Addition and Subtraction

Addition and Subtraction is a large component of level 3 mathematics (Year 5 and 6)


               Maths Strategy Groups

There are 3 groups  Yellow       Green           Red
   
Yellow are working at the start and middle of stage 5

Green are working at the end of stage 5, and the beginning of stage 6

Red are working at the end of stage 6 and beginning of stage 7

Previous Strategy	Current strategy	Future strategy
	Solve addition problems by compensation from tidy numbers Year 5 strategy	Solve subtractions problems when one number is close to 10 - Year 4 review strategy Solve addition problems by using compensation from tidy numbers (equal additions) Year 5 strategy
	Year 5 Strategy	Year 5 Strategy

Current strategy	Future strategy
Solve addition problems using compensation from tidy numbers 387 + 89 = as   387 + 89        +13     - 13    300  + 76 = 376	Solve subtraction problems by using compensation from tidy numbers (equal additions) Year 5 strategy Year 6 strategy
	Year 5 Strategy             Year 6 Strategy

Number Knowledge Focus

- Stage 5 yellow  addition and subtraction to 20




- Stage 5 green numbers that equal 100




- Stage 6 red numbers that equal 1000

Addition and subtraction strategies follow a progression and successively build on earlier strategies and number knowledge. 

In the lower levels (year 1-4) students are exposed to a number of strategies to solve particular maths problems.

 At year 5 and 6 students are expected to have a larger range of strategies and be able to chose the best strategy to solve a particular maths problem.

In short, the number of strategies increases as students get older.

Stages explained

Stage 0: Emergent	The student is unable to consistently count a given number of objects because they lack knowledge of counting sequences and/or one-to-one correspondence.
Stage 1: One-to-one counting	The student is able to count a set of objects or form sets of objects but cannot solve problems that involve joining and separating sets.
Stage 2: Counting from one on materials	The student is able to count a set of objects or form sets of objects to solve simple addition and subtraction problems. The student solves problems by counting all the objects.
Stage 3: Counting from one by imaging	The student is able to visualise sets of objects to solve simple addition and subtraction problems. The student solves problems by counting all the objects.
Stage 4: Advanced counting	The student uses counting on or counting back to solve simple addition or subtraction tasks.
Stage 5: Early additive part-whole	The student uses a limited range of mental strategies to estimate answers and solve addition or subtraction problems. These strategies involve deriving the answer from known basic facts (for example doubles, fives, making tens).
Stage 6: Advanced additive/early multiplicative part-whole	The student can estimate answers and solve addition and subtraction tasks involving whole numbers mentally by choosing appropriately from a broad range of advanced mental strategies (for example place value positioning, rounding and compensating or reversibility). The student uses a combination of known facts and a limited range of mental strategies to derive answers to multiplication and division problems (for example doubling, rounding or reversibility).
Stage 7: Advanced multiplicative part-whole	The student is able to choose appropriately from a broad range of mental strategies to estimate answers and solve multiplication and division problems. These strategies involve partitioning one or more of the factors (for example place value partitioning, rounding and compensating, reversibility).
Stage 8: Advanced proportional part-whole	The student can estimate answers and solve problems involving the multiplication and division of fractions and decimals using mental strategies. These strategies involve recognising the effect of number size on the answer and converting decimals to fractions where appropriate.  These students have strongly developed number sense and algebraic thinking.

Where should my child be?

To be AT the expectation you should be at ...

                                STAGE 6                     

B - beginning Starting out	P = proficient Got it	A = advanced Ready to move on to the next level
Year 5	Year 6	Year 6

==================================================================

STRATEGIES

Below is a list of the strategies for each stage, with video and powerpoint links.

I appreciate it is a little different from how we did it. Please note that these are strategies to solve maths problems, they are NOT the only strategy. Students need to learn a range of strategies, and choose the more efficient.

The good old way we learned of   234

                                                   +  145

                                                   -------

                                                       379

is still a strategy, and should be taught.

