UNIVERSITY OF SOUTHERN QUEENSLAND EDX3280 MATHEMATICS CURRICULUM & PEDAGOGY Lesson...

UNIVERSITY OF SOUTHERN QUEENSLAND

EDX3280 MATHEMATICS CURRICULUM & PEDAGOGY

Lesson Plan Assessment

Must be submitted electronically through EASE

Due: 13th May, 2011

STUDENT NAME: Kerry Murren (0050085735) INSTRUCTOR: David Martin

Students must select an element of the Mathematics P-10 Curriculum at a level broadly applicable across the 4 maths strands of the course. Students plan a sequence of three to four lessons, including making provision for a diverse range of learning styles/speeds. Provision must be made for how student learning is to be evaluated. The teaching strategies are explained and justified.

Marking Criteria- Unit Lesson Plan with Web Quest

3 - 4 Unit Lesson Plan Sequence / Web Quest content – Consider the criteria below as to what will make this a high standard resource.

Minimal standard 0-1 marks

Satisfactory standard 2-3 marks

High standard 4-5 marks

1. Use of QLD Essential Learnings in lesson Plans: [Ways of Working], [Knowledge and Understanding], [Aims and Goals aligned with EL and SLO], [Prerequisite Knowledge], See #1 of Teaching Episode Rubric Guideline

2. Use of planning template and P-12 Curriculum Documents: [Specific Learning Outcome Statements], [Teaching / Learning Strategies], [Assessment, as a demonstration of the Specified Learning Outcomes]. See #2, #3, and #4 of Teaching Episode Rubric Guideline

3. Written rationale as to your reasoning for the sequence of planning (Language Model), teaching strategies, resources and assessment strategies you chose. i.e. What pedagogical and theoretical knowledge do you now identify with which brought you to these planning decisions? 500 words max. and placed at the end of the lesson plan sequence See #4, #5, and #6 of Teaching Episode Rubric Guideline

4. Individual reflection on the value of the Web quest in the teaching of mathematics content in the 21st century. 250 words maximum and placed following your written rationale See #7 of Teaching Episode Rubric Guideline

5. Age appropriateness of the content of the Unit / Web quest. Do websites open in their own windows? How do you return to the webquest after navigating to external sites? Is it useful as a teacher resource? See #8 of Teaching Episode Rubric Guideline

6. Investigative nature of the Web quest. Does your Web quest design require students to search and acquire new knowledge on their own? Does your design require students to use deductive reasoning? #8 of Teaching Episode Rubric Guideline

7. English communication and referencing See #9 of Teaching Episode Rubric Guideline

8. Standards of the 1st and 2nd steps of the 6-step process of Web Quest. See Web Quest Rubric Guideline

9. Standards of the 3rd and 4th steps of the 6-step process of Web Quest. See Web Quest Rubric Guideline

10. Standards of the 5th and 6th steps of the 6-step process of Web Quest. See Web Quest Rubric Guideline

Total / 50 Comments: Your assignment – must be in .doc or .docx format. After your lesson plans, insert your rationale and reflection

Unit overview The four lessons attached are part of a larger unit that is designed to assist in the learning of algebraic concepts for twenty-four, grade five students. A Web Quest has been implemented within the unit, to allow students to apply and demonstrate their new or already learnt skills. The mathematical topic of measurement is also implemented within the Web Quest. Students are already familiar with some measurement concepts.

Lesson one: This introductory lesson introduces the algebraic concept: determining the relationship of number patterns. Students will need to apply the skills they develop from learning the algebraic concept, in order to complete their Web Quest. Lesson two: This reinforcement lesson encourages students to further develop their skills, understanding and knowledge; using the same algebraic concept from lesson one. This is to ensure that the students have a complete understanding of the concept. The Web Quest is also introduced within this lesson and students begin their quest. Lesson three: This lesson introduces the algebraic concept: the meaning of the equality symbol. Again, the students need to apply the skills that they have developed from learning the algebraic concept, in order to complete their Web Quest. Students should complete their Web Quest by the end of the lesson. Students will demonstrate their skills and be evaluated by the teacher, as part of their Web Quest reflection. Lesson four: This lesson introduces the algebraic concept: commutative operations. Students should be able to solve commutative operations by the end of the lesson.

Name: Kerry Murren Day 1:

Curriculum Area: Mathematics Specific Topic: Algebra (Determining the relationship of number patterns)

Year Level: 5

Essential Learning’s (knowledge, understandings, and ways of working) to be addressed: Algebra K&U- Patterns in space and number, and relationship between quantities, including equivalence, can be represented using concrete and pictorial materials, lists, tables and graphs (QSA, Essential Learning’s, 2007). Algebra WOW – >Students should be able to identify and describe mathematical concepts required to generate solutions. > Students should be able to communicate and justify thinking and reasoning, using everyday and mathematical language, concrete materials, visual representation and technologies. > Students will then reflect on their learning to identify new understandings and future applications.

