Victorian Essential Learning Standards) students completing this lesson should be at progression point 3.5-3.75 and progressing towards level 4. ???At level 4 students classify and sort shapes and solids (for example, prisms, pyramids, cylinders and cones) using the properties of lines (orientation and size) angles (less than, equal to, or greater than 90 degrees) and surfaces . The proficiency strand that is an integral part of the Australian Curriculum , ???problem solving??™ includes ???formulating and solving authentic problems using numbers and measurements, creating transformations and representing secondary data and calculating angles for year 6??™s and identifying line and rotational symmetries .
The teacher taking this lesson can effectively choose and link activities over 1 week and rotate the students between a teacher focus group and small group focus activities that best suit the needs of the class to follow an effective pedagogical ethos that will help deliver the mathematical objectives of the lesson. Teacher??™s will assess students to see if they can:
Construct, identify and explain the features of a range of lines (vertical, horizontal, parallel, diagonal, curved and zigzag lines.
Use protractors to measure angles.
Identify right angles, obtuse angles and acute angles.
Theory linked with mathematical pedagogy.
This particular lesson plan has a very strong connection with current mathematical pedagogy for teaching ???lines and angles??™. A terrific lesson plan such as this one includes ???a whole-class focus??™ to introduce the concept and prompt discussion and questioning, modeling the appropriate mathematical language in discussion throughout the week: Lines, vertical line, horizontal line, parallel line, diagonal line, curved line, zigzag line, right angle, obtuse angel, acute angle and degrees.
Marzano??™s High Effect Strategies to Support Student Learning (2001) discusses in chapters 8 and 9 the importance of co-operative learning such as grouping strategies were students are organized based on the same abilities encouraging students to approach their activity using the ???sink and swim??™ strategy which tests their thinking and most importantly allows them to make discoveries. After reading chapter 9, ???setting objectives and providing feedback??™ I was able to make a strong connection between the features of the lesson plan and the strategies mentioned in this chapter. This lesson plan sets goals and keeps students focused and on task through various hands on activities that use non-linguistic manipulative??™s that keep the lesson ???real??™. With the use of different approaches and strategies throughout the lesson helps students bring their ideas together together and stimulates their thinking.
Features of the Lesson Plan.
When researching to find a terrific lesson plan I was looking for features throughout the lesson plan that included learning objectives such as ???construct, solve, reflect upon, draw conclusions, present, build, discuss etc. This lesson plan ???lines and angles??™ breaks the lesson into 3 parts; ???Whole class focus- Introducing the concept??™ and has pictures next to each activity linking the common activities, their is a different activity for each day to keep students engaged and keen to make new discoveries. The second part of the lesson plan is all about ???Applying the concept??™ through small group focus task; A teacher focus group can monitor assessment for learning. The activities in the lesson plan instruct the teacher step by step how to set out each group and provides the resources at the back of the book for teachers to photocopy and enlarge, e.g. BLM 8 in the lesson plan are ???line and angle cards??™ that teachers can cut out and laminate. This is a terrific lesson plan because it includes questioning, explanations, modeling and thinking through generating mental pictures that go along with information creating graphic representations known as ???Dual-coding??™ an information storage strategy that includes ???linguistic and imagery??™ (Marzano, RJ 2001, chapter 6). Example, activity using a protractor to demonstrate to students how angles are measured using an overhead projector protractor and ask students questions such as, ???How so I ensure that the protractor is in the correct position to measure the angle??™ The last part of the lesson involves a ???whole- class share time??™ which asks students to review and demonstrate their thinking that was involved with their activity. An example of this, ???Have students explain how to use their protractors. Record this as a set of instructions on a class chart. Have individuals share the shapes they made on the student book page using their protractors. Feedback is so important in a terrific lesson plan because it involves all students and ask??™s questions such as, ???What was correct what was incorrect Why ???I want to know.. I want to know more..??™
I highly recommend this type of lesson plan from ???Nelson Maths for Victoria??™ for teachers and pre-service teachers because the lesson plans feature everything a terrific, detailed and credible lesson plan should contain. The learning outcomes throughout the lesson explicitly share objectives with the students which also helps teachers monitor the students progress. The selection of activities that can be rotated during 1 week allows teachers to constantly evaluate if the activities have delivered the objectives of the lesson to avoid fruitless and wasteful activities. The structure throughout the lesson plan has taught me how to plan keeping in mind the ???bigger picture??™ to develop strategies for future learning. A terrific lesson plan such as this one ???begins to look at… adds to students knowledge and allows them to make discoveries.??™
Lesson Plan 2: ???Magazine Data??™
The second lesson plan that I wanted to find was one that was ICT based and one that demonstrates exceptional enjoyment and progress of the learners. I wanted to find a lesson that involved more than students simply using ICT to solve maths equations using ICT maths programs such as ???National Library of Virtual Manipulatives??™. As effective as these ICT programs might be I decide I wanted a lesson that involved students throughout the gathering of the data process that encourages them to make their own individual discoveries and then to compare their results will fellow classmates. The following lesson plan is on ???Data??™ and was designed by Miss Amanda Sullivan at West Meadows Primary School and is called ???Magazine Data??™.
