MATHEMATICS K-12 LEARNING OUTCOMES & BENCHMARKS

Transcription

1 MATHEMATICS K-12 LEARNING OUTCOMES & BENCHMARKS

2 Learning Outcomes and Benchmarks Below you will find the Learning Outcomes and Benchmarks for the International Baccalaureate Primary Years Programme, Middle Years Programme and Diploma Programme at ISS. This document covers the Learning Outcomes and Benchmarks that will be covered from Kindergarten to Grade 12 at ISS. It is an important document in ensuring that the students at ISS have a World Class education. An education that provides an ever deepening level of understanding of the world from when they join us to when they leave. Explanation of terms: Different curriculum use the terms Outcomes and Benchmarks in slightly different ways. At ISS we use the terms to mean: Learning Outcomes: the concepts, skills, attributes and knowledge that a student in the relevant Grade Level is expected to understand, demonstrate and apply. Learning outcomes complete the statement: students will be able to... Benchmarks: specific performance indicators for each grade level Benchmarks complete the statement: students will be able to show their understanding by... It is important to note that a Learning Outcome is not a limitation. Through differentiated teaching teachers ensure that all students are given the maximum opportunity to reach the Learning Outcomes for their Grade Level and to extend those who are capable of surpassing the Learning Outcomes.

3 Learning Outcomes and Benchmarks Subject : MATHEMATICS Strand : NUMBER Grade/Phase Grade 12 Learning Outcome Students will be able to... Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current IB Curriculum Guide documents which can be accessed by the links below; Mathematics Standard Level Mathematics Higher Level Mathematical Studies Further Mathematics Benchmarks: Students will be able to show their understanding by... Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current IB Curriculum Guide documents which can be accessed by the links below; Mathematics Standard Level Mathematics Higher Level Mathematical Studies Further Mathematics Grade 11 Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current IB Curriculum Guide documents which can be accessed by the links below; Mathematics Standard Level Mathematics Higher Level Mathematical Studies Further Mathematics Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current IB Curriculum Guide documents which can be accessed by the links below; Mathematics Standard Level Mathematics Higher Level Mathematical Studies Further Mathematics Grade 10 Express equivalent forms of expressions involving indices and surds classifying numbers from a list, which includes radical numbers such as root(2) as rational or irrational accurately adding, subtracting, multiplying and dividing radical numbers converting accurately between root form and rational exponent form estimating values of numbers with rational exponents using surds within computations, both in root form and with rational exponents using multiplication principles to correctly rationalise denominators for monomial and binomial square root radicals applying all the strategies learned to algebraic expressions which include real number terms converting between negative rational exponents and their positive radical equivalent form applying the laws of exponents to simplify expressions containing positive and negative integer and rational exponents

4 describing the meaning and development of irrational numbers and the relationship between irrational numbers and radicals such as root(2) rationalizing denominators for monomial and binomial square root radicals applying laws of positive and negative rational exponents Grade 9 Extension Perform operations involving complex numbers Number Skills Students will be able to understand the distinction between rational and irrational numbers, make reasonable estimates, compute fluently and solve problems Extension Simplifying surds involving negative roots Solving quadratic equations involving imaginary roots Number Skills recognizing and classifying numbers in different number systems including the set of positive integers and zero (N), integers (Z), rational numbers (Q), irrational numbers (Q ) and real numbers (R) and show visually the relationships amongst the different sets. marking approximate locations of various types of real numbers (including numbers with repeating decimals, fractions, and irrational numbers) on a number line. computing, comparing and ordering real numbers expressed in a variety of forms; and demonstrating the difference between exact and approximate values of equivalent forms of numbers. Exponents Exponents Students will be able to understand positive and negative integer exponents, scientific notation, and exponent laws, make reasonable estimates, compute fluently and solve problems when working with exponents Extension accurately adding, subtracting, multiplying and dividing numbers in scientific notation form, with and without a calculator applying scientific notation to real-life problems Using the rules of indices to simplify numerical expressions involving radicals and fractional exponents

5 Grade 8 Number Skills Understand rational numbers, make reasonable estimates using rounding and significant figures, compute fluently and solve problems when working with rational numbers and begin to develop understanding of irrational numbers Number Skills Identifying numbers as rational or irrational and provide appropriate justification Finding equivalent forms for rational numbers including integers, fractions, repeating and terminating decimals, exponents, scientific notation and square root radicals and convert from one form to another Accurately carrying out multi step operations with rational numbers Making reasonable estimates when finding sums, differences, products and quotients of rational numbers and judge the reasonableness of estimates Solving problems involving application and calculation of simple interest Rounding numbers to a given number of significant figures Exponents Understand positive and negative integer exponents, scientific notation, and exponent laws, make reasonable estimates, compute fluently and solve problems when working with exponents Exponents Applying the laws of exponents to simplify expressions containing integer exponents and zero exponents Using exponents to model simple growth and decay (such as 2 x or 2 -x ) Converting between scientific/standard form (including E notation from scientific calculators) Grade 7 Rational Numbers Understand integers, make reasonable estimates, compute fluently and solve problems when working with rational numbers Rational Numbers Reading, writing, comparing and ordering rational numbers and finding their approximate locations on a number line Accurately carrying out multi step calculations with rational numbers Using common divisibility rules, factors, multiples, and prime factorizations to solve problems including finding greatest common factor (GCF) and lowest common multiple (LCM) Exponents Exponents Using index notation to express and simplify powers of integers