(QSA, Essential Learning’s, 2007)

General Teaching Aim or Goal: This introductory lesson will allow students to reinforce their knowledge and understanding of identifying and describing patterns and relationships between objects and numbers. By the end of the lesson students should then be able to determine the relationship of the number patterns, identified and described, using visual and concrete materials and gradually progressing towards symbolic language. Students will achieve this aim by determining the relationship of written linear number patterns and the creation of their own linear number patterns. The linear number patterns will involve the use of the four operations. Students’ Prerequisite knowledge / understanding / concepts / skills: Students should already be able recognise relationships between objects or numbers, by describing patterns and simple rules with concrete materials (QSA, Essential Learning’s, Y3, 2007). Therefore, students are already familiar with the concept of identifying & describing patterns and relationships and should be able to apply these skills to the learning of the symbolic language of algebra. Students also have deep understanding and acquired skills of the four operations.

Specific Learning Outcomes for this

Lesson

Time Req.

Teaching / Learning Strategies Organisation Resources Type of formative or summative assessment

Orientating Phase / Introduction Students should be able to identify, describe & continue a number pattern using concrete materials.

10 Minutes

> Teacher introduces the lesson outcome. > Teacher engages the student’s interest by introducing a ‘Number Pattern’: Stacking cups in multiples of 3 (3,6,9 & 12) > Teacher labels each collection of cups: Step 1, step 2, step 3 & step 4 & creates a table (step 1 – 7). > Teacher asks: “Who can identify what is happening with the cups as the steps progress?” & “ How many cups are there in step 1, step 2 etc…?” > Students recall on their prior knowledge to identify the pattern. >Teacher completes part of the table (step 1-4). > Teacher asks, “Who can describe the pattern?” > Students recall on their prior knowledge to describe the pattern. > Teacher asks “Who can define the word determine?” > Teacher brainstorms the student’s answers & provides a ‘student friendly’ definition. > Teacher asks, “Who can determine how many numbers of cups we will need for step 5,6, & 7?” & “Why do you think we will need to add that many cups as the steps progress?” & “Who can determine the relationship of the pattern?”

Teacher models the number pattern at the front of the classroom. Whole class approach. Teacher & student directed. Students are first located on the carpet. Group activity: Students are located at their tables.

Whiteboard: Lesson outcome. Table – Stacking cups Plastic cups x30 Cards – step 1-4 Interactive Whiteboard: Table & brainstorm Marker pen Paddle pop sticks x 270

Formative: Observation, answers to questions & determining the next three steps of the number pattern.

> Students determine the relationship of the pattern. > In their table groups, students apply their learnt knowledge by creating the next 3 steps of the pattern, using paddle pop sticks. > Teacher & the students complete the rest of the table (step 5-7).

Students should be able to create their own linear number patterns.

40 Minutes

> Teacher asks the students to write the following multiplication pattern:

3,6,9,12,15,18,21. > Teacher reinforces that the number pattern is the same pattern used previously, but uses numbers rather than cups. > Teacher demonstrates how the pattern can be identified, described & determined the same way as it was previously. > Teacher & students complete a second number pattern using the operation - Addition. > Teacher writes two more patterns, using two of the four operations. > Students are to complete a table, identifying & describing the two patterns. They also are to complete the next three steps of the patterns, in order to determine the relationship. >Students are to create their own number patterns using the four operations & ask their partner to solve it. > Teacher introduces the website ‘IXL Patterns’ to the students & explains the task. > Students interact with the website by

Teacher assists the students learning. Teacher & student directed. Students are located at their desks. Pair activity Group activity Interactive Website: Whole class approach. Group points reward system is used.

Maths book Pencil Ruler Pen Interactive Whiteboard: Website, patterns & table Marker pens Laminated Hundreds Chart x 5

Formative: Observation & solving, creating & identifying number patterns.

extending number patterns, finding missing numbers & determining the relationship of number patterns using the four operations. . > Teacher introduces the group game: ‘Patterns in a Hundred Chart’. Each table is to identify as many patterns as they can, using a laminated hundreds chart. The group with the most identified patterns wins 10 group points.

Synthesising Phase / Conclusion Students should be able to determine the relationship of a linear number pattern, justify their reasoning & reflect on their learning.

10 Minutes

> Students demonstrate & apply their learnt skills by identifying, describing & determining the relationship of the number patterns found in their hundreds chart (through explanation). > Teacher writes each pattern that is identified. > Teacher asks “How can we apply the skills we developed today in other math topics?” & “How can we use these skills in our everyday life?” >Teacher & the students have a class discussion on number patterns. This enables the teacher to identify any misunderstandings or assumptions & allows the students to justify their thinking & reasoning. > Teacher & students reflect on the lesson.

Whole class discussion. Student directed Students are located on the carpet.

