Lesson+plan+example

// MS3.3 // Selects and uses the appropriate unit to estimate and measure volume and capacity, including the volume of rectangular prisms.
 * **__ Unit of Work Outline __**
 * Key Learning Area: ** Mathematics |||| ** Strand: ** Measurement |||| ** Substrand: ** Volume and Capacity |||| ** Stage / Year: ** Stage 3 / Year 5 ||
 * ** Unit Aim: ** For students to be able to select and use the appropriate unit to measure volume and capacity, including the volume of rectangular prisms. |||| ** Duration: ** Three fifty-minute lessons ||
 * ** Unit Outcomes: **


 * // Working Mathematically //**
 * // WMS3.1 //**// Questioning // Asks questions that could be explored using mathematics in relation to Stage 3 content


 * // WMS3.2 //**// Applying Strategies // Selects and applies appropriate problem-solving strategies, including technological applications, in undertaking investigations.
 * // WMS3.3 //**// Communicating // Describes and represents a mathematical situation in a variety of ways using mathematical terminology and some conventions


 * // WMS3.4 //**// Reasoning // Gives a valid reason for supporting one possible solution over another

Using repeated addition to find the volume of rectangular prisms - Estimating, measuring and comparing volumes and capacities - Estimate the number of cubic metres in a variety of objects such as a cupboard, car, bus, classroom - Using the cubic metre as a formal unit for measuring larger volumes - Recognising the need for a unit larger than the cubic centimetre - Using the abbreviation for cubic metre - Estimating then measuring the capacity of rectangular containers by packing with cubic centimetre blocks - Constructing rectangular prisms using cubic centimetre blocks - Selecting the appropriate unit to measure volume and capacity - Finding the relationship between the length, breadth, height and volume of rectangular prisms - Estimate the amount of cups needed to fill a container with a capacity of one litre - Estimating the size of a cubic metre, half a cubic metre and two cubic metres - Identify situations where cubic metres are used to measure volume - Calculating the volume of rectangular prisms - Predict and use cubic metres to measure volume - Explain that the volume of rectangular prisms can be found by finding the number of cubes in one layer and multiplying by the number of layers || ü Observation checklist on students predicting and measuring the capacity of a range of rectangular prisms ü Post-it notes with more detailed comments of children’s understanding on measuring the volume of rectangular prisms ü Observation of students calculating volume using cubic centimetres ü Collect completed volume worksheet to assess students learning in the first lesson ü Observation of students participation in the classroom discussion ü Observation of students work in pairs to make a measuring device ü Observation of students level of understanding on mL and L ü Collect the students recording sheets ü Observation of students calculating volume ü Collect Recording sheets – measuring in mL and L ü Post-it notes recording children’s verbal responses to worksheet – making a cubic metre, ü Checklist – students predictions on using the cubic metre to measure objects ü Collect and mark the end of unit assessment task – Volume and Capacity Quiz ü Collect students recording measurement sheets || Overall, the unit was successful in achieving its outcomes. Some indicators still need to be revisited, which have been included in individual lesson evaluations, however most of them were reached. The students engaged in a lot of very meaningful learning activities which allowed them to explore the concepts surrounding volume and capacity. The students all appeared to enjoy the unit as most of the time they were engaged and concentrating on their tasks. The students really seemed to grasp a good knowledge on the concepts surrounding volume and capacity that were explored in the lesson. Students were given the opportunity to make links to previous work in earlier stages. We need to improve our timing of lessons, making the tasks more concerned with quality rather than quantity. We also need to improve our questioning techniques and explanations as this will only enhance the quality of the lessons. Overall, this was a successful mini unit and the students learnt a lot about volume and capacity. One student, Rhiannon, requires a lot more work in this area, preferably one-on-one, as she appears to understand a lot of the content, and then cannot explain it and performed poorly in assessment tasks. || // Aim - // To determine the students’ prior knowledge on volume and capacity and explore how students can predict and measure the volume and capacity of certain objects. |||||||| ** Assessment: **
 * // WMS3.4 //**// Reflecting // Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Stage 3 content. |||||||| ** Knowledge & Skills Indicators **
 * * ** Assessment **
 * ** Evaluation: **
 * **__ Lesson 1: Finding the Volume of Rectangular Prisms __**
 * **__ Lesson 1: Finding the Volume of Rectangular Prisms __**

