Number & Algebra
Number & Place Value
| Number & Place Value | Resource Link | Australian Curriculum | Big Mathematical Idea | Year Levels | Task Attributes | |||
| Open Middle Task | Dot Card Counting | F: Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point | Counting enables us to find out how many altogether. | F-3 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
| Maths Association of Victoria Card Game | Snap! One More, One Less | F: Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond | Numbers are a naming system. | F-1 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Supports formative assessment practices Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| Prime Number Magazine Warm up/Investigation | Paper Plates | F: Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond | Numbers are a naming system. | F-4 | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| Maths Association of Victoria Warm-up Activity | Horseshoe Numbers | F: Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond | Numbers are a naming system. | F-4 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Students see how mathematical ideas are connected across different strands and sub-strands of the mathematics curriculum. |
| Kerri Smith Warm up Activity | Write and Wriggle | F: Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond | We write numerals the same way so that they are easy for us, and for others, to read and understand. | F-2 | Students learn by doing | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. |
| Maths 300 Investigation (subscription) | Cookie Count (& The Doorbell Rang) | F: Represent practical situations to model addition and sharing | Fairness in sharing often involves division into equal parts. | F-4 | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. |
| Steve Wyborney Lesson Sequence | Splat! | F: Represent practical situations to model addition and sharing | Counting enables us to find out how many altogether. | F-6 | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| Martin Holt Investigation | One is a Snail... | Y1: Count collections to 100 by partitioning numbers using place value | We can combine different numbers together to make new numbers. | F-1 | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| reSolve Investigation | Skip Counting: How Many Birds? | Y1: Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero (VCMNA086) | Building to benchmark numbers can help us count large collections. | F-2 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. |
| Mathforlove 5 Lesson Sequence | Cuisenaire Rods | Y1: Count collections to 100 by partitioning numbers using place value | We can combine different numbers together to make new numbers. | F-2 | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. | Extends knowledge in new contexts Introduces students to forms of knowledge in contexts that probably exists outside of their experience and the contexts of everyday life. |
| NRICH Virtual Manipulative Puzzle |
| Y1: recognise, represent and order numbers to at least 120 using physical and virtual materials, numerals, number lines and charts | Place value helps us compare and order very large and very small numbers. | 1-2 | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths.
| Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. |
| Maths Association of Victoria Warm-up | Sticky Labels | Y1: Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line | Place value helps us compare and order very large and very small numbers. | F-6 | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| Martin Holt Assessment Task | F-2 Place Value Thinkboard | Y1: Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line | Numbers are connected to each other in many different ways. | F-2 | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. | Extends knowledge in new contexts Introduces students to forms of knowledge in contexts that probably exists outside of their experience and the contexts of everyday life. |
| MAV Learning Activity | Salute | Y1: Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts | Some ways of adding are more efficient than others. | 1-4 | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. |
| Maths Association of Victoria Warm-up | Flip 10 | Y1: Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts | We can combine different numbers together to make new numbers. | F-2 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| NRICH Investigation | I'm Eight | Y2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies (VCMNA107) | The 4 basic operations help us find different ways to represent numbers. | 1-4 | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress.
| Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. |
| Dr Paul Swan warm-up | Hokey Pokey | Y2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies | We can combine different numbers together to make new numbers. | F-4 | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. |
| Dr James Russo game | Nearest to the Gnarly Number | Y2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies | Some ways of adding are more efficient than others. | 2-4 | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
| Michael Ymer game | Place Value Paths | Y2: Recognise, model, represent and order numbers to at least 1000 | All numbers are made up of the digits 0-9. | 1-5 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. |
| 3-Act-Tasks Graham Fletcher | The Cookie Monster | Y2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies | An array has the same number of objects in each row. We can sometimes use arrays to solve problems. | F-2 | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| Michael Ymer Card Game | Ten in a Row | Y2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies | The 4 basic operations are related to one another and are used to process information and solve problems. | 2-4 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
| reSolve Investigation | Place Value Cards | Y2: Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting. | The place-value properties of a number can be represented additively and multiplicatively. | 2-3 | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. |
| reSolve Investigation | Counting Large Collections | Y2: Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting. | Ten is really just a group of 10 ones. | 1-3 | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. |
| Mathematics Task Centre Investigation | Truth Tiles | Y2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies | The 4 basic operations are related to one another and are used to process information and solve problems. | 2-4 | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. |
| Mathematics Task Centre Investigation | Bob's Buttons | Y2: Recognise and represent division as grouping into equal sets and solve simple problems using these representations | When we make equal groups, there is sometimes a remainder. | 2-6 | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. |
| YouCubed Game | How Close to 100 | Y2: Recognise and represent multiplication as repeated addition, groups and arrays | We can think about multiplication as repeated addition. | 2-4 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. |
| Kentucky Centre for Maths Game | Multiplication Match - 3 in a Row | Y2: Recognise and represent multiplication as repeated addition, groups and arrays | We can think about multiplication as repeated addition. | 2-4 | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
| NRICH Investigation | Make 37 | Y3: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation | Some ways of adding are more efficient than others. | 2-4 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. |
| Michael Ymer Card Game | Target 100 | Y3: Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies | We can think about multiplication as repeated addition. | 3-4 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
| NRICH Investigation | Magic Vs | Y3: Investigate the conditions required for a number to be odd or even and identify odd and even numbers | Recognising odd and even numbers numbers can help us organise collections and solve problems. | 2-5 | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| Martin Holt Assessment Task | 3-6 Place Value Thinkboard | Y3: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems | One of these is 10 of those. | 3-6 | Promotes formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. |
| Mathematics Task Centre Investigation | Dominoes | Y4: Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems | The base 10 place value system is used to represent numbers and number relationships. The base 10 place value system is used to represent numbers and number relationships. | 2-6 | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. |
| Michael Ymer Investigation | What does ten thousand look like? | Y4: Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems | The place value system helps us keep track of, and organise large numbers. | 3-5 | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Promotes formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| Maths Association of Victoria Warm-up Game | Beat the Teacher | Y4: Recognise, represent and order numbers to at least tens of thousands | The place value system helps us keep track of, and organise large numbers. | 1-5 | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
| Maths Association of Victoria Challenging Task | The 1,2,3,4 Problem | Y4: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder | The 4 basic operations are related to one another and are used to process information and solve problems. | 3-6 | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. |
| Top Drawer Teachers Game | Facts and Models | Y4: Recall multiplication facts up to 10 × 10 and related division facts | The 4 basic operations are related to one another and are used to process information and solve problems. | 3-5 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. |
| Martin Holt investigation | Connecting Times Tables | Y4: Recall multiplication facts up to 10 × 10 and related division facts | The 4 basic operations are related to one another and are used to process information and solve problems. | 4-6 | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. |
| Math4Love game | Damult Dice | Y4: Recall multiplication facts up to 10 × 10 and related division facts | The 4 basic operations are related to one another and are used to process information and solve problems. | 3-6 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
| Mathematics Task Centre Investigation | Crosses | Y4: Investigate and use the properties of odd and even numbers | Recognising odd and even numbers can help us organise collections and solve problems. | 4-6 | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. |
| Math4Love Warm-up / Investigation | The Broken Calculator | Y5: Use efficient mental and written strategies and apply appropriate digital technologies to solve problems | We can combine different numbers together to make new numbers. | 2-6 | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. |
| Mathematics Task Centre Investigation | Fay's Nines | Y5: Use efficient mental and written strategies and apply appropriate digital technologies to solve problems | To identify a pattern is to begin to understand how maths applies to the world in which we live. | 4-6 | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. |