Interactive whiteboard: Pattern

Formative: Observation, demonstration, answers to questions, & explanation. .

Assessment Strategies (link to Learning Outcomes): The formative assessment strategies used for this lesson are: >Observation of student’s application of skills. >Answers to questions and questions they may ask (feedback). >Explanations to justify their thinking & reasoning. >Demonstration of solving, identifying, describing and determining the relationship of number patterns.

What’s next? Where to from this lesson? Next lesson students will reinforce their new learnt knowledge by identifying, describing, determining & creating their own number patterns during math rotations. Students will also be introduced to their ‘Lost in Space’ Web Quest & should understand the requirements of their summative assessment (Lost in Space portfolio). Students should also understand the group and independent expectations of their Web Quest.

Reference List: Queensland Studies Authority. (2007). Mathematics essential learning’s by the end of year 5. Retrieved on April 17th, 2011, from

http://www.qsa.qld.edu.au/downloads/early_middle/qcar_el_maths_yr5.pdf

Queensland Studies Authority. (2007). Mathematics essential learning’s by the end f year 3. Retrieved on April 17th, 2011, from


The Australian Curriculum: Mathematics (n.d.). Year 5. Retrieved on April 17th, 2011, from

http://usqstudydesk.usq.edu.au/file.php/19093/Webquest_Assessment_1/Lesson_Plan_Resource_Folder/australian_curriculum.pdf

Activities IXL Website. (2011).Patterns. Retrieved on April 17th, 2011, from http://au.ixl.com/math/year-5/increasing-growth-patterns Martin, A, D. (2011). EDX3280 Mathematics curriculum & pedagogy course notes. Fraser Coast: University of Southern Queensland. Van De Walle, A. J., & Karp, S. K., & Bay-Williams, M. J. (2010). Elementary & middle school mathematics (7ed.). United States of America: Pearson

Name: Kerry Muren Day 2:

Curriculum Area: Mathematics Specific Topic: Algebra (Symbolic Language and number patterns) Year Level: 5

Essential Learning’s (knowledge, understandings, and ways of working) to be addressed: Algebra K&U Web Quest & Lesson- Patterns in space and number, and relationship between quantities, including equivalence, can be represented using concrete and pictorial materials, lists, tables and graphs (QSA, Essential Learning’s, 2007). Measurement K&U Web Quest – Timelines, clocks, calendars and timetables are used to sequence, schedule and calculate timed events (QSA, Essential Learning’s, 2007). Algebra and Measurement WOW – > Students should be able to identify, describe mathematical concepts required to generate solutions. > Students should be able to pose questions and make predictions based on experiences in similar situations. > Students should be able to make statement, predictions, inferences and decisions based on mathematical interpretations. > Students will reflect on learning to identify new understandings and future applications.

(QSA, Essential Learning’s, 2007) General Teaching Aim or Goal: This reinforcement lesson will allow students to recall on their prior knowledge and develop their knowledge and understanding by determining the relationship of number patterns. Students will do this, by applying their learnt skills during math rotations. At the end of the lesson the teacher can determine if students have developed ‘number sense’, in determining the relationship of number patterns. Students will also be introduced to their mathematical Web Quest and their summative assessment (Lost in Space portfolio). Students should understand the assessment, requirements, group and individual expectations required for their Web Quest. The Web Quest will focus on the topics algebra and measurement.

Students’ Prerequisite knowledge / understanding / concepts / skills: Students should have developed their knowledge by determining the relationship of linear number patterns during the previous math lesson. Students should then be familiar with identifying, describing and determining relationships between numbers patterns. Students have prior experience of group and independent activities, math rotations and interaction with technology. Students have a strong understanding, great prior knowledge and developed skills, regarding the measurement ‘knowledge and understanding’ stated above. Therefore, they will be able to demonstrate their learnt skills regarding the measurement tasks provided within their Web Quest. Specific Learning Outcomes for this

Lesson

Time Req.


Orientating Phase / Introduction Students should be able to recall on their prior knowledge to identify, describe & continue a number pattern using symbolic language.

5 minutes

>Teacher introduces the lesson outcome. >Teacher asks “Who can remind me what we did last lesson?” & “Who can tell me what we did last lesson?” >Teacher & students recall on the previous lesson by identifying, describing & determining a number pattern.

Teacher & students located on the carpet. Whole class approach.

Whiteboard: Lesson outcome & number pattern.

Formative: Answers to questions & solving the number pattern.

Enhancing Phase / Body Students should reinforce their understanding by describing, continuing & creating number patterns, using the four operations during math rotations.

45 minutes

> Teacher introduces & explains each maths rotation. > R1: Using a 10x10 number grid, write what to you notice when counting from 0 in 3’s, 6’s, 5’s & 9’s? > R2: Describe & extend number patterns. > R3: Fill in the missing numbers & write the relationship. > R4: Create your own number patterns, using laminated numbers & ask a group member to determine the relationship. > Teacher checks for understanding &

Extra teacher assistance when required. Students move in a clockwise direction to each rotation. Teacher & student directed.

