International School of Lausanne

Mathematics

Philosophy

Students from Reception to Year 6 use the Everyday Mathematics program as a foundation for the development of mathematical knowledge. This program is grounded in the belief that repeated exposure through topics and strands build students’ mathematical knowledge from the basics to higher-order and critical problem solving. These strands are numeration and order, operation and computation, patterns, algebra and functions, geometry and spatial sense, measurement, data analysis and probability. These strands are revisited and built upon in each year group. The ISL math curriculum also includes a variety of mathematical resources from around the world to extend and support Everyday Mathematics.

Aims

Development of conceptual understanding

The curriculum builds conceptual understanding while maintaining mastery of basic skills
Concepts and skills are taught in a repeated fashion and not in isolation from one another

Problem solving for everyday situations

Effective multiple strategies for problem solving are encouraged

Developing readiness through hands-on activities

Reading, writing and drawing are integral parts of mathematics
Explorations and projects are integral parts of the program
Children receive instruction and opportunity on the use of a variety of mathematics tools for example, calculators, computers, measuring tools and number lines

Establishing links between past experiences and explorations of new concepts

Children share their thinking and strategies
Mental math is supported, developed and encouraged to be used whenever possible

Sharing ideas through discussion

Discussion is encouraged because talking about mathematics is an important part of learning about mathematics

Cooperative learning through partner and small-group activities

Children learn to work together in cooperative situations
Individual needs, abilities and interests and learning styles can be accommodated

Practice through games

Frequent practice is a necessity to attain mastery of basic facts and algorithms

Ongoing review throughout the year

Repeated exposure to key ideas are built into the program

Daily routines

Routines help students to develop a sense of order and responsibility while reinforcing mathematical concepts
Language and design of program are consistent throughout the primary years

Informal and Formal assessment

Assessments and unit reviews are built into the program

Home and school partnership

Learning is more optimal for children when child, teacher and parents work together
Students are led to see the relevance and value of mathematics and to use their knowledge and skills in the context of everyday life
Provides students with the understanding and knowledge that allows for their transfer into other schools and other education systems

	Reception 3	Reception 4	Year 1	Year 2
Number	Students should be able to:
	* explore the language and meaning of numbers 1 - 5 using concrete materials * have some knowledge of one to one correspondence * count objects to 10 * recognise positional words such as first and last	* explore the language and meaning of numbers 1 - 10 using concrete materials * count objects to 20 * write numbers 1 - 20 * recognise positional words such as first and last, top, bottom, left, right explore and develop the concept of cardinal and ordinal numbers from 0-10 using concrete materials make equivalent sets through one-to one correspondence	* use basic comparison, positional vocabulary * classify objects by attributes of size, shape, colour, kind etc. * recognise, copy, extend and create patterns * continue counting patterns * identify, write, count and order groups 0-20, including estimates * add, subtract one digit numbers without regrouping* associate symbols to sets * recognise equal parts (pairs) * introduce plus, minus and equal signs	* represent numbers as tens and ones up to two digits * apply place value to whole number operations* explore relationship between place value and order * revise, order, compare, write numbers (0 to 20) * identify ordinal numbers to twelfth * understand positional vocabulary * recognise, copy, extend and create patterns * identify, order, compare, write numbers to 100 * count by ones, twos, fivesand tens using simple number patterns * demonstrate operation of addition and subtraction * explore the use of plus, minus and equal signs * introduce > and < signs * introduce regrouping in addition andsubtraction * explore calculator to develop counting patterns * mentally add or subtract 10s to/from any number * begin mental arithmetic for adding two digit numbers

	Reception 3	Reception 4	Year 1	Year 2
Fractions	Students should be able to:
				* develop understanding of equal parts * understand one half, third, fourth of a region * explore/use equal parts of a set

	Reception 3	Reception 4	Year 1	Year 2
Measure	Students should be able to:
	* have some understanding of comparative measures, e.g. taller than, shorter than, etc * explore shapes through construction	* have some understanding of comparative measures, e.g. taller than, shorter than, etc * explore shapes through construction * time - duration (more time, less time) * time - daily routines * volume - empty, half full, full *compare weights using approriate vocabulary, e.g. lighter than, heavier than	* compare, sort, classify and order by size, length, capacity & temperature * explore length using arbitrary units * explore capacity using appropriate language (full, empty, more than…) * time - during (more/less time), night day, calendar language * simulate payment for services with Swiss currency	* length - estimate, order and measure with arbitrary and metric (cm and m) units * capacity measures - standard and non-standard measures * mass/weight - use of a variety of scales and balances * temperature - read and compare * time - day divided into hours, read time to hour and half hour * calendar language, days of the week * money - value of all coins in a denomination, counting * show amount of money in different coin combinations * exchange coins for a given amount * compare coin values * create and solve money stories

