Question: Lesson 1 Unit/Lesson Title Lesson duration 60 minutes Stage 2 Year 4 Rationale This lesson develops and reinforces ideas of place value and the understanding
Lesson 1
| Unit/Lesson Title | Lesson duration 60 minutes | Stage 2 Year 4 | |
| Rationale This lesson develops and reinforces ideas of place value and the understanding of applying mental strategies to add and subtract. It is important to understand problem-solving strategies such as algorithms, number lines, and compensation strategies, as well as recognise aspects of money and represent amounts. This lesson sets students up for success in thecompletion of lesson 2. | Syllabus Outcomes MA2-AR-01-selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers MA2-AR-02 completes number sentences involving addition and subtraction by finding missing values MA2-MR-01-represents and uses the structure of multiplicative relations to 10 10 to solve problems MAO-WM-01 Working mathematically (WM)-develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly | Syllabus Content
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Prior Knowledge Students should have prior experience using mental strategiessuch as algorithms, number lines, and compensation strategies. They should be familiar with identifying hundreds, tens, and ones in place value and distinguishing between dollars and cents. | Risk Assessment
The teacher should actively supervise students throughout theentire activity/lesson. | Resources
| ||||
| Learning Outcomes/Time Guide: (20 min) We are learning to:
Success Criteria:
| Content/Learning Experiences Introduction (Engagement) Gather students as a class group seated facing the whiteboard and interactive smartboard. The teacher begins by engaging them in the lesson about "Revising mental strategies for addition and subtraction and the importance of place value when adding and subtracting money." Ask students what key mental strategies they know and think, pair and share with their learning partner, andcreate a class discussion with students on what they discussed with their peers. Begin to discuss with student's what key mental strategies you are going to be looking at as a class. "This lesson, we are going to look at using algorithms, number lines and the compensation strategy with 2-digit numbers". Display the number line (Appendix 3) on the interactive smartboardto students, "The first strategy we are going to look at is the number line strategy, so who can tell me if I have 57+8 how can I use the number line to help figure this out?". Invite a student to come up and demonstrate how they would figure it out on the IWB and allow other students to do the same on their whiteboards. Once the student has completed the example, break down the steps for completing the strategy. "The first thing to do is to figure out which number is closest to the nearest decade, so which number is that "57" and what do we need to add to it to make it 60, "3" isperfect, so we add three, by drawing our line adding three up the top and our new number is 60. Our next step is if we have added 3 from needing to add 8 how much do we have left "5", perfect we draw our line adding 5 up the top and our final answer is "65". So we know now that 57+8= 65". Provide students with another example and allow them to work it out using their whiteboards again. After the students have attempted the questions together as a class, complete them on the number line and begin to look at the compensation strategy. Using the IWB, display the compensation strategy PowerPoint is shownto the students (Appendix 4). Work through each slide, beginning with looking at rounding numbers to the nearest decade by adding or subtracting 1 or 2. Continue onto the next slide and look continuing the same thing but within a sum explaining to students, "what you do to one side, you must do the same to the other, so if we have 28+65 if we plus 2 to 28 that becomes 30 we then need to take away 2 from 65 which will become 63". Continue working through the slide, showing the students the correct way of displaying working out and the use of place value. Allow students to independently complete equations on their whiteboards and discuss themas a class altogether. After completing the final question together, begin to watch the YouTube clip on adding and subtracting money (Appendix 8). In the video, students revise the mental strategy using algorithms and are taught the importance of the decimal point and place value when adding and subtracting money. Provide students with an example so they can work independently to complete the equation on their whiteboards and discuss it as a class. Body (Exploration/Transformation/Presentation) Explain to students their activity today; they are going to rotate in groups of three. They will be using technology, their Chromebooks, to complete online games usingalgorithms, number lines and the compensation strategy with 2-digit numbers. "The first group will start with the adding and subtracting number line game (Appendix 5), the second group will begin with the algorithm online game (Appendix 6), and the final group will be playing the adding and subtracting money online game (Appendix 7), students will use their maths books for each rotation to answer at least five questions and show their strategy used in their books while completing the online activity. Additional support:Each online activity can be adjusted to cater for students' levels. Teachers can change the level so that students can use smaller digit numbers and also provide concrete resources to complete activities like suing counters or fake money as a visual aidfor students. Extension support:The teacher can adjust the levels for students, creating more difficulty. Students can use 3-digit numbers to perform the algorithms, number lines, and compensation strategy within the online activity. Conclusion (Presentation/Reflection) Gather students on the floor and begin a reflective discussion that will spark ideas for the continuum of this lesson onto the next lesson;