6 Understand positive integer exponents, make reasonable estimates and solve problems when working with exponents Using squares and cubes of integer numbers and square roots in computation Using index notation to express and simplify powers of rational numbers expressed in fractional form including squares, cubes, square roots and cube roots Ratio, Rate and Percentage Understand ratios, rates, percentage and proportions and develop understanding and fluency when applying proportional thinking Ratio, Rate and Percentage Using ratio as a comparison of quantities of the same kind Using rate as a comparison of quantities of different kinds Using proportions as statements of equivalent ratios Using fractions, decimals, and percentage to make estimations and perform calculations Comparing and order fractions, decimals and percentage Developing meaning for percent greater than 100 and less than 1 Calculating a given percentage of a quantity and express one quantity as a percentage of another Calculating the percent increases and decreases of a quantity by using a multiplier Developing, analysing and explaining methods for solving proportions such as equivalent ratios, cross multiplication and scaling Grade 6 Multiples and factors Rounding Identify prime numbers, prime factors and multiples Round to a specific number of places and assess the reasonableness of their results Order of Operations Evaluate calculations with a number of Multiples and factors Rounding Using common divisibility rules, factors, multiples, and prime factorization to solve problems including finding greatest common factor (GCF) and lowest common multiple (LCM) Rounding decimal numbers to a given number of decimal places Using appropriate forms of rounding to estimate results Applying basic rounding rules to solve simple problems in authentic real-life contexts and assess reasonableness of results Order of Operations Accurately carrying out multi-step calculations with integers, decimals

7 operations and fractions involving multiplication, division, subtraction and addition Fractions, Decimals and Percentages Exponents Understand the relationship between decimals, decimals and percentages Convert between index form to expanded form to standard form fluently Fractions, Decimals and Percentages Exponents Reading, writing, comparing and ordering fractions, mixed numbers, decimals and percentages and finding their approximate location on a number line Demonstrating multiple ways to represent fractions and decimals Writing fractions in equivalent and simplest forms Converting between fractions, decimals, and percentages Developing and using strategies to make reasonable estimates of fraction and decimal sums, differences, products and quotients Accurately adding, subtracting, multiplying and dividing fractions, decimals and percentages Demonstrating percent as a comparison with the whole amount which is 100% Expressing one quantity as a percentage of another Using fractions, decimals and percentages to solve a wide variety of simple problems and assess reasonableness of results Multiplying and dividing by powers of 10 Using index notation to express numbers in index and expanded form Identifying the first 10 square numbers Applying square numbers, cube numbers and their inverse (square roots and cube roots) Using square and cube numbers in computations Grade 5 Number/Notation Understand how to read, represent, compare and order numbers to 1 million Demonstrate an understanding of magnitude by counting forwards and backwards by 0.01 Number/Notation Representing, comparing, and ordering numbers from 0.01 to 1 million Using the properties of odd and even numbers to check the accuracy of calculations Counting forwards by hundredths from any decimal number expressed to two decimal places, using concrete materials and number lines

8 Understand how to add and subtract with negative numbers Applying understanding of negative numbers when adding and subtracting, using a variety of strategies Understand place value in whole numbers and decimal numbers from 0.01 to 1 million Applying place value to partition, rearrange and regroup numbers from 0.01 to 1 million to assist calculations and solve problems Demonstrate an understanding of rounding numbers to the nearest tenth Rounding decimal numbers to the nearest tenth Addition and Subtraction Understand how to use a range of efficient mental and written strategies to solve problems involving the addition and subtraction of multi-digit whole numbers and decimal numbers to hundredths Addition and Subtraction Solving problems involving the addition and subtraction of five digit numbers to three decimal places, mentally, or using concrete materials, estimation and algorithms Using estimation when solving problems to help judge the reasonableness of a solution Multiplication and Division Understand how to use a range of efficient mental and written strategies to solve problems involving the multiplication of multidigit numbers, using efficient mental and written strategies. Multiplication and Division Recalling all multiplication facts from, up to and including 12x12 Solving multiplication operations involving 4 and 5 digit numbers by up to 2 digits, using a variety of strategies Multiplying whole and simple decimals by 10, 100 and 1,000, using a variety of strategies Applying techniques for multiplication such as the area model, the Italian lattice method, arrays, or partitioning of numbers and explain calculation strategies Understand how to use a range of efficient mental and Using known multiplication facts to calculate related division facts

