MATHEMATICS - International IB school | ISS International …€¦ · · 2017-06-01Grade 12 Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current

K-12 LEARNING OUTCOMES & BENCHMARKS

MATHEMATICS

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.

Learning Outcomes and Benchmarks Subject : MATHEMATICS Strand : NUMBER

Grade/Phase Learning Outcome Students will be able to...

Benchmarks: Students will be able to show their understanding by .......................

Grade 12 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 11



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

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Extension

● Perform operations involving complex numbers

● 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

Extension

● Simplifying surds involving negative roots ● Solving quadratic equations involving imaginary roots

Grade 9

Number Skills

● Students will be able to understand the distinction between rational and irrational numbers, make reasonable estimates, compute fluently and solve problems

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

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

● accurately adding, subtracting, multiplying and dividing numbers in scientific notation form, with and without a calculator

● applying scientific notation to real-life problems

Extension

● Using the rules of indices to simplify numerical expressions involving radicals and fractional exponents

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

Exponents

● Understand positive and negative integer exponents, scientific notation, and exponent laws, make reasonable estimates, compute fluently and solve problems when working with exponents

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

● Applying the laws of exponents to simplify expressions containing integer exponents and zero exponents

● Using exponents to model simple growth and decay (such as 2x 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

Exponents

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

● Using index notation to express and simplify powers of integers

● Understand positive integer exponents, make reasonable estimates and solve problems when working with exponents

Ratio, Rate and Percentage

● Understand ratios, rates, percentage and proportions and develop understanding and fluency when applying proportional thinking

● 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

● 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

● Identify prime numbers, prime factors and multiples

Rounding

● 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

● Using common divisibility rules, factors, multiples, and prime factorization to solve problems including finding greatest common factor (GCF) and lowest common multiple (LCM)

●

Rounding

● 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

operations

Fractions, Decimals and Percentages

● Understand the relationship between decimals, decimals and percentages

Exponents

● Convert between index form to expanded form to standard form fluently

and fractions involving multiplication, division, subtraction and addition


● 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

Exponents

● 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

● Understand how to add and subtract with negative

numbers

● Understand place value in whole numbers and decimal numbers from 0.01 to 1 million

● Demonstrate an understanding of rounding 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

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.

● Understand how to use a range of efficient mental and

● Applying understanding of negative numbers when adding and subtracting,

using a variety of strategies

● Applying place value to partition, rearrange and regroup numbers from 0.01 to 1 million to assist calculations and solve problems

● Rounding decimal numbers to the nearest tenth 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

● 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

● Using known multiplication facts to calculate related division facts

written strategies to solve problems involving the the division of multidigit numbers by 2-digit numbers


● Understand how to use a variety of strategies to represent, compare and convert simple fractions, decimal numbers to hundredths, and percentages

● 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

Financial Mathematics

● Apply strategies to solve money related problems up to $10,000

● Explain the importance of financial plans and apply

● 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


● 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

● Adding and subtracting fractions with like denominators

● Adding and subtracting decimal numbers to hundredths, using concrete materials and student-generated algorithms


● 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

understanding

● Apply calculations of a percentage of a number in a an everyday context

● Creating a simple budget

● Identifying the GST component of invoices and receipts

● Calculating percentage discounts

Grade 4


order numbers to 100,000

● Demonstrate an understanding of magnitude by counting forward and backwards by 0.1 and by fractional amounts

● Understand how to move between negative and positive integers, -10 and 10

● Understand that the place-value pattern is built on the operations of multiplication or division of tens


● 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



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

● 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

● Applying understanding of negative integers by ordering them from -10 to 10

● Rounding four-digit whole numbers to the nearest ten, hundred, and thousand 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


● Recalling all multiplication facts from, up to and including 10x10

written strategies to solve problems involving the multiplication of two and three digit numbers.

● Understand how to use a range of efficient mental and written strategies to solve problems involving the the division of three digit numbers


● Understand how to use a variety of strategies to represent, compare and convert simple fractions and decimal numbers to tenths

● 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

● 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

● 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

● 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

● 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 =


● Apply strategies to solve money related problems up to $1000

25%= 0.25, 1/2 = 50%, 3/4 = 75%, 1/10 = 10%, 1/5 = 20%) Financial Mathematics

● Estimating, counting and representing the value of a collection of coins and notes with a maximum value of $1000



Grade 3


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

● Understand five-digit numbers are comprised of ten thousands, thousands, hundreds, tens and ones/units

● Demonstrate an understanding of rounding numbers to the nearest 10 and 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)

● Applying place value to partition, rearrange and regroup numbers to at least 10,000 to assist calculations and solve problems

● Rounding three digit numbers to the nearest ten and hundred Addition and Subtraction

● Solving problems involving the addition and subtraction of three-digit

written strategies to solve problems involving the addition and subtraction of two and three digit numbers


● Understand how to use a range of efficient mental and written strategies to solve problems involving the multiplication of one and two digit numbers.