| Class Organisation For this lesson, students engage in collaborative learning. They work in pairs and groups throughout the lesson allocated by the teacher. Working in pairs allows them to share their understanding, promote confidence and engagement, and learn to take responsibility for what they sayas they become involved in the learning process of their partners and the whole class. The picking of students at random by the teacher is a student who are gifted and talented and a student who are at a sound levelpromotes more respectful sharing, a chance for students to mingle with other classmates. | Teaching strategies Modelling: The teacher shows and guides students through a framework of problem-solving solutions, such as Algorithms or number lines. Explicit Language: The teacher adopts a systematic approach that facilitates important instructional interactionsbetween the class using words like "sum, add, digit, tens, ones". Questioning: The teacher allows students to explain their mathematical thinking. -Dialogic teaching Scaffolding:problem-solving process by step-by-step explaining. Use of ICT: Online games and interactive PowerPoints, YouTube videos and explanations. | Assessment Techniques Observation: The teacher observes students and how they engage with the lesson. The teacher observes how students' complete addition and subtraction problems and how they effectively use strategy and place value. Feedback: The teacher marks and examines the students' work as they complete the activity. At the end of the lesson, the teacher marks the students' workand leaves feedback for students to read. Peer & Self-assessment: Students work together in pairs to complete the task, providing guidance and feedback to one another while self-reflecting on their understanding. | ||
| Transitions to next lesson | ||||||
Lesson 2:
| Unit/Lesson Title Shopping for School Supplies | Lesson duration 60 minutes | Stage 2 Year 4 | |
| Rationale This is a problem-solving lesson in which students apply their knowledge of using written addition and subtraction strategies and understanding of place value to find solutions to a problem. | Syllabus Outcomes MA2-AR-01- selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers MA2-MR-01- represents and uses the structure of multiplicative relations to 10 10 to solve problems MAO-WM-01 Working mathematically (WM)-develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly | Syllabus Content
| |
|
Prior Knowledge Students should have prior experience in partitioning, rearranging, and regrouping numbers for addition and subtraction problems, identifying unknown quantities in number sentences, solving problems using written and mental calculations, and representing equivalent amounts of money using different denominations. | Risk Assessment
The teacher should actively supervise students throughout theentire activity/lesson. | Resources
| ||||
| Learning Outcomes/Time Guide:
We are learning to:
Success Criteria:
(30 min) (15 min) | Content/Learning Experiences Lesson 2 follows the ELPSARA framework and is delivered as an active process in which studentsconstructtheir own ways of knowing through both individual thinking andsocialinteractions with others. Introduction (Engagement) E(Experience): Gather students on thefloor area facing the interactive Smartboard or TV screen. The teacher begins by engaging them that today's lesson is about "Shopping with a budget." The teacher asks the students, "Have you ever purchased school supplies beforemaybe pencils or a ruler?" "If so, how much do you think these items would cost, and how would you calculate your total if you were to purchase more than one thing?". L(Language): A discussion follows as students think pair and share strategies for calculating theirtotal when shopping for school supplies. The teacher brainstorms with students their responses using 2-3-digit numbers and prior learning from lesson 1 and constructs a mind map rethinking algorithms, number lines, the compensation strategy, etc. P(Pictorial): On the interactive Smart Board, the teacher displays "Shopping for School Supplies"(Appendix 1). Discuss the price of the items with students and begin to look at the question. Explain to students that they only have $10 to spend, and they needto select as many efficient strategies and combinations as possible to make $10. Remind students they will need to complete a number sentence involving addition or subtractions with 3-digit numbers using a strategy they have studied in prior lessons and record and show they're working out using standard place value form. S- (Symbolic): Ask students to "select any four supplies and the price for each, and what strategy might you use to find the total amount?". Remind students they can buy more than one of each item. Write the response on the whiteboard.