9 written strategies to solve problems involving the the division of multidigit numbers by 2-digit numbers Dividing whole and decimal numbers by 10 and 100 Solving division operations involving 4 and 5 digit numbers by up to 2 digits Expressing remainder of a division problem as fractions Fractions, Decimals and Percentages Understand how to use a variety of strategies to represent, compare and convert simple fractions, decimal numbers to hundredths, and percentages Fractions, Decimals and Percentages Using knowledge of fractions to demonstrate equivalences between fractions, decimal notation and percentages Representing, comparing and ordering decimal numbers to hundredths, using standard decimal notation Representing, comparing and ordering fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using standard fractional notation Converting mixed numbers to improper fractions and vice versa Be able to convert a given fraction into a decimal and percentage Understand how to use a range of efficient strategies to solve problems involving the addition and subtraction of fractions with related denominators and of decimals Adding and subtracting fractions with like denominators Adding and subtracting decimal numbers to hundredths, using concrete materials and student-generated algorithms Financial Mathematics Apply strategies to solve money related problems up to $10,000 Financial Mathematics Estimate, count and represent the value of a collection of coins and bills with a maximum value of $10,000 Adding and subtracting money amounts, using a variety of tools, to make simulated purchases and providing change for amounts up to $1000 Explain the importance of financial plans and apply

10 understanding Creating a simple budget Identifying the GST component of invoices and receipts Grade 4 Apply calculations of a percentage of a number in a an everyday context Number/Notation Understand how to read, represent, compare and order numbers to 100,000 Calculating percentage discounts Number/Notation Representing, comparing, and ordering numbers from 0.1 to 100,000 Using the properties of odd and even numbers to check the accuracy of calculations Demonstrate an understanding of magnitude by counting forward and backwards by 0.1 and by fractional amounts Counting forwards by quarters, halves, thirds, fourths and tenths to beyond one whole, using concrete materials and number lines Counting forwards by tenths from any decimal number expressed to one decimal place, using concrete materials and number lines Understand how to move between negative and positive integers, -10 and 10 Applying understanding of negative integers by ordering them from -10 to 10 Understand that the place-value pattern is built on the operations of multiplication or division of tens Rounding four-digit whole numbers to the nearest ten, hundred, and thousand Addition and Subtraction Understand how to use a range of efficient mental and written strategies to solve problems involving the addition and subtraction of single- and multi-digit whole numbers, including the addition and subtraction of decimal numbers to tenths Addition and Subtraction Solving problems involving the addition and subtraction of four-digit numbers, mentally, or using concrete materials, student-generated algorithms and standard algorithms Using estimation when solving problems to help judge the reasonableness of a solution Multiplication and Division Understand how to use a range of efficient mental and Multiplication and Division Recalling all multiplication facts from, up to and including 10x10

11 written strategies to solve problems involving the multiplication of two and three digit numbers. Solving multiplication operations involving 3 digits by 1 or 2 digit numbers, using a variety of strategies Multiplying whole numbers by 10, 100 and 1000 using mental strategies Using known facts and strategies, such as commutativity, doubling and halving for multiplication when there is no remainder Understand how to use a range of efficient mental and written strategies to solve problems involving the the division of three digit numbers Using known multiplication facts to calculate related division facts Dividing whole numbers by 10 and 100, using mental strategies Solving division operations involving 3 digits by 1 or 2 digit numbers Fractions, Decimals and Percentages Understand how to use a variety of strategies to represent, compare and convert simple fractions and decimal numbers to tenths Fractions, Decimals and Percentages Using knowledge of fractions to demonstrate equivalences between fractions and decimal notation Representing, comparing and ordering decimal numbers to tenths, using standard decimal notation Comparing and ordering fractions (halves, thirds, fourths, fifths, tenths) by considering the size and the number of fractional parts Converting mixed numbers to improper fractions and vice versa Understand how to use a range of efficient strategies to solve problems involving the addition and subtraction of fractions with related denominators and of decimals Adding and subtracting simple common fractions with like denominators Adding and subtracting decimal numbers to tenths, using concrete materials and student-generated algorithms Know commonly used fraction, decimal, and percentage conversions.(1/4 =