Whiteboard: Rotations 1-4 Pen R1: 10X10 Grid, Maths book & Pen R2: Worksheet & Pen

Formative: Observation & answers on worksheets during math rotations.

Students should understand the Web Quest requirements, assessment, group & independent expectations.

groups the students according to their ‘maths learning ability’. Teacher works with each group during rotation 3. >Students complete the four rotations. > Teacher & students go to the E-learning room. >Teacher introduces the Web Quest ‘Lost in Space’ >Teacher explains how the Web Quest works, the topics of the Web Quest and what the students are to do. > Teacher asks questions regarding the topic of measurement. E.g. “Who can remind me what we learnt about, when we looked at the topic measurement?” >Students answer the questions & recall on their prior knowledge. >Teacher explains the summative assessment (Lost in Space portfolio), requirements, group & independent expectations regarding the Web Quest. > Teacher checks for understanding by asking the students to repeat back the given explanations. > Students ask any questions concerning the Web Quest, assessment & requirements. >Teacher groups the students in groups of three, according to their maths learning ability.

Students on the carpet for Web Quest introduction. Students in groups of 3 per computer.

R3: Worksheet & Pen R4: Laminated numbers. E-Learning room Interactive whiteboard d: Web Quest Pencil

Synthesising Phase / Conclusion Students should demonstrate their knowledge & understanding of measurement &

20 Minutes

> In their groups, students begin their mission stated on the introduction page of their Web Quest. > Students continually demonstrate their knowledge & understanding by interacting

3 students per computer. Extra teacher assistance if

E-Learning room Computers Lost in Space

Formative: Observation & demonstration of their applied skills through

algebraic concepts through interaction with their Web Quest.

with the Web Quest & completing provided tasks. > Teacher hands each students their ‘Lost in Space’ portfolio, when asked. > Teacher asks, “Are there any questions about your Web Quest or assessment?” > Teacher & the students have a class discussion about their Web Quest. This allows the teacher to recognise, which students may require, extra assistance. > Teacher & the students reflect on the lesson.

required. Student directed Students progress through their Web Quest at their own rate. Inquiry approach

portfolio Pen Web Quest worksheets

interaction with their Web Quest.

Assessment Strategies (link to Learning Outcomes): The formative assessment strategies used for this lesson are: >Observation of student’s application of skills during math rotations and interaction with their Web Quest. >Answers to questions and questions they may ask (feedback). Also, the answers stated on their rotation worksheets. >Demonstration of solving, identifying, describing and determining number patterns during the math rotations.

What’s next? Where to from this lesson? Providing all students fully understand the concept ‘determining the relationship of number patterns’, next lesson students will be introduced to the meaning of the equality symbol. Students should also complete their ‘Lost in Space’ Web Quest & hand in their ‘Lost in Space’ portfolio (summative assessment).

Reference List: Queensland Studies Authority. (2007). Mathematics essential learning’s by the end of year 5: Algebra. Retrieved on April 17th, 2011, from




Van De Walle, A. J., & Karp, S. K., & Bay-Williams, M. J. (2010). Elementary & middle school mathematics (7ed.). United States of America: Pearson Rotations Activities: Primary Resources. (2011). Maths: Numbers and the number system. Retrieved on April 18th, 2011, from

http://www.primaryresources.co.uk/maths/mathsB3.htm#1


Curriculum Area: Mathematics Specific Topic: Algebra (Meaning of the equality symbol) Year Level: 5

Essential Learning’s (knowledge, understandings, and ways of working) to be addressed: Algebra K&U Lesson & Web Quest– Generalisations associated with the four operations are built upon commutative operations (QSA, Essential Learning’s, 2007). Web Quest- Patterns in space and number, and relationship between quantities, including equivalence, can be represented using concrete and pictorial materials, lists, tables and graphs (QSA, Essential Learning’s, 2007) Measurement K&U Web Quest- Timelines, clocks, calendars and timetables are used to sequence, schedule and calculate timed events (QSA, Essential Learning’s, 2007). Algebra and Measurement WOW – > Students should be able to identify and describe the mathematical concepts, strategies and procedures required to generate solutions. > Students should be able to pose questions and make predictions based on experiences in similar situations. >Students should be able to make statements, predictions, inferences and decisions based on mathematical interpretations. > Students will evaluate their own thinking and reasoning, in relation to the application of mathematical ideas, strategies and procedures. > Students will reflect on mathematics and identify the contribution of mathematics to personal activities. > Students will reflect on learning to identify new understandings and future applications.