● Understand how to use a range of efficient mental and written strategies to solve problems involving the division of two digit numbers


● Understand how concrete materials and standard notation can be used to represent fractions

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

● 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

● 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

● 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


● Understand how concrete materials can be used to represent money amounts to $100


● 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


order numbers to 1000

● Demonstrate an understanding of magnitude by counting to and from 1000, using multiples of various numbers as starting points


● Understand four-digit numbers as comprised of thousands, hundreds, tens and one/units

● Demonstrate an understanding of rounding numbers to the nearest 10

● Understand how to use a range of efficient mental and written strategies to solve problems involving the addition and subtraction two digit numbers

Number/Notation ● Representing, comparing and ordering whole numbers to 1000

● Classifying one and two digit numbers as odd and even

● 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

● Grouping, partitioning and rearranging collections up to 1000 in thousands, hundreds, tens and ones to facilitate more efficient counting

● Rounding two digit numbers to the nearest ten

● 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


● Understand and represent multiplication as repeated addition, groups and arrays.

● Understand and represent division as grouping into equal sets and solve simple problems using these representations.


● Understand how to interpret a fraction as division of the numerator by the denominator


● Understand how concrete materials can be used to represent money amounts to $10


● Using concrete materials, represent and explain multiplication as the combining of equal groups

● Representing array problems with available materials and explain reasoning

● 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

● 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

● 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

Grade 1 Number/Notation ● Understand how to read, represent, compare and

order whole numbers to 100

● Demonstrate an understanding of magnitude by counting to and from 100, starting at any number

● Understand partitioning of numbers and the importance of grouping in tens


● 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


● Understand how concrete materials can be used to investigate fractions


● Understand how concrete materials can be used to investigate money amounts to 50 cents

Number/Notation

● Representing, comparing and ordering whole numbers to 100

● Classifying one digit numbers as odd and even

● 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

● Counting collections to 100 by partitioning numbers using place value 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


● 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)


● Representing money amounts to 50 cents, using coin manipulatives

● Adding and subtracting money amounts to 50 cents, using coin manipulatives and drawings

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


● Understand how to use a range of efficient strategies to solve problems involving addition and subtraction of single digit numbers

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


● 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

Learning Outcomes and Benchmarks Subject : MATHEMATICS Strand : DATA HANDLING - STATISTICS & PROBABILITY





Grade 11



Grade 10 (Either probability or statistics unit in G10)

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

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.

















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

Grade 9 (Either probability or statistics unit in G9)

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

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

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

● Understand and apply basic skills and concepts of probability to calculate and compare theoretical and experimental probability

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

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

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

● 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

● 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

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.

● 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)

Chance and Probability

● Understand how to list outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions

● Understand that probabilities range from 0 to 1


● 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

● 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

● Understand how to evaluate the effectiveness of different display in illustrating data features including variability

● 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

● Understand basic statistical concepts and conventions, such as median


● Comparing the effectiveness of different methods of collecting data

● Choosing and explaining the most effective way to collect data for particular investigations

● 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

● 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

● Calculating the median of a set of data and interpreting these statistics in the context of data


● Understand how to describe possible everyday events and order their chances of occurring

● Understand how to identify everyday events where one cannot happen if the other happens


● Using lists of familiar events familiar and ordering them from 'least likely' to 'most likely' to occur

● 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

● Understand how to interpret and compare data displays

● Understand how to collect data, organise into categories and create displays, with and without the use of digital technologies


● Understand how to conduct chance experiments, identify and describe possible outcomes and recognise variation in results

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

● Comparing various student-generated data representations and describe their similarities and differences

● 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)


● Conducting repeated trials of chance experiments such as tossing a coin or drawing a ball from a bag and identifying the variations between trials

Grade 2


● Understand how to identify a question of interest based on one categorical variable and gather data relevant to the question

● Understand how to create displays of data using lists, table and picture graphs and interpret them

● Understand how to collect data, organise into categories and create displays


● 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'


● Using a prepared table to record observations

● Creating picture graphs to represent data using one-to-one correspondence

● Comparing the usefulness of different data 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


● Classifying a list of everyday events according to how likely they are to happen, using the language of chance, and explaining reasoning

Grade 1 Collect, Record Organise and Interpret Data ● Understand how to choose simple questions, gather

responses and make simple inferences

● Understand how to represent data with objects and drawings where one object or drawing represents one data value and describe the displays

● Understand how to collect, check and classify data

Collect, Record Organise and Interpret Data ● Determining which questions will gather appropriate responses for a simple

investigation

● Demonstrating one-to-one correspondence

● Describing displays by identifying categories with the greatest or least number of objects

● Recognising the usefulness of tally marks and recording them accurately

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'


● Justifying that some events are certain or impossible

K2 Collect, Record Organise and Interpret Data ● Understand how to answer yes/no questions to collect

information and make simple inferences

● Understand how to collect and record information related to own experiences

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?")

● Observing and recording information using drawings and labels

K1 Collect, Record Organise and Interpret Data ● Understand how to collect and record information

related to own experiences

Collect, Record Organise and Interpret Data ● Observing and recording information using drawings

Learning Outcomes and Benchmarks Subject : MATHEMATICS Strand : ALGEBRA





Grade 11



Grade 10 Factorization of algebraic expressions:

● Understand how to factorize quadratic expressions. Integer and fractional exponents:

● Know the the laws of exponents. (Including negative 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.