12 25%= 0.25, 1/2 = 50%, 3/4 = 75%, 1/10 = 10%, 1/5 = 20%) Financial Mathematics Apply strategies to solve money related problems up to $1000 Financial Mathematics Estimating, counting and representing the value of a collection of coins and notes with a maximum value of $1000 Grade 3 Number/Notation Understand how to read, represent, compare and order whole numbers to 10,000 Demonstrate an understanding of magnitude by counting forward and backwards by various numbers and from various starting points Understand the number line can go below zero Adding and subtracting money amounts, using a variety of tools, to make simulated purchases and providing change for amounts up to $100 Number/Notation Representing, comparing, and ordering whole numbers to 10,000 Explaining the conditions required for a number to be even or odd Counting forward by 10's and 100's to 10,000 from various starting points and by 25's to 10,000 starting from multiples of 25, using a variety of tools and strategies Counting backwards by 100's from 10,000 and any number less than 10,000, using a variety of tools and strategies Explaining how positive and negative numbers represent quantities in real-world contexts (e.g., temperature above/below zero, elevation above/below sea level) Understand five-digit numbers are comprised of ten thousands, thousands, hundreds, tens and ones/units Applying place value to partition, rearrange and regroup numbers to at least 10,000 to assist calculations and solve problems Demonstrate an understanding of rounding numbers to the nearest 10 and 100 Rounding three digit numbers to the nearest ten and hundred Addition and Subtraction Understand how to use a range of efficient mental and Addition and Subtraction Solving problems involving the addition and subtraction of three-digit

13 written strategies to solve problems involving the addition and subtraction of two and three digit numbers numbers, with and without regrouping, mentally or using concrete materials, student-generated algorithms, and standard algorithms Using estimation when solving problems to help judge the reasonableness of a solution Multiplication and Division Understand how to use a range of efficient mental and written strategies to solve problems involving the multiplication of one and two digit numbers. Multiplication and Division Recalling multiplication facts of two, three, five and 10 Solving multiplication operations involving 2 digits by 1 digit numbers, using a variety of strategies Multiplying whole numbers by 10 and 100, using a variety of strategies Understand how to use a range of efficient mental and written strategies to solve problems involving the division of two digit numbers Using known multiplication facts to calculate related division facts when there is no remainder Dividing whole numbers by 10 and 100 Dividing two digit whole numbers by one digit whole numbers, using a variety of tools and student-generated algorithms Fractions, Decimals and Percentages Understand how concrete materials and standard notation can be used to represent fractions Fractions, Decimals and Percentages Dividing whole objects and sets of objects into equal parts and identifying the parts using fractional names (one half, three thirds, two fourths or two quarters) Modeling and representing unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole Comparing fractions using concrete materials, using standard fractional notation

14 Financial Mathematics Understand how concrete materials can be used to represent money amounts to $100 Financial Mathematics Estimating, counting and representing, using the $ or other national symbol, the value of a collection of coins and notes with a maximum value of $100 Grade 2 Number/Notation Understand how to read, represent, compare and order numbers to 1000 Adding and subtracting money amounts, using a variety of tools, to make simulated purchases and providing change for amounts up to $50 Number/Notation Representing, comparing and ordering whole numbers to 1000 Classifying one and two digit numbers as odd and even Demonstrate an understanding of magnitude by counting to and from 1000, using multiples of various numbers as starting points Counting forward by 5, 10's and 25's to 1000, using number lines and hundreds charts, starting from multiples of 1, 2, 5 and 10 Counting backwards by 1's and 10's from 1000, and any number less than 1000, with and without the use of concrete materials and number lines Addition and Subtraction Understand four-digit numbers as comprised of thousands, hundreds, tens and one/units Addition and Subtraction Grouping, partitioning and rearranging collections up to 1000 in thousands, hundreds, tens and ones to facilitate more efficient counting Demonstrate an understanding of rounding numbers to the nearest 10 Rounding two digit numbers to the nearest ten Understand how to use a range of efficient mental and written strategies to solve problems involving the addition and subtraction two digit numbers Solving problems involving the addition and subtraction of two-digit numbers, with and without regrouping, mentally, or using concrete materials, student-generated algorithms, and standard algorithms

15 Multiplication and Division Understand and represent multiplication as repeated addition, groups and arrays. Multiplication and Division Using concrete materials, represent and explain multiplication as the combining of equal groups Representing array problems with available materials and explain reasoning Understand and represent division as grouping into equal sets and solve simple problems using these representations. Identifying the difference between dividing a set of objects into three equal groups and dividing the same set of objects into groups of three Using concrete materials, represent and explain division as the sharing of a quantity equally Fractions, Decimals and Percentages Understand how to interpret a fraction as division of the numerator by the denominator Fractions, Decimals and Percentages Using concrete materials, determine the relationship between the number of fractional parts of a whole and the size of the fractional part (halves, fourths/quarters, eighths) Regrouping fractional parts into wholes, using concrete materials Comparing fractions using concrete materials, without using standard fractional notation Financial Mathematics Understand how concrete materials can be used to represent money amounts to $10 Financial Mathematics Estimating, counting and representing the value of a collection of coins and notes with a maximum value of $10 Adding and subtracting money amounts to $10, using a variety of tools and strategies

