Math syllabus Kindergarten 1 Number strand: • Count forward and backwards to 10 • Identify numbers to 10 on a number line • Use ordinal numbers first (1st) to fifth (5th) correctly • Recognize and play with money Pattern strand: • Identify basic repeating patterns with one attribute Shape and space strand: • Identify shapes in the environment • Identify common 2-­‐dimensional shapes • Describe locations of objects or people using basic positional language Measurement strand: • Relate events to morning, afternoon, evening and night Data handling strand: • Organize objects into categories by sorting and classifying Kindergarten 2 Number strand: • Identify numbers to 20 on a number line • Recognize and match number names to 10 • Investigate, through play, how something can be divided into parts • Use ordinal numbers to twentieth (20th) correctly • Understand that money varies in value • Play with money to understand that sometimes we need change back Pattern strand: • Identify, describe, create and extend basic repeating patterns with one attribute Shape and space strand: • Identify shapes in the environment • Describe and sort 2-­‐dimensional shapes • Compose patterns, pictures and designs, using common 2-­‐
dimensional shapes • Describe similarities and differences between everyday objects and 3-­‐dimensional figures • Identify the 2-­‐dimensional faces of 3-­‐dimensional figures, using concrete models • Describe locations of objects or people using positional language Measurement strand: • Compare and order 2 to 3 everyday objects using the vocabulary of large, heavy, short, wide, high, early, and the comparatives and superlatives • Describe their daily routine • Relate temperature to experiences of the seasons Data handling strand: • Gather data, as an entire class, to answer a question, using a simple survey with a limited number of responses • Collect and organize data using graphs and concrete materials • Organize objects into categories and describe informal sorting experiences • Answer questions about collected data • Describe the likelihood that everyday events will occur Grade 1 Number strand: • Count forward by 1’s, 2’s, 5’s, and 10’s to 100, using various tools and strategies • Count backwards from 20 by 2’s and 5’s • Locate whole numbers to 50 on a number line • Order whole numbers to 50 • Read and write numbers, in words, to 20 • Identify and represent the value of a digit in a number (up to 50) according to its position in the number • Round to the nearest 5 or 10 • Add and subtract one-­‐digit numbers using concrete materials • Mentally solve single digit addition and subtraction • Solve word problems up to the value of 10 • Recognize simple fractions -­‐ 1/2, 1/4 and whole • Use ordinal numbers to fiftieth • Identify and describe various euro coins, and state their value • Show different ways of making €1 • Add and subtract money amounts to 50¢ Pattern strand: • Identify, describe, create and extend repeating patterns involving two attributes • Identify and extend numeric repeating patterns using materials • Determine, using a “balance” model and whole numbers to 10, the number of identical objects that must be added or subtracted to establish equality Shape and space strand: • Identify, describe, sort and classify common 2-­‐dimensional shapes by their attributes • Identify and describe shapes within other shapes • Locate shapes in the environment that have symmetry, and describe the symmetry. • Create and describe symmetrical designs • Make connections between 3-­‐dimensional figures and everyday objects • Identify the various 2-­‐dimensional shapes in 3-­‐dimensional forms • Identify, describe, sort and classify common 3-­‐dimensional figures by their attributes • Build 3-­‐dimensional structures using concrete materials • Describe the location of an object • Describe the locations of objects on self-­‐made maps Measurement strand: • Use the metre as a benchmark for measuring length, and compare the metre with non-­‐standard units • Estimate, measure, and record lengths, heights, and distances • Describe, using concrete materials, the relationship between the size of a unit and the number of units needed to measure length • Measure and describe area using non-­‐standard units • Estimate, measure, and describe the capacity and/or mass of an object, using non-­‐standard units • Compare and order objects by their measurements, using the same non-­‐standard unit • Estimate, measure, and describe the passage of time, using nonstandard units • Read digital and analogue clocks, and use them to tell and write time to the hour and half-­‐hour in everyday settings • Name the months of the year in order, and read the date on a calendar • Describe how changes in