Ask students to work out the given word problem using their whiteboards. Ask two to three different students to see what strategies they used and what answers they came up with. Select one and demonstrate it on the whiteboard.
Looking at the given totals, you have calculated, "Is this less than or more than 10? Have we gone over our budget?". Ensure you have talked through trading and the place value of the numbers and decimal points in the algorithm and provide enough examples for students. Body (Exploration/Transformation/Presentation) A-(Application): Invite students to work in pairs to try and select efficient strategies to help solve the problems. Explain to students they will go back to their desks with their learning partners to complete this task. "You will need to collect the working out table and worksheet(Appendix 2) from the teacher" and go back and complete it. "You are to think of all the different combinations you can spend $10 shopping for school supplies; you must think of at least ten different solutions". Encourage students to use a whiteboard to think of strategies and work themout before filling them out into their given worksheet table(Appendix 2). Before sending students off to complete the task, think of prompts like
Additional Support: Provide students with concrete materials such as MAB materials to model solving the problem. Allow students to work using whole numbers and not cents and alter the budget to $5, allowing students to find combinations of school supplies. Extension Support:Provide students with the same questions but use different figures to make it more challenging. Students can use place value to solve the addition and subtraction questions and complete the same task using different prices and budgets. Scenario:Imagine you are buying supplies for school. You have a budget of $20. You need to buy the following items:
What are all the different ways you could spend exactly $20 Conclusion (Presentation/Reflection) R(Reflection): Once the teacher can see the students have completed themajority of the task, the task gets closer to the end. Gather students onto the floor to sit next to their partners. Carry out a formal discussion of the task, asking students, "How many different ways did you spend $10, and what combinations did you come up with?". Allow students to come up and share their working out and justify their strategy used. Ask them how they used their knowledge from prior lessons to help solve this problem. Show the class on the interactive board the ten possible solutions. Ask students, "Have you figured out all 10, with correct working out and calculations?". | Class Organisation For this lesson, students engage in collaborative learning. They work in pairs throughout the lesson allocated by the teacher. Working in pairs allows them to share their understanding, promote confidence and engagement, and learn to take responsibility for what they sayas they become involved in the learning process of their partners and the whole class. The picking of students at random by the teacher is a student who are gifted and talented and a student who are at a sound levelpromotes more respectful sharing, a chance for students to mingle with other classmates. | Teaching strategies Modelling: The teacher shows and guides students through a framework of problem-solving solutions, such as Algorithms or number lines. Explicit Language: The teacher adopts a systematic approach that facilitates important instructional interactionsbetween the class using words like "sum, add, digit, tens, ones". Questioning: The teacher allows students to explain their mathematical thinking. | Assessment Techniques Observation: The teacher observes students and how they engage with the lesson. The teacher observes how students complete addition and subtraction problems and how they effectively use strategy and place value. Feedback: The teacher marks and examines the students' work as they complete the activity. At the end of the lesson, the teacher marks the students' workand leaves feedback for students to read. Peer & Self-assessment: Students work together in pairs to complete the task, providing guidance and feedback to one another while self-reflecting on their understanding. | ||
| Transitions to next lesson Discuss with the students the importance of selecting the appropriate addition or subtraction strategy to solve an equation, as well as the importance of place value. "Next lesson, we are going to continue using addition and subtraction strategies and continue working with money where we begin to look at reverse operations". | ||||||
Lesson 1
| Unit/Lesson Title | Lesson duration 60 minutes | Stage 2 Year 4 | |
| Rationale This lesson develops and reinforces ideas of place value and the understanding of applying mental strategies to add and subtract. It is important to understand problem-solving strategies such as algorithms, number lines, and compensation strategies, as well as recognise aspects of money and represent amounts. This lesson sets students up for success in thecompletion of lesson 2. | Syllabus Outcomes MA2-AR-01-selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers MA2-AR-02 completes number sentences involving addition and subtraction by finding missing values MA2-MR-01-represents and uses the structure of multiplicative relations to 10 10 to solve problems MAO-WM-01 Working mathematically (WM)-develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly | Syllabus Content
