Students demonstrate a large jump in skills at the intermediate levels. Typically for students in grades three through five these levels assume basic fluency with positive base ten numeration in the first century, introducing the thousands. Once whole number base ten numeration is established students are introduced to decimals and using decimals to represent parts of whole numbers. Students are introduced to fractions and using fractions and improper numbers to represent and communicate about quantities. Students continue to use inequalities to compare pairs of whole numbers, fractions and decimals as well as being able to use number lines to compare and order several numbers. Students also dive deep into composition and decomposition, working with increasing flexibility and a wider range of operations to break down the numbers.

Domainskill groupskill descriptor678
Numbers and countingrecognizes numbersspoken100010 000100 000
fractionsdecimals 
written100010 000100 000
fractionsdecimals 
subitizingdots4050 
2 colour dots3040 
with objects4050 
copy with objects4050 
Countingforward by ____ from zero      3      6      11
4712
 8 
 9 
forward by from any number3611
4712
 8 
 9 
backward by from a given number3611
4712
 8 
 9 
groups objects by ____ for effective counting10100 
Fractionsidentify fractionsas parts of a whole equivalent fractions
as parts of a group  
 with x/2 as a common denominator 
 with x/3 as a common denominator 
 with x/4 as a common denominator 
 with x/5 as a common denominator 
 with x/8 as a common denominator 
 with x/8 as a common denominator 
 with x/10 as a common denominator 
 using 0 as a benchmark 
 using 1/2as a benchmark 
 using 1 as a benchmark 
Representing Numberswhole numberswith objects100010 000100 000
with drawings100010 000100 000
with numerals100010 000100 000
 represent fractions…with objectswith objectsequivalent fractions with objects
with drawingswith drawingsequivalent fractions with drawings
with numeralswith numeralsequivalent fractions numerals
with equal partitioningwith equal partitioning as part of a group 
 with equal partitioning as part of a set 
Decimalsrepresent decimals… tenths with objectsthousandths with objects
 tenths with drawingsthousandths with drawings
 tenths with numeralsthousandths with numerals
 tenths with coins 
 hundredths with objects 
 hundredths with drawings 
 hundredths with numerals 
 hundredths with coins 
Place Valuebase 10 numeration – whole numbersrepresents numbers with base ten blocks to1 00010 000 
uses a place value chart to represent numbers to1 00010 000100 000
identifies the value of the numbers in each place to1 00010 000100 000
record numbers in standard notation from a place value chart1 00010 000100 000
Base 10 numeration – decimalsrepresents numbers with base ten blocks to 1 decimal place3 decimal places
 2 decimal places 
uses a place value chart to represent numbers to 1 decimal place3 decimal places
 2 decimal places 
identifies the value of the numbers in each place to 1 decimal place3 decimal places
 2 decimal places 
record numbers in standard notation from a place value chart 1 decimal place3 decimal places
 2 decimal places 
Number Relationshipscomposition and decompositioncomposes numbers to___ in many ways using objects1 00010 000100 000
composes numbers to___ in many ways using pictures1 00010 000100 000
compose numbers to____ using numerals and mathematical notation1 00010 000100 000
uses base 10 blocks to compose numbers to ___ in many ways1000  
decomposes numbers to___ in many ways using objects1 00010 000100 000
decomposes numbers to___ in many ways using pictures1 00010 000100 000
decompose numbers to____ using numerals and mathematical notation1 00010 000100 000
uses base 10 blocks to decompose numbers to ___ in many ways1000  
composes numbers to___ in many ways using objects 1 decimal place3 decimal places
 2 decimal places 
composes numbers to___ in many ways using pictures 1 decimal place3 decimal places
 2 decimal places 
compose numbers to____ using numerals and mathematical notation 1 decimal place3 decimal places
 2 decimal places 
decomposes numbers to___ in many ways using objects 1 decimal place3 decimal places
 2 decimal places 
decomposes numbers to___ in many ways using pictures 1 decimal place3 decimal places
 2 decimal places 
decompose numbers to____ using numerals and mathematical notation 1 decimal place3 decimal places
 2 decimal places 
comparing and ordering – base 10 numerationcompares quantities to1 00010 000100 000
compare pairs of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to)1 00010 000100 000
compare groups of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to)1 00010 000100 000
uses place value to compare numbers100010 000100 000
uses place value toorder numbers100010 000100 000
order numbers to ___1 00010 000100 000
place numbers to ___ on a number line1 00010 000100 000
uses benchmarks to compare and order numbers100100010 000
500500050 000
compare pairs of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to) 1 decimal place3 decimal places
 2 decimal places 
compare groups of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to) 1 decimal place3 decimal places
 2 decimal places 
order numbers to ___ 1 decimal place3 decimal places
 2 decimal places 
place numbers to ___ on a number line 1 decimal place3 decimal places
 2 decimal places 
comparing and ordering – fractionscompares fractions to benchmarks 0 1/4
  1/2 3/4
 1 
orders fractions on a number line with like and unlike denominatorsimproper fractions
compare pairs of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to) with like and unlike denominatorsimproper fractions
compare groups of numbers to a maximum number of ___ using inequalities notation (greater than/ less than / equal to) with like and unlike denominatorsimproper fractions
equivalencyFractions equivalent fractionsequivalent improper fractions
decimals fraction tenths to decimal tenths 
 fraction hundredths to decimal hundredths 

Early Years
Primary
Intermediate
Middle Years
Number Sense Progressions by Level
Number Sense Progressions