Factorization of algebraic expressions:

● Carrying out activities with the factorizing of quadratic expressions Integer and fractional exponents:

● Investigate the laws of exponents 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

















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.

Extensions Polynomial Functions

● Solve and graph polynomial functions Rational Functions

● Solve and graph rational functions Logarithmic and Exponential Functions

● Apply properties of logarithms and solve exponential and logarithmic equations

● Graph exponential and logarithmic functions

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

● 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

● Simplifying rational expressions including the multiplication, division, addition and subtraction rational expressions

● Solving rational equations ● Graphing rational functions including asymptotes and intercepts

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

Grade 9

Addition, subtraction, multiplication and division of algebraic terms:

● Know how to expand and simplify algebraic expressions.

Factorization of algebraic expressions:

Addition, subtraction, multiplication and division of algebraic terms:

● Expanding and simplifying linear algebraic expressions Factorization of algebraic expressions:

● Know how to factorize linear expressions. 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

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

● Using substitution to evaluate expressions including quadratics and cubics 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. 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


● 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

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 Relationships and Graphing

● Understand, represent and analyse linear functions

● Factoring algebraic expressions by greatest common factor ● rearranging (linear and quadratic) expressions to change the subject

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

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

Grade 7


● Write, interpret and use algebraic expressions to represent and analyse mathematical situations and structures

Linear Equations

● Write, interpret and use linear equations to represent and analyse mathematical situations and structures and solve simple problems

Tables, Graphs and Patterning

● Understand, represent and analyse patterns and relationships using tables, equations and graphs


● Writing algebraic expressions to represent word phrases or simple real life situations

● Evaluating an expression and evaluate algebraic expressions and formulas for given values which require the use of order of operations with integers

● Simplifying expressions and simplifying simple algebraic expressions by applying associative and commutative properties to collect like terms

● Applying the distributive property and expanding expressions containing monomial multiplied by polynomial

● Recognizing that factoring is the inverse operation of expanding ● Factoring algebraic expressions by using the greatest common factor ● Simplifying, adding, subtracting, multiplying and dividing simple

algebraic fractions

Linear Equations

● Recognizing the difference between an expression and an equation ● Solving linear equations (including multiple operations and equations

written in fractional form) by inspection, trial-and-error, and inverse operations

● Checking the validity of a solution by substitution ● Solving simple word problems using a variety of methods including

translating into algebraic equations ● Simplifying, multiplying, dividing, adding and subtracting simple

algebraic fractions

Tables, Graphs and Patterning

● Representing, analysing and generalizing a variety of patterns and simple relationships using different forms of representation including words, tables, graphs, and where possible equations (i.e. symbolic rules) and compare the different forms

● Identifying patterns and develop understanding in a variety of number sequences including linear, quadratic, triangular and Fibonacci

sequences, and beginning to develop the rules which describe them ● Describing relationships as linear or nonlinear and contrast their

properties from tables, graphs or equations ● Developing understanding of slope as a ratio which compares vertical

change to horizontal change ● Investigating and developing understanding of relationship between

the equation of a linear relationship and the graph of a line ● Investigating and developing understanding of different techniques

that can be used to draw the graph of a linear relation including: table of values and y=mx+b form

Grade 6

Algebraic Expressions ● Write, interpret and use algebraic expressions

to represent and analyse mathematical situations and structures


● Constructing a table for a linear pattern, writing an equation for n terms of the pattern and drawing a graph based on the table

● Writing algebraic expressions to represent word phrases or simple real life situations

● Evaluating linear algebraic expressions and formulas by substituting the variables with given values

● Simplifying linear algebraic expressions by collecting like terms ● Solving linear equations using a variety of strategies including inspection, trial

and error, and inverse operations

Grade 5

● Determine, through investigation using a table of values, relationships in growing and shrinking patterns, and investigate repeating patterns involving translations

● Understand the use of variables in equations

● Recognising more challenging sequences such as the Fibonacci sequence and applying this knowledge to finding a future term in the sequence

● Extending and creating repeating patterns that result from translations, using

a variety of tools (e.g., pattern blocks, dynamic geometry software, dot paper)

● Determining the missing number in equations involving addition, subtraction, multiplication, or division and one-or two-digit numbers

● Identifying and using variables as changing quantities, given equations with

letters or other symbols that describe relationships involving simple rates (e.g. C = 3 x n)

Grade 4

● Understand how to describe, extend and create a variety of numeric and geometrical patterns, make predictions related to the patterns and investigate repeating patterns involving reflections

● Understand the concept of equality between pairs of expressions, using addition, subtraction and multiplication

● Creating a number pattern involving addition, subtraction or multiplication, given a pattern rule expressed in words

● Extending, describing and creating repeating, growing and shrinking patterns

● Extending and creating repeating patterns that result from reflections, using a

variety of tools

● Identifying and using the commutative property of multiplication to facilitate computation with whole numbers