(QSA, Essential Learning’s, 2007)

General Teaching Aim or Goal: Students are introduced to a new algebraic concept that is the meaning of the equality symbol. By the end of the lesson should be able to understand the meaning and definitions of the equality symbol and balance equations. Students should be able to recognise that the equality symbol does not necessarily mean ‘get the answer’. Students should also complete their ‘Lost in Space’ Web Quest. Each student will need to ensure that all requirements are met and hand in their ‘Lost in Space’ portfolio (summative assessment). Students’ Prerequisite knowledge / understanding / concepts / skills: Students are familiar with the symbol for equality but may not know the correct meaning. Students have already completed some of the tasks provided in their ‘Lost in Space’ Web Quest. Students should be familiar with their assessment, requirements, group and independent expectations. Specific Learning Outcomes for this

Lesson

Time Req.


Orientating Phase / Introduction Students should recall on their prior knowledge to solve an addition equation.

5 minutes

>Teacher introduces the lesson outcome. > Teacher engages the students interest by writing he addition equation on the whiteboard: 8+4=+6 > Teacher asks “What number do you think belongs in the box?” >Students are to write the equation & their chosen answer in a box. > Teacher asks four students to share their answers & asks, them to explain why they choose that answer. > Teacher draws an equality symbol on the whiteboard & asks, “What do you think this symbol represents?” >Students provide explanations & the teacher takes note of their assumptions.

Teacher and students located on the carpet. Whole class approach. Students are located at their desk to complete the equation. Teacher & student directed.

Whiteboard: Lesson outcome, equation and equality symbol. Maths book Pencil

Formative: Answers to questions, chosen number & explanations of their answer.

Enhancing Phase / Body Students should be able to describe equations has ‘equal to’ or ‘same as’ and recognise that the value of an equation stays the same, after being arranged.

30 Minutes

>Teacher reminds students how they previously determined relationships using number patterns & explains how the equality symbol represents the relationship within the number system. > Teacher reinforces that the equality symbol does not necessarily mean ‘find the answer’. > Teacher asks, “What does the word equality mean?” & “ What does the word balance mean?” & “What does the word equivalence mean? > Students use their dictionaries to find the definition of each word. > Teacher asks three students to read the dictionary definition for each word. > Teacher asks, “What are the similarities of each definition?” & “What are the differences of each definition?” > Teacher & students reinforce that all three words mean the same. > Teacher uses a set of scales & various weights to demonstrate balance and equality of objects. > Teacher writes the balance equation in a symbolic form. E.g. 50g + 50g = 1kg > Teacher states how both pans of weights are equal to one another. Teacher rotates the weights to reinforce the statement. E.g. 50g + 50g = 1kg. > Teacher explains how both weights are equivalent (both provide the same answer) no matter how they are arranged. >Teacher & the students create another

Teacher models at the front of the classroom. Whole class approach: Scale & weights example. Group activity Teacher & student directed.

Whiteboard: Equality, balance & equivalence definition, & symbolic forms. Scales x5 Weights: various sizes E-Learning room Pen Math’s book: symbolic forms

Formative: Observation, answers to questions, observation, explanations & marking of their symbolic forms. .

balance equation. > Teacher asks a student to swap the weight around and asks “Are the weights equivalent to one another?” >Teacher asks another student to write the balance equation in symbolic form. >Teacher provides each table of students with a set of scales and various sized weights. > In groups students create their own balancing operations, using the scales and weights. Ensuring they are equal. They are to then write the symbolic form. >Teacher refers back to the previous addition equation & asks; “Now who can tell me what number belongs in the box?” > Teacher & the students have a class discussion on the answer. > Teacher and students go to the E-learning room. >Teacher answers any questions the students may have concerning their Web Quest, assessment, requirements, group & independent expectations.

Synthesising Phase / Conclusion Students should demonstrate their knowledge & understanding of measurement & algebraic concepts through interaction with their Web Quest.

30 minutes

> In their groups, students progress through the rest of their mission stated on the task page of their Web Quest. > Students continually demonstrate their knowledge & understanding by interacting with their Web Quest. > Students should complete each task provided on their Web Quest before completing their mission. > Students evaluate & reflect on their

3 students per computer. Extra teacher assistance if required. Student directed Inquiry based

E-Learning room Computers Lost in Space portfolio Pen

Summative: Observation, completed tasks on Web Quest and portfolio.

learning by completing a ‘Reflection of Your Web Quest’ worksheet. The worksheet allows the students to further demonstrate their knowledge and understanding of the concepts algebra & measurement that has previously been learnt. > Students hand in their ‘Lost in Space’ portfolio. > Teacher & the students celebrate the end of their Web Quest with a small party.

approach

Web Quest – Worksheets Party resources: Cupcakes Hats Music Games

Assessment Strategies (link to Learning Outcomes): The formative assessment strategies used for this lesson are: >Observation of student’s application and skills during the group activity. >Answers to questions and questions they may ask (feedback). >Explanations of the equality symbol (justify their reasoning). The Summative assessment strategies used for this unit are: > Evaluation of group work, independent work & interaction with their Web Quest > Answers on task sheets provided in their Web Quest. > Demonstration of their applied skills to solve all tasks provided in their Web Quest. > Marking and evaluation of their Web Quest using the ‘student friendly rubric’. * For more information please see Lost in Space Web Quest*

What’s next? Where to from this lesson? Next lesson, students will develop their knowledge & reinforce their understanding on the meaning on the equality symbol through a game activity. Students will also be introduced to commutative operations. The students Web Quest will be marked and assessed against a student rubric. The teacher will provide feedback for the students by implementing a one on one conferencing session that will take place throughout the rest of the unit.



