Describe probabilities using fractions, decimals and percentages; recognise that probabilities lie on numerical scales of 0–1 or 0%–100%; use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals
<ul>
<li>recognising that the probability of an event occurring can be represented numerically as either a number ranging from zero to one or a percentage from 0% to 100% where zero or 0% means it will not happen and one or 100% means it is certain to happen</li>
<li>using a scale of zero to one or 0% to 100% to estimate chances of events</li>
<li>listing the different possible outcomes for rolling a dice and using a scale to locate the relative probability by considering the chance of more than or less than for each possible event, for example, the probability of getting a number greater than 4</li>
<li>recognising the language used to describe situations involving uncertainty, such as what it means to be ‘lucky’, a ‘75% chance’ of rain or a ‘1-in-100 years’ flood</li>
<li>exploring Aboriginal and/or Torres Strait Islander children’s instructive games, such as Weme from the Warlpiri Peoples of Central Australia, to investigate and assign probabilities that events will occur, indicating their estimated likelihood</li>
</ul>
List the possible outcomes of chance experiments involving equally likely outcomes and compare to those that are not equally likely
<ul>
<li>discussing what it means for outcomes to be equally likely and comparing the number of possible and equally likely outcomes of chance events; for example, when drawing a card from a standard deck of cards there are 4 possible outcomes if you are interested in the suit, 2 possible outcomes if you are interested in the colour or 52 outcomes if you are interested in the exact card</li>
<li>discussing how chance experiments that have equally likely outcomes can be referred to as random chance events; for example, if all the names of students in a class are placed in a hat and one is drawn at random, each person has an equally likely chance of being drawn</li>
<li>commenting on the chance of winning games by considering the number of possible outcomes and the consequent chance of winning</li>
<li>investigating why some games are fair and others are not; for example, drawing a track game to resemble a running race and taking it in turns to roll 2 dice, where the first runner moves a square if the difference between the 2 dice is zero, one or 2 and the second runner moves a square if the difference is 3, 4 or 5, and responding to the questions ‘Is this game fair?’, ‘Are some differences more likely to come up than others?’ and ‘How can you work that out?’</li>
<li>comparing the chance of a head or a tail when a coin is tossed, whether some numbers on a dice are more likely to be facing up when the dice is rolled, or the chance of getting a 1, 2 or 3 on a spinner with uneven regions for the numbers</li>
<li>discussing supermarket promotions such as collecting stickers or objects and whether there is an equal chance of getting each of them</li>
</ul>
Describe and perform translations, reflections and rotations of shapes, using dynamic geometry software where appropriate; recognise what changes and what remains the same, and identify any symmetries
<ul>
<li>understanding and explaining that translations, rotations and reflections can change the position and orientation of a shape but not its shape or size</li>
<li>using pattern blocks and paper, tracing around a shape and then conducting a series of one-step transformations and tracing each resulting image, and then finally copying the original position and end position on a new sheet of paper</li>
<li>demonstrating how different combinations of transformations can produce the same resulting image</li>
<li>challenging classmates to select a combination of transformations to move from an original image to the final image, noting the different combinations by using different colours to trace images</li>
<li>investigating how animal tracks can be interpreted by Aboriginal and Torres Strait Islander Peoples using the transformation of their shapes, to help determine and understand animal behaviour</li>
</ul>
Estimate, construct and measure angles in degrees, using appropriate tools, including a protractor, and relate these measures to angle names
<ul>
<li>using a protractor to measure angles in degrees and classifying these angles using angle names; for example, an acute angle is less than 90°, an obtuse angle is more than 90° and less than 180°, a right angle is equal to 90° and a reflex angle is more than 180° and less than 360°</li>
<li>estimating the size of angles in the environment using a clinometer and describing the angles using angle names</li>
<li>using a ruler and protractor to construct triangles, given the angle measures and side lengths</li>