16 Grade 1 Number/Notation Understand how to read, represent, compare and order whole numbers to 100 Number/Notation Representing, comparing and ordering whole numbers to 100 Classifying one digit numbers as odd and even Demonstrate an understanding of magnitude by counting to and from 100, starting at any number Counting forward by 1 s, 2 s, 5 s and 10 s to 100, using a variety of tools and strategies Counting backwards by 1's, 2's and 5's from 100 with and without the use of concrete materials and number lines Understand partitioning of numbers and the importance of grouping in tens Counting collections to 100 by partitioning numbers using place value Addition and Subtraction Understand how to use a range of efficient mental and written strategies to solve problems involving the addition and subtraction of one and two digit numbers Addition and Subtraction Solving problems involving the addition and subtraction of one and two-digit numbers, without regrouping, mentally, or using concrete materials, student-generated algorithms, and standard algorithms Fractions, Decimals and Percentages Understand how concrete materials can be used to investigate fractions Fractions, Decimals and Percentages Using concrete materials, divide whole objects into parts and identify and describe equal-sized parts of the whole, using fractional names (halves and fourths/quarters) Financial Mathematics Understand how concrete materials can be used to investigate money amounts to 50 cents Financial Mathematics Representing money amounts to 50 cents, using coin manipulatives Adding and subtracting money amounts to 50 cents, using coin manipulatives and drawings

17 K2 Number/Notation Understand how to read, represent, compare and order numbers, including zero, up to 50 Demonstrate an understanding of magnitude by counting to and from 50, starting at any number Number/Notation Representing, comparing and ordering whole numbers to 50 Counting forward by 1's, 5's and 10's to 50, using a variety of tools and strategies Counting backwards by 1's from 50, with and without the use of concrete materials and number lines Addition and Subtraction Addition and Subtraction Understand how to use a range of efficient strategies to solve problems involving addition and subtraction of single digit numbers Solving a variety of problems involving the addition and subtraction of whole numbers to 10, mentally or using concrete materials and drawings K1 Number/Notation Understand how to recognise, count and write numbers up to 20 Demonstrate an understanding of magnitude by naming the number that comes before and after a given number from 0-20 Number/Notation Identifying, counting and writing numbers up to 20 Identifying the number before and after a given number up to 20, using a variety of tools and strategies

18 Learning Outcomes and Benchmarks Subject : MATHEMATICS Strand : DATA HANDLING - STATISTICS & PROBABILITY Grade/Phase Grade 12 Grade 11 Grade 10 (Either probability or statistics unit in G10) Learning Outcome Students will be able to... Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current IB Curriculum Guide documents which can be accessed by the links below; Mathematics Standard Level Mathematics Higher Level Mathematical Studies Further Mathematics Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current IB Curriculum Guide documents which can be accessed by the links below; Mathematics Standard Level Mathematics Higher Level Mathematical Studies Further Mathematics Probability: Know how to calculate probabilities of simple events, with and without replacement Understand and know how to calculate probabilities of independent events, mutually exclusive events and combined events Have the skills to solve problems using tree diagrams and Venn diagrams Statistics: Understand the skills to use survey (digital/paper) to collect data Know how to construct and interpret graphs to represent statistical data. Understand how to draw the line of best fit from scatter graph Be able to select samples and making inferences about Benchmarks: Students will be able to show their understanding by... Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current IB Curriculum Guide documents which can be accessed by the links below; Mathematics Standard Level Mathematics Higher Level Mathematical Studies Further Mathematics Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current IB Curriculum Guide documents which can be accessed by the links below; Mathematics Standard Level Mathematics Higher Level Mathematical Studies Further Mathematics Probability: Experimenting with the probability of a simple event through games Identify and classify events as independent, or mutually exclusive. Calculate the probability of independent, mutually exclusive and combined events through simple game theory Calculating the probability of successive trials for both replacement and without replacement. Using Venn diagrams to illustrate probabilities and sets Create and trial probability games Statistics: Constructing, analysing and representing pie charts, histograms, line graphs, scatter plots and box-and-whisker plots Collecting data through the process of random sampling Calculating mean, mode, median, quartile, percentile for discrete and continuous data Constructing, analysing and representing cumulative frequency curves.

19 Grade 9 (Either probability or statistics unit in G9) populations Know the steps for calculating the mean, median and mode, and how to choose the best measure of central tendency Know how to calculate the interquartile range from cumulative frequency curves and stem and leaf diagrams Probability: Know how to calculate probabilities of simple events, with and without replacement Understand and know how to calculate probabilities of independent events, mutually exclusive events and combined events Have the skills to solve problems using tree diagrams and Venn diagrams Statistics: Understand the skills to use survey (digital/paper) to collect data Know how to construct and interpret graphs to represent statistical data. Understand how to draw the line of best fit from scatter graph Be able to select samples and making inferences about populations Know the steps for calculating the mean, median and mode, and how to choose the best measure of central tendency Know how to calculate the interquartile range from cumulative frequency curves and stem and leaf diagrams Measuring and analysing of dispersion by the use and applications of range, and interquartile range for discrete and continuous data Probability: Experimenting with the probability of a simple event through games Identify and classify events as independent, or mutually exclusive. Calculate the probability of independent, mutually exclusive and combined events through simple game theory Calculating the probability of successive trials for both replacement and without replacement. Using Venn diagrams to illustrate probabilities and sets Create and trial probability games Statistics: Constructing, analysing and representing pie charts, histograms, line graphs, scatter plots and box-and-whisker plots Collecting data through the process of random sampling Calculating mean, mode, median, quartile, percentile for discrete and continuous data Constructing, analysing and representing cumulative frequency curves. Measuring and analysing of dispersion by the use and applications of range, and interquartile range for discrete and continuous data Grade 8 Statistics Select and use appropriate statistical methods to collect, organize, display and analyse data Statistics Identifying graphs and data that do not follow standard conventions and discuss the possible reasons why Designing an investigation to collect, organize, present and analyse data Selecting, creating, using and analysing appropriate graphical