Queensland Studies Authority Mathematics Syllabus. (2004).Years 1 to 10 syllabus. Retrieved on April 17th, 2011, from

http://www.qsa.qld.edu.au/downloads/early_middle/kla_maths_syll.pdf



Activities: Martin, A, D. (2011). EDX3280 Mathematics curriculum & pedagogy course notes. Fraser Coast: University of Southern Queensland. Van De Walle, A. J., & Karp, S. K., & Bay-Williams, M. J. (2010). Elementary & middle school mathematics (7ed.). United States of America: Pearson


Curriculum Area: Mathematics Specific Topic: Algebra (Commutative Operations) Year Level:5

Essential Learnings (knowledge, understandings, and ways of working) to be addressed: Algebra K&U –Generalisations associated with the four operations are built upon commutative operations (QSA, Essential Learning’s, 2007). Algebra WOW >Students should be able to identify and describe mathematical concepts, strategies and procedures required to generate solutions. > Students should be able to make predictions based on experience in similar situations. > Students will make statements, inferences and decisions based on mathematical interpretations. >Students will reflect on learning to identify new understandings and future applications.

(QSA, Essential Learning’s, 2007) General Teaching Aim or Goal: Students will be introduced to a new algebraic concept that is commutative operations. By the end of the lesson students should be able to know how to solve commutative operations and understand that commutative operations only work with the operations addition and multiplication. This lesson, also allows the teacher to determine which students understand the meaning of the equality symbol and which students may require more teacher assistance. Students should use their prior knowledge and similar experiences to answer questions and solve problems regarding the equality symbol concept. Students will reinforce and demonstrate their knowledge and understanding through whole class, group and independent activities. Students’ Prerequisite knowledge / understanding / concepts / skills: Students have already been introduced to the meaning of the equality symbol and will have prior knowledge on the concept. Therefore, students should already have some understanding that the equality symbol represents ‘balance’. Students also have deep understanding and acquired skills of the four operations.

Specific Learning Outcomes for this

Lesson

Time Req.


Orientating Phase / Introduction Students should be able to recognise & describe the equivalence of two sides of a multiplication equation.

10 minutes

>Teacher introduces the lesson outcome. > Teacher asks “What did you learn last lesson about the equality symbol?” & “How do we know when two equations are balanced?” > Students recall on their prior knowledge to answer the questions. > Teacher & the students have a class discussion on the concept. > Teacher engages the student’s interest by introducing the ‘Tilt or Balance’ game. > Teacher draws a balance scale & writes an equation in each pan. E.g. 5x7 & 7x5 > Teacher asks, “Will the scales balance or tilt?” & “How do you know this?” > Students share & explain their answers. > Teacher swaps the equations around & asks, “Does the scale still balance?” > Teacher explains that when equations can be swapped around & still share the same answer it is known as a commutative operation. > Teacher writes the term commutative operations & asks, “Who can think of a definition to explain the term commutative?” > Students share their definitions. > Together, the teacher & the students

Teacher & students located on the carpet. Whole class approach. Teacher & student directed.

Whiteboard: Lesson outcome & commutative definition Interactive whiteboard: Scales & equations. Marker pen

Formative: Answers to questions, explanations & solving commutative operations.

create a ‘student friendly’ definition for the term commutative. > Teacher & the students carry on with the game using only addition & multiplication equations.

Enhancing Phase / Body Students should be able to work out and write the equivalence in equations that involve combinations of multiplication & addition.

30 minutes

>Teacher writes the equations 54/3 & 3/54 on the drawn scale. > Teacher asks, “Do these division equations balance?” > Students share their answers. > Teacher asks, “How do we know that these division equations do not balance?” & “What does each equation need to have in order to balance?” > Teacher encourages the students to explain why two division equations do not balance. > Teacher writes the equations 63 – 17 & 17 – 63 on the drawn scale. > Teacher asks, “Do these subtraction equations balance?” > Again, the teacher encourages the students to explain why two subtraction equations do not balance. > Teacher reinforces that only addition & multiplication equations are commutative. Division & multiplication are non-commutative, because the answer changes when you swap the two equations around. > Teacher introduces the group activity and gives each table a piece of A3 paper (divided in two columns), various numbers, addition, multiplication & equality symbols and a glue stick.