● Identifying and using the distributive property of multiplication to facilitate

computation with whole numbers

● Determining the missing number in equations involving multiplication of one-and two-digit numbers

● Identifying and using variables as unknown quantities represented by a letter or other symbol

Grade 3

● Understand how to describe, extend and create a variety of numeric and geometrical patterns

● Representing simple geometrical patterns using a number sequence, a number line or bar graph

● Creating repeating pattern involving more than two attributes (i.e. size, colour,

orientation, number)

● Identifying and describing number patterns involving addition, subtraction and multiplication, represented on a number line, on a calendar and on a hundreds chart

● Extending repeating, growing and shrinking number patterns

● Identifying the properties of zero and one in multiplication

● Explaining how the pattern of multiplication results from repeating addition

● Explaining how the pattern of division results from repeating subtraction

● Understand the concept of equality between pairs of expressions, using addition and subtraction of one and two digit numbers

● Determining the missing number in equations involving addition and subtraction of one and two digit numbers

● Determining the inverse relationship between multiplication and division

● Identifying and using the associative property of addition to facilitate

computation with whole numbers

Grade 2

● Understand how to identify, describe, extend and create repeating patterns, growing patterns and shrinking patterns

● Understand the concept of equality between pairs of expressions, using concrete materials, symbols, and addition and subtraction to 20

● Identifying, describing and extending geometric repeating patterns involving more than one attribute

● Creating repeating patterns by combining attributes (i.e. colour and shape;

colour and size)

● Identifying, extending and creating numeric repeating patterns

● Identifying, describing and creating growing and shrinking patterns generated by the repeated addition or subtraction of 1's, 2's, 5's, 0's and 25's, using a variety of strategies (i.e. number line, hundreds chart)

● Identifying how the pattern of multiplication results from repeating addition

● Identifying how the pattern of division results from repeating subtraction

● Determining the missing number in equations involving addition and subtraction to 20

● Representing, with concrete materials and pictures, two number expressions

that are equal, using the equal sign

● Determining the inverse relationship between addition and subtraction

● Identifying and using the commutative property of addition to facilitate computation with whole numbers

● Identifying the properties of zero in addition and subtraction

Grade 1 ● Understand how to identify, describe, extend and create repeating patterns

● Understand the concept of equality, using concrete materials and addition and subtraction to 10

● Identifying, describing, and extending geometric repeating patterns involving one attribute

● Creating repeating patterns involving one attribute (i.e. size, colour, shape,

sound)

● Identifying and extending numeric repeating patterns

● Creating a set in which the number of objects is greater than, less than or equal to the number of objects in another given set

● Using a 'balance' model to show examples of equality

K2 ● Understand how to sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings

● Creating and describing patterns using materials, sounds, movement or drawings

K1 ● Understand how to sort familiar objects and describe patterns in various ways

● Sorting real objects by attributes, including colour, size, and shape

Learning Outcomes and Benchmarks Subject : MATHEMATICS Strand : GEOMETRY





Grade 11



Grade 10 Transformational Geometry ● Perform 2D transformations of geometric shapes

Trigonometry

● Apply the Law of Sines and the Law of Cosines, including the ambiguous case for sine.

● Graph sine and cosine waves

Transformational Geometry Students will be able to show their understanding by:

● describing an algebraic rule that defines translations, reflections and dilations; eg: reflection over the x-axis described as (x,y) → (x, -y)

● applying algebraic rules for transformations to generate a table of co-ordinates for an image given the co-ordinates of the pre-image

Extension:

● apply shearing transformations Trigonometry

● using Pythagorean triples when solving right triangles ● determining the exact values of sine, cosine and tangent for 30-60-90 and

45-45-90 using special triangles ● choosing appropriate formulae (right triangle trigonometric ratio, Sine Law,

Cosine Law) to calculate unknown sides and angles in right and non-right-angled triangles

● given a graph, stating the amplitude and period of a sine or cosine curve

















Vectors

● Work with 2D vectors

including vertical (but not horizontal) translations Extension:

● converting between degrees and radians ● using radians to solve trigonometric problems ● using the unit circle to find exact values of trigonometric functions of special

angles ● using simple trigonometric identities to simplify expressions and solve

equations where 0°≤θ≤360° ( )in x os x , tanxs 2 + c 2 = 1 = sinxcosx

Vectors

● writing vectors in column form and unit form ● graphing vectors and calculating magnitude ● adding and subtracting vectors (algebraically and graphically) ● multiplying by a scalar and graphing the resultant ● determining whether or not vectors are parallel or perpendicular ● writing vectors as position vectors ● applying the dot product to vectors ●

Extension: ● calculating the dot product of two vectors and scalar in 3D ● applying the vector equation of a line

Grade 9

Deductive Geometry ● Apply the properties of similar and congruent triangles

Co-ordinate Geometry

● Apply the properties of two dimensional shapes on a coordinate plane

Deductive Geometry ● determining whether two triangles are similar, congruent or neither, giving

proof to support their claim ● determining the lengths of sides and sizes of angles in two similar or

congruent shapes, with emphasis on triangles Extension:

● Justify and provide proof of similarity and/or congruence using applicable theorems.

