Stage 6 : Advanced Additive PartWhole
Stage Six: Advanced Additive PartWhole
Students at the Advanced Additive stage are learning to choose appropriately from a repertoire of partwhole strategies to solve and estimate the answers to addition and subtraction problems.
They see numbers as whole units in themselves but also understand that “nested” within these units is a range of possibilities for subdivision and recombining. Simultaneously, the efficiency of these students in addition and subtraction is reflected in their ability to derive multiplication answers from known facts.
These students can also solve fraction problems using a combination of multiplication and additionbased reasoning.
For example, 6 x 6 as (5 x 6) + 6;
or ¾ of 24 as ¼ of 20 is 5 because 4 x 5 = 20, so ¾ of 20 is 15, and ¼ of 4 is 1 because 4 x 1 = 4,so ¾ of 4 is 3. Therefore of 24 is 15 + 3, namely 18.
Here are examples of the addition and subtraction strategies used by Advanced Additive PartWhole