LISA-JUNIOR
International Primary School
Aubrunnerweg 43, 4040 Linz
[email protected]
www.lisa-junior.at
Mathematics
PYP 1
Learning Objectives :
Number Sense
Number formation
Number bonds up to 10
Difference between digit and number
Establish the understanding for the decadal system
Numbers to 30
Numbers to 100 in steps of 10
Illustrate numbers by using number rays, different symbols, etc
Comparison: <, >, =, ≠
Place value: Tens, Units
Data handling: make and read bar graph
Arithmetic Operations
Numbers to 30 – calculating without crossing the tens boundary
Numbers to 30 - (calculating with crossing the tens boundary)
Calculating up to 100 in 10s
Calculation within the 30 range: addition, subtraction
Fact families (3+5=8, 5+3=8, 8-3=5, 8-5=3)
Commutative law (4+2=6, 2+4=6)
Intro. to multiplication – repeated addition as basic multiplying
Odd and even numbers
Ordinal numbers
Double and halve numbers up to 20
6 + 6 = 12,
4 = 2+2,
10+10 = 20, etc.
Real-life word problems – one step
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LISA-JUNIOR
International Primary School
Aubrunnerweg 43, 4040 Linz
[email protected]
www.lisa-junior.at
Measurement
Telling the Time (full and half hour)
Introduction in Measurement: non-standard and standard units
Measurement Length: cm
Measurement Money: Euro and Cent
Measurement Time: Date (months of the year / days of the week)
Comparing weight: heavier and lighter
Geometry
Symmetry - grid animals
Shapes: 2D
Use of ruler
Recognizing and finishing patterns (shapes, numbers)
Free “play” with cubes and different shapes
Position and direction: left, right, up, down
Sorting and classifying by attributes (size, colour, shape, etc.)
Data Handling
Read and create own graph (pictogram, bar chart)
Read a pie chart
PYP 2
Learning Objectives :
Number Sense
Review grade 1: + and - up to 30 with and without crossing the ten
Develop number conception up to 100 by:
 Using the number ray
 Estimation
 Arranging numbers in order
 Using the symbols =, ≠, <, >
 Working with place value
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LISA-JUNIOR
International Primary School
Aubrunnerweg 43, 4040 Linz
[email protected]
www.lisa-junior.at
 Finding the difference between number and digit
 Delving into different operation number relations: finding the neighbours,
breaking down numbers (64 = 60 + 4, 80 = 2 x 40), comparing numbers (10
+ 2 = 6 x 2)
Interpret data by using different types of graphs
Arithmetic Operations
Understand the operations: add, take away, share, multiply, to add to, by doing
Learn the right terminology: addition = add, subtraction= minus division = divided
by, multiplication = multiply
Introduce and use the correct signs: +, -, x, :
Add and subtract up to 100 without crossing the ones/tens
Add and subtract up to 100 with crossing the ones/tens
Finding real-world relations for multiplications (eg. egg carton..)
Apply different ways to illustrate multiplication
Develop times tables from 1x1 to 10x10 (if possible 11 times table additionally) by
using continued addition (3 x 4 = 4 + 4 + 4), doubling ( 5 + 5 = 2 x 5)
Develop division tables from 1:1 to 100 :10 by measuring, halving, parting ( 18 = 6
groups of 3…)
Using board games to apply the knowledge
Solve “magic squares” or any other game that gives “food for thought”
Finding real world word problems to the different arithmetic operations
Formulate a correct answer to a question
Use pictures, drawings and illustrations to solve a word problem
Role play a word problem
Measurements – never exceed the number range of 100
Discover different real life measurements
Measuring length: m, cm should be explained and converted
Measuring weight: kg, g should be explained and converted
Measuring volume: l
Measuring time: sec, min, hour, day, week, month, year and convert
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LISA-JUNIOR
International Primary School
Aubrunnerweg 43, 4040 Linz
[email protected]
www.lisa-junior.at
Measuring money: Euro and cent and convert
Finding real world word problems to go with the measurements
Telling the time (full hour, half past, quarter past, quarter to) analog and digital
clocks
Geometry
Get to know the terms: above/under, left/right, before/behind, inside/outside, next
to, between, in the middle
Exercise for orientation – easy maps, treasure hunts
Get to know the terms: round/angled, straight/bent, open/closed
Form geometrical bodies
Discover symmetries (term symmetry axis), fold paper
Invent own patterns with figures and numbers
Continue existing patterns with figures and numbers
Draw and measure different lines with a ruler
Name different 2D shapes
PYP 3
Learning Objectives :
Number Sense
Number Review from Grade 2 – up to 100
Extend the number range to 1000 using number rays, different number pictures,
symbols; explain the decadal system