	Reception 3	Reception 4	Year 1	Year 2
Geometry Spacial Sence	Students should be able to:
	* use everyday language to describe shape * recognise, continue and create simple repeating patterns with real objects	* use everyday language to describe shape * recognise, continue and create simple repeating patterns with real objects	* identify 2D and 3D shapes * identify objects that are of the same length, which is longer or shorter * solve problems by recognising and extending patterns	* identify and compare properties of 2D and 3D shapes * identify similarities, differences and patterns in shapes, including reflection and simple tessellation * construct simple geometric shapes * explore with pattern blocks and attribute blocks

	Reception 3	Reception 4	Year 1	Year 2
Data and Chance	Students should be able to:
	* sort real life objects into sets by attributes * graph real life objects	* sort real life objects into sets by attributes * graph real life objects * interpret simple data	* make and interpret real graphs/picture graphs * make and interpret simple bar graphs * explore with pattern blocks * talk about possible/impossible events	* develop/interpret picture graphs and simple bar graphs * collect, sort and organise data for graphs in tables * use a variety or recording strategies

	Reception 3	Reception 4	Year 1	Year 2
Problem Solving	Students should be able to:
		raise questions observe, test, predict	* select and apply appropriate stategy * identify relevant language * evaluate solutions	* select and apply appropriate stategy * identify relevant information * evaluate and create strategies and solutions

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	Year 3	Year 4	Year 5	Year 6
Number	Students should be able to:
	* read, write and compare numbers up to 999 * use ordinal numbers to 20th * introduce thousands and zero as placeholder * count by ones, fives, tens and hundreds * recognise that all numbers are created from 0-9 * use > and <symbols for comparison * compare and order numbers to hundreds * addition - sums to 20 * subtarction - difference to 20 * add and subtract two-digit numbers with and without regrouping * create number stories with both addition and subtraction * add a multiple of 10 to any two-digit number * add two three-digit numbers with and without regrouping * multiplication - readiness by counting repeated addition, arrays and factors to 5 * division - grouping/sharing equal sets, create number stories * introduce squared paper for written work as appropriate	* explore place value relationships * identify the place value of a digit to millions * write whole numbers to ten thousands * introduce hundred thousands to millions * compare and order numbers to ten thousands * round numbers to the nearest ten or hundred * develop identification of odd and even numbers * explore square numbers * introduce concept of negative numbers * mental maths facts mastered to 20 * exposure to strategies of addition and subtraction of multipple digits * multiplication - factors to 10 * develop multiplication strategies 2 digits x I digit * introduce division strategies, 2 digits x 1 digit with equal sharing, including remainders * develop greater accuracy with estimation	* explore/identify concepts of place value from 100s to 100000s to M * read/write whole numbers to 100000 in figures and word form * compare and order whole numbers and decimals to 100000s * round numbers to the nearest ten or hundred * round decimals to tenths * multiply and divide numbers by 10s * addition/subtraction mental recall of facts to 20 * multiplication - factors to 12 * develop multiplication and division of 4 digit numbers by 1 digit number * dividion - factors to 12 * develop strategies for dividing 4 digit numbers by 1 digit with remainders * use calculator to multiply and divide numbers by 1 or 2 digit numbers * devel understanding of square numbers * further developpatterns for identifying odd/even numbers and positive/negative numbers * use brackets correctly * develop greater accuracy with estimation	* identify the place value of a digit to millions * compare and order numbers to millions * round numbers to the nearest 1, 10,100 or 1000 * add or subtract any numbers to 6 digits * estimate with percentages * estimate sums, differences, products and quotients * multiply any number to 4 digits by any number to 3 digits * divide any 4 digit number by a 1 digit number * use a calculator to add, subtract, multiply or divide numbers * find patterns in number sequences * understand multiples, factors and prime numbers * additiona and subtraction of negative numbers * parentheses to make number sentences true * algebraic expressions

	Year 3	Year 4	Year 5	Year 6
Fractions	Students should be able to:
	* identify, write and compare fractional parts * recognise half, third, quarter, sixth and eighth of a region or set * explore fractional equivalencies	* explore equivalent fractions * calculate simple fractions of quantities * identify fractions on a number line * learn to identify fractional equivalencies	* numerator/denominator as terms * compare fractions with like * use >, <, +, = signs * order fractions with like denominator * find fractional parts of a number, money and shapes	* round fractions to the nearest whole amount * compare and order fractions (equivalent fractions) * add and subtract like and unlike fractions, and mixed numbers * multiplication of fractions, whole numbers and mixed numbers * interchange mixed numbers and improper fractions * explore multiplication of fractions * find fractional parts of a number