Co-ordinate Geometry

● calculating the distance between two points using the distance formula

Trigonometry

● Apply right triangle trigonometry in a variety of contexts Three Dimensional Geometry

● Apply geometric properties to three-dimensional shapes

● calculating the perpendicular distance between a point and a line ● calculating a midpoint using the midpoint formula ● geometric construction involving loci ● determining the location of intersection between lines and circles ● relating the distance formula between two points to Pythagoras’ theorem

Extension:

● Apply coordinate geometry methods to three-dimensional questions to calculate distances and midpoints

Trigonometry

● finding the lengths of sides and angle measures of right-angled triangles using trigonometric ratios (sine, cosine and tangent)

● solving real-life problems using trigonometric ratios such as applying and understanding of the angles of elevation and depression, finding unknown heights, and finding three-figures-bearings (and so on)

● applying trigonometry to three-dimensional problems Three-Dimensional Geometry

● finding volumes and surface areas of prisms, cones, cylinders, pyramids and spheres

● finding and applying planes of symmetry

Grade 8

2D and 3D Shapes

● Understand and analyse characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

2D and 3D Shapes

● Calculating perimeter and area of polygons and circles, including composite shapes

● Calculating surface area and volume of prisms ● Applying Pythagorean theorem and Pythagorean triples to solve for

missing sides of right triangles in 2D shapes and 3D solids ● Identifying similarity and congruency in 2D shapes

Grade 7

2D and 3D Shapes

● Understand and analyse characteristics and properties of two and three-dimensional geometric shapes, and understand volume and surface area as attributes of three dimensional shapes

● Understand and analyse characteristics and properties of angles in parallel lines and polygons

2D and 3D Shapes ● Calculating the area and perimeter of composite 2D shapes ● Calculating the circumference and area of circles ● Using Pythagorean Theorem to solve for the unknown side of right angle

triangles ● Using angle properties to calculate unknown angles in parallel lines ● Calculating the sum of interior and exterior angles in polygons ● Using nets of three-dimensional objects to visualize component shapes of 3D

shapes and develop and justify formulae for surface areas and volumes of prisms, pyramids, and cylinders

● Applying formulae to calculate volume and surface area of prisms

Grade 6

Coordinate Geometry

● Specify locations and describe spatial relationships using coordinate geometry and begin to apply transformations and use symmetry to analyse mathematics in the real world.

2D and 3D Shapes

● Understand and analyse characteristics and properties of triangles, quadrilaterals and other regular polygons and understand perimeter and area as attributes of two dimensional shapes

● Understand and analyse characteristics and properties of angles in triangles and quadrilaterals

● Identify simple 3D shapes and calculate volume of rectangular prisms and cubes

Coordinate Geometry

● Accurately reading and plotting coordinate points on a Cartesian plane using the form (x,y)

● Using the Cartesian plane to plot points and draw graphs of patterns and relations in all four quadrants

● Using the Cartesian plane to plot simple figures and determine their image under translations, rotations and reflections

● Determining reflectional symmetry of an object in a vertical or horizontal line ● Determining the center and order of rotation of an object ● Describing transformations to an object by describing the coordinates of the

image

2D and 3D Shapes

● Applying scale and accurately reading a map using the scale ● Drawing simple to scale maps ● Convert units in the metric system in length, area and volume ● Selecting and using appropriate units to measure angles, perimeter,

area and volume ● Investigating and developing understanding of relationship amongst

interior angles of triangles and quadrilaterals ● Finding unknown angles in geometric figures using angle theorems ● Selecting and applying techniques and tools to accurately find length,

perimeter, area, and angle measures to appropriate levels of precision

● Using a protractor to accurately construct and measure all angles ● Using appropriate formulae to determine perimeter and area of

triangles, quadrilaterals, and other regularly and irregularly shaped polygons

● Naming simple 3D shapes; cube, rectangular prism, cylinder, triangular prism, pyramid, sphere

● Calculating the volume of rectangular prisms and cubes

Grade 5

Coordinate Geometry

○ Specify locations and describe spatial relationships using coordinate geometry and begin to apply transformations and use symmetry to analyse mathematics in the real world.

2D and 3D Shapes

● Understand how to identify and classify two-dimensional shapes by side and angle properties, and compare and sort three dimensional figures

● Understand how to identify and construct nets of prisms and pyramids

Symmetry Understand how to apply transformations and use symmetry to

Coordinate Geometry

Accurately read and plot coordinate points on a Cartesian plane using the form (x,y)

○ Develop understanding of the different components of the Cartesian plane (origin, horizontal axis, vertical axis, quadrants)

○ Use the Cartesian plane to plot points and draw graphs of patterns and relations in the first quadrant

2D and 3D Shapes

● Recognising the properties of regular polygons (number of interior angles; sum of interior angles etc) and apply these to solve problems involving unknown sides and angles

● Distinguishing among prisms, right prisms, pyramids, and other three-dimensional figures

● Measuring and constructing angles up to 180 degrees, using a protractor.