Formative: Summative: // Working Mathematically // // Applying Strategies // Selects and applies appropriate problem-solving strategies, including technological applications, in undertaking investigations. // Communicating // Describes and represents a mathematical situation in a variety of ways using mathematical terminology and some conventions // Reasoning // Gives a valid reason for supporting one possible solution over another // Reflecting // Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Stage 3 content. ||||||||^  ||
 * Thorough observation of students’ participation in discussion and group interaction throughout the lesson using an observational checklist. Using post-it notes with more detailed comments of children’s understanding as we observe them solving problems and recording data.
 * The completed volume sheet and recording sheet will be used to assess students’ understanding and achievement of the lessons outcomes. ||
 * ** Outcomes: **// MS3.3 // Selects and uses the appropriate unit to estimate and measure volume and capacity, including the volume of rectangular prisms.
 * ** Teaching and Learning ** |||| ** Indicators ** |||| ** Assessment ** || ** Resources ** ||
 * **// Ordering objects according to volume //**

**// Aim: //**// Use direct comparison, estimation and informal //

// measurement from Level 1 to 3 of the measurement //

// framework to elicit prior knowledge //

A variety of containers (rectangular prisms) are introduced to the students and asked //Which container do you think holds the most?// Students will be asked to explain their reasons why they think different containers hold more than others and then asked //How could we find out if our predictions are correct? What kinds of materials do we need to find out the volume of these rectangular prisms?// (WM: reasoning)

Students will work together, using cubic centimetre blocks to determine the volume of each shape after predicting how many blocks they think they’ll need to fill each container (WM: applying strategies). Students will be asked if they notice relationships between any of the objects, and students should be able to explain that objects with the same volume can have different shapes (communicating, reflecting).Students will then record the volume of each object in their tables and compare these with their predictions.

Students will be asked to think of other ways to determine the volume of objects that are too big to fill with blocks. Students should be able to explain that the volume of rectangular prisms can be found by finding the number of cubes in one layer and multiplying by the number of layers (WM: applying strategies, reflecting).

Students will use this to identify the relationship between the length, breadth and height of the shape to find the volume of the rectangular prism (WM: applying strategies, communicating). |||| * Estimating then measuring the capacity of rectangular containers by packing with cubic centimetre blocks (WM: applying strategies)
 * Selecting the appropriate unit to measure volume and capacity (WM: applying strategies)
 * Using repeated addition to find the volume of rectangular prisms
 * Finding the relationship between the length, breadth, height and volume of rectangular prisms (WM: applying strategies) |||| * Observational checklist
 * Post-it notes with more detailed comments of children’s understanding
 * Post-it notes recording students comments regarding the relationship of shape and volume
 * Pencils
 * Stencil of estimation table for each student
 * Variety of rectangular prisms
 * Lots of cubic centimetre blocks ||  ||
 * **// Using rulers to find the volume of objects //**

**// Aim: //**// Consolidate understanding by practice to find the volume of a variety of rectangular prisms using rulers //

Allow opportunities for students to practice finding the volume of an object using a ruler and a variety of objects. Encourage students to draw diagrams of the prisms they measure, including units, to demonstrate their understanding of how to find volume (WM: communicating). Students will be given a sheet with a variety of rectangular prisms with varying dimensions to allow further practice |||| * Calculating the volume of rectangular prisms (WM: communicating)
 * Observation of students calculating volume
 * Completed volume worksheet
 * Ruler
 * Rectangular prisms sheet
 * pencils ||||  ||   ||
 * **// Constructing prisms //**

**// Aim: //**// To estimate, measure and record the volume of rectangular prisms in cubic centimetres by packing. //

Pairs of student make a rectangular prism with centimetre blocks. They commence with a base which has 12 blocks. Ask students, //Using 12 blocks, how can I change the shape of the base?// (WM: communicating, reflecting). Students record the number of blocks and array pattern in the first layer. Two more layers are added and the total number of blocks recorded. Ask students, //How many blocks are in each shape? What is different about the shapes? What does this tell you about volume?// Students should be able to explain that objects with the same volume can have a different shape (WM: communicating, reflecting). Students look at the number pattern of the layers to predict how many blocks will be needed for five layers. |||| * Constructing rectangular prisms using cubic centimetre blocks and counting to determine volume (WM: applying strategies)
 * Explain the objects with the same volume may have different shapes (WM: communicating, reflecting)
 * Observation of students participation in the classroom discussion
 * Observation of students work in pairs, their level of understanding
 * The students recording sheets
 * Cubic centimetre blocks
 * Pencils
 * Paper ||||  ||   ||
 * ** Lesson Evaluation **