	Year 3	Year 4	Year 5	Year 6
Decimals	Students should be able to:
		* add and subtract numbers to two decimal places, including money * extend decimals to thousandths using metric units of length * compare and order decimals < > and equivalencies	* develop place value of decimals to thousandths * round given amounts of money * add and subtract decmals and money * estimate sums and differences * multiply decimals to tenths, by whole numbers * explore equivalence between decimal fractions and common fractions	* order and compare decimals * use place value to thousandths * write decimals as fractions and fractions as decimals * round decimals and money using various currencies * add and subtract decimals with different decimal places * multiply/divide decimals and whole numbers * estimate sums, differences and products

	Year 3	Year 4	Year 5	Year 6
Ratio Percent	Students should be able to:
				* introduce ratio as a fraction * interpret scale drawing with ratios * write fractions as % and a decimal * calculate simple percentages * write number models for ratio number stories

	Year 3	Year 4	Year 5	Year 6
Measure	Students should be able to:
	* compare linear measurement with cm., mm., m. and km. * categorise measures of length, weight and capacity * explore equivalence between units of measure * find perimeter and area of object * solve problems about temperature differences * read and measure time to the nearest min, hour and half hour * use calendars * explore digital clocks and relate to clock face * read decimal notation of money * make change for a given amount of money * compare prices	* use linear measures * use capacity, mass and weight measures * explore simple equivalent metric measures * draw to a given measure and label line segments * determine appropriate types of scale * write the values of coins using decimal notation * apply monetary knowledge to find best prices for realistic situations * explore currencies from around the world * revisit counting on to give change explore temperature using Celsius, introduce negative temperatures * estimate reasonably in all areas of measurement * review measuring of perimeter, area and volume * use vocabulary of time * explore calendar concepts * money - addition and subtraction, differences in currencies	* accurately estimate and measure linear measurements * find equivalent linear measures * capacity - litre and millilitre * mass/weight - kilogram and gram * choose appropriate measuring tools and appropriate units of measure * calculate perimeter and area of shapes * solve problems involving perimeter and area * tell time to the minute * find elapsed time * money - add, subtract, multiply and divide given amounts * explore degrees of angles, develop appropriate vocabulary (right, obtuse acute) * measure and construct angles with a protractor	* measure linear, capacity and weight amounts accurately * discover relations between measures of volume and capacity * explore equivalencies between metric and customary measures * measure time to seconds * find Celsius and Fahrenheit equivalencies * calculate perimter and area of rectangles and irregular shapes * calculate volume of rectangular prisms * use time zones, timetables change units of time add and subtract time

	Year 3	Year 4	Year 5	Year 6
Geometry Spatial Sense	Students should be able to:
	* identify and explore the properties of 2D and 3D shapes * explore bases, faces and corners of slids * identify congruent figures * explore symmetry * explore tessellation * construct simple geometric shapes	* explorfe similarities and differences in 3D shapes * draw/name points in segments/lines * introduce parallel and perpendicular lines * explore attributes of triangles and quadrilaterals * identify lines of symmetry * form angles by making turns * order a set of angles by size	* identify lines, parallel, intersecting lines and their angles * count faces, edges and vertices of 3D shapes * identify and name polygons and congruent figures * identify lines of symmetry * create tessellating patterns	* identify lines, parallel, intersecting lines and their angles * identify plane and solid figures * draw measure and classify angles * calculate angles using a protractor * classify polygons and congruent shapes * find circumference of a circle * identify lines of symmetry and rotational symmetry

	Year 3	Year 4	Year 5	Year 6
Data and Chance	Students should be able to:
	* collect and organise data for graphs * make and interpret picture and bar graphs * develop language for probability and record outcomes of probability in everyday situations	* read/make/interpret picture graphs, bar, frequency and pie charts * explore data in a table * explore probability * find mean, median and mode	* read/make/interpret picture graphs, bar, frequency and pie charts * use simple conversion graphs * conduct probability experiments and record outcomes * calculate the mean, mode, median, range, maximum and minimum * introduce percentages * links between fractions, decimals and percentages * use computer to gather and display information in a variety of forms	* read/make/ interpret picture graphs, bar, frequency and pie charts * collect, organise and interpret data * use a computer to gather and display data in a variety of forms * introduce coordinates * record outcomes and find fractional probabilities * calculate the mean, mode, median, range, maximum and minimum

	Year 3	Year 4	Year 5	Year 6
Problem Solving	Students should be able to:
	* select and apply appropriate strategy * identify relevant information * develop strategies * evaluate solutions	* select and apply appropriate strategy * identify relevant information * develop strategies * evaluate solutions	* select and apply appropriate strategy * identify relevant information * develop strategies * evaluate solutions	* select and apply appropriate strategy * identify relevant information * develop strategies * evaluate solutions