GermanEuropeanSchool of Singapore–Pre-School Mathematics Scope and Sequence - DRAFT

NUMBER SKILLS

Kindergarten (3-5 year olds)* / Pre-Primary (5-6 year olds) / Grade 1 (6-7 year olds)
Number Line / 1-1 correspondence to 5 (10)
Counts, models and reads numbers to 5 (10) / Counts and models numbers to 20
Reads numbers to 10 / Reads and writes numerals to 100
Counts to 100 FW/BW
Number Relationships / Orders numbers to 5 (10)
Uses ordinal numbers to describe position in a sequence to 5
Uses vocabulary of:
first, last, next, more, less / Orders numbers to 20
Compares numbers to 20 / Orders numbers to 100
Compares numbers to 100
Uses Base Ten blocks to represent numbers up to 100
Pattern/Function
Number Facts / Shows understanding of size, colour and shape
Names and classifies by colour
Recognizes and finds pairs
Creates and continues patterns of one variable (eg., colour or size or shape)
Explores conservation of number using concrete materials (number is constant unless materials are added or removed) / Recognizes, describes, creates and continues repeating patterns of 2 or 3 variables (eg., colour, size, shape or number)
Explores concepts of addition and subtraction in real life contexts / 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
Operations / Compares groups to identify more, less or same number
Adds on to make “more”
Takes part of a group away to make “less” / Uses vocabulary:
plus and minus
Demonstrates meaning of addition and subtraction
Begins to explore:
-modelling equal groups or rows
-grouping and sharing equal collections of objects / 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
Estimation / Estimates quantities to 5 (10) / Estimates quantities to 10 / Uses the vocabulary of estimation
Estimates quantities to 100
Estimates reasonableness of an answer to a problem
Rounds whole numbers to nearest 10
Pre-Primary (5-6 year olds) / Grade 1 (6-7 year olds)
Fractions and Decimals / Uses fraction name “half” to describe whole and part relationships
Divides whole objects into halves / Uses fraction names: halves, quarters, fourths and thirds to describe whole and part relationships
Divides whole objects in halves, quarters and fourths

NUMBER SKILLS (continued)

Kindergarten (3-5 year olds)* / Pre-Primary (5-6 year olds) / Grade 1 (6-7 year olds)
Space:
Length
Volume
Mass / Begins to compare and describe objects using vocabulary of measurement:
Long(er)/short(er)
Big(ger)/small(er)
More/less
Heavy(ier)/light(er)
Empty/full
Hot(ter)/cold(er) / Compares and describes objects using vocabulary of measurement:
Long(er)/short(er)
Big(ger)/small(er)
Heavy(ier)/light(er)
Empty/full
Hot(ter)/cold(er)
Thick(er)/thin(ner)
Wide(r)/narrow(er)
Using non-standard units:
Estimates, compares and measures length, mass and volume / 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
Money / Becomes familiar with denominations of currency (coins, etc)
Uses money to model simple addition and subtraction
Time / Begins to use concepts of time:
Day/night
Morning/afternoon
Before/after
Tomorrow/today/yesterday
Identifies and sequences events in daily routine / Uses everyday language to sequence events in a school day
Names the days of the week and months of the year
Reads time to the hour on analogue clocks; explores relationship between digital and analogue clocks / 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

MEASUREMENT

Kindergarten (3-5 year olds)* / Pre-Primary (5-6 year olds) / Grade 1 (6-7 year olds)
2-D and 3-D Geometry / Names 2-D shapes:
circle, triangle, square, rectangle
Manipulates and sorts 2-D shapes according to size and form: circle, triangle, square, rectangle / Names and creates 2-D shapes:
circle, triangle, square, rectangle, oval
Manipulates and sorts 2-D shapes according to size and form: circle, triangle, square, rectangle, oval
Names 3-D shapes: cube, cone, cylinder, sphere (ball)
Describes features of 3-D objects using everyday language / 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
Position/Orientation / Explores and describes their immediate environment:
Inside/outside
Up/down
In/out/on
Next to, behind, in front of
Near/far / Explores and describes their immediate environment:
Inside/outside
Up/down
Above/below/under
In/out/on
Next to, beside, behind, in front of
Near/far
Forwards/backwards
Gives and follows simple directions: left, right, forward, backward / 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 the immediate environment
Symmetry / Finds symmetry in the natural environment
Creates simple symmetrical designs / Finds symmetry in the natural environment
Creates and explains simple symmetrical designs in 2-D and 3-D

SHAPE AND SPACE

DATA HANDLING

Kindergarten (3-5 year olds)* / Pre-Primary (5-6 year olds) / Grade 1 (6-7 year olds)
Probability / Begins to discuss outcomes that will or won’t happen / Discusses and identifies outcomes that will happen, won’t happen and might happen / Discusses and identifies outcomes that will happen, won’t happen and might happen
Graphing / Sorts real-life objects into sets by one attribute (colour, size, shape, purpose, etc)
Creates a graph of real-life objects and compares quantities using number / Collects and sorts objects by one or more attribute (colour, size, shape, purpose, etc)
Creates a pictograph from a set of real-life objects and compares quantities using number / 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 and bar graphs

MATHEMATICAL THINKING

Kindergarten (3-5 year olds)* / Pre-Primary (5-6 year olds) / Grade 1 (6-7 year olds)
Questioning
Applying Strategies
Communicating
Reasoning
Reflecting / Asks questions and explores environment to further mathematical understanding
Uses objects, actions, images and/or trial and error to explore concepts
Attempts to explain observations and reasoning
Connects mathematical learning to everyday understandings and observations / Asks questions and explores environment to further mathematical understanding
Uses objects, actions, images and/or trial and error to explore concepts
Attempts to explain observations and reasoning
Uses concrete materials and/or pictures to support conclusions
Connects mathematical learning to everyday understandings and observations / Asks questions that further mathematical understanding
Uses objects, actions, images and/or trial and error to explore concepts
Attempts to explain reasoning
Solves and creates simple word problems
Uses concrete materials and/or pictures to support conclusions
Connects mathematics to everyday knowledge and observations

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