According the the VELS- Victorian Essential Learning Standards students should be at progression point 3.25 to 3.75 and progressing towards the standard at level 4. By level 4, ???students recognize and give consideration to different data types in forming questionnaires and sampling. They distinguish between categorical and numerical data and classify numerical data as discrete (from counting) or continuous (from measurement). Students present data is appropriate displays (e.g. pie chart for eye colour data and a histogram for grouped data of students heights). They also learn to calculate and interpret measures of certainty (mean, median and mode) and data spread (range). The year 5 and 6 achievement standard from the Australian Curriculum expects students to ???pose questions to gather data and construct, describe and interpret different data sets??™ .
The specific mathematical objectives for this lesson plan comes under the mathematical domain of ???chance and data;. This lesson plan posses questions and the collection of data to design and prepare surveys and experiments and answer questions or test conjectures and predictions. ???Magazine Data??™ requires students to count the number of advertisements in the first 25 pages of a magazine and think of ways to classify the ads; size of the add, number of people in the add, product type and another choice. Students then have to record their findings using various graphs. It is a key objective for this lesson that students are able to interpret, discuss and compare data displays including how well they communicate information.
Links to Mathematical Pedagogy
This lesson plan is a terrific lesson plan that focuses on non-linguistic representations and co-operative learning through interactive approaches and visual manipulatives to enhance learning. Marzano??™s High Effect Strategies to Support Students Learning states that by creating graphic representation and by engaging in kinesthetic activity around the classroom increases and stimulates activity in the brain (Marzano, RJ et al, chapter9, 2001). What I really liked about this lesson is that it is a teacher directed based lesson plan so he/she can effectively plan according to students different needs and by using ICT based manipulatives it allows for interaction of real life situations.
The rise of ICT use in classrooms has placed increasing demand on teachers to include a wide array of ICT based activities in lessons and in mathematics it is important students are able to make sense of maps, charts, number lines and graphs as means of communication. Combining ICT with mathematics is very important.
Features of the Lesson Plan
One of the most important features of this lesson is that it is designed for students to collect their data individually and correct it in a sufficient manor were they can present their data on various graphs using MS Excel. If students are having difficulties using MS Excel, attached to the lesson plan is a copy of ???Creating Charts- Easy to see numbers from Excel made easy- A beginners guide including how -to skills and Projects, by Ewan Arthur. As a whole class focus to introducing the topic another key feature of the lesson involves students collecting the weather information over 1 week, either from the internet or newspaper and guide students in creating a table for maximum temperatures and show them how to locate, read and record the data. At the end of the lesson as a whole-class reflection the students share with the class their findings and what they can read from the graph, demonstrating to the teacher of they can communicate mathematical data. The features of this lesson helps students to identify and learn whether the intent of the graph is to provide a context or present mathematical information and by presenting the information of different types of graphs let??™s them see the data from variable perceptions which strengthens their understanding ( Diezman et al,2009).
This mathematical lesson plan on ???Chance and data??™ is a quality lesson plan that teachers can alter the features of it to suit there students needs.It is a quality lesson plan for both teachers and pre-service teachers to use because it is important we address the structure and the nature of the different types of graphs that we can represent information in. This lesson plan is very useful because it can be used as an assessment strategy to see if students are able to understand mathematical data and present it visually.
Lesson Plan 3: Geometry – ???Volume and Surface Area??™
I was very fortunate to use the ICT based resources at West Meadows Primary to find an exceptional detailed lesson plan. Lesson planet is a search engine for teachers that has over 200,000 teacher approved lesson plans; the website is . I typed in geometry and I located a terrific lesson plan that was sourced from ???TrickyBags- NewZealand Maths . Grade 5/6 teacher MIss Amanda Sullivan has used this lesson plan and emphasized to me that by following this lesson plan and by following attention to detail you can run a fantastic lesson on the ???Concept Attainment Model- Volume and Surface Area (Geometry) and the concept of this lesson is defining volume and surface area.
