These Addition and Subtraction professional learning videos are designed to deepen **YOUR **understanding of the levels of understanding that children go through as they develop **THEIR** understanding of adding and subtracting using place value.

Children develop their understanding of addition and subtraction in **Years 1 and 2, when the focus of their learning is on additive thinking** about Addition, Subtraction and Place Value. Even Multiplication and Division is additive in Years 1 and 2, as children skip count!

In **Year 1**, children begin to **add and subtract single-digit numbers**, initially **using counters**, **then** as they develop their number sense that a number always represents the same amount, by **counting on or back**.

They then begin to **add and subtract single-digit numbers using the additive place value concepts** of standard and non-standard place value of teen and two-digit numbers, friends of 10, 20 and any decade, and partitioning single-digit, teen and two-digit numbers, bridging to 10, then to 20 and then to any decade.

In **Year 2**, children begin to **add and subtract tens numbers, using the additive place value concepts** of standard and non-standard place value of two-digit and three-digit numbers, friends of 100, and partitioning two-digit and three-digit numbers, before **putting it all together to add and subtract two-digit numbers**.

**After this, there is really nothing else to understand about addition, subtraction or additive place value**, as children apply their understanding to add three- and four-digit numbers in Year 3, five-digit numbers in Year 4, fractions and decimals in Years 5 and 6.

Developing this additive understanding during Years 1 and 2 frees children to focus their learning in Years 3 to 6 on thinking multiplicatively about Multiplication and Division, multiplicative Place Value and Fractions.

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).