The lesson was very successful. We were able to elicit the students’ prior knowledge and engage them in meaningful learning activities to increase their knowledge on volume and capacity. The students enjoyed the lesson however became a bit bored when they had to measure the volume of all of the containers using the cubic centimetres. This could have been avoided by not having as many containers to measure the volume of. The students understood some of the concepts surrounding volume and capacity such as recognising how to measure which container was bigger than the other and having to order them although students had trouble explaining their predictions and recording their measurements. Perhaps the recording table needed to be explained in more depth as students wasted a lot of time in the lesson making mistakes and being unsure about what to write in the table. Having less objects to estimate and measure would have contributed to a less confusing table. Students were able to make links to their previous work and background knowledge on volume and capacity and had the opportunity to think about how the concepts they learnt could be applied to real-world examples. The time specified for the lesson was perfect as we managed to get all of the explanations, questioning, and reflecting done amongst the learning tasks. To improve the overall quality of the lesson we need to continue to think of ways to keep the students interested and engaged in the lesson. We must also now focus on the individual students’ needs and abilities in order to maximise their learning. More open questions should be asked so that students get the opportunity to verbalise their opinions and thoughts. ||
 * **__ Lesson 2: __**
 * **__ Lesson 2: __**

// Aim - // To consolidate learning from the previous lesson regarding finding the volume of rectangular prisms and to estimate and find the capacity of a variety of containers in a liquid measure. |||||||| ** Assessment: ** // Formative // // Summative //
 * Thorough observation throughout the lesson using an observational checklist. Using post-it notes with more detailed comments of children’s understanding.
 * The completed volume worksheet and recording sheet will be used to formally assess students’ understanding by the teacher to and their achievement of the lesson outcomes. ||
 * ** Outcomes: **// MS3.3 // Selects and uses the appropriate unit to estimate and measure volume and capacity, including the volume of rectangular prisms.

// Working Mathematically //

// Applying Strategies // Selects and applies appropriate problem-solving strategies, including technological applications, in undertaking investigations.

// Communicating // Describes and represents a mathematical situation in a variety of ways using mathematical terminology and some conventions

// Reasoning // Gives a valid reason for supporting one possible solution over another

// Reflecting // Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Stage 3 content. ||||||||^  ||
 * ** Teaching and Learning ** |||| ** Indicators ** |||| ** Assessment ** || ** Resources ** ||
 * **// Introduction Activity //**

**// Aim: //**// to consolidate understanding from last lesson where students learnt to find the volume of shapes using centimetre cubes and rulers. //

Teacher and students work together through worksheet. Questions involve using the number of cubes in the base, side and height to predict how many cubes make up the volume of the shape (WM: Reasoning). Other questions supply side measurements in cm and students use this to find the volume (WM: Applying strategies). Teachers can use this activity to question students about the relationship between layering and volume and determine students’ understanding of volume and capacity so far. |||| * Finding the relationship between the length, breadth, height and volume of rectangular prisms
 * Calculating the volume of rectangular prisms (WM: applying strategies)
 * Explain that the volume of rectangular prisms can be found by finding the number of cubes in one layer and multiplying by the number of layers (WM: applying strategies, reflecting)
 * Observation of students calculating volume
 * Post-it notes recording children’s verbal responses to worksheet ||||  || * Volume worksheets
 * Pencils
 * Rulers ||
 * **// Introducing capacity in liquid //**

**// Aim: //**// Use direct comparison, estimation and informal measurement from Level 1 to 3 of the measurement framework to elicit prior knowledge //