● Recognising that the angle sum of a triangle is 180 and using this knowledge to calculate unknown angles of a triangle

● Identifying prisms and pyramids from their nets ● Constructing nets of prisms and pyramids, using a variety of tools ● Match images of 3D objects to their plan views (top, side, front and

back)

Symmetry ● Creating and analysing designs by translating and/or reflecting a

analyse mathematical situations Directions and Mapping

● Understand how to identify and describe the location of an object, using cardinal directions in terms of degrees

shape, or shapes, using a variety of tools ● Identifying, performing and describing translations, using a variety of

tools

Directions and Mapping ● Expressing cardinal directions in terms of degrees (5 degrees North)

Grade 4

2D and 3D Shapes

● Understand how to identify polygons and three-dimensional figures and classify them by their geometric properties, and compare various angles to benchmarks

● Understand how to construct three-dimensional figures, using two dimensional shapes

2D and 3D Shapes

● Identifying and comparing different types of polygons and sort and classify them by their geometric properties (number of interior angles; number of right angles)

● Identifying and describing prisms and pyramids, and classify them by their geometric properties, using concrete materials

● Identifying benchmark angles (45,90,180 degrees), using a reference tool,

and comparing other angles to these benchmarks

● Relating the names of the benchmark angles (right angle and straight line) to their measures in degrees

● Drawing and describing the net of rectangular and triangular prisms

● Constructing prisms and pyramids from given nets

Symmetry

● Understand how to create symmetrical patterns, pictures and shapes with and without digital technologies

Directions and Mapping

● Understand how to identify and describe the location of an object, using ordinal directions

Symmetry

● Creating and analysing symmetrical designs by reflecting shape or shapes, using a variety of tools and identify the congruent shapes in the designs

● Identifying, performing and describing reflections, using a variety of tools


● Identifying and locating an object using ordinal directions (i.e. Northeast, Southeast, etc.), using various types of maps

Grade 3

2D and 3D Shapes ● Understand how to compare two dimensional shapes

and three dimensional figures and sort and classify them by their geometric properties

● Understand how to describe relationships between two-dimensional shapes, and between two-dimensional shapes and three-dimensional figures

2D and 3D Shapes ● Identifying and comparing various polygons (triangles, quadrilaterals,

pentagons, hexagons, heptagons, octagons) and sort them by their geometric properties (number of faces, edges and vertices)

● Comparing and sorting prisms and pyramids by geometric properties, using

concrete materials

● Using a reference tool (paper corner, pattern block) to identify right angles and to describe angles as greater than, less than or equal to a right angle

● Comparing various angles, using concrete materials and pictorial

representations, and describe angles as bigger than, smaller than, or about the same as other angles

● Identifying and describing the two dimensional shapes that can be found in a three dimensional figure

● Constructing three-dimensional figures, using congruent shapes

Symmetry

● Understand how to recognise and explain symmetrical patterns, including tessellations, in the environment


● Understand how to identify and describe the location of an object, using cardinal directions

Symmetry

● Completing and describing designs and pictures of images that have vertical, horizontal or diagonal lines of symmetry

● Identifying reflections, translations and rotations, using concrete materials and

physical motion Directions and Mapping

● Identifying and describing the location of an object using cardinal directions (North, South, East, West)

Grade 2

2D and 3D Shapes

● Understand how to identify common two-dimensional shapes and three-dimensional figures and sort and classify them by their geometric properties

● Understand how to compose and decompose common two-dimensional shapes and three-dimensional figures

Symmetry

● Understand how to recognise and explain symmetrical patterns, including simple transformations, in the environment

2D and 3D Shapes

● Identifying and describing various polygons (triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons) and sort and classify them by their geometric properties (number of edges, vertices and faces), using concrete materials and pictorial representations

● Identifying and describing various three-dimensional figures (cubes, prisms,

pyramids) and sort and classify them by their geometric properties (number and shape of faces), using concrete materials

● Composing and describing pictures, designs and patterns by combining two-dimensional shapes

● Constructing three-dimensional figures (cubes, prisms, pyramids), using a

variety of tools Symmetry

● Locating the line of symmetry in two dimensional shapes

● Creating and describing symmetrical designs using a variety of tools (pattern blocks, tangrams, paper and pencil)


● Understand how to identify and describe the locations and movements of shapes and objects

● Identifying flips, slides and turns using concrete materials and physical motion


● Describing movement from one location to another using various maps

Grade 1 2D and 3D Shapes ● Understand how to identify common two-dimensional

shapes and three-dimensional figures and sort and classify them by their attributes

● Understand how to compose and decompose common two-dimensional shapes and three-dimensional figures

Symmetry

● Understand how to identify symmetry in the environment

2D and 3D Shapes ● Identifying and describing common two dimensional shapes (circles, triangles,

rectangles, squares) and sort and classify them by their attributes ( size, number of sides), using concrete materials and pictorial representations

● Identifying and describing common three-dimensional figures (cubes, cones,

cylinders, spheres, rectangular prisms) and sort and classify them by their attributes, using concrete materials and pictorial representations

● Identifying the two dimensional faces of three-dimensional figures, using concrete models