20 representations for discrete numerical data and grouped discrete numerical data including histograms, box and whisker plots, stem-and-leaf plots and frequency tables Describing distribution of data using terms such as symmetrical, positively skewed, negatively skewed, outliers Finding the measures of central tendency of sets of data including grouped data and interpret the significance of these values Calculating measures of spread of data including range and interquartile range and interpret the significance of these values Using appropriate mathematical concepts and skills to solve problems involving statistics including those in real-life contexts and assess reasonableness of results Grade 7 Probability Probability Understand and apply basic skills and concepts of probability to calculate and compare theoretical and experimental probability Developing understanding of key terms including chance, probability, outcome, event, frequency, relative frequency, sample space Determining the likelihood of events happening by investigating using manipulatives such as dice, coins, spinners, cards Developing understanding of theoretical probability as the theoretical chance of an event occurring Using lists, tree diagrams and grids to illustrate sample spaces and determine theoretical probabilities of given events Using appropriate mathematical concepts and skills to solve problems involving probability Formulating questions, designing studies and collecting experimental data to investigate probability of an event and comparing it to theoretical probability Grade 6 Displaying Data and Statistics Develop an understanding of the various statistical methods to collect, organize, display and analyse data and develop and evaluate inferences in order to make decisions and predictions based on the data Displaying Data and Statistics Defining key terms; population, sample, random sample, census, survey, categorical data and numerical data Formulating questions, designing studies and collecting data about characteristics shared by two populations or different characteristics within one population Selecting, creating and using appropriate graphical representations for categorical data including tally and frequency tables, column graphs, bar charts and pie charts Selecting, creating and using appropriate graphical representations

21 for numerical data including stem and leaf charts, frequency tables and bar graphs Calculating the mean, median, mode and range of a set of data and interpreting the significance of these values Identifying and creating a hypothesis to explain trends in graphical representations of data Identifying misleading graphs and statistics Venn Diagrams and Sets Understand and apply the skills and concepts of sets and Venn diagrams to represent and analyse abstract and practical mathematical situations Venn Diagrams and Sets Using terminology and notation involved in sets and set operations (union, intersection, complement, empty set, subset, universal set) Using Venn Diagrams to represent sets and use these diagrams to solve problems Grade 5 Collect, Record Organise and Interpret Data Understand how to pose questions and collect categorical or numerical data by observation and survey Understand how to describe and interpret different data sets in context Collect, Record Organise and Interpret Data Posing questions, collecting data and explaining observations and data Using and comparing data representations (i.e. column/bar graphs, carroll diagrams, pie charts) for different data sets to help decision making Identify and create a hypothesis to explain simple trends in graphs. Understand basic statistical concepts and conventions, such as mean Understand how to construct displays appropriate for data type, with and without the use of digital technologies Calculating the mean for a small set of data and using it to describe the shape of the data set across its range of values, using charts, tables and graphs Using the best methods to present data to illustrate the results of investigations and justifying the choice of representations (using column graphs, Venn Diagrams, dot plots, pie charts, tables)

22 Chance and Probability Understand how to list outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions Chance and Probability Explaining the likelihood of winning simple games of chance by considering the number of possible outcomes and the consequent chance of winning in simple games of chance Understand that probabilities range from 0 to 1 Assigning numerical values (fractions, simple decimals and simple percentages) to describe the probability of simple chance events, such as scoring a given number on a spinner or dice Grade 4 Collect, Record Organise and Interpret Data Understand how to select and trial methods for data collection, including survey questions and recording sheets Collect, Record Organise and Interpret Data Comparing the effectiveness of different methods of collecting data Choosing and explaining the most effective way to collect data for particular investigations Understand how to evaluate the effectiveness of different display in illustrating data features including variability Interpreting data representations in the media and other forums in which symbols represent more than one data value Suggesting questions that can be answered by a given data display and using the display to answer questions Understand how to construct suitable data displays, with and without the use of digital technologies, from given or collected data, using many-to-one correspondence Presenting data and showing the results of investigations (using tables, column graphs, Venn Diagrams and pie charts) Creating data displays where one picture can represent many data values Understand basic statistical concepts and conventions, such as median Calculating the median of a set of data and interpreting these statistics in the context of data