A range of containers are shown to students. Students are asked to predict and order which containers hold the most, and record this in a table. Ask students //Why do you think that container will hold more than this one? (WM: Reasoning, applying strategies)// to discover strategies that students are using. Students pour liquid between containers to make direct comparisons to determine the order of volume. Students draw a diagram demonstrating the correct order of shapes in capacity and discuss how this activity changes their ideas about the shape of a container and its capacity. |||| * Estimate and measure the capacity of containers (WM: applying strategies)
 * Observe students closely to determine their understanding
 * Post-it notes recording children’s verbal responses and diagrams
 * A range of different sized containers
 * A bucket of water
 * Recording sheet
 * pencils ||||  ||   ||
 * **// Measure and record capacity in L and mL //**

**// Aim: //**// To make a measuring container and use this to find the capacity in mL and L’s of a variety of containers //

Explain that the students will be making a measuring container. Ask students //How many 100mL cups of water are needed to fill a 1000mL container? (WM: reasoning, applying strategies).// Students then mark 100mL graduation on an empty plastic container, using water poured from a measuring jug of 100mL to make their own measuring device, up to 1 litres.

Students then problem solve to measure the containers compared in the previous activity, and record to the nearest 100mL their findings on their diagrams. |||| * Estimating, measuring and comparing volumes and capacities (to the nearest litre)
 * Estimate the amount of cups needed to fill a container with a capacity of one litre (//WM: Applying Strategies//)
 * Observation checklist of students responses
 * Post it notes recording responses
 * Recording sheets
 * Measuring jugs
 * Clear 2L plastic containers
 * Marking pens
 * Recording sheets
 * Pencils
 * Variety of containers ||||  ||   ||
 * ** Lesson Evaluation ** The lesson achieved a lot of its indicators and students are working towards achieving the unit outcome. All of the students really seemed to enjoy this lesson where they were using water and making their own measuring devices. They were constantly engaged in the lesson which really showed in their responses and level of learning and knowledge. Lilly understood all of the concepts surrounding volume and capacity taught in the lesson and offered very valuable questions and answers which really helped the other students. Jarvis showed a thorough understanding of the concept of measuring volume using water and showed an understanding of the relationship between mL and L and how to record the volume of different containers. Rhiannon is working towards understanding the concepts and does not yet appear to understand the relationship between mL and L and that the volume of a container takes up the entire space. In the lesson students revisited links to previous work and their background knowledge on volume and capacity where they confidently filled in a work sheet and engaged in discussion about how to find the volume of a variety of containers. The time specified for each activity was not adequate. We tried to fit too many learning activities and indicators into the lesson that just didn’t realistically fit into the 50 minute time slot. The lesson would have been more successful if it only focused on a few indicators as this would have provided us with the time to do more questioning and have a chance to do a strong lesson conclusion. To improve the overall quality of the lesson, the time must be more evenly distributed and we must continue to work on our questioning and explanation techniques. ||
 * **__ Lesson 3: __**
 * **__ Lesson 3: __**

// Aim - // For students to learn how to know and represent large units by calculating volume in cubic metres. |||||||| ** Assessment: **

// Formative // // Summative //
 * Thorough observation throughout the lesson using an observational checklist. Using post-it notes with more detailed comments of children’s understanding.
 * The completed volume worksheet and recording sheet will be used to formally assess students’ understanding by the teacher to and their achievement of the lesson outcomes. Final assessment task. ||
 * ** Outcomes: **// MS3.3 // Selects and uses the appropriate unit to estimate and measure volume and capacity, including the volume of rectangular prisms.

// Working Mathematically //

// Applying Strategies // Selects and applies appropriate problem-solving strategies, including technological applications, in undertaking investigations.

// Communicating // Describes and represents a mathematical situation in a variety of ways using mathematical terminology and some conventions

// Reasoning // Gives a valid reason for supporting one possible solution over another

// Reflecting // Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Stage 3 content. ||||||||^  ||
 * ** Teaching and Learning ** |||| ** Indicators ** |||| ** Assessment ** || ** Resources ** ||
 * **// Introduction Activity – Making a cubic metre //**

**// Aim: //**// to recap on prior work regarding finding the volume of a rectangular prism. Students make a cubic metre as a visualisation tool, understand the need for a unit larger than a centimetre and understand the relationship between length, breadth and height) //

Begin lesson by recapping first lesson and how to find the volume of a rectangular prism. //Ask students What is the relationship between the length, breadth, and height of a rectangular prism when finding the volume? Ask students to demonstrate their understanding of this formula using an example.// Ask students //How would you find the volume of a larger space?// Suggest garbage bin, storeroom or classroom for example. Students may suggest measuring in metres instead of centimetres.