<li>using a protractor to measure angles when creating a pattern or string design within a circle</li>
<li>recognising the size of angles within shapes that do and do not tessellate, measuring the angles and using the sum of angles to explain why some shapes will tessellate and other shapes do not</li>
</ul>
Compare 12- and 24-hour time systems and solve practical problems involving the conversion between them
<ul>
<li>using timetables written in 24-hour time, such as flight schedules, to plan an overseas or interstate trip, converting between 24- and 12-hour time</li>
<li>converting between the digital and analog representation of 24-hour time, matching the same times represented in both systems; for example, setting the time on an analog watch from a digital alarm clock</li>
</ul>
Solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units
<ul>
<li>investigating problem situations involving perimeter, for example, ‘How many metres of fencing are required around a paddock, or around a festival event?’</li>
<li>using efficient ways to calculate the perimeters of rectangles, such as adding the length and width together and doubling the result</li>
<li>solving measurement problems such as ‘How much carpet would be needed to cover the entire floor of the classroom?’, using square metre templates to directly measure the floor space</li>
<li>creating a model of a permaculture garden, dividing the area up to provide the most efficient use of space for gardens and walkways, labelling the measure of each area, and calculating the amount of resources needed, for example, compost to cover the vegetable garden</li>
<li>using a physical geoboard or a virtual geoboard app to recognise the relationship between area and perimeter and solve problems; for example, investigating what is the largest and what is the smallest area that has the same perimeter</li>
<li>exploring the designs of fishing nets and dwellings of Aboriginal and Torres Strait Islander Peoples, investigating the perimeter, area and purpose of the shapes within the designs</li>
</ul>
Choose appropriate metric units when measuring the length, mass and capacity of objects; use smaller units or a combination of units to obtain a more accurate measure
<ul>
<li>ordering metric units from the largest unit to the smallest, for example, kilometre, metre, centimetre, millimetre</li>
<li>recognising that some units of measurement are better suited to some tasks than others; for example, kilometres are more appropriate than metres to measure the distance between 2 towns</li>
<li>deciding on the unit required to estimate the amount of paint or carpet for a room or a whole building, and justifying the choice of unit in relation to the context and the degree of accuracy required</li>
<li>measuring and comparing distances (for example, measuring and comparing jumps or throws using a metre length of string and then measuring the part metre with centimetres and/or millimetres) and explaining which unit of measure is most accurate</li>
<li>researching how the base units are derived for the International System of Units (SI), commonly known as the metric system of units, recognising that the metric unit names for the attributes of length and mass are international standards for measurement</li>
</ul>
Find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations
<ul>
<li>using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that 3 × 5 = 15 and 30 ÷ 2 = 15, then 3 × 5 = 30 ÷ 2, and therefore the solution to 3 × 5 = 30 ÷ □ is 2</li>
<li>using relational thinking, and an understanding of equivalence and number properties to determine and reason about numerical equations; for example, explaining whether an equation involving equivalent multiplication number sentences is true, such as 15 ÷ 3 = 30 ÷ 6</li>
<li>using materials, diagrams and arrays to demonstrate that multiplication is associative and commutative but division is not – for example, using arrays to demonstrate that 2 × 3 = 3 × 2 but 6 ÷ 3 does not equal 3 ÷ 6; demonstrating that 2 × 2 × 3 = 12 and 2 × 3 × 2 = 12 and 3 × 2 × 2 = 12; and understanding that 8 ÷ 2 ÷ 2 = (8 ÷ 2) ÷ 2 = 2 but 8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8</li>
<li>using materials, diagrams or arrays to recognise and explain the distributive property, for example, where 4 × 13 = 4 × 10 + 4 × 3</li>
<li>constructing equivalent number sentences involving multiplication to form a numerical equation, and applying knowledge of factors, multiples and the associative property to find unknown values in numerical equations; for example, considering 3 × 4 = 12 and knowing 2 × 2 = 4, then 3 × 4 can be written as 3 × (2 × 2) and, using the associative property, (3 × 2) × 2 so 3 × 4 = 6 × 2 and so 6 is the solution to 3 × 4 = □ × 2</li>
</ul>
Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including simple financial planning contexts; formulate the problems, choosing operations and efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation
<ul>
<li>modelling an everyday situation and determining which operations can be used to solve it using materials, diagrams, arrays and/or bar models to represent the problem; formulating the situation as a number sentence; and justifying their choice of operations in relation to the situation</li>
<li>modelling a series of contextual problems, deciding whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved</li>
<li>modelling financial situations such as creating financial plans; for example, creating a budget for a class fundraising event, using a spreadsheet to tabulate data and perform calculations</li>
<li>investigating how mathematical models involving combinations of operations can be used to represent songs, stories and/or dances of Aboriginal and Torres Strait Islander Peoples</li>
</ul>
Check and explain the reasonableness of solutions to problems, including financial contexts using estimation strategies appropriate to the context
<ul>
<li>interpreting a series of contextual problems to decide whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved</li>
<li>recognising the effect of rounding addition, subtraction, multiplication and division calculations, and rounding both numbers up, both numbers down, and one number up and one number down; and explaining which estimation is the best approximation and why</li>
<li>considering the type of rounding that is appropriate when estimating the amount of money required; for example, rounding up or rounding down when buying one item from a store using cash, compared to rounding up the cost of every item when buying groceries to estimate the total cost and not rounding when the financial transactions are digital</li>
</ul>
Solve problems involving division, choosing efficient mental and written strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction
<ul>
<li>interpreting and solving everyday division problems such as ‘How many buses are needed if there are 436 passengers and each bus carries 50 people?’, deciding whether to round up or down in order to accommodate the remainder and justifying choices</li>
<li>solving division problems mentally, such as 72 divided by 9, 72 ÷ 9, by thinking, ‘How many nines make 72?’, □ x 9 = 72, or ‘Share 72 equally 9 ways’</li>
<li>using the fact that equivalent division calculations result if both numbers are divided by the same factor</li>
</ul>
Solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient mental and written calculation strategies and using digital tools where appropriate; check the reasonableness of answers
<ul>
<li>solving multiplication problems such as 253 × 4 using a doubling strategy, for example, 2 × 253 = 506 and 2 × 506 = 1012</li>
<li>solving multiplication problems like 15 × 16 by thinking of factors of both numbers, 15 = 3 × 5, 16 = 2 × 8, and rearranging the factors to make the calculation easier, 5 × 2 = 10, 3 × 8 = 24 and 10 × 24 = 240</li>
<li>using an array to show place value partitioning to solve multiplication, such as 324 × 8, thinking 300 × 8 = 2400, 20 × 8 = 160, 4 × 8 = 32 then adding the parts, 2400 + 160 + 32 = 2592; and connecting the parts of the array to a standard written algorithm</li>
<li>using different strategies used to multiply numbers, and explaining how they work and if they have any limitations; for example, discussing how the Japanese visual method for multiplication is not effective for multiplying larger numbers</li>
</ul>
Solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies
<ul>
<li>using different ways to add and subtract fractional amounts by subdividing different models of measurement attributes; for example, adding half an hour and three-quarters of an hour using a clock face, adding a 3/4 cup of flour and a 1/4 cup of flour, subtracting 3/4 of a metre from 2 1/4 metres</li>
<li>representing and solving addition and subtraction problems involving fractions by using jumps on a number line, or bar models, or making diagrams of fractions as parts of shapes</li>
<li>using materials, diagrams, number lines or arrays to show and explain that fraction number sentences can be rewritten in equivalent forms without changing the quantity, for example, 1/2 + 1/4 is the same as 2/4 + 1/4</li>
</ul>
Compare and order common unit fractions with the same and related denominators, including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line
<ul>
<li>using pattern blocks to represent equivalent fractions; selecting one block or a combination of blocks to represent one whole, and making a design with shapes; and recording the fractions to justify the total</li>