● Composing patterns, pictures and designs, using common two-dimensional

shapes

● Describe similarities and differences between everyday objects and three dimensional figures

● Constructing three-dimensional figures (cubes, cones, cylinders, spheres,

rectangular prisms), using a variety of tools Symmetry

● Locating shapes in the environment that have symmetry and describing the symmetry

● Creating symmetrical designs and pictures, using concrete materials and

describing the relative location of the parts


● Understand how to describe and represent the relative location of objects, and represent objects on a map


● Describing the relative locations (i.e. beside, two steps to the right of) and the movements of objects on a map (i.e. 'The path shows that he walked around the desk, down the aisle, and over to the window')

● Drawing simple maps of familiar settings, and describing the relative locations

of objects on the maps

K2 2D and 3D Shapes ● Understand how to sort, describe and name familiar

two-dimensional shapes and three dimensional figures in the environment


● Understand how to describe the relative locations of objects using positional language

2D and 3D Shapes ● Sorting and describing squares, circles, triangles, rectangles, spheres and

cubes Directions and Mapping

● Describing the relative locations of objects or people using positional language (i.e. over, under, above, below, in front of, behind, inside, outside, beside, between, along)

● Describing the relative location of objects on concrete maps created in the

classroom

K1 2D and 3D Shapes ● Understand how to use everyday language to describe

shapes Directions and Mapping

● Understand how to describe position and movement

2D and 3D Shapes ● Using words such as 'raindrop', 'egg shape', 'curved', 'bent', and 'round' to

describe shapes Directions and Mapping

● Interpreting the everyday language of location and direction, such as 'between', 'near', 'next to', 'forward', 'toward'

● Following and giving simple directions to guide a peer around an obstacle

path and vice versa

Learning Outcomes and Benchmarks Subject : MATH Strand : MEASUREMENT **Measurement is NOT a strand in the ISS/ IBO MYP curriculum. Topics that are somewhat related to Measurement are reallotted to Strands in NUMBER and SHAPE AND SPACE.



Grade 5

Length - Weight - Capacity - Volume ● Understand how to estimate, measure,

compare and record length, perimeter, area, mass, capacity and volume, using a variety of strategies

Length - Weight - Capacity - Volume ● Identifying and explaining the

relationship between equivalent standard units

● Selecting and justifying the most

appropriate standard unit to measure length, height, width and distance (millimetre, centimetre, decimetre, metre, kilometre)

● Solving problems requiring conversion

from metres to centimetres and from kilometres to metres

● Estimating, measuring, comparing and

recording the area of regular and irregular polygons using a variety of tools (i.e. grid paper, geoboard, formulas A=LxW)


recording the perimeter of regular and irregular polygons using a variety of tools (i.e. grid paper, geoboard,

Time

● Understand how to estimate, measure, compare and record elapsed time, using a variety of strategies

Temperature

● Understand how to estimate, measure, compare and record temperature change using a variety of strategies

formulas P=(2xL)+(2xW))

● Determining the relationship between capacity and volume by comparing the volume of an object with the amount of liquid it can contain or displace

● Selecting and justifying the most

appropriate standard unit to measure mass (i.e. milligram, gram, kilogram, tonne)

● Measuring, comparing and discussing

the relationship between area, perimeter and volume

Time

● Solving problems that involve the relationship between a 12-hour clock and a 24-hour clock

● Reading, writing, estimating and

measuring time using analogue and digital clocks to the nearest second

● Estimating and determining elapsed

time, with and without using a timeline, given the durations of events expressed in five-minute intervals, hours, days, weeks, months or years

Temperature

● Measuring and recording temperatures to determine and represent temperature changes over time

Angles ● Understand the relationships between

angles of intersecting lines

Angles ● Recognising and applying angle

relationships associated with intersecting lines (i.e. recognise that vertically opposite angles are equal)

Grade 4

Length - Weight - Capacity - Volume ● Understand how to estimate, measure,

compare and record length, perimeter, area, mass, capacity and volume, using a variety of strategies

Length - Weight - Capacity - Volume

● Identifying the relationship between equivalent standard units


recording length, height and distance using standard units (millimetre, centimetre, metre, kilometre)

● Drawing items using a ruler, given

specific lengths in millimetres

● Estimating, measuring, comparing and recording the area of polygons using a variety of tools and strategies (i.e.centimetre grid paper, geoboard)

● Calculating and comparing the area of

triangles

● Estimating, measuring, comparing and recording the perimeter of two-dimensional shapes, using standard units


recording the capacity of containers, using the standard units of the litre and the millilitre


Time

● Understand how to estimate, measure, compare and record elapsed time, using a variety of strategies

Temperature

● Understand how to estimate, measure, compare and record temperature using standard units

Angles

● Understand how to estimate, measure, compare and construct angles using a protractor and degrees

recording the mass of objects using the standard units of the kilogram and gram


recording volume, and relating volume to the space taken up by an object

Time

● Solving problems involving the relationship between years and decades, and between decades and centuries, using a variety of tools (i.e. calendars, calculators)