23 Chance and Probability Understand how to describe possible everyday events and order their chances of occurring Chance and Probability Using lists of familiar events familiar and ordering them from 'least likely' to 'most likely' to occur Understand how to identify everyday events where one cannot happen if the other happens Identifying example of mutually exclusive events such as weather, which cannot be dry and wet at the same time Grade 3 Collect, Record Organise and Interpret Data Understand how to identify questions or issues for categorical variables, identify data sources, and plan methods of data collection and recording Collect, Record Organise and Interpret Data Refining questions and planning and carrying out investigations that involve collecting data Choosing the most effective way to collect data for a given investigation Understand how to interpret and compare data displays Comparing various student-generated data representations and describe their similarities and differences Understand how to collect data, organise into categories and create displays, with and without the use of digital technologies Using meaningful and increasingly efficient ways to record data, and representing and reporting the results of investigations (using lists, tables, pictographs and column/bar graphs) Chance and Probability Understand how to conduct chance experiments, identify and describe possible outcomes and recognise variation in results Chance and Probability Conducting repeated trials of chance experiments such as tossing a coin or drawing a ball from a bag and identifying the variations between trials

24 Grade 2 Collect, Record Organise and Interpret Data Understand how to identify a question of interest based on one categorical variable and gather data relevant to the question Collect, Record Organise and Interpret Data Using a prepared table to record observations Creating picture graphs to represent data using one-to-one correspondence Understand how to create displays of data using lists, table and picture graphs and interpret them Comparing the usefulness of different data displays Understand how to collect data, organise into categories and create displays Using meaningful ways to record data, and representing and reporting the results of investigations (using lists, tables, pictographs and simple column/bar graphs) Identifying categories of data and using them to sort data Grade 1 Chance and Probability Understand how to identify practical activities and everyday events that involve chance, describe outcomes as 'likely' or 'unlikely' and identify some events as 'certain' or 'impossible' Collect, Record Organise and Interpret Data Understand how to choose simple questions, gather responses and make simple inferences Chance and Probability Classifying a list of everyday events according to how likely they are to happen, using the language of chance, and explaining reasoning Collect, Record Organise and Interpret Data Determining which questions will gather appropriate responses for a simple investigation Understand how to represent data with objects and drawings where one object or drawing represents one data value and describe the displays Demonstrating one-to-one correspondence Describing displays by identifying categories with the greatest or least number of objects Understand how to collect, check and classify data Recognising the usefulness of tally marks and recording them accurately

25 K2 Chance and Probability Understand how to identify outcomes of familiar events involving chance and describing them using everyday language such as 'will happen', 'won't happen' or 'might happen' Collect, Record Organise and Interpret Data Understand how to answer yes/no questions to collect information and make simple inferences Chance and Probability Justifying that some events are certain or impossible Collect, Record Organise and Interpret Data Posing questions about themselves, familiar objects and environment Representing responses to questions using simple displays, including grouping students according to their answers Using data displays to answer simple questions (i.e. "How many students answered 'yes' to having brown hair?") K1 Understand how to collect and record information related to own experiences Collect, Record Organise and Interpret Data Understand how to collect and record information related to own experiences Observing and recording information using drawings and labels Collect, Record Organise and Interpret Data Observing and recording information using drawings

26 Learning Outcomes and Benchmarks Subject : MATHEMATICS Strand : ALGEBRA Grade/Phase Grade 12 Grade 11 Grade 10 Learning Outcome Students will be able to... Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current IB Curriculum Guide documents which can be accessed by the links below; Mathematics Standard Level Mathematics Higher Level Mathematical Studies Further Mathematics Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current IB Curriculum Guide documents which can be accessed by the links below; Mathematics Standard Level Mathematics Higher Level Mathematical Studies Further Mathematics Factorization of algebraic expressions: Understand how to factorize quadratic expressions. Benchmarks: Students will be able to show their understanding by... Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current IB Curriculum Guide documents which can be accessed by the links below; Mathematics Standard Level Mathematics Higher Level Mathematical Studies Further Mathematics Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current IB Curriculum Guide documents which can be accessed by the links below; Mathematics Standard Level Mathematics Higher Level Mathematical Studies Further Mathematics Factorization of algebraic expressions : Carrying out activities with the factorizing of quadratic expressions Integer and fractional exponents : Know the the laws of exponents. (Including negative exponents. Integer and fractional exponents : Investigate the laws of exponents Patterns and sequences : Understand the steps required to find and justify or prove general rules/formulae for sequences. Algorithms: Be able to analyse and use well-defined procedures for solving complex problems. Patterns and sequences : Working with patterns in quadratic sequences Finding and justifying or proving general rules/formulae for sequences such as Fibonacci, linear and quadratic sequences Algorithms Changing the subject of real-life formula (quadratic, cubic and radicals) and developing an algebraic approach