<li>creating a fraction wall from paper tape to model and compare a range of different fractions with related denominators, and using the model to play fraction wall games</li>
<li>connecting a fraction wall model and a number line model of fractions to say how they are the same and how they are different; for example, explaining 1/4 on a fraction wall represents the area of one-quarter of the whole, while on the number line 1/4 is identified as a point that is one-quarter of the distance between zero and one</li>
<li>using an understanding of factors and multiples as well as equivalence to recognise efficient methods for the location of fractions with related denominators on parallel number lines; for example, explaining on parallel number lines that 2/10 is located at the same position on a parallel number line as 1/5 because 1/5 is equivalent to 2/10</li>
<li>converting between mixed numerals and improper fractions to assist with locating them on a number line</li>
</ul>
Express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another
<ul>
<li>using a certain number of blocks to form different rectangles and using these to list all possible factors for that number; for example, 12 blocks can form the following rectangles: 1 × 12, 2 × 6 and 3 × 4</li>
<li>researching divisibility tests and explaining each rule using materials; for example, using base-10 blocks to test if numbers are divisible by 2, 5 and 10</li>
<li>using divisibility tests to determine if larger numbers are multiples of one-digit numbers; for example, testing if 89 472 is divisible by 3 using 8 + 9 + 4 + 7 + 2 = 30, as 30 is divisible by 3 then 89 472 is a multiple of 3</li>
<li>demonstrating and reasoning that all multiples can be formed by combining or regrouping; for example, multiples of 7 can be formed by combining a multiple of 2 with the corresponding multiple of 5: 3 × 7 = 3 × 2 + 3 × 5, and 4 × 7 = 4 × 2 + 4 × 5</li>
</ul>
Interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line
<ul>
<li>making models of decimals including tenths, hundredths and thousandths by subdividing materials or grids, and explaining the multiplicative relationship between consecutive places; for example, explaining that thousandths are 10 times smaller than hundredths, or writing numbers into a place value chart to compare and order them</li>
<li>renaming decimals to assist with mental computation; for example, when asked to solve 0.6 ÷ 10 they rename 6 tenths as 60 hundredths and say, ‘If I divide 60 hundredths by 10, I get 6 hundredths’ and write 0.6 ÷ 10 = 0.06</li>
<li>using a number line or number track to represent and locate decimals with varying numbers of decimal places and numbers greater than one and justifying the placement; for example, 2.335 is halfway between 2.33 and 2.34, that is, 2.33 < 2.335 < 2.34, and 5.283 is between 5.28 and 5.29 but closer to 5.28</li>
<li>interpreting and comparing the digits in decimal measures, for example, the length or mass of animals or plants, such as a baby echidna weighing 1.78 kilograms and a platypus weighing 1.708 kilograms</li>
<li>interpreting plans or diagrams showing length measures as decimals, placing the numbers into a decimal place value chart to connect the digits to their value</li>
</ul>
Choose appropriate metric units when measuring the length, mass and capacity of objects; use smaller units or a combination of units to obtain a more accurate measure
Describe and perform translations, reflections and rotations of shapes, using dynamic geometric software where appropriate; recognise what changes and what remains the same, and identify any symmetries
Recognise that probabilities lie on numerical scales of 0 – 1 or 0% – 100% and use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals
Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems, choosing operations and efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms
Solve problems involving division, choosing efficient strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction
Solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers
Compare and order fractions with the same and related denominators including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line
Interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line
Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division
Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies
20 Numeracy Exit Ticket activities for students to provide evidence of their learning progress.
This teaching resource is an assessment tool for students to show evidence of their learning. Use Exit Tickets after a numeracy skill has been taught to show evidence that they have acquired the skill and are ready to move to the next learning goal.
These Numeracy Exit tickets collect evidence for basic Year 5 curriculum requirements. Use the editable Word version to create your own class-specific learning goals.