Read and write numbers without calculating
Place Value
Number Placement
Difference between digit and number
Rounding to the nearest H, T, U
Discover the big numbers by comparing to the small ones and using different
symbols: = , ≠, <, >; 200 + 100 = 400 - 100
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LISA-JUNIOR
International Primary School
Aubrunnerweg 43, 4040 Linz
[email protected]
www.lisa-junior.at
To arrange numbers in order
Interpret data by using different types of graphs
Introduce the Roman Numerals: I, V, X, L, C, D, M
Arithmetic Operations
Understand the structure of different operations and interpret them by doing (role
play)
Revise the times tables from 1x 1 to 10x10 introduce 11s and 12s
Revise the division tables without remainder
Introduce division with remainder
Written addition (numbers on top of each other) – review of 2 digit plus 2 digit with
and without crossing the 10s
Written addition – 3 digit plus 3 digit (not going into the thousands) with and without
carrying
Written subtraction – review of 2 digit minus 2 digit with and without crossing the
10s
Written subtraction – 3 digit minus 3 digit with and without borrowing
Written Multiplication – up to 3 digit times 1 digit
Written Division – up to 3 digit divided by 1 digit
Introduce the terms: sum, difference, product, and quotient
Real-life word problems (2- and 3-steps) using the new operations
Estimate before calculate
Get to know relations of the operations
“Rechenvorteile” – eg. +9= +10 -1
Measurements
Review measurements from grade 2
Create relation of measurements: 1000:1
Measurement Length (Review): km, m, cm, mm; explain dm
Measurement Length: Convert mm to cm and dm to m
Measurement Time: Convert years to days, days to minutes / seconds
Telling time review: full hour, half past, quarter past, quarter to, analog and digital
clock
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LISA-JUNIOR
International Primary School
Aubrunnerweg 43, 4040 Linz
[email protected]
www.lisa-junior.at
Measurement Money: Convert Euro to Cent
Measurement Volume: Introduce L
Measurement Weight: Introduce ton and kg
Real-life (2- and 3-steps) word problems with all kinds of measurement
Geometry
Read plans and maps, getting to know positions
Describe the way from A to B
Work with different shapes (2D and 3D)
Terms: edge, corner, side, parallel, right angle
Find differences and similarities of different shapes
Develop the term “perimeter”
Find different ways to calculate the perimeter; define the most effective one
Construct different 2D and 3D shapes by using different materials e.g. tooth picks
Use a ruler to measure different lengths and draw given distances
Draw parallel lines, right angles, different shapes
Start to use the compass by investigating and inventing
PYP 4
Learning Objectives :
Numbers Sense
Number Revision (Grade 3) up to 1000
Extend the number range to 1 000 000 by using number rays, different number
pictures, symbols; use the decadal system
Read and write numbers without calculation
Counting
ordering
Rounding off
Develop number sense by comparing and using different symbols e.g. 7000 –
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LISA-JUNIOR
International Primary School
Aubrunnerweg 43, 4040 Linz
[email protected]
www.lisa-junior.at
2000 = 4000 + 1000
Interpret data by using different types of graphs
Arithmetic Operations
Revise division and multiplication by a 1-digit number
Mental arithmetic in the number range of 10 000 ; later up to 100 000
Expand the written addition and subtraction to the number ranges
Estimate before calculate
Multiplying by tens
Multiplying by a 2-digit number
Dividing by 2-digit numbers
Continue to use the correct terms for the different operations, also correct spelling;
(addend, sum); (minuend, subtrahend, difference); (multiplicand, multiplier,
product); (multiplicand, multiplier, product)
Real-life 2 or 3 step word problems
Calculating mean, median, and mode
Measurements
Revise all measurements and conversions from grade 3
Introduce m2 to dm2; km2 to m2 by interaction and investigation
Mearsurement Time: Seconds, 24h-clock, duration of time;
Difference between duration and point of time
Calculate with area and perimeter:
 Rectangles
 Squares
 Composite figures
Real-life word problems
Geometry
Naming angles and correct spelling
Estimating and measuring angles
8-point compass
Drawing angles
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LISA-JUNIOR
International Primary School
Aubrunnerweg 43, 4040 Linz
[email protected]
www.lisa-junior.at
Horizontal lines and vertical lines
Drawing perpendicular lines using a ruler and a set square
Drawing parallel lines using a rules and a set square
Rectangles
Squares
Tables
Line graphs
Symmetric figures and line of symmetry
Completing symmetric figures
PYP 5
Learning Objectives :
