Curriculum Topics Directory

recognise, represent and order numbers to at least 120 using physical and virtual materials, numerals, number lines and charts

partition one- and two-digit numbers in different ways using physical and virtual materials, including partitioning two-digit numbers into tens and ones

quantify sets of objects, to at least 120, by partitioning collections into equal groups using number knowledge and skip counting

add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies

use mathematical modelling to solve practical problems involving additive situations including simple money transactions; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem

use mathematical modelling to solve practical problems involving equal sharing and grouping; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem

recognise, continue and create pattern sequences, with numbers, symbols, shapes and objects, formed by skip counting, initially by twos, fives and tens

recognise, continue and create repeating patterns with numbers, symbols, shapes and objects, identifying the repeating unit

compare directly and indirectly and order objects and events using attributes of length, mass, capacity and duration, communicating reasoning

measure the length of shapes and objects using informal units, recognising that units need to be uniform and used end-to-end

describe the duration and sequence of events using years, months, weeks, days and hours

make, compare and classify familiar shapes; recognise familiar shapes and objects in the environment, identifying the similarities and differences between them

give and follow directions to move people and objects to different locations within a space

acquire and record data for categorical variables in various ways including using digital tools, objects, images, drawings, lists, tally marks and symbols

represent collected data for a categorical variable using one-to-one displays and digital tools where appropriate; compare the data using frequencies and discuss the findings

recognise, represent and order numbers to at least 1000 using physical and virtual materials, numerals and number lines

partition, rearrange, regroup and rename two- and three-digit numbers using standard and non-standard groupings; recognise the role of a zero digit in place value notation

recognise and describe one-half as one of 2 equal parts of a whole and connect halves, quarters and eighths through repeated halving

add and subtract one- and two-digit numbers, representing problems using number sentences, and solve using part-part-whole reasoning and a variety of calculation strategies

multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies

use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the situation

recognise, describe and create additive patterns that increase or decrease by a constant amount, using numbers, shapes and objects, and identify missing elements in the pattern

recall and demonstrate proficiency with addition facts to 20; extend and apply facts to develop related subtraction facts

recall and demonstrate proficiency with multiplication facts for twos; extend and apply facts to develop the related division facts using doubling and halving

measure and compare objects based on length, capacity and mass using appropriate uniform informal units and smaller units for accuracy when necessary

identify common uses and represent halves, quarters and eighths in relation to shapes, objects and events

identify the date and determine the number of days between events using calendars

recognise and read the time represented on an analog clock to the hour, half-hour and quarter-hour

identify, describe and demonstrate quarter, half, three-quarter and full measures of turn in everyday situations

recognise, compare and classify shapes, referencing the number of sides and using spatial terms such as “opposite”, “parallel”, “curved” and “straight”

locate positions in two-dimensional representations of a familiar space; move positions by following directions and pathways

acquire data for categorical variables through surveys, observation, experiment and using digital tools; sort data into relevant categories and display data using lists and tables

create different graphical representations of data using software where appropriate; compare the different representations, identify and describe common and distinctive features in response to questions

recognise, represent and order natural numbers using naming and writing conventions for numerals beyond 10 000

recognise and represent unit fractions including \(\frac12\), \(\frac13\), \(\frac14\), \(\frac15\) and \(\frac1{10}\) and their multiples in different ways; combine fractions with the same denominator to complete the whole

add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator

multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies

estimate the quantity of objects in collections and make estimates when solving problems to determine the reasonableness of calculations

use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation

follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns

recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences

extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator

recall and demonstrate proficiency with multiplication facts for \(3, 4, 5\) and \(10\); extend and apply facts to develop the related division facts

identify which metric units are used to measure everyday items; use measurements of familiar items and known units to make estimates

measure and compare objects using familiar metric units of length, mass and capacity, and instruments with labelled markings

recognise and use the relationship between formal units of time including days, hours, minutes and seconds to estimate and compare the duration of events

describe the relationship between the hours and minutes on analog and digital clocks, and read the time to the nearest minute

identify angles as measures of turn and compare angles with right angles in everyday situations

recognise the relationships between dollars and cents and represent money values in different ways

make, compare and classify objects, identifying key features and explaining why these features make them suited to their uses