Describe probabilities using fractions, decimals and percentages; recognise that probabilities lie on numerical scales of 0–1 or 0%–100%; use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals
<ul>
<li>recognising that the probability of an event occurring can be represented numerically as either a number ranging from zero to one or a percentage from 0% to 100% where zero or 0% means it will not happen and one or 100% means it is certain to happen</li>
<li>using a scale of zero to one or 0% to 100% to estimate chances of events</li>
<li>listing the different possible outcomes for rolling a dice and using a scale to locate the relative probability by considering the chance of more than or less than for each possible event, for example, the probability of getting a number greater than 4</li>
<li>recognising the language used to describe situations involving uncertainty, such as what it means to be ‘lucky’, a ‘75% chance’ of rain or a ‘1-in-100 years’ flood</li>
<li>exploring Aboriginal and/or Torres Strait Islander children’s instructive games, such as Weme from the Warlpiri Peoples of Central Australia, to investigate and assign probabilities that events will occur, indicating their estimated likelihood</li>
</ul>
List the possible outcomes of chance experiments involving equally likely outcomes and compare to those that are not equally likely
<ul>
<li>discussing what it means for outcomes to be equally likely and comparing the number of possible and equally likely outcomes of chance events; for example, when drawing a card from a standard deck of cards there are 4 possible outcomes if you are interested in the suit, 2 possible outcomes if you are interested in the colour or 52 outcomes if you are interested in the exact card</li>
<li>discussing how chance experiments that have equally likely outcomes can be referred to as random chance events; for example, if all the names of students in a class are placed in a hat and one is drawn at random, each person has an equally likely chance of being drawn</li>
<li>commenting on the chance of winning games by considering the number of possible outcomes and the consequent chance of winning</li>
<li>investigating why some games are fair and others are not; for example, drawing a track game to resemble a running race and taking it in turns to roll 2 dice, where the first runner moves a square if the difference between the 2 dice is zero, one or 2 and the second runner moves a square if the difference is 3, 4 or 5, and responding to the questions ‘Is this game fair?’, ‘Are some differences more likely to come up than others?’ and ‘How can you work that out?’</li>
<li>comparing the chance of a head or a tail when a coin is tossed, whether some numbers on a dice are more likely to be facing up when the dice is rolled, or the chance of getting a 1, 2 or 3 on a spinner with uneven regions for the numbers</li>
<li>discussing supermarket promotions such as collecting stickers or objects and whether there is an equal chance of getting each of them</li>
</ul>
Describe and perform translations, reflections and rotations of shapes, using dynamic geometry software where appropriate; recognise what changes and what remains the same, and identify any symmetries
<ul>
<li>understanding and explaining that translations, rotations and reflections can change the position and orientation of a shape but not its shape or size</li>
<li>using pattern blocks and paper, tracing around a shape and then conducting a series of one-step transformations and tracing each resulting image, and then finally copying the original position and end position on a new sheet of paper</li>
<li>demonstrating how different combinations of transformations can produce the same resulting image</li>
<li>challenging classmates to select a combination of transformations to move from an original image to the final image, noting the different combinations by using different colours to trace images</li>
<li>investigating how animal tracks can be interpreted by Aboriginal and Torres Strait Islander Peoples using the transformation of their shapes, to help determine and understand animal behaviour</li>
</ul>
Estimate, construct and measure angles in degrees, using appropriate tools, including a protractor, and relate these measures to angle names
<ul>
<li>using a protractor to measure angles in degrees and classifying these angles using angle names; for example, an acute angle is less than 90°, an obtuse angle is more than 90° and less than 180°, a right angle is equal to 90° and a reflex angle is more than 180° and less than 360°</li>
<li>estimating the size of angles in the environment using a clinometer and describing the angles using angle names</li>
<li>using a ruler and protractor to construct triangles, given the angle measures and side lengths</li>
<li>using a protractor to measure angles when creating a pattern or string design within a circle</li>
<li>recognising the size of angles within shapes that do and do not tessellate, measuring the angles and using the sum of angles to explain why some shapes will tessellate and other shapes do not</li>
</ul>