Teacher models at the front of the classroom Students are located at their desks. Group activity Teacher & Student directed

Laminated paper x5 Marker pens x5 Whiteboard: Scale drawing 7 equations Pen A3 paper Numbers (mix) Symbols (+, -, =) Glue stick Group point system.

Formative: Observation & answers to questions.

> In their table groups the students are to create five commutative equations, using the numbers & symbols. They are to glue each commutative equation on the A3 paper in each column. Example:

Left Equation Right Equation 11 + 9 = 9 + 11

> The first group to create five commutative operations wins 10 group points. > Teacher writes the following a addition equation on the whiteboard: 14 + = 7 + 14 > Teacher asks, “Who can tell me what numbers belong in the box? > Students share their answers. > Teacher asks, “Why do you think the number … belongs in the box?” > Students explain their reasoning. > Teacher & students write the correct numbers in the box. > Teacher writes a multiplication equation, but with two missing boxes: 3 x = 4 x > Teacher asks, “Who can identify what numbers belong in both boxes?” > Students share their answers. > Teacher asks, “How can we work it out?” > Students explain their working out. > Teacher reinforces that the each number (on the opposite side) belongs in the box.

Synthesising Phase / Conclusion Students should demonstrate their knowledge & understanding by using equivalent

20 Minutes

>Teacher hands each student a worksheet ‘What Goes in the Box?’& Explains what the students are to do. >Students are to demonstrate their knowledge & understanding by completing

Students directed Independent activity to

Worksheets x24 Pen

Formative: Observation, answers to questions, demonstration &

number equations involving addition & multiplication to find unknown quantities.

the worksheet. Students are to a table. Students are to write the correct missing number in the box provided (1st part of the table), to make the two number equations balance. They are to then write the equation & answer for the left hand side equation (2nd part of the table) & the right hand side equation (3rd part of the table). They are to state if the full equation is balanced or not (4th part of the equation). > Teacher asks, students to share their answers. > Teacher asks, “Did anyone get a different answer?” > Students compare their answers. > Teacher asks, “How did you know that was the answer?” > Students explain their working out and justify their thinking & reasoning. > Teachers ensure all students recognise the correct answer. > Teacher & the students reflect on the lesson.

complete worksheet Students are located at their desk to complete the worksheet. Whole class discussion

explanation.

Assessment Strategies (link to Learning Outcomes): The formative assessment strategies used for this lesson are: >Observation of student’s application and skills throughout the lesson. > Explanations to justify their thinking & reasoning. >Answers to questions and questions they may ask (feedback). > Demonstration of their knowledge & understanding on their worksheet.

What’s next? Where to from this lesson? This unit will extend longer then the four lesson planned. Students will further their skills & knowledge in the concept of algebra throughout the rest of the unit; enabling them to maximise their full learning potential. The new algebra concepts that will next be introduced are associative, distributive properties and inverse operations.



Queensland Studies Authority Mathematics Syllabus. (2004). Years 1 to 10 syllabus. Retrieved on April 17th, 2011, from

http://www.qsa.qld.edu.au/downloads/early_middle/kla_maths_syll.pdf



Activities and Worksheet: Van De Walle, A. J., & Karp, S. K., & Bay-Williams, M. J. (2010). Elementary & middle school mathematics (7ed.). United States of America: Pearson Department of Education and Early Childhood Development. (2010). The meaning of the equals sign. Retrieved on April 22nd, 2011, from

http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathscontinuum/structure/St25001P.htm#a3

Written Rationale - Justification of Decisions The four mathematical lessons attached are designed to assist in twenty-four grade five

students’ learning, in the mathematical topic Algebra. During the four lessons students will be

determining the relationship of number patterns, understanding the meaning of the equality

symbol and learning how to solve commutative operations. All learning outcomes are based

on the Queensland Studies Authority (2007) Mathematical Essential Learning’s: By the end of

year 5, the QSA syllabus (2004) and the Australian Mathematics Curriculum (n.d.). The unit

is designed to reinforce prior teaching of algebra concepts.

Algebra is an introductory concept that grade five students must learn. Therefore lesson one

introduces one concept of algebra, determining the relationship of number patterns. Lesson

one engages the student’s interest through the use of concrete materials, visual representation

and technology. Students use concrete materials because they are a familiar resource, in which

students can relate to. As the lesson progresses’ students are gradually introduced to

mathematical and symbolic language. This refers to the ‘Language Model of Mathematics’

(EDX3280, Week two, 2011).

Lesson two reinforces prior teaching, again focusing on determining the relationship of

number patterns. This type of lesson was chosen to ensure that all students have a grasp of the

teachings before moving onto the next concept.

Lesson three introduces the meaning of the equality symbol. Students need to understand this

concept before moving onto lesson four, which introduces commutative operations. Again,

each lesson that introduces a new algebraic concept refers to the ‘Language Model of

Mathematics’.