Students will first discuss together what a cubic metre is. Explain that they will make a cubic metre using cardboard and tape. Ask them how they think they might go about this (What they would use to measure sides etc) Make sure that students know how many cm there are in 100m. Once made, students play with cube, comparing it to parts of their body. Students draw their cubes and record the measurements. |||| * using the abbreviation for cubic metre
 * recognising the need for a unit larger than the cubic centimetre (WM: reasoning)
 * finding the relationship between the length, breadth, height and volume of rectangular prisms (WM: applying strategies)
 * calculating the volume of rectangular prisms (WM: applying strategies)
 * Identify situations where cubic metres are used to measure volume (WM:reflecting)
 * Estimate and use cubic metres to measure volume (WM: applying strategies)
 * Observation checklist
 * Post-it notes recording children’s verbal responses to worksheet
 * Collect students’ recording measurement sheets ||||  || * Cardboard
 * Scissors
 * Masking tape
 * Marking pen
 * Rectangular container
 * 30cm rulers ||
 * **// Measuring using a cubic metre //**

Take students on a ‘volume walk’ pointing out different shapes, objects and spaces around the school playground and //ask them to estimate the volume of these objects and spaces//. Encourage students to verbalise their strategies and discuss together the reasons for their predictions. Ensure the students have opportunities to estimate in multiple cubic metres and half/quarter metres. Ensure the students understand that measurement is never perfectly accurate by nature and that it is not always going to be possible to find our the exact dimensions of a space they want to measure, and in these cases estimations can be very useful as an informal means of measuring. Suggest some examples, and //ask the students for examples of when it might be useful to estimate the volume of an object or space.// |||| * Using the cubic metre as a formal unit for measuring larger volumes (WM: applying strategies)
 * Estimating the size of a cubic metre, half a cubic metre and two cubic metres (WM: applying strategies)
 * Estimate the number of cubic metres in a variety of objects such as a cupboard, car, bus, classroom (WM: Applying strategies)
 * Observe students closely to determine their understanding
 * Checklist – students predictions ||||  || * Student-made cubic metres (one layer)
 * Playground objects ||
 * **// Assessment Task - test //**

**// Aim: //**// To determine students’ level of understanding and achievement of outcomes in the unit //

Allow the students ten to fifteen minutes to complete the test. The test assesses students understanding of the last two classes; finding volume in terms of mL’s/L’s and cubic metres. |||| Assessing outcomes - **//MS3.3//** Selects and uses the appropriate unit to estimate and measure volume and capacity, including the volume of rectangular prisms. The lesson was successful in achieving the majority of its indicators. Each learning activity explored in sufficient depth working mathematically outcomes and provided opportunities for students to question, explore, communicate and reason with volume and capacity concepts. The students were engaged with the lesson as they had built up enough previous knowledge to know exactly what to do and therefore were able to understand the leaning tasks. They all appeared to enjoy the lesson. Lilly and Jarvis understood the majority of concepts surrounding volume and capacity however Rhiannon is still working towards achieving most of them. Lilly requires extra work on volume and capacity as although she was engaged with these tasks, they were slightly below her ability level. The assessment task allowed students to make links to their previous work on volume and capacity. The time specified for each task was suitable and allowed enough time for questioning and reflecting. No major changes need to be made to improve the quality of this lesson other than to perhaps identify some objects around the playground that students can estimate and measure previous to the lesson. ||
 * // WM //** //Applying Strategies// Selects and applies appropriate problem-solving strategies, including technological applications, in undertaking investigations. |||| * Collect and mark this end of unit assessment task.
 * 3 copies of the assessment task
 * Pencils
 * Rulers ||  ||
 * ** Lesson Evaluation **
 * ** References **

Board of Studies (2002). //Mathematics K-6: Syllabus//. Sydney: Board of Studies.

Department of Education and Training, Professional Support and Curriculum Directorate (2003). //Teaching measurement: Stage2 and 3.// Sydney: Department of Education and Training. ||