● Reading, writing, estimating and

measuring time using analogue and digital clocks to the nearest minute

● Estimating and determining elapsed

time, with and without using a timeline, given the durations of events expressed in five-minute intervals, hours, days and weeks

Temperature

● Estimating, reading and recording temperatures to the nearest degree Celsius, including negative degrees

Angles

● Measuring and constructing angles using both 180 degrees and 360 degree protractors

● Classifying angles as acute, right,

obtuse and reflex

Grade 3


● Understand how to estimate, measure, compare and record length, perimeter, area, mass, and capacity using standard units


● Explaining the importance of using common units of measurement


recording length, height and distance using standard units (centimetre, metre, kilometre)

● Drawing items using a ruler, given

specific lengths in centimetres

● Estimating, measuring, comparing and recording area (i.e. using centimetre grid paper, arrays) using standard units

● Describing the relationship between the

size of a unit of area and the number of units needed to cover a surface


recording the perimeter of polygons using a variety of tools and strategies (i.e. centimetre grid paper, geoboard)


recording the capacity of containers using the standard unit of the litre or parts of a litre (i.e. half or quarter of a litre)


recording the mass of objects, using

Time

● Understand how to estimate, measure, compare and record time using standard units

Temperature

● Understand how to estimate, measure, compare and record temperature using standard units

Angles

● Understand how to estimate, measure, compare and construct angles using a protractor and degrees

the standard unit of the kilogram or parts of a kilogram (i.e. half or quarter of kilogram)

Time

● Solving problems involving the relationships between minutes and hours, hours and days, days and weeks, and weeks and years, using a variety of tools (i.e. clocks, calendars, calculators)

● Reading and writing time using

analogue and digital clocks to the nearest five minutes

● Using calendars to locate specific

information and identifying personally or culturally specific days

Temperature

● Estimating, reading and recording positive temperatures to the nearest degree Celsius

Angles

● Measuring and constructing angles using both 180 degrees and 360 degree protractors

● Classifying angles as acute, right, obtuse and reflex

Grade 2


● Understand how to estimate, measure, compare and record length, perimeter, area, mass, and capacity using non-standard and standard units

Time

● Understand how to estimate, measure, compare and record time using non-standard and standard units


● Selecting and justifying the choice of a standard unit or a nonstandard unit to measure length


recording lengths, heights and distances using standard units (centimetre, metre) and non-standard units


recording the distance around objects, using non-standard units


recording area, using a variety of non-standard units

● Describing the relationship between the

size of a unit of area and the number of units needed to cover a surface


recording the capacity and/or mass of an object, using a variety of non-standard units

Time

● Determining the relationship between days and weeks and between months and years


analogue and digital clocks to the quarter hour

Temperature

● Understand how to estimate, measure, compare and record temperature using non-standard and standard units

● Using calendars to locate specific information and identifying personally or culturally specific days

Temperature

● Describing how changes in temperature affect everyday experiences

● Using a standard thermometer to

determine whether temperature is rising or falling

Grade 1 Length - Weight - Capacity - Volume ● Understand how to estimate, measure,

describe and compare length, area, mass and capacity using nonstandard units of the same size

Length - Weight - Capacity - Volume ● Justifying why non-standard units must

be the same size when measuring

● Comparing two or three objects using measurable attributes and describing the objects using relative terms (e.g. taller, heavier, faster, bigger, warmer)

● Estimating, measuring and describing

lengths, heights and distances in non standard units

● Using concrete materials to describe

the relationship between the size of a unit and the number of units need to measure length


area using nonstandard units

Time ● Understand how to estimate, measure and

describe time using nonstandard and standard units

Temperature

● Understand how to estimate, measure and describe temperature using nonstandard units of the same size

Time ● Reading the date on a calendar


analogue and digital clocks to the hour and half hour


the passage of time using nonstandard units (i.e. number of sleeps, number of claps, number of flips of a sand timer)

Temperature

● Relating temperature to experiences of the seasons

K2 Length - Weight - Capacity - Volume ● Understand how to direct and indirect

comparisons to decide which is longer, heavier, or holds more, and explain reasoning in everyday language

Time

● Understand how to compare and order duration of events using everyday language of time

Length - Weight - Capacity - Volume ● Using suitable language associated

with measurement attributes, such as 'tall' and 'taller', 'heavy' and 'heavier, 'holds more' and 'holds less'

● Comparing objects directly, by placing

one object against another to determine which is longer or by pouring from one container into the other to see which holds more

Time

● Identifying the days of the week and linking specific days to familiar events

● Sequencing familiar events in time

order ● Naming the months of the year in order

K1 Length - Weight - Capacity - Volume ● Understand how to compare a group of

objects and describe them by their length and height

Time

● Understand how to describe a duration of time

Length - Weight - Capacity - Volume ● Ordering two items by length or height

● Comparing the length of an object by

lining up multiple units Time

● Identifying the continuity of time such as day into night and night into day

Documents

MATHEMATICS - International IB school | ISS International …€¦ · · 2017-06-01Grade 12 Learning outcomes and benchmarks for IB Diploma subjects are prescribed by the current