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
solve add compensation from tidy numbers year 5 strategy




Year 5 Strategy

equal additions subtraction yr5





Current strategy
Future strategy


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


Compensation from tidy numbers year 6


 Year 5 Strategy
equal additions subtraction yr5
            Year 6 Strategy

equal additions subtraction yr6






Number Knowledge Focus

- Stage 5 yellow  addition and subtraction to 20




- Stage 5 green numbers that equal 100

adding to 100 stage 5 passport


- Stage 6 red numbers that equal 1000

adding to 1000 stage 6 passport




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: EmergentThe 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 countingThe 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 materialsThe 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 imagingThe 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 countingThe student uses counting on or counting back to solve simple addition or subtraction tasks.
Stage 5: Early additive part-wholeThe 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-wholeThe 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-wholeThe 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-wholeThe 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

Year 1
Strategy 1

Year 2
Strategy 1

Year 3
Strategy 1

Year 4
Strategy 1

Year 5
Strategy 1

Year 6
Strategy 1

Year 7
Strategy 1

Year 8
Strategy 1





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
8 + 7 = 15  as 8 + 2 = 10, 10 + 5 = 15
Tim has 14, Steve has 18. 
                                                 How many more does Steve have?
   As 14 + 4 = 18, 18 - 4 = 14










Early Additive/ Advanced Additive
286 + ? = 400
29 + ? = 63
54 - 29 =    as 29 + ? = 54


AND SOME OF
Advanced Additive
55 + 98 as 53 + 100 = 153  ( + - strategy)
173 - 98  as  175 - 100 = 75 ( + + strategy)


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
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





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