KEY STRATEGIES 

at each year level

Addition and Subtraction Year 0 Strategy 1 Strategy 2 Year 1 Strategy 1 Strategy 2 Year 2 Strategy 1 Strategy 2 Strategy 3 Strategy 4 Year 3 Strategy 1 Strategy 2 Strategy 3 Strategy 4 Year 4 Strategy 1 Strategy 2 Year 5 Strategy 1 Strategy 2 Year 6 Strategy 1 Strategy 2 Year 7 Strategy 1 Strategy 2 Strategy 3 Strategy 4 Year 8 Strategy 1 Strategy 2

Year 4 strategies EA =  early additive	Year 5 strategies late EA + AA = advanced additive	Year 6 strategies AA =  advanced additive  + EM = early multiplicative
The student uses a limited range of mental strategies to estimate answers and solve addition or subtraction problems. These strategies involve deriving the answer from known basic facts (for example doubles, fives, making tens).	The student can estimate answers and solve addition and subtraction tasks involving whole numbers mentally by choosing appropriately from a broad range of advanced mental strategies (for example place value positioning, rounding and compensating or reversibility). The student uses a combination of known facts and a limited range of mental strategies to derive answers to multiplication and division problems (for example doubling, rounding or reversibility).	As with year 5 plus students are now staring to use multiplcation strategies to solve problems
Early Additive Adding in parts 8 + 7 = 15  as 8 + 2 = 10, 10 + 5 = 15 Addition in parts (Video) Comparisons More comparisons (video) Tim has 14, Steve has 18.                                                   How many more does Steve have?    As 14 + 4 = 18, 18 - 4 = 14 Subtraction in parts How many ten-dollar notes
	Early Additive/ Advanced Additive Saving hundreds 286 + ? = 400 Saving hundreds (video) Jumping the number line 29 + ? = 63 Jumping the number line (video) Don't subtract add 54 - 29 =    as 29 + ? = 54 Don't subtract add (video)
	AND SOME OF	Advanced Additive Problems like 23 + ? = 71 Problems like 23 + ? = 71 (video) How many tens and hundreds Problems like 37 + ? = 79 Problems like 37 + ? = 79 (video) Problems like ? + 29 = 81 When one number is near 100 When 1 number is near 100 -add (video) 55 + 98 as 53 + 100 = 153  ( + - strategy) When 1 number is near 100 -sub (video) 173 - 98  as  175 - 100 = 75 ( + + strategy) Problems like 73 - 19 = ? Problems like 73 - 19 = ? (video) Equal additions People's ages People's Ages (video) A balancing act A balancing act (video) Near doubles Near doubles (video) Three or more at a time Three or more at a time (video) Problems like 67 - ? = 34 Large numbers roll over Large numbers roll over - addition (video) Large numbers roll over - subtraction (video) Standard written form for addition Standard written form for addition (video) Decomposition Decomposition (video) Estimation as a check

Previous Strategies

Students should have covered the following strategies prior to year 5. To review, practice, consolidate these strategies, click on the links below.

AC = Stage 4 strategies 

Counting on the the biggest number first             3, 66 -->   66 + 3 = 69

Change unknown                                                   4 + ? = 7

Counting back to solve subtraction problems       12 - 3 = ?

Adding tens                                                            14 + 30 = ?

Subtracting tens                                                      37 - 20 = ?

Adding ones and tens                                             23 + 32 = ?

Subtracting ones and tens                                       37 - 15 = ?

Missing ones and tens                                             32 + ? = 45          

AC/EA = late stage 4 / early stage 5      

Making tens                             6 + 2 + 4 as   6 +  4 = 10 + 2 = 12

Compatible numbers               3 + 4 + 2 - 6     as  4 + 2 = 6 so 6 -6 = 0 (3 are left)

Subtraction in parts                 14 - 6 = ?  as 14 - 4 = 10, 10 - 2 = 8

Up and over tens                      8 + ? = 14