There are various teaching strategies used within the four lesson plans. One strategy

implemented is ‘modelling’. Modelling is an explicit demonstration that the teacher uses in

order to verbalise the process involved (Wing Jan, 2009). At the end of the modelling

demonstration, students should be able to understand the thinking process and physical actions

required to complete a task (Wing Jan, 2009). In order for the students to accomplish their

lesson outcome, they first need to know what is required of them. Which is why ‘modelling’ is

a key strategy.

Another strategy used throughout the unit is questioning. Questioning plays an important role

and is a useful technique that all teachers should use within their teaching pedagogy (Eggen &

Kauchak, 2006). Questions asked in the four lesson plans range from simple questions to

higher order thinking questions, in order to suit all diverse learning abilities. Questions were

frequently asked, to allow the students to provide explanations and justify their reasoning.

Throughout each lesson students will work in the following situations: a whole class

approach, group and independent work. A whole class approach allowed all students to

compare answers on the algebra concept being learnt and provided an opportunity for students

to discuss their assumptions. It also allowed the teacher to recognise any student

misconceptions.

Independent work was implemented to allow each student to demonstrate their personal

ability and skills to solve algebra patterns and equations. It also allows each student to

individually reflect on their new learning without interruption.

Group work was implemented within the unit to allow students to collaborate with one

another, improving their co-operation skills. Also, group work allows students to realise their

competitive nature through a group point reward system. A range of lesson resources and

assessment strategies were chosen to cater for all learning styles and needs of the students.

A constructivist approach to learning was the theory used that underpinned the unit created. A

constructivist approach allows students to construct their own knowledge from their

experiences (Williams & Burden, 1997). The constructivist approach was developed by the

theories Piaget (Williams & Burden, 1997). Each lesson provides an opportunity for students

to construct their own knowledge, through hands-on tasks. Therefore, allowing students to be

responsible for their own learning. However, teacher assistance will still be needed to assist

learners who require it.

References:

EDX3280 Mathematics Curriculum and Pedagogy: Week Two Lecture Notes (2011). Fraser Coast: University

of Southern Queensland.

Eggen, D. P., & Kauchak, P. D. (2006). Strategies and models for teachers: Teaching content and thinking

skills (5th ed). America: Pearson Education.

Queensland Studies Authority. (2007). Mathematics essential learning’s by the end of year 5: Algebra.

Retrieved on April 17th, 2011, from


Queensland Studies Authority Mathematics Syllabus. (2004). Years 1 to 10 syllabus. Retrieved on April 17th,

2011, from http://www.qsa.qld.edu.au/downloads/early_middle/kla_maths_syll.pdf

Williams, M., & Burden, L. R. (1997). Psychology for language teachers: A constructivist approach. Retrieved

on May 9th, 2011, from

http://books.google.com.au/books?hl=en&lr=&id=7AGfCHsAgGMC&oi=fnd&pg=PR8&dq=construct

ivist+approach+theory&ots=lVL8zymm-

r&sig=3gG1F02jjNpoHP9RWbbY6hfqiu0#v=onepage&q=constructivist%20approach%20theory&f=f

alse

Wing Jan, L. (2009). Write Ways: Modeling Writing Forms (3rd ed). Australia: Oxford University Press.


http://usqstudydesk.usq.edu.au/file.php/19093/Webquest_Assessment_1/Lesson_Plan_Resource_Folde

r/australian_curriculum.pdf

Reflection

In order to create my Web Quest I had to ensure my understanding of the topics algebra and

measurement were prominent. I felt that the Web Quest clarified my understanding of the topic

measurement, and had little difficulty implementing the topic within my Web Quest. However, I had

difficulty implementing the topic algebra within my Web Quest. This is more so, because I needed to

understand a concept of algebra, before I felt comfortable implementing it within my Web Quest.

Therefore, I can clarify that step one of learning an algebra concept needs to be evident, before

moving on to another.

One idea that I have gained during the completion of my Web Quest is that the Web Quest can be

used to incorporate a whole unit, rather than from lesson to lesson. Another idea I gained is that Web

Quests assists with ‘edutainment’ within a classroom environment. Therefore, keeping students

engaged, yet still maximising their learning potential. A third idea I gained when creating my Web

Quest is that they can be adapted to assist a learner’s preference. The Web Quest provides visual

stimulation for visual learners, audio can be embedded to cater for audio learners and the Web Quest

can provide hands-on tasks for kinaesthetic learners.

I believe the Web Quest that I created, is a valuable resource that I can and will implement within my

future teaching career. The Web Quest is a great tool for enquiry-based learning and student centred

approach.

UNIVERSITY OF SOUTHERN QUEENSLAND EDX3280 MATHEMATICS CURRICULUM & PEDAGOGY Lesson...

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