interpret and create two-dimensional representations of familiar environments, locating key landmarks and objects relative to each other

acquire data for categorical and discrete numerical variables to address a question of interest or purpose by observing, collecting and accessing data sets; record the data using appropriate methods including frequency tables and spreadsheets

create and compare different graphical representations of data sets including using software where appropriate; interpret the data in terms of the context

conduct guided statistical investigations involving the collection, representation and interpretation of data for categorical and discrete numerical variables with respect to questions of interest

identify practical activities and everyday events involving chance; describe possible outcomes and events as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ explaining reasoning

conduct repeated chance experiments; identify and describe possible outcomes, record the results, recognise and discuss the variation

recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals

explain and use the properties of odd and even numbers

find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation

count by fractions including mixed numerals; locate and represent these fractions as numbers on number lines

solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits

develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder

choose and use estimation and rounding to check and explain the reasonableness of calculations including the results of financial transactions

use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation

follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns

find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations

recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator

interpret unmarked and partial units when measuring and comparing attributes of length, mass, capacity, duration and temperature, using scaled and digital instruments and appropriate units

recognise ways of measuring and approximating the perimeter and area of shapes and enclosed spaces, using appropriate formal and informal units

solve problems involving the duration of time including situations involving “am” and “pm” and conversions between units of time

estimate and compare angles using angle names including acute, obtuse, straight angle, reflex and revolution, and recognise their relationship to a right angle

represent and approximate composite shapes and objects in the environment, using combinations of familiar shapes and objects

create and interpret grid reference systems using grid references and directions to locate and describe positions and pathways

recognise line and rotational symmetry of shapes and create symmetrical patterns and pictures, using dynamic geometric software where appropriate

acquire data for categorical and discrete numerical variables to address a question of interest or purpose, using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information that has been created

analyse the effectiveness of different displays or visualisations in illustrating and comparing data distributions, then discuss the shape of distributions and the variation in the data

conduct statistical investigations, collecting data through survey responses and other methods; record and display data using digital tools; interpret the data and communicate the results

describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring; identify independent or dependent events

conduct repeated chance experiments to observe relationships between outcomes; identify and describe the variation in results

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

express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another

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

recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents

solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies

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

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

check and explain the reasonableness of solutions to problems including financial contexts using estimation strategies appropriate to the context

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 of the situation

create and use algorithms involving a sequence of steps and decisions and digital tools to experiment with factors, multiples and divisibility; identify, interpret and describe emerging patterns

recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts

find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations

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

solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units

compare 12- and 24-hour time systems and solve practical problems involving the conversion between them

estimate, construct and measure angles in degrees, using appropriate tools including a protractor, and relate these measures to angle names

connect objects to their nets and build objects from their nets using spatial and geometric reasoning

construct a grid coordinate system that uses coordinates to locate positions within a space; use coordinates and directional language to describe position and movement

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

acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables, to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data

interpret line graphs representing change over time; discuss the relationships that are represented and conclusions that can be made

plan and conduct statistical investigations by posing questions or identifying a problem and collecting relevant data; choose appropriate displays and interpret the data; communicate findings within the context of the investigation

list the possible outcomes of chance experiments involving equally likely outcomes and compare to those which are not equally likely

conduct repeated chance experiments including those with and without equally likely outcomes, observe and record the results; use frequency to compare outcomes and estimate their likelihoods

recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane

identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations

apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order

apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers

solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions

multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers

solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies and using digital tools where appropriate

approximate numerical solutions to problems involving rational numbers and percentages, including financial contexts, using appropriate estimation strategies

use mathematical modelling to solve practical problems involving natural and rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made

recognise and use rules that generate visually growing patterns and number patterns involving rational numbers

find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations

create and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns

convert between common metric units of length, mass and capacity; choose and use decimal representations of metric measurements relevant to the context of a problem

establish the formula for the area of a rectangle and use it to solve practical problems

interpret and use timetables and itineraries to plan activities and determine the duration of events and journeys

identify the relationships between angles on a straight line, angles at a point and vertically opposite angles; use these to determine unknown angles, communicating reasoning

compare the parallel cross-sections of objects and recognise their relationships to right prisms

locate points in the 4 quadrants of a Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the plane

recognise and use combinations of transformations to create tessellations and other geometric patterns, using dynamic geometric software where appropriate

interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using comparative displays or visualisations and digital tools; compare distributions in terms of mode, range and shape

identify statistically informed arguments presented in traditional and digital media; discuss and critique methods, data representations and conclusions

plan and conduct statistical investigations by posing and refining questions or identifying a problem and collecting relevant data; analyse and interpret the data and communicate findings within the context of the investigation