This lesson plan can be used for both years 5 and 6 however it would be more suitable to use towards the end of the school year for the grade 5??™s. According the Victorian Essential Learning Standards the domain for this lesson plan falls under ???Measurement, chance and Data??™ and the progression points are between 3.25 – 3.75 progressing towards the standard at level 4 which demonstrates ???students use metric units to estimate and measure length, perimeter, area, surface area, mass, volume, capacity and time ( for example, L-mL, sec to min). In terms of working mathematically, by level 4 students recognize and investigate the use of mathematical structure of problems to choose strategies for solutions. It is important that from this lesson students are able to explain their reasoning and procedures and be able to create new problems based on familiar problem structures . As part of the Australian Curriculum Grade 6 ???Measurement and Geometry??™ students need to be able to demonstrate using units of measurement that they can convert between common metric units of length, mass and capacity and in conjunction for this lesson and the Australian Curriculum students need to be able to connect volume and capacity and their units of measurement .
The concept of this lesson is for students to be able to define volume and surface area. The general objective of this lesson is that the students will investigate and solve practical problems involving volume and surface area of rectangular solids (prisms), cylinders, cones and pyramids. Not only has this lesson plan included it??™s general objective it has gone into detail to summarize the learning outcomes and the content outline, which outlines the definition of volume; ???The amount of space inside a 3 dimensional shape (capacity).
Links to Mathematical Pedagogy
After reading Booker??™s Teaching Primary Mathematics, chapter 6 on Geometry I could see the link between the content of the lesson plan and the theory related to teaching the topic. ???The study of geometry is about understanding the spacial world in which we live- thinking about how things look, how they are arranged, where they are, how they move??™ (booker et al,2010).
This lesson plan does an amazing job in reflecting current mathematical pedagogy because it offers students an opportunity to engage in mathematical thinking that allows them to make new discoveries. There is a lot of questioning and discussion in the lesson plan and good questioning techniques have long been regarded as a fundamental tool of effective teachers( Way, J 2008). Going back to Marzano??™s High Effect Strategies to Support Student Learning, (Marzano, RJ et al, 2001) using hands on approaches and visual and physical manipulatives enhance learning, adding to students knowledge by helping them retain what they are learning by encouraging them to make discoveries ( Marzano RJ, 2001, chapter 7).
Features of the Lesson Plan
Looking at this lesson plan from the perspective of a pre-service teacher it??™s a fantastic lesson to deliver to students to understand the concepts of defining volume and surface area. What makes it such a terrific lesson plan is that it explains in detail in the content outline the definition of volume, the key attributes and positive and negative examples of various objects and filled with liquid/sand, other objects are a picture of a swimming pool and a picture of an ice cream cone filled with ice-cream. To introduce the topic and help students develop a concept definition two column headings are to be put on the board: ???negative and positive features and students are to list the features as they see each example. Following this whole-class focus activity their is a ???discuss??™ were the teacher asks ???starter questions??™ to stimulate higher order thinking; ??? What is it that you did with the concept of volume??? ???How did you come to that conclusion??? ??? What is the difference between volume and area???
Throughout the lesson plan it uses questions to question mathematical thinking and the key attributes of the lesson plan includes sections that ???develop??™ ???give examples??™ ???discuss??™ ???define??™ ???attributes??™ and then various activities that assist the students to discuss to focus on particular strategies, connect to previous experiences and help them to see patterns and relationships (Way, U, Pages 22-27, 2008).
This lesson plan is an example of a detailed and pedagogical lesson plan that I highly recommend for teachers and pre-service teachers. Pre-service teachers can use this as a guide to master the attention to detail that a stimulating and engaging lesson requires in it??™s planning. In conclusion to this lesson plan it helps teachers understand not only the concepts but the methods of evaluation, differentiation of instruction and subject matter extension. The structure of this lesson plan gradually transfers responsibility of the tasks to the students to continue to scaffold their mathematical thinking.
Way, J. Using questioning to stimulate mathematical thinking. [online]. Australian Primary Mathematics Classroom; v.13 n.3 p.22-27; 2008. Availability: ISSN: 1326-0286. [cited 03 August 2011].
Diezmann, Carmel; Lowrie, Tom; Sugars, Lindy and Logan, Tracy. The visual side to numeracy : students sensemaking with graphics. [online]. Australian Primary Mathematics Classroom; v.14 n.1 p.16-20; 2009. Availability: ISSN: 1326-0286. [cited 04 August 2011].
Booker et al,2003, Teaching Primary Mathematics, Pearson Australia, NSW.
Feely, J 2003, Teacher??™s Resource, Nelson Maths for Victoria, Thomson Australia, Vic.
Lesson Education 2011, Lesson planet, lesson plan sourced from TrickyBags NZ Maths viewed on Tuesday 2nd of August, 2011
Department of Education and Early Childhood Development 2010, VELS mathematics continuum, viewed on 4 August 2011,
Department of Education and Early Childhood Development 2010,Developmental Overviews, viewed on 4 August 2011,
Australian Curriculum 2010, Mathematics Rationale, viewed on 4 August 2011,
Lesson Plans/ resources and information was taken from grade 5/6 classroom at West Meadows Primary School on Tuesday 2nd of August,2011.