LET’S BRING IN ADDITION AND SUBTRACTION!

As students develop their understanding of place value concept levels, they immediately apply their understanding to adding and subtracting using place value. (See the diagram below.) (For Professional Learning on Place Value, select Professional Learning above, Learn by Concept, Number and Algebra, Addition and Subtraction Professional Learning.)

Students begin investigating place value concepts informally in Kindergarten/Prep/Reception (PV 1, 2, 3, 4, 5).

Students begin to investigate addition and subtraction formally in Year 1, counting by ones with, then without counters (AS 1, 2, 3, 4, 5) as they simultaneously investigate Place Value formally including friends of 10, partitioning and place value of teen numbers (PV 6, 7, 8). They then use their understanding to add and subtract bridging 10 using place value (AS 6, 7) while they begin to investigate friends of 20, friends of any decade and two-digit place value (PV 9, 10, 11) and then use their understanding to add and subtract single-digit numbers over 20, then any decade (AS 8, 9). Students investigate Patterns and Algebra concepts of adding and subtracting 0, adding using the associative property, and addition and subtraction equivalent number sentences (AS 10, 11, 12).

Students begin to investigate counting forwards and backwards by 10 on and off the decade (PV 12, PA 11) in Year 2, then use their understanding to add and subtract 10s numbers, and 10s numbers and two-digit numbers counting by 10s (AS 13, 15). They investigate partitioning 10s numbers, friends of 100 and three-digit place value (PV 13, 14, 15) then use their understanding to add and subtract 10s numbers, 10s and two-digit numbers, and two-digit numbers bridging to 100 (AS 14, 16, 17). Students investigate Money and Financial Mathematics concept of adding and subtracting coins and notes (AS 18 MF 7), and Patterns and Algebra concepts of seeing difference in 3 ways, and addition and subtraction word problems as number sentences. (AS 19, 20 PA 13, 14).

Students begin to investigate counting by 100s and four-digit place value (PV 16, 17, PA 12, 16) in Year 3, then use their understanding to add and subtract three- and four-digit numbers (AS 21) including as money (AS 23, MF 9). They begin their investigation of multiplicative place value, with an investigation of multiplicative place value of whole numbers (PV 18). Students investigate Patterns and Algebra concept of addition and subtraction equivalent number sentences (AS 22, PA 19). 

Students begin to investigate five-digit place value (PV 19, PA 20) in Year 4, then use their understanding to add and subtract five-digit numbers, including as money (AS 24 MF10). Students investigate Patterns and Algebra concepts of adding and subtracting odd and even numbers (AS 25, PA 21). They continue their investigation of additive and multiplicative place value, with an investigation of tenths and hundredths (PV 20, 21, FD 11, 12), money as decimal to 2 places (PV 22, FD 16), and rounding decimals (PV 23, FD 17). Students investigate fractions in number patterns (AS 26, FD 15, PA 22).  

Students begin to investigate using multiplicative place value to multiply and divide by 10, 100 and 1000 (PV 24, FD 18) in Year 5, and extend their investigation of additive and multiplicative place value to thousandths (PV 25 FD 21). They investigate ordering numbers to thousandths and number patterns with decimals (PV 26, 27, FD 22, 24, PA  27). Students investigate adding and subtracting fractions with the same denominator (AS 28, FD 23). 

Students begin to investigate additive and multiplicative place value of numbers of any size (PV 28, FD 25) in Year 6, multiplying and dividing by decimals (PV 29, MD 25, FD 26) and probabilities using fractions, decimals and percentages (PV 30, FD 31, SP 16). They investigate patterns with fractions and decimals (PV 31, AS 31, FD 34, PA 28), and add and subtract decimals and fractions with related denominators (PV 32, AS 29,30, FD 32, 33). Students investigate the Patterns and Algebra concepts of negative numbers (AS 32, PA 30) and order of operations and grouping symbols (AS 33, MD 29, PA 31).                

AS and PV