German European School of Singapore - European Section: Primary Math Scope and Sequence
NUMBER SKILLS
Grade 1 / Grade 2 / Grade 3 / Grade 4 / Grade 5Number Line / Reads and writes numerals to 100
Counts to 100 FW/BW / Recognizes and writes numerals to 1000
Counts to 1000 FW/BW / Reads and writes numbers to 100,000
Counts to 100,000 FW/BW
Is aware of Roman numerals / Reads and writes numbers to a million
Reads and writes decimal fractions to tenths / Reads, writes and models numbers to a million or beyond
Reads and writes decimal fractions to hundredths
Number Relationships / Orders numbers to 100
Compares numbers to 100
Uses Base Ten Blocks to represent numbers up to 100 / Orders numbers to 1000
Compares numbers to 1000
Recognizes odd and even numbers
Uses Base Ten Blocks to represent numbers up to 1000 / Compares and orders numbers to 100,000 / Recognizes negative numbers in real-life situations
Represents using base 10 system and compares:
-Whole numbers to million
-Decimal fractions to tenths
-Fractions / Interchanges fractions, percentages and decimals
Reads, writes and models percentages
Pattern and Function/
Number Facts / Recognizes, describes, creates and continues repeating patterns in colour, size, shape and number
Can skip count in:
2’s to 20
5’s to 100
10’s to 100
Recalls addition and subtraction facts to 10
Recalls doubles to 20 / Recognizes, creates, represents and continues a variety of number patterns
Supplies missing elements in a number pattern
Can skip count in:
2’s to 100
5’s to 100
10’s to 100
100’s to 1000
Recalls addition and subtraction facts to 20
Doubles to 20
Multiplication: 2 5 10 / Generates, describes and records number patterns
Supplies missing elements in a number pattern
Can skip count:
2’s to 20
3’s to 30
4’s to 40
5’s to 50
9’s to 90
10’s to 100
Multiplication:
2 3 4 5 9 10 / Generates, describes and records number patterns
Supplies missing elements in a number pattern
Can skip count:
6’s to 60
7’s to 70
8’s to 80
9’s to 90
Recalls number facts to 100
Multiplication:
2 3 4 5 6 7 8 9 10 / Records, analysis and describes geometric and number patterns that involve one operation using tables and words
Constructs, verifies and completes number sentences involving the four operations with a variety of numbers
Recalls and uses number facts to 100 (addition, subtraction, multiplication, division)
Understands and applies multiplication strategies for numbers larger than 100
Operations / Uses vocabulary and symbols: plus (+) and minus (-)
Reads and writes plus and minus sentences to 20
Demonstrates meaning of addition and subtraction
Uses vertical and horizontal layout for + and –
Models multiplication as grouping
Models division as sharing / Using a range of mental strategies and informal recording:
Adds to 100:
without and with regrouping
Subtracts to 100:
without and with regrouping
Models multiplication and division using concrete materials / Models with and without grouping:
- Addition to 1000
- Subtraction from 1000
Uses vocabulary and symbols: groups of, times(×), product, divide (÷), quotient
Uses a variety of strategies to add, subtract, multiply and divide / Calculates corresponding division facts for multiplication facts
Applies mental strategies for all operations
Creates and solves double-digit multiplication
Creates and solves single-digit division
Models and solves addition and subtraction to million / Models addition and subtraction facts to million or beyond
Creates and solves multiple digit multiplication and division of two multiples or divisors
NUMBER SKILLS (continued)
Estimation / Uses the vocabulary of estimationEstimates quantities to 100
Estimates reasonableness of an answer to a problem
Rounds whole numbers to nearest 10 / Estimates quantities to 1000
Rounds to the nearest 10
Estimates reasonableness of an answer to a problem / Estimates answers rounding up or down to nearest 10’s, 100’s, 1000’s
Estimates reasonableness of an answer to a problem / Estimates reasonably:
-Sums, differences, products, quotients
Rounds whole numbers to 100,000 / Estimates reasonableness of an answer to a problem
Rounds whole numbers to one million
Rounds decimals to hundredths
Fractions
and Decimals / Uses fraction names: halves, quarters, fourths and thirds to describe whole and part relationships
Divides whole objects in halves, quarters and fourths / Describes, models and compares halves, quarters, eighths and thirds of objects and numbers
Represents fractions using fractional notation: halves, thirds, quarters and fifths
Understands and models equivalence to 1: two halves = 1, etc. / Compares and orders fractions of different denominators using fraction pieces
Models addition and subtraction of fractions of different denominators
Models, compares and represents commonly used fractions and decimals
Adds and subtracts decimals to two decimal place, and interprets everyday percentages / Converts improper fractions to mixed numbers and vice versa
Reads, writes and models: addition and subtraction of fractions with related denominators
Reads, writes and models improper fractions and mixed numbers
Models equivalent fractions
Uses vocabulary: improper, mixed numbers, denominators, numerators, equivalent
Reads, models and solves addition and subtraction of decimal fractions to tenths
Relates simple fractions to decimal equivalents
Orders, adds, subtracts and multiplies decimals
Can solve simple problems
using percentages / Reads, writes and models addition and subtraction of fractions with unrelated denominators
Reads, writes and models improper fractions and mixed numbers
Compares, simplifies, orders and calculates fractions, decimals and simple percentages
Models equivalent fractions
Begins reading, writing, and modeling multiplication and division of decimals to hundredths
MEASUREMENT
Space:
Length
Area
Perimeter
Volume
Capacity
Mass
Temperature / Using standard and/or non-standard units:
Makes reasonable estimates of length, mass and volume
Compares objects’ length, mass and volume
Measures and records length, mass and volume
Understands the need for standard units / Estimates, measures, records and compares length and distance:
m cm km g kg
Understands numeric relations among units (100 cm = 1 m)
Uses appropriate tools
Measures to the half unit
Estimates, measures and compares using standard and/or non-standard units:
Perimeter
Area (sq cm)
Volume (cubic cm)
Capacity (litres, ml) / Using standard units estimates, measures, records and compares:
- Length and distance (mm, cm, m, km)
- Perimeter
- Area (sq. cm and sq m)
- Volume (cubic cm)
- Capacity (litres, ml)
- Mass (g, kg)
- Temperature (degrees C)
Uses appropriate tools and units / Using standard units estimates, measures, records and compares:
- Length and distance (mm, cm, m, km)
- Perimeter
- Area (sq. cm and sq m)
- Volume (cubic cm)
- Capacity (litres, ml, ounces, pints, quarts)
- Mass (g, kg)
- Temperature (degrees C)
Understands and uses the formula to calculate area in words (length X breadth)
Understands and uses relationships among units of capacity and of mass
Develops procedures to find area and perimeter
Understands relationship between area and perimeter
Uses standard units to estimate, measure, record, and compare area and perimeter to tenths / Selects and uses standard units and tools accurately
Understands that various factors affect the accuracy of measurement
Develops procedures for finding volume
Determines the relationship between area, perimeter, and volume
Uses formulae to estimate, measure, record and compare perimeter, area and volume of any shape
Uses decimal notation in measurement
Identifies, measures and constructs angles to 360°
Money / Becomes familiar with denominations of currency (coins, etc)
Uses money to model simple addition and subtraction / Uses money to model simple addition and subtraction / Uses money to model addition and subtraction, including making change / Uses money to model addition and subtraction problem, including making change, using all coins and notes
Can convert between currencies / Models +/- in a variety of currencies
Models ×/÷ to decimal hundredths
Can convert between currencies
Time / Uses everyday language to sequence and describe duration of events
Uses a calendar to recognize the date, weekdays and months
Reads and writes time to the quarter-hour, half hour and hour on analogue and digital clocks / Estimates, measures and compares time in: seconds minutes hours
Reads and writes time to the 5-minute increment on analogue and digital clocks
Places events on a timeline in chronological order / Reads and writes time to 5 minutes using analogue and digital clocks
Solves simple elapsed time problems / Reads and records time to 1-minute intervals
Understands duration of seconds, minutes and hours
Reads 24-hr clock and uses 24-hr notation
Constructs and uses timetables (12h clock)
Solves elapsed time problems / Constructs and uses timetables (12h and 24h clock) and time lines
Understands and converts time zones
SHAPE AND SPACE
Grade 1 / Grade 2 / Grade 3 / Grade 4 / Grade 52-D
and 3-D
Geometry / Names, creates and describes 2-D shapes:
circle, semi-circle, square, rectangle, triangle, oval, hexagon, octagon
Creates and describes 3-D shapes:
sphere, cube, triangular prism, cone, cylinder, pyramid
Understands and uses vocabulary: side, corner, edge, curved, flat, point, face
Finds and identifies 2-D shapes within 3-D shapes / Recognizes, sorts, describes and models: 2-D shapes:
circle, semi-circle, square, triangle, rectangle, rhombus, trapezoid, hexagon, oval, pentagon, octagon
Understands regular and irregular shapes
Combines 2-D shapes
Recognizes 2D and 3D shapes in pictures and objects
Sorts, describes, creates, models and sketches 3-D shapes:
cone, pyramid, rectangular prism, cube, triangular prism, hexagonal prism, sphere, cylinder, square pyramid, triangular pyramid
Understands and uses vocabulary: side, corner, edge, curved, flat, point, face / Sorts, describes and models polygons:
triangle, quadrilateral, square, rectangle, parallelogram, rhombus, trapezoid, pentagon, hexagon, octagon
Understands and uses vocabulary: acute/obtuse/right angle, corner, side, parallel, diverging, converging lines
Combines and transforms 2-D shapes
Compares 3-D shapes: cone, pyramid, rectangular prism, cube, triangular prism, hexagonal prism, sphere, cylinder, square pyramid, triangular pyramid
Understands and uses vocabulary: face, edge, vertex, base
Knows that angles are measured in degrees
Can identify and make simple nets / Uses language of geometry for 2-D and 3-D shapes
Describes circles in terms of radius and diameter
Classifies and describes all sorts of triangles and quadrilaterals:
scalene, isosceles, equilateral, right-angled, rhombus, trapezoid, parallelogram, square, rectangle
Uses a protractor to measure and compare angles in degrees
Can explain: obtuse, acute, right, straight, reflex
Visualizes, describes and models 3-D prisms: rectangular, triangular, hexagonal, square
Beginning to draw 3-D shapes using depth and perspective
Builds 3-D models based on drawings of different views
Turns a 2-D shape net into a 3-D shape and vice versa / Uses language of geometry for 2-D and 3-D shapes, including line, ray, segment, parallel and perpendicular
Describes circles in terms of radius, diameter and circumference
Classifies and constructs all sorts of triangles and quadrilaterals:
scalene, isosceles, equilateral, right-angled, rhombus, trapezoid, parallelogram, square, rectangle
Uses formulae to measure perimeter and area of circles, triangles and quadrilaterals
Turns a 2-D shape net into a 3-D shape and vice versa
Confidently classifies, describes and models 3-D shapes
SHAPE AND SPACE, continued
Position/Orientation / Gives and follows simple directions: left, right, forward, backward
Makes whole, half or quarter turns to the left or right
Recognizes the right angle
Describes and begins to map features of immediate environment / Locates and understands cardinal directions (north, south, west and east)
Describes the position of objects using models and everyday language
Locates features on a grid using coordinates / Understands angle as a measure of rotation: whole turn, half turn, quarter turn, clockwise, counterclockwise
Locates cardinal directions N, S, W, E, NW, NE, SW, SE) on a compass
Plots points on a grid using a compass
Uses simple maps and grids to represent position and follow routes
Describes the location of objects using coordinates / Reads and plots coordinates in 4 quadrants / Reads and plots coordinates in 4 quadrants
Uses the language and notation of bearing to describe position
Finds and uses scale to enlarge and reduce shapes
Uses maps and grids to represent position and follow routes
Symmetry / Finds symmetry in natural environment
Creates and explains simple symmetrical designs in 2-D and 3-D / Creates and describes symmetrical patterns
Identifies 2 lines of symmetry in shapes
Recognizes that some shapes tessellate / Creates symmetrical designs and tessellations using reflection, translation and rotational symmetry / Creates symmetrical designs and tessellations using reflection, translation and rotational symmetry / Identifies lines and axes of reflective and rotational symmetry
DATA HANDLING
Probability / Discusses and identifies outcomes that will happen, won’t happen and might happen / Recognizes and describes the element of chance in everyday events
Discusses and predicts outcomes in order: impossible, possible, unlikely, likely, certain
Uses probability to predict fair and unfair outcomes / Uses probability to determine fair and unfair games and to explain possible outcomes / Uses probability to determine fair and unfair games and to explain possible outcomes / Uses a probability scale of 0% to 100% to calculate odds
Graphing / Compares data from different diagrams
(tree, Carroll, Venn)
Collects, organizes and displays data in simple tables
Interprets data by comparing quantities:
more, fewer, less than, greater than
Understands the purpose of graphing
Creates simple pictographs or bar graphs / Compares, discusses and organizes data on different diagrams (tree, Carroll and Venn)
Collects and interprets data from a survey
Understands that a database can be used to answer questions and solve problems
Creates pictographs and bar graphs / Compares and creates sets and subsets from data on different diagrams (tree, Carroll and Venn)
Designs a survey to collect data
Creates bar graphs with quantities > 10
Identifies and explains the mode in a set of data / Designs a survey to collect, organize and record data in graphs (bar, picto, line)
Creates, interprets and compares data displays
Reads and interprets graphs with scales of many-to-one correspondence / Conducts investigations to answer questions
Creates and compares data displays (picto, pie bar and line)
Identifies and explains the range, mode, median and mean in a set of data
Creates and uses an electronic database
Sets a spreadsheet, manipulates data and creates graphs
MATHEMATICAL THINKING