Compare 12- and 24-hour time systems and solve practical problems involving the conversion between them
<ul>
<li>using timetables written in 24-hour time, such as flight schedules, to plan an overseas or interstate trip, converting between 24- and 12-hour time</li>
<li>converting between the digital and analog representation of 24-hour time, matching the same times represented in both systems; for example, setting the time on an analog watch from a digital alarm clock</li>
</ul>
Solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units
<ul>
<li>investigating problem situations involving perimeter, for example, ‘How many metres of fencing are required around a paddock, or around a festival event?’</li>
<li>using efficient ways to calculate the perimeters of rectangles, such as adding the length and width together and doubling the result</li>
<li>solving measurement problems such as ‘How much carpet would be needed to cover the entire floor of the classroom?’, using square metre templates to directly measure the floor space</li>
<li>creating a model of a permaculture garden, dividing the area up to provide the most efficient use of space for gardens and walkways, labelling the measure of each area, and calculating the amount of resources needed, for example, compost to cover the vegetable garden</li>
<li>using a physical geoboard or a virtual geoboard app to recognise the relationship between area and perimeter and solve problems; for example, investigating what is the largest and what is the smallest area that has the same perimeter</li>
<li>exploring the designs of fishing nets and dwellings of Aboriginal and Torres Strait Islander Peoples, investigating the perimeter, area and purpose of the shapes within the designs</li>
</ul>
Choose appropriate metric units when measuring the length, mass and capacity of objects; use smaller units or a combination of units to obtain a more accurate measure
<ul>
<li>ordering metric units from the largest unit to the smallest, for example, kilometre, metre, centimetre, millimetre</li>
<li>recognising that some units of measurement are better suited to some tasks than others; for example, kilometres are more appropriate than metres to measure the distance between 2 towns</li>
<li>deciding on the unit required to estimate the amount of paint or carpet for a room or a whole building, and justifying the choice of unit in relation to the context and the degree of accuracy required</li>
<li>measuring and comparing distances (for example, measuring and comparing jumps or throws using a metre length of string and then measuring the part metre with centimetres and/or millimetres) and explaining which unit of measure is most accurate</li>
<li>researching how the base units are derived for the International System of Units (SI), commonly known as the metric system of units, recognising that the metric unit names for the attributes of length and mass are international standards for measurement</li>
</ul>
Find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations
<ul>
<li>using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that 3 × 5 = 15 and 30 ÷ 2 = 15, then 3 × 5 = 30 ÷ 2, and therefore the solution to 3 × 5 = 30 ÷ □ is 2</li>
<li>using relational thinking, and an understanding of equivalence and number properties to determine and reason about numerical equations; for example, explaining whether an equation involving equivalent multiplication number sentences is true, such as 15 ÷ 3 = 30 ÷ 6</li>
<li>using materials, diagrams and arrays to demonstrate that multiplication is associative and commutative but division is not – for example, using arrays to demonstrate that 2 × 3 = 3 × 2 but 6 ÷ 3 does not equal 3 ÷ 6; demonstrating that 2 × 2 × 3 = 12 and 2 × 3 × 2 = 12 and 3 × 2 × 2 = 12; and understanding that 8 ÷ 2 ÷ 2 = (8 ÷ 2) ÷ 2 = 2 but 8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8</li>
<li>using materials, diagrams or arrays to recognise and explain the distributive property, for example, where 4 × 13 = 4 × 10 + 4 × 3</li>
<li>constructing equivalent number sentences involving multiplication to form a numerical equation, and applying knowledge of factors, multiples and the associative property to find unknown values in numerical equations; for example, considering 3 × 4 = 12 and knowing 2 × 2 = 4, then 3 × 4 can be written as 3 × (2 × 2) and, using the associative property, (3 × 2) × 2 so 3 × 4 = 6 × 2 and so 6 is the solution to 3 × 4 = □ × 2</li>
</ul>
Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including simple financial planning contexts; formulate the problems, choosing operations and efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation
<ul>
<li>modelling an everyday situation and determining which operations can be used to solve it using materials, diagrams, arrays and/or bar models to represent the problem; formulating the situation as a number sentence; and justifying their choice of operations in relation to the situation</li>
<li>modelling a series of contextual problems, deciding whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved</li>
<li>modelling financial situations such as creating financial plans; for example, creating a budget for a class fundraising event, using a spreadsheet to tabulate data and perform calculations</li>
<li>investigating how mathematical models involving combinations of operations can be used to represent songs, stories and/or dances of Aboriginal and Torres Strait Islander Peoples</li>
</ul>
Check and explain the reasonableness of solutions to problems, including financial contexts using estimation strategies appropriate to the context
<ul>
<li>interpreting a series of contextual problems to decide whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved</li>
<li>recognising the effect of rounding addition, subtraction, multiplication and division calculations, and rounding both numbers up, both numbers down, and one number up and one number down; and explaining which estimation is the best approximation and why</li>
<li>considering the type of rounding that is appropriate when estimating the amount of money required; for example, rounding up or rounding down when buying one item from a store using cash, compared to rounding up the cost of every item when buying groceries to estimate the total cost and not rounding when the financial transactions are digital</li>
</ul>
Solve problems involving division, choosing efficient mental and written strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction
<ul>
<li>interpreting and solving everyday division problems such as ‘How many buses are needed if there are 436 passengers and each bus carries 50 people?’, deciding whether to round up or down in order to accommodate the remainder and justifying choices</li>
<li>solving division problems mentally, such as 72 divided by 9, 72 ÷ 9, by thinking, ‘How many nines make 72?’, □ x 9 = 72, or ‘Share 72 equally 9 ways’</li>
<li>using the fact that equivalent division calculations result if both numbers are divided by the same factor</li>
</ul>
Solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient mental and written calculation strategies and using digital tools where appropriate; check the reasonableness of answers
<ul>
<li>solving multiplication problems such as 253 × 4 using a doubling strategy, for example, 2 × 253 = 506 and 2 × 506 = 1012</li>
<li>solving multiplication problems like 15 × 16 by thinking of factors of both numbers, 15 = 3 × 5, 16 = 2 × 8, and rearranging the factors to make the calculation easier, 5 × 2 = 10, 3 × 8 = 24 and 10 × 24 = 240</li>
<li>using an array to show place value partitioning to solve multiplication, such as 324 × 8, thinking 300 × 8 = 2400, 20 × 8 = 160, 4 × 8 = 32 then adding the parts, 2400 + 160 + 32 = 2592; and connecting the parts of the array to a standard written algorithm</li>
<li>using different strategies used to multiply numbers, and explaining how they work and if they have any limitations; for example, discussing how the Japanese visual method for multiplication is not effective for multiplying larger numbers</li>
</ul>
Solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies
<ul>
<li>using different ways to add and subtract fractional amounts by subdividing different models of measurement attributes; for example, adding half an hour and three-quarters of an hour using a clock face, adding a 3/4 cup of flour and a 1/4 cup of flour, subtracting 3/4 of a metre from 2 1/4 metres</li>
<li>representing and solving addition and subtraction problems involving fractions by using jumps on a number line, or bar models, or making diagrams of fractions as parts of shapes</li>
<li>using materials, diagrams, number lines or arrays to show and explain that fraction number sentences can be rewritten in equivalent forms without changing the quantity, for example, 1/2 + 1/4 is the same as 2/4 + 1/4</li>
</ul>
Compare and order common unit fractions with the same and related denominators, including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line
<ul>
<li>using pattern blocks to represent equivalent fractions; selecting one block or a combination of blocks to represent one whole, and making a design with shapes; and recording the fractions to justify the total</li>
<li>creating a fraction wall from paper tape to model and compare a range of different fractions with related denominators, and using the model to play fraction wall games</li>
<li>connecting a fraction wall model and a number line model of fractions to say how they are the same and how they are different; for example, explaining 1/4 on a fraction wall represents the area of one-quarter of the whole, while on the number line 1/4 is identified as a point that is one-quarter of the distance between zero and one</li>
<li>using an understanding of factors and multiples as well as equivalence to recognise efficient methods for the location of fractions with related denominators on parallel number lines; for example, explaining on parallel number lines that 2/10 is located at the same position on a parallel number line as 1/5 because 1/5 is equivalent to 2/10</li>
<li>converting between mixed numerals and improper fractions to assist with locating them on a number line</li>
</ul>
Express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another
<ul>
<li>using a certain number of blocks to form different rectangles and using these to list all possible factors for that number; for example, 12 blocks can form the following rectangles: 1 × 12, 2 × 6 and 3 × 4</li>
<li>researching divisibility tests and explaining each rule using materials; for example, using base-10 blocks to test if numbers are divisible by 2, 5 and 10</li>
<li>using divisibility tests to determine if larger numbers are multiples of one-digit numbers; for example, testing if 89 472 is divisible by 3 using 8 + 9 + 4 + 7 + 2 = 30, as 30 is divisible by 3 then 89 472 is a multiple of 3</li>
<li>demonstrating and reasoning that all multiples can be formed by combining or regrouping; for example, multiples of 7 can be formed by combining a multiple of 2 with the corresponding multiple of 5: 3 × 7 = 3 × 2 + 3 × 5, and 4 × 7 = 4 × 2 + 4 × 5</li>
</ul>
Interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line
<ul>
<li>making models of decimals including tenths, hundredths and thousandths by subdividing materials or grids, and explaining the multiplicative relationship between consecutive places; for example, explaining that thousandths are 10 times smaller than hundredths, or writing numbers into a place value chart to compare and order them</li>
<li>renaming decimals to assist with mental computation; for example, when asked to solve 0.6 ÷ 10 they rename 6 tenths as 60 hundredths and say, ‘If I divide 60 hundredths by 10, I get 6 hundredths’ and write 0.6 ÷ 10 = 0.06</li>
<li>using a number line or number track to represent and locate decimals with varying numbers of decimal places and numbers greater than one and justifying the placement; for example, 2.335 is halfway between 2.33 and 2.34, that is, 2.33 < 2.335 < 2.34, and 5.283 is between 5.28 and 5.29 but closer to 5.28</li>
<li>interpreting and comparing the digits in decimal measures, for example, the length or mass of animals or plants, such as a baby echidna weighing 1.78 kilograms and a platypus weighing 1.708 kilograms</li>
<li>interpreting plans or diagrams showing length measures as decimals, placing the numbers into a decimal place value chart to connect the digits to their value</li>
</ul>
Choose appropriate metric units when measuring the length, mass and capacity of objects; use smaller units or a combination of units to obtain a more accurate measure
Describe and perform translations, reflections and rotations of shapes, using dynamic geometric software where appropriate; recognise what changes and what remains the same, and identify any symmetries
Recognise that probabilities lie on numerical scales of 0 – 1 or 0% – 100% and use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals
Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems, choosing operations and efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms
Solve problems involving division, choosing efficient strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction
Solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers
Compare and order fractions with the same and related denominators including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line
Interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line
Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division
Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies
Use estimation and rounding to check the reasonableness of answers to calculations
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Thank you for another helpful resource. These Exit Tickets can be useful for pre- and post testing or fast finisher work.
Paul (Teach Starter)
·
You're most welcome, Zuriette! Thank you for sharing your tip on how the exit tickets can be used!
ST Mary MacKillop College
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I love the idea of Exit tickets and am going to use them this semester. Are you planning to create more please?
Janeen
·
Hi ST Mary MacKillop College
Thanks for getting in touch with us!
Might I suggest that you make a new resource request and list specifically what you were after? You can do so on our Requests page. https://www.teachstarter.com/request-a-resource/
Your fellow Teach Starter members can then vote for it and, if it proves popular, we would love to make it for you!
Kind regards
Janeen
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Thank you for another helpful resource. These Exit Tickets can be useful for pre- and post testing or fast finisher work.
You're most welcome, Zuriette! Thank you for sharing your tip on how the exit tickets can be used!
I love the idea of Exit tickets and am going to use them this semester. Are you planning to create more please?
Hi ST Mary MacKillop College Thanks for getting in touch with us! Might I suggest that you make a new resource request and list specifically what you were after? You can do so on our Requests page. https://www.teachstarter.com/request-a-resource/ Your fellow Teach Starter members can then vote for it and, if it proves popular, we would love to make it for you! Kind regards Janeen