| |
|
Prior Knowledge Students should have prior experience using mental strategiessuch as algorithms, number lines, and compensation strategies. They should be familiar with identifying hundreds, tens, and ones in place value and distinguishing between dollars and cents. | Risk Assessment
The teacher should actively supervise students throughout theentire activity/lesson. | Resources
| ||||
| Learning Outcomes/Time Guide: (20 min) We are learning to:
Success Criteria:
| Content/Learning Experiences Introduction (Engagement) Gather students as a class group seated facing the whiteboard and interactive smartboard. The teacher begins by engaging them in the lesson about "Revising mental strategies for addition and subtraction and the importance of place value when adding and subtracting money." Ask students what key mental strategies they know and think, pair and share with their learning partner, andcreate a class discussion with students on what they discussed with their peers. Begin to discuss with student's what key mental strategies you are going to be looking at as a class. "This lesson, we are going to look at using algorithms, number lines and the compensation strategy with 2-digit numbers". Display the number line (Appendix 3) on the interactive smartboardto students, "The first strategy we are going to look at is the number line strategy, so who can tell me if I have 57+8 how can I use the number line to help figure this out?". Invite a student to come up and demonstrate how they would figure it out on the IWB and allow other students to do the same on their whiteboards. Once the student has completed the example, break down the steps for completing the strategy. "The first thing to do is to figure out which number is closest to the nearest decade, so which number is that "57" and what do we need to add to it to make it 60, "3" isperfect, so we add three, by drawing our line adding three up the top and our new number is 60. Our next step is if we have added 3 from needing to add 8 how much do we have left "5", perfect we draw our line adding 5 up the top and our final answer is "65". So we know now that 57+8= 65". Provide students with another example and allow them to work it out using their whiteboards again. After the students have attempted the questions together as a class, complete them on the number line and begin to look at the compensation strategy. Using the IWB, display the compensation strategy PowerPoint is shownto the students (Appendix 4). Work through each slide, beginning with looking at rounding numbers to the nearest decade by adding or subtracting 1 or 2. Continue onto the next slide and look continuing the same thing but within a sum explaining to students, "what you do to one side, you must do the same to the other, so if we have 28+65 if we plus 2 to 28 that becomes 30 we then need to take away 2 from 65 which will become 63". Continue working through the slide, showing the students the correct way of displaying working out and the use of place value. Allow students to independently complete equations on their whiteboards and discuss themas a class altogether. After completing the final question together, begin to watch the YouTube clip on adding and subtracting money (Appendix 8). In the video, students revise the mental strategy using algorithms and are taught the importance of the decimal point and place value when adding and subtracting money. Provide students with an example so they can work independently to complete the equation on their whiteboards and discuss it as a class. Body (Exploration/Transformation/Presentation) Explain to students their activity today; they are going to rotate in groups of three. They will be using technology, their Chromebooks, to complete online games usingalgorithms, number lines and the compensation strategy with 2-digit numbers. "The first group will start with the adding and subtracting number line game (Appendix 5), the second group will begin with the algorithm online game (Appendix 6), and the final group will be playing the adding and subtracting money online game (Appendix 7), students will use their maths books for each rotation to answer at least five questions and show their strategy used in their books while completing the online activity. Additional support:Each online activity can be adjusted to cater for students' levels. Teachers can change the level so that students can use smaller digit numbers and also provide concrete resources to complete activities like suing counters or fake money as a visual aidfor students. Extension support:The teacher can adjust the levels for students, creating more difficulty. Students can use 3-digit numbers to perform the algorithms, number lines, and compensation strategy within the online activity. Conclusion (Presentation/Reflection) Gather students on the floor and begin a reflective discussion that will spark ideas for the continuum of this lesson onto the next lesson;