temperature, using degrees, affect everyday experiences Data handling strand: • Collect information and organize into different types of graphs • Organize objects into two different categories • Read and comprehend a variety of graphs • Ask and answer questions about collected information • Describe the likelihood that everyday events will occur Grade 2 Number strand: • Count forward by 1’s, 2’s, 5’s, 10’s, and 25’s to 200 • Count backwards by 1’s from 50, and count backwards by 10’s from 100 • Order whole numbers to 100 • Read and write numbers, in words, to 50 • Locate whole numbers to 100 on a number line • Round to the nearest 10 in two-­‐digit numbers • Identify and represent the value of a digit in a number (up to 100) according to its position in the number • Add and subtract two-­‐digit numbers, using concrete materials • Use concrete materials to show division of two-­‐digit numbers • Mentally solve whole number addition and subtraction problems to 20 • Mentally multiply whole numbers by 10 • Solve word problems up to the value of 100 • Understand simple fractions -­‐ 1/2, 1/3, 1/4, 1/8, and whole • Understand equivalent fractions, using real objects • Write ordinal numbers and words • Convert money, up to €5, between coins and notes • Add and subtract money amounts to €1 • Show different ways of making €5 Pattern strand: • Create a pattern results from repeating an operation • Identify, describe, and create patterns involving addition and subtraction, with1’s, 2’s, 5’s, 10’s, and using materials • Demonstrate an understanding of the concept of equality by partitioning whole numbers to 20 in a variety of ways, using concrete materials • Determine the missing number in equations involving addition and subtraction to 20, using various tools and strategies • Identify and use the commutative property of addition • Identify the properties of zero in addition and subtraction Shape and space strand: • Use 2-­‐dimensional shapes to make other 2-­‐dimensional shapes • Locate the line of symmetry in a 2-­‐dimensional shape • Create and describe symmetrical designs using a variety of tools • Identify, describe, sort, and classify various 2-­‐dimensional shapes by their geometric properties • Build 3-­‐dimensional forms using various materials, and describe their characteristics • Identify, describe, sort, and classify various 3-­‐dimensional figures by their geometric properties • Describe 3-­‐dimensional figures and everyday objects using mathematical language • Build a structure using 3-­‐dimensional figures and describe the 2-­‐
dimensional & 3-­‐dimensional shapes used • Draw simple maps of familiar settings, and describe the relative locations of objects on the maps • Describe the location of an object and give directions to find it Measurement strand: • Choose personal referents for a centimetre and a metre to help perform measurement tasks • Investigate, estimate, measure and record length, height, and distance, using standard and non-­‐standard units • Estimate, measure, and record capacity, area and perimeter, using non-­‐standard units • Describe the relationship between the size of a unit of area and the number of units needed to cover a surface • Compare and order a collection of objects by mass and/or capacity, using non-­‐standard units • Construct tools for measuring time intervals in non-­‐standard units • Tell and write time to the quarter-­‐hour • Determine the relationship between days and weeks and between months and years • Use a standard thermometer to determine whether temperature is rising or falling • Describe how changes in temperature, using degrees, affect everyday experiences Data handling strand: • Conduct simple surveys • Collect information and organise into different types of graphs, labeling the axes • Organise objects into two or more separate categories • Read, comprehend, and compare a variety of graphs • Ask and answer questions about collected information represented in graphs • Describe the probability that an event will occur, through investigation and experiments Grade 3 Number strand: • Count forward by 1’s, 2’s, 5’s, 10’s, and 100’s to 1000 from various starting points, and by 25’s to 1000, using various tools and strategies • Count backwards by 2’s, 5’s, and 10’s from 100 • Read and write, in words, whole numbers to 100 • Recognize relationships between numbers up to 1000 • Locate whole numbers to 1,000 on a number line • Understand the value of a digit in a number according to its position in the number • Represent, estimate and order whole numbers up to 1000 • Round three-­‐digit numbers to the nearest 10 and 100 • Add and subtract three-­‐digit numbers, using concrete materials • Multiply 1-­‐digit numbers, using a variety of tools • Divide