| reSolve Investigation | Bakery Challenge | Y5: Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies | Arrays can help us make sense of large numbers. | 5-6 | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| Youcubed Investigation | The Four 4s | Y6: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers | Brackets make it clear which part of a calculation is to be done first. | 3-6+ | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Extends knowledge in new contexts Introduces students to forms of knowledge in contexts that probably exists outside of their experience and the contexts of everyday life. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. |
| NRICH Investigation | Make 100 | Y6: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers | Brackets make it clear which part of a calculation is to be done first. | 5-6 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| reSolve: Maths by Inquiry game | The Elevator Challenge | Y6: Investigate everyday situations that use integers. Locate and represent these numbers on a number | A vertical number line can help us solve problems involving negative numbers. | 5-6 | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Extends knowledge in new contexts Introduces students to forms of knowledge in contexts that probably exists outside of their experience and the contexts of everyday life. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. |
Fractions & Decimals
| Fractions & Decimals | Resource Link | Australian Curriculum | Big Mathematical Idea | Year Levels | Task Attributes | |||
| Number Talk Images | Number Talk Images | Y2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections | A fraction of a shape may not always be a single part but may be made up of lots of different sized small parts. | F-6 | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. |
| reSolve Investigation | Bottle Flipping | Y3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole. | We can model, order and compare fractions to make sense of them. | 2-5 | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Extends knowledge in new contexts Introduces students to forms of knowledge in contexts that probably exists outside of their experience and the contexts of everyday life. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. |
| Wonder in Mathematics Investigation (Dr. Amie Albrecht) | Y3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole | We can use pictures and symbols to represent fractions. | 3-6 | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | |
| Steve Wyborney Lesson Sequence | Fraction Splat! | Y4: Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line | We can count, compare and add fractions just like we do for whole numbers | 2-6 | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| Maths Association of Victoria Warm-up | Sticky Labels | Y4: Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation | We can model, order and compare fractions and decimals to make sense of them. | F-6 | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| Peter Sullivan Warm-Up Activity | Directions | Y4: Count by quarters halves and thirds, including with mixed numerals. | We can model, order and compare fractions to make sense of them. | F-6 | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. |
| Fractiontalks.com | Fraction Talks | Y4: Investigate equivalent fractions used in contexts | We can model, order and compare fractions to make sense of them. | 3-6 | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. |
| Dr. Chris Shore Lesson Ideas | The Clothesline | Y5: Compare and order common unit fractions and locate and represent them on a number line | There are always numbers between two other numbers. | 3-6+ | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. |
| Michael Ymer Game | Decimal Number Path | Y5: Compare, order and represent decimals | We can model, order and compare decimals to make sense of them. | 4-6 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. |
| NRICH Game / Investigation | Spiralling Decimals | Y5: Compare, order and represent decimals | We can model, order and compare decimals to make sense of them. | 4-6 | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. |
| Martin Holt Game | Y5: Compare and order common unit fractions and locate and represent them on a number line | Benchmarks on number lines help us understand the relative magnitude of proper and improper fractions. | 4-6 | High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | |
| maththinkingseen.com Game / Investigation Carla Dawson
| Y6: Compare fractions with related denominators and locate and represent them on a number line | A fraction of a shape may not always be a single part but may be made up of lots of different sized small parts. | 5-6 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | |
| NZMaths Lesson Sequence | Cuisenaire Rod Fractions | Y6: Solve problems involving addition and subtraction of fractions with the same or related denominators | A fraction of a shape may not always be a single part but may be made up of lots of different sized small parts. | 4-6 | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. |
| Youcubed Investigation (Mark Driscoll) | Paper Folding | Y6: Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies | When we divide an object or a group into equal parts we are creating fractions. | 4-6 | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. |
| 3-Act Tasks Graham Fletcher | The Big Pad | Y6:Solve problems involving addition and subtraction of fractions with the same or related denominators | A fraction of a shape may not always be a single part but may be made up of lots of different sized small parts. | 5-6 | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Extends knowledge in new contexts Introduces students to forms of knowledge in contexts that probably exists outside of their experience and the contexts of everyday life. |
| openmiddle.com Challenging Task | Adding Decimals | Y6: Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers | To identify a pattern is to begin to understand how maths applies to the world in which we live. | 5-6 | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
| Rob Vingerhoets | Fraction Inbetweenies | Y6: Make connections between equivalent fractions, decimals and percentages | Fractions, decimals and percentages help us make sense of quantities, including numbers that lie between whole numbers. | 4-7 | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. |
Money
| Money | Resource Link | Australian Curriculum | Big Mathematical Idea | Year Levels | Task Attributes | |||
| Kerri Smith Challenging Task | Bakery Mystery | Y1: Recognise, describe and order Australian coins according to their value | There is often more than one way to make an amount. | F-1 | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. |
| Dr. Paul Swan Game | Money Match | Y2: Count and order small collections of Australian coins ... according to their value. | There is often more than one way to make an amount. | 2 | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
| Martin Holt Warm-up Activity | Money Make | Y3: Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents. | There is often more than one way to make an amount. | 2-3 | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily.
| Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |
| Robert Kaplinsky Problem-solving Task | How much Money were those Pennies? | Y3: Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents | The notes and coins in our money system have been designed make it easier to calculate totals. | 3-6 | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. |
| Would You Rather? John Stevens Investigation | Cookie Sale | Y4: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies | Value can be measured by money. | 3-6 | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. |
| Jennifer Bowden Challenging Task | Sushi Plates | Y4: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies | The notes and coins in our money system help us efficiently calculate amounts and change. | 4 | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Extends knowledge in new contexts Introduces students to forms of knowledge in contexts that probably exists outside of their experience and the contexts of everyday life. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. |
Pattern & Algebra
| Pattern & Algebra | Resource Link | Australian Curriculum | Big Mathematical Idea | Year Levels | Task Attributes | |||
| NRICH Investigation | Three Blocks Towers | F: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings | Patterns repeat and grow. | F-2 | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. |
| NRICH Investigation | Snakes | F: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings | Patterns repeat and grow. | F-2 | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. |
| Martin Holt Warm-up | Come to my Party | Y1: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings. | We can sort any number once we find the rule. | F-6 | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. |
| NZMaths | Staircases | Y1: Investigate and describe number patterns formed by skip-counting and patterns with objects | Patterns repeat and grow. | 1-4 | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. |
| NRICH Investigation | Magic Plant | Y2: Apply repetition in arithmetic operations, including multiplication as repeated addition and division as repeated subtraction (VCMNA114) | Growing patterns increase in a systematic way. | 1-3 | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. |
| Warm-up / Investigation | Visual Patterns | Y2: Describe patterns with numbers and identify missing elements | To identify a pattern is to begin to understand how maths applies to the world in which we live. | F-6 | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. |
| NRICH Puzzle | Frogs | Y6: Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (VCMNA219) | To identify a pattern is to begin to understand how maths applies to the world in which we live. | 3-6 | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. |
| Maths Association of Victoria 10 Lesson for Algorithmic Thinking | Number Code | Y3: Describe, continue, and create number patterns resulting from performing addition or subtraction | The repetitive features of pattern can be identified and described as generalised rules called ‘functions’. | 3 | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. |
| Youcubed investigation | Squares Upon Squares | Y3: Describe, continue, and create number patterns resulting from performing addition or subtraction | By analysing patterns and identifying rules for patterns it is possible to make predictions. | 3-6 | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. | |
| Youcubed Investigation | Messing with Pascal | Y3: Describe, continue, and create number patterns resulting from performing addition or subtraction | To identify a pattern is to begin to understand how maths applies to the world in which we live. | 3-6 | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Students see the maths of others Students see other ways of knowing and working mathematically. The sharing of concrete, visual and abstract strategies and solutions significantly raises the level of thinking. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. |
| Mathematics Task Centre Investigation | Add the Pack | Y4: Explore and describe number patterns resulting from performing multiplication | Recognising patterns helps us estimate and calculate the total. | 4-6 | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. |
| The Maths Projects Journal (Dr. Chris Shore) | I'm Thinking of a Number… | Y5: Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division | Patterns can often be generalised using algebraic expressions, equations or functions. | 4-6 | Supports formative assessment practices Helps teachers and students identify where the student is at, recognise where they are going and plan how they will get there with an emphasis on student growth. Self, peer and teacher feedback guide this process. | Builds student understanding of the ‘why’ and ‘how’ of mathematics. Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big ideas) in different ways. e.g. developing number sense, place value. | Develops fluency Performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. | Promotes reasoning and critical thinking Logical, rational and critical thinking. e.g. Estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
| NRICH Investigation | Summing Consecutive Numbers | Y5: Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction | By analysing patterns and identifying rules for patterns it is possible to make predictions. | 5-6 | Inspires creative thinking and/or visualising Students invent, discover and imagine new ways to solve a problem. Task includes a visual component that helps students make connections and “see” relationships. e.g. visualise the problem, represent solutions using visual stimuli. | Stimulates curiosity and imagination High student interest, motivation, enjoyment and sense of purpose can be anticipated and/or observed. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. |
| Martin Holt Investigation | The King's Chessboard | Y6: Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence | Exponential notation is a powerful way to express repeated products of the same number. | 3-6+ | Students learn by doing Students are moving, designing, constructing etc. They actively solve problems in the physical space which may include an outdoor space. Experiential learning plays a crucial role in helping students understand patterns and relationships in maths. | Provides multiple entry and exit points Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. | Problem solving is required to overcome obstacles Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. | Encourages collaboration and discourse Students share and challenge each others' ideas. They recognise efficient strategies in the work of their peers. |