| Class Organisation For this lesson, students engage in collaborative learning. They work in pairs and groups throughout the lesson allocated by the teacher. Working in pairs allows them to share their understanding, promote confidence and engagement, and learn to take responsibility for what they sayas they become involved in the learning process of their partners and the whole class. The picking of students at random by the teacher is a student who are gifted and talented and a student who are at a sound levelpromotes more respectful sharing, a chance for students to mingle with other classmates. | Teaching strategies Modelling: The teacher shows and guides students through a framework of problem-solving solutions, such as Algorithms or number lines. Explicit Language: The teacher adopts a systematic approach that facilitates important instructional interactionsbetween the class using words like "sum, add, digit, tens, ones". Questioning: The teacher allows students to explain their mathematical thinking. -Dialogic teaching Scaffolding:problem-solving process by step-by-step explaining. Use of ICT: Online games and interactive PowerPoints, YouTube videos and explanations. | Assessment Techniques Observation: The teacher observes students and how they engage with the lesson. The teacher observes how students' complete addition and subtraction problems and how they effectively use strategy and place value. Feedback: The teacher marks and examines the students' work as they complete the activity. At the end of the lesson, the teacher marks the students' workand leaves feedback for students to read. Peer & Self-assessment: Students work together in pairs to complete the task, providing guidance and feedback to one another while self-reflecting on their understanding. | ||
| Transitions to next lesson | ||||||
Lesson 2:
| Unit/Lesson Title Shopping for School Supplies | Lesson duration 60 minutes | Stage 2 Year 4 | |
| Rationale This is a problem-solving lesson in which students apply their knowledge of using written addition and subtraction strategies and understanding of place value to find solutions to a problem. | Syllabus Outcomes MA2-AR-01- selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers MA2-MR-01- represents and uses the structure of multiplicative relations to 10 10 to solve problems MAO-WM-01 Working mathematically (WM)-develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly | Syllabus Content
| |
|
Prior Knowledge Students should have prior experience in partitioning, rearranging, and regrouping numbers for addition and subtraction problems, identifying unknown quantities in number sentences, solving problems using written and mental calculations, and representing equivalent amounts of money using different denominations. | Risk Assessment
The teacher should actively supervise students throughout theentire activity/lesson. | Resources
| ||||
| Learning Outcomes/Time Guide:
We are learning to:
Success Criteria:
(30 min) (15 min) | Content/Learning Experiences Lesson 2 follows the ELPSARA framework and is delivered as an active process in which studentsconstructtheir own ways of knowing through both individual thinking andsocialinteractions with others. Introduction (Engagement) E(Experience): Gather students on thefloor area facing the interactive Smartboard or TV screen. The teacher begins by engaging them that today's lesson is about "Shopping with a budget." The teacher asks the students, "Have you ever purchased school supplies beforemaybe pencils or a ruler?" "If so, how much do you think these items would cost, and how would you calculate your total if you were to purchase more than one thing?". L(Language): A discussion follows as students think pair and share strategies for calculating theirtotal when shopping for school supplies. The teacher brainstorms with students their responses using 2-3-digit numbers and prior learning from lesson 1 and constructs a mind map rethinking algorithms, number lines, the compensation strategy, etc. P(Pictorial): On the interactive Smart Board, the teacher displays "Shopping for School Supplies"(Appendix 1). Discuss the price of the items with students and begin to look at the question. Explain to students that they only have $10 to spend, and they needto select as many efficient strategies and combinations as possible to make $10. Remind students they will need to complete a number sentence involving addition or subtractions with 3-digit numbers using a strategy they have studied in prior lessons and record and show they're working out using standard place value form. S- (Symbolic): Ask students to "select any four supplies and the price for each, and what strategy might you use to find the total amount?". Remind students they can buy more than one of each item. Write the response on the whiteboard.
Ask students to work out the given word problem using their whiteboards. Ask two to three different students to see what strategies they used and what answers they came up with. Select one and demonstrate it on the whiteboard.