objects into equal parts, and identify the parts • Solve problems involving the addition and subtraction of two-­‐digit numbers, using various strategies • Multiply whole numbers by 10 and 100 and divide whole numbers by 10, using various strategies • Recognise the relationship between fractions, using concrete materials and drawings • Compare fractions with same numerators • Represent and describe the relationships between coins and bills up to €10 • Estimate, count, and write amounts of money to €10 • Add and subtract money amounts to €5, using a variety of tools Pattern strand: • Identify, extend, and create a pattern involving two attributes, using a variety of tools • Explain that a pattern results from repeating an action • Create a number pattern involving addition or subtraction • Identify and use the associative property of addition • Identify the properties of zero and one in multiplication Shape and space strand: • Solve problems involving 2-­‐dimensional shapes • Explain the relationships between different types of quadrilaterals • Identify congruent 2-­‐dimensional shapes by matching concrete materials • Complete and describe designs and pictures that have a vertical, horizontal, or diagonal line of symmetry • Identify flips, slides, and turns • Identify and compare various 2-­‐dimensional shapes and sort them by their geometric properties • Compare and sort prisms and pyramids by geometric properties • Identify and describe the 2-­‐dimensional shapes that can be found in a 3-­‐dimensional figure • Construct rectangular prisms and describe geometric properties of the prisms • Describe and name prisms and pyramids by the shape of their base • Compare various angles, and describe angles as bigger than, smaller than, or about the same as other angles • Describe movement from one location to another using a grid map Measurement strand: • Use the most appropriate standard unit for length, mass and capacity • Compare and order units of length, mass and/or capacity • Estimate, measure, and record length, height, and distance, using standard units • Estimate, measure, compare and record the perimeter and area of 2-­‐dimensional shapes • Estimate, measure, and record the mass of objects, using standard units • Estimate, measure, and record the capacity of containers, using standard units • Estimate, measure, and represent time intervals to the nearest hour • Read time using analogue clocks, to the nearest five minutes, and using digital clocks, and represent time in 12-­‐hour notation • Solve problems involving time, using a variety of tools • Estimate, read, and record positive temperatures to the nearest degree Celsius Data handling strand: • Collect data by conducting a survey or an experiment, and record observations or measurements • Collect and organize data and display the data in charts, tables, and graphs, with appropriate titles and labels • Organize objects into categories, using two or more attributes simultaneously, using multiple diagrams • Read data presented in charts, tables, and graphs, then describe the data • Interpret and draw conclusions from data presented in charts, tables, and graphs • Identify the mode in a set of data • Create a fair game and relate this to the occurrence of equally likely outcomes • Predict the frequency of an outcome in a simple probability experiment or game, then perform the experiment, and compare the results with the predictions Grade 4 Number strand: • Count forwards and backwards with fractions • Read and write, in words, whole numbers to 1000 • Order whole numbers and decimal numbers from 0.1 to 10 000 • Determine place value of whole numbers and decimal numbers from 0.1 to 10 000 • Locate whole numbers to 10,000 on a number line • Round and estimate 4-­‐digit numbers to the nearest tenth, ten, hundred, and thousand • Add and subtract 4-­‐digit numbers to tenths • Multiply and divide whole numbers by 10, 100, and 1000 • Multiply 1-­‐digit by 2-­‐digit numbers, 1 digit by 3-­‐digit numbers and 2-­‐digit by 2-­‐digit numbers • Divide 2-­‐digit by 1-­‐digit numbers, with or without a remainder • Know the times tables to 10 • Convert fractions to decimals, to one place behind the decimal • Recognise equivalent fractions • Represent and describe the relationships between coins and bills up to €100 Pattern strand: • Make predictions related to repeating geometric and numeric patterns • Extend repeating number patterns • Identify and use the commutative property of multiplication • Determine, through investigation, the inverse relationship between multiplication and division Shape and space strand: • Identify and compare different quadrilaterals, and sort and classify them by their geometric properties • Identify and describe