27 Properties of functions Be able to describe properties of standard functions such as quadratics, exponentials and sinusoidal. Be able to describe simple transformations of the above functions. Be able to graph the above functions on graph paper as well as using GDC and Desmos.com. Properties of functions Describing transformed linear, quadratic, exponential, and sine and cosine functions Example: f(x) = a (x h) 2 + k Note: Sine and cosine functions are limited to the form f(x) = a sin(bx) + c and f(x) = a cos(bx) + c Graphing different types of functions and understanding their characteristics Determining the range, given the domain translating, reflecting and dilating functions Extensions Polynomial Functions Solve and graph polynomial functions Extensions Polynomial Functions Solving polynomial cubic and quartic polynomial functions by listing potential factors and dividing by long division and synthetic division Graphing polynomial functions using x-intercepts and using a sign chart to find positive and negative ranges Rational Functions Solve and graph rational functions Rational Functions Simplifying rational expressions including the multiplication, division, addition and subtraction rational expressions Solving rational equations Graphing rational functions including asymptotes and intercepts Grade 9 Logarithmic and Exponential Functions Apply properties of logarithms and solve exponential and logarithmic equations Graph exponential and logarithmic functions Addition, subtraction, multiplication and division of algebraic terms: Know how to expand and simplify algebraic expressions. Factorization of algebraic expressions: Logarithmic and Exponential Functions Using the definition of logarithm, the laws of logarithms, and the change of base rule to simplify a variety of exponential and logarithmic expressions and to solve a variety of exponential and logarithmic equations Showing that exponential and logarithmic functions are inverses of one another and graphing both exponential and logarithmic functions including asymptotes Solving a variety of applied problems particularly exponential growth and decay type problems Addition, subtraction, multiplication and division of algebraic terms: Expanding and simplifying linear algebraic expressions Factorization of algebraic expressions:

28 Know how to factorize linear expressions. Using substitution to evaluate expressions including quadratics and cubics Substitution: Know how to use substitution to evaluate expressions. Algebraic fractions: Be able to solve equations involving algebraic fractions. Systems of equation: Be able to solve systems of equations by the substitution, elimination, graphical methods and by graphical display calculators Substitution: Working with linear functions, f(x) = mx + b, its graph, gradient and y-intercept, parallel and perpendicular lines and the relationships between their gradients and by the process of graphically Recognizing that in a linear relationship the rate of change is constant whereas in non-linear relationships the rate of change varies as a more formal approach with links to the sciences Algebraic fractions: Multiplying through by the GCF to eliminate the denominator Systems of equation Solving linear equations involving algebraic fractions Solving equations algebraically and graphically Solving and graphing of linear inequalities algebraically Using the GDC App of Plysmlt2 to solve system of inequalities and equations Using the Trace, Calc, Intersect functions on the GDC to solve the system of linear equations. Extension: Solve systems of equations in three variables Word problems: Know the steps to solve word problems using a variety of methods including translating into algebraic equations Word problems: Solving and graphing linear programming problems and it s applications Grade 8 Algebraic Expressions Write, interpret and use algebraic expressions to represent and analyse mathematical situations and structures Algebraic Expressions demonstrating understanding of the terms: variable, term, coefficient, like terms, constant, polynomial, monomial, binomial, trinomial, simplify, evaluate, factor, expand, expression simplifying algebraic expressions by collecting like terms using the distributive property to multiply a monomial by a polynomial, two or more binomials or two or more polynomials

29 Factoring algebraic expressions by greatest common factor rearranging (linear and quadratic) expressions to change the subject Linear Equations and Systems Write, interpret and use linear equations, inequalities and systems of linear equations to represent and analyse mathematical situations and structures and solve a variety of problems Linear Equations and Systems mastering understanding of what an equation is (with emphasis on linear equation) and what it means to solve an equation solving a variety of linear equations including those with parentheses, fractions, decimals and variables on both sides solving word problems using a variety of methods including translating into algebraic equations developing understanding of what it means to find the solution to a system of linear equations graphically solving word problems involving a system of linear equations Lin ear Relationships and Graphing Understand, represent and analyse linear functions Linear Relationships and Graphing Graphing a line given an equation in y = mx+b form and determining the equation of a line in y = mx+b form given a graph Recognizing that in a linear relationship the rate of change is constant whereas in non-linear relationships the rate of change varies Investigating and developing understanding of the meaning of slopes which are positive, negative, zero, and undefined Investigating and understanding the characteristics of special lines including vertical, horizontal, parallel, perpendicular lines Determining whether a given point satisfies the equation of a line geometrically and algebraically Applying linear functions as tools for mathematical modelling and model and solve contextualized real-life problems that involve linear relationships