Looking at the given totals, you have calculated, "Is this less than or more than 10? Have we gone over our budget?". Ensure you have talked through trading and the place value of the numbers and decimal points in the algorithm and provide enough examples for students. Body (Exploration/Transformation/Presentation) A-(Application): Invite students to work in pairs to try and select efficient strategies to help solve the problems. Explain to students they will go back to their desks with their learning partners to complete this task. "You will need to collect the working out table and worksheet(Appendix 2) from the teacher" and go back and complete it. "You are to think of all the different combinations you can spend $10 shopping for school supplies; you must think of at least ten different solutions". Encourage students to use a whiteboard to think of strategies and work themout before filling them out into their given worksheet table(Appendix 2). Before sending students off to complete the task, think of prompts like
Additional Support: Provide students with concrete materials such as MAB materials to model solving the problem. Allow students to work using whole numbers and not cents and alter the budget to $5, allowing students to find combinations of school supplies. Extension Support:Provide students with the same questions but use different figures to make it more challenging. Students can use place value to solve the addition and subtraction questions and complete the same task using different prices and budgets. Scenario:Imagine you are buying supplies for school. You have a budget of $20. You need to buy the following items:
What are all the different ways you could spend exactly $20 Conclusion (Presentation/Reflection) R(Reflection): Once the teacher can see the students have completed themajority of the task, the task gets closer to the end. Gather students onto the floor to sit next to their partners. Carry out a formal discussion of the task, asking students, "How many different ways did you spend $10, and what combinations did you come up with?". Allow students to come up and share their working out and justify their strategy used. Ask them how they used their knowledge from prior lessons to help solve this problem. Show the class on the interactive board the ten possible solutions. Ask students, "Have you figured out all 10, with correct working out and calculations?". | Class Organisation For this lesson, students engage in collaborative learning. They work in pairs throughout the lesson allocated by the teacher. Working in pairs allows them to share their understanding, promote confidence and engagement, and learn to take responsibility for what they sayas they become involved in the learning process of their partners and the whole class. The picking of students at random by the teacher is a student who are gifted and talented and a student who are at a sound levelpromotes more respectful sharing, a chance for students to mingle with other classmates. | Teaching strategies Modelling: The teacher shows and guides students through a framework of problem-solving solutions, such as Algorithms or number lines. Explicit Language: The teacher adopts a systematic approach that facilitates important instructional interactionsbetween the class using words like "sum, add, digit, tens, ones". Questioning: The teacher allows students to explain their mathematical thinking. | Assessment Techniques Observation: The teacher observes students and how they engage with the lesson. The teacher observes how students complete addition and subtraction problems and how they effectively use strategy and place value. Feedback: The teacher marks and examines the students' work as they complete the activity. At the end of the lesson, the teacher marks the students' workand leaves feedback for students to read. Peer & Self-assessment: Students work together in pairs to complete the task, providing guidance and feedback to one another while self-reflecting on their understanding. | ||
| Transitions to next lesson Discuss with the students the importance of selecting the appropriate addition or subtraction strategy to solve an equation, as well as the importance of place value. "Next lesson, we are going to continue using addition and subtraction strategies and continue working with money where we begin to look at reverse operations". | ||||||
- Construct a reflective essay (800 words), based on integrated recommendations from current mathematics literature, that justifies: your choice of problem/investigations (demonstrate mathematical purpose achieved, such as knowledge and skills, and a clear and succinct explanation for both the reasoning developed and the mathematical significance of the problem); and lesson designs, re: pedagogical models and practices (teaching and learning strategies, such as problem-based activities) for primary mathematics.
- Appraise (evaluate) the lesson planning process, including the peer review process associated with your chosen investigation/problem and extension activity, and interpret the place of this primary mathematics content within the K-12 continuum of learning.
- Analyse the function of mathematics as a numerate and literate practice to meet cognitive, social, cultural and aesthetic needs of children. For example, discuss how your lessons promote inclusivity, challenge, social interactions, relevance and enthusiasm, whilst also developing a supportive knowledge-building culture.
- Please ensure that you model appropriate academic integrity and accurately cite a minimum of four appropriate academic sources (including 1 recent peer-reviewed journal article), adhering to APA (7th edition) referencing guidelines.
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