prisms and pyramids, and classify them by their geometric properties, using concrete materials. • Construct a 3-­‐dimensional figure from a picture or model of the figure, using connecting cubes • Identify and describe nets of rectangular and triangular prisms • Identify right angles, using a reference tool, and compare other angles to these • Identify and describe the location of an object using a grid system Measurement strand: • Choose appropriate standard unit to measure things • Estimate, measure, record and compare length, height, and distance, using standard units • Work out the perimeter of regular shapes • Determine the relationship between the side lengths of a rectangle and its perimeter and area • Estimate and measure the mass of objects • Estimate and measure volume using displacement • Determine the relationship between millilitres and litres • Read time using analogue and digital clocks, to the nearest one minute • Estimate and read negative temperatures to the nearest degree Celsius • Measure and record temperatures to determine and represent temperature changes over time Data handling strand: • Collect data by conducting a multiple question survey and display data in charts, tables, and graphs • Read, interpret, and draw conclusions from data • Describe the shape of a set of data across its range of values, using charts, tables, and graphs • Predict the frequency of an outcome in a simple probability experiment, conduct the experiment and compare the result with the prediction Grade 5 Number strand: • Count forwards by 2’s, 5’s, and 10’s from 100 and count backwards by 100’s from 1000 • Read and write, in words, whole numbers to 10,000 • Order whole, negative and decimal numbers • Order fractions and percentages • Locate whole numbers to 100,000 on a number line • Determine place value of whole numbers and decimal numbers from 0.01 to 100 000 • Round and estimate 6-­‐digit numbers decimal numbers up to the nearest hundredth, hundred thousand • Add and subtract 6-­‐digit numbers to hundredths • Add and subtract fractions • Multiply whole and decimal numbers • Divide whole and decimal numbers • Know the times tables up to 12 • Recognise equivalent fractions • Simplify fractions • Convert fractions to decimals to percentages • Represent and describe the relationships between coins and bills up to €1000 • Calculate percentage discounts Pattern strand: • Create, identify, and extend numeric and geometric patterns, using a variety of tools • Make a table of values for a pattern that is generated mathematically, given either the sequence or the pattern rule in words • Extend and create repeating patterns that result from translations, through investigation, using various tools Shape and space strand: • Identify triangles, and classify them according to angle and side properties • Distinguish among 2-­‐dimensional shapes, regular shapes and irregular shapes • Distinguish among prisms, right prisms, pyramids, and other 3-­‐
dimensional figures • Identify and classify acute, right, obtuse, and straight angles • Measure and construct angles up to 90º, using a protractor • Compare grid systems commonly used on maps • Locate an object using the cardinal directions and a coordinate system Measurement strand: • Choose appropriate standard unit to measure length, height, width, and distance • Convert centimetres <-­‐> metres <-­‐> kilometres • Find the perimeter and area of regular and irregular shapes using formulas • Determine the relationship between the height, the area of the base, and the volume of a rectangular prism, and turn it into a formula • Determine the relationship between capacity and volume • Select the most appropriate standard unit to measure mass • Read time using analogue and digital clocks, to the nearest one second • Solve problems involving the relationship between a 12-­‐hour clock and a 24-­‐hour clock • Estimate and determine elapsed time expressing the durations of events • Measure and record temperatures to freezing and below Data handling strand: • Collect data by conducting a survey or an experiment and display concrete and continuous data in charts, tables, and graphs • Distinguish between discrete data and continuous data • Read, interpret, and draw conclusions from data presented in charts, tables, and graphs and describe whether the methods of collection were appropriate. • Describe the shape of the data set across its range of values, comparing similarities and differences • Calculate mode, median, mean and range • Determine and represent all the possible outcomes in a simple probability experiment • Pose simple probability problems and solve them by conducting probability experiments and selecting appropriate methods of recording the results