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

conduct repeated chance experiments and run simulations with an increasing number of trials using digital tools; compare observations with expected results and discuss the effect on variation of increasing the number of trials

describe the relationship between perfect square numbers and square roots, and use squares of numbers and square roots of perfect square numbers to solve problems

represent natural numbers as products of powers of prime numbers using exponent notation

represent natural numbers in expanded notation using place value and powers of 10

find equivalent representations of rational numbers and represent rational numbers on a number line

round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions

use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies

compare, order and solve problems involving addition and subtraction of integers

recognise, represent and solve problems involving ratios

use mathematical modelling to solve practical problems, involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation

recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown

formulate algebraic expressions using constants, variables, operations and brackets

solve one-variable linear equations with natural number solutions; verify the solution by substitution

describe relationships between variables represented in graphs of functions from authentic data

generate tables of values from visually growing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane

manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables

solve problems involving the area of triangles and parallelograms using established formulas and appropriate units

solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units

describe the relationship between \(π\) and the features of circles including the circumference, radius and diameter

identify corresponding, alternate and co-interior relationships between angles formed when parallel lines are crossed by a transversal; use them to solve problems and explain reasons

demonstrate that the interior angle sum of a triangle in the plane is 180° and apply this to determine the interior angle sum of other shapes and the size of unknown angles

use mathematical modelling to solve practical problems involving ratios; formulate problems, interpret and communicate solutions in terms of the situation, justifying choices made about the representation

represent objects in 2 dimensions; discuss and reason about the advantages and disadvantages of different representations

classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships

describe transformations of a set of points using coordinates in the Cartesian plane, translations and reflections on an axis, and rotations about a given point

design and create algorithms involving a sequence of steps and decisions that will sort and classify sets of shapes according to their attributes, and describe how the algorithms work

acquire data sets for discrete and continuous numerical variables and calculate the range, median, mean and mode; make and justify decisions about which measures of central tendency provide useful insights into the nature of the distribution of data

create different types of numerical data displays including stem-and-leaf plots using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and mode

plan and conduct statistical investigations involving data for discrete and continuous numerical variables; analyse and interpret distributions of data and report findings in terms of shape and summary statistics

identify the sample space for single-stage events; assign probabilities to the outcomes of these events and predict relative frequencies for related events

conduct repeated chance experiments and run simulations with a large number of trials using digital tools; compare predictions about outcomes with observed results, explaining the differences

recognise irrational numbers in applied contexts, including square roots and \(π\)

establish and apply the exponent laws with positive integer exponents and the zero-exponent, using exponent notation with numbers

recognise terminating and recurring decimals, using digital tools as appropriate

use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate

use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model

create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties

graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution

use mathematical modelling to solve applied problems involving linear relations, including financial contexts; formulate problems with linear functions, choosing a representation; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model

experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns

solve problems involving the area and perimeter of irregular and composite shapes using appropriate units

solve problems involving the volume and capacity of right prisms using appropriate units

solve problems involving the circumference and area of a circle using formulas and appropriate units

solve problems involving duration, including using 12- and 24-hour time across multiple time zones

recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure

use Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles

use mathematical modelling to solve practical problems involving ratios and rates, including financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model

identify the conditions for congruence and similarity of triangles and explain the conditions for other sets of common shapes to be congruent or similar, including those formed by transformations

establish properties of quadrilaterals using congruent triangles and angle properties, and solve related problems explaining reasoning

describe the position and location of objects in 3 dimensions in different ways, including using a three-dimensional coordinate system with the use of dynamic geometric software and other digital tools

design, create and test algorithms involving a sequence of steps and decisions that identify congruency or similarity of shapes, and describe how the algorithm works

investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques

analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques to select and study samples

compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation

plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences about the population and report findings, acknowledging uncertainty

recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts

determine all possible combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific outcomes in practical situations

conduct repeated chance experiments and simulations, using digital tools to determine probabilities for compound events, and describe results

recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools

apply the exponent laws to numerical expressions with integer exponents and extend to variables

simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions

find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane

identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate

use mathematical modelling to solve applied problems involving change including financial contexts; formulate problems, choosing to use either linear or quadratic functions; interpret solutions in terms of the situation; evaluate the model and report methods and findings

experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns

solve problems involving the volume and surface area of right prisms and cylinders using appropriate units

solve problems involving very small and very large measurements, time scales and intervals expressed in scientific notation

solve spatial problems, applying angle properties, scale, similarity, Pythagoras’ theorem and trigonometry in right-angled triangles

calculate and interpret absolute, relative and percentage errors in measurements, recognising that all measurements are estimates

use mathematical modelling to solve practical problems involving direct proportion, rates, ratio and scale, including financial contexts; formulate the problems and interpret solutions in terms of the situation; evaluate the model and report methods and findings

recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity

apply the enlargement transformation to shapes and objects using dynamic geometry software as appropriate; identify and explain aspects that remain the same and those that change

design, test and refine algorithms involving a sequence of steps and decisions based on geometric constructions and theorems; discuss and evaluate refinements

analyse reports of surveys in digital media and elsewhere for information on how data was obtained to estimate population means and medians

analyse how different sampling methods can affect the results of surveys and how choice of representation can be used to support a particular point of view

represent the distribution of multiple data sets for numerical variables using comparative representations; compare data distributions with consideration of centre, spread and shape, and the effect of outliers on these measures

choose appropriate forms of display or visualisation for a given type of data; justify selections and interpret displays for a given context

plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions

list all outcomes for compound events both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes

calculate relative frequencies from given or collected data to estimate probabilities of events involving “and”, inclusive “or” and exclusive “or”

design and conduct repeated chance experiments and simulations, using digital tools to compare probabilities of simple events to related compound events, and describe results

recognise the effect of using approximations of real numbers in repeated calculations and compare the results when using exact representations

expand, factorise and simplify expressions and solve equations algebraically, applying exponent laws involving products, quotients and powers of variables, and the distributive property

solve linear inequalities and simultaneous linear equations in 2 variables; interpret solutions graphically and communicate solutions in terms of the situation

recognise the connection between algebraic and graphical representations of exponential relations and solve related exponential equations, using digital tools where appropriate

use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; interpret solutions in terms of the situation; evaluate and modify models as necessary and report assumptions, methods and findings

experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns

solve problems involving the surface area and volume of composite objects using appropriate units

interpret and use logarithmic scales  in applied contexts involving small and large quantities and change

solve practical problems applying Pythagoras’ theorem and trigonometry of right-angled triangles, including problems involving direction and angles of elevation and depression

identify the impact of measurement errors on the accuracy of results in practical contexts

use mathematical modelling to solve practical problems involving proportion and scaling of objects; formulate problems and interpret solutions in terms of the situation; evaluate and modify models as necessary, and report assumptions, methods and findings

apply deductive reasoning to proofs involving shapes in the plane and use theorems to solve spatial problems

interpret networks and network diagrams used to represent relationships in practical situations and describe connectedness

design, test and refine solutions to spatial problems using algorithms and digital tools; communicate and justify solutions

analyse claims, inferences and conclusions of statistical reports in the media, including ethical considerations and identification of potential sources of bias

compare data distributions for continuous numerical variables using appropriate data displays including boxplots; discuss the shapes of these distributions in terms of centre, spread, shape and outliers in the context of the data

construct scatterplots and comment on the association between the 2 numerical variables in terms of strength, direction and linearity

construct two-way tables and discuss possible relationship between categorical variables

plan and conduct statistical investigations of situations that involve bivariate data; evaluate and report findings with consideration of limitations of any inferences

use the language of “if ... then”, “given”, “of”, “knowing that” to describe and interpret situations involving conditional probability

design and conduct repeated chance experiments and simulations using digital tools to model conditional probability and interpret results