Number
Number Revision (Grade 4) up to 1 000 000 with the use of number rays, number
pictures, use the base 10 system
Rounding numbers (revision)
Estimate before calculate
Automatically recall and use basic number facts
Continue to use the correct terms for the different operations, also correct spelling;
(addend, sum); (minuend, subtrahend, difference); (multiplicand, multiplier,
product); (dividend, divisor, quotient);
Interpret data by using different types of graphs
Use of the calculator
Create and solve multiple digit multiplication and division
Gain insight of whole numbers with the help of divisors and multiples
Read, write and model integers
Select and defend the most appropriate and efficient method of solving a problem:
mental estimation, mental arithmetic
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LISA-JUNIOR
International Primary School
Aubrunnerweg 43, 4040 Linz
[email protected]
www.lisa-junior.at
Apply linear equations
Apply different algorithms:
Commutative law: a + b = b + a; a x b = b x a
Associative law: (a + b) + c = a + (b + c); (a x b) x c = a x (b x c)
Distributive law: a × (b + c) = a × b + a × c
Fractions
Factors
Common Factors
Multiples
Common Multiples
Mixed numbers
Improper Fractions
Express mixed numbers as improper fractions
Express improper fractions as mixed or whole numbers
Adding fractions
Subtracting fractions
Fractions of a set and product of a fraction and whole number
Real-life word problems
Read, write and model addition and subtraction of fractions with the same and
related denominators
Read, write and model improper fractions and mixed numbers
Compare and order fractions
Model equivalency of fractions: 2/4 = ½
Simplify fractions
Use the mathematical vocabulary of fractions: improper, mixed numbers, reduced
to lowest terms
Decimals
Read, write and model the addition and subtraction of decimals to the thousandths
Round decimals to a given place or whole number
Read, write and model percentages
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LISA-JUNIOR
International Primary School
Aubrunnerweg 43, 4040 Linz
[email protected]
www.lisa-junior.at
Interchange fractions, percentages and decimals
Tenths, hundredths, and thousandths
Comparing and ordering
Multiplying decimals with 1 digit whole number
Dividing decimals by 1 digit whole number
Word problems with decimals
Measurement
Revision of measurement : length and conversions
Revision of measurement: area and conversions
Revision of measurement: volume and conversions
Revision of measurement: time and conversions
Revision of measurement: weight and conversions
Real-life word problems connected to measurement
Revision: Calculate with area and perimeter
Calculate the volume and the surface of cuboids
Apply and interpret mathematical formula
Understand that the accuracy of a measurement depending on the situation and
the precision of the tools
Determine the relationship between area, perimeter and volume
Use decimal notation in measurement: 3.2 cm, 1.47kg, 1.63 €
Measure and construct angles in degrees
Shape and Space
Describe, classify and model 3-D shapes (revision grade 4)
Turn a 2-D net into a 3-D shape and vice versa
Draw sketches of rectangles, circles, segment of circles, cuboids, etc
Use different plotting instruments for constructing different 2-D and 3-D shapes
Understand and use the vocabulary of lines, rays and segments: parallel,
perpendicular
Find and use scale (ratio) to enlarge and reduce shapes
Plot to scale and calculate the real length
Read and plot coordinates in four quadrants
Symmetrical figures and line of symmetry
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LISA-JUNIOR
International Primary School
Aubrunnerweg 43, 4040 Linz
[email protected]
www.lisa-junior.at
Completing symmetrical figures
Identifying tessellations
Tessellating
Data Handling
Design a survey and systematically collect, organize and record the data in
displays: pictograph, bar graph, circle graph, line graph
Create interpret, discuss and compare data displays (pictograph, bar graph, circle
graph, line graph) including how well they communicate information
Find, describe and explain the range, mode, median and mean in a set of data and
understand their use
Create and manipulate an electronic database for their own purposes
Set up a spreadsheet
Identify different linearity (proportionality): quantity of goods to costs, distance to
time
Pattern and Functions
Revision grade 4: understand and use the relationship between multiplication and
addition
Revision grade 4: understand and use the relationship between multiplication and
division (inverse function)
Revision grade 4: understand and use the relationship between division and
subtraction
Use real-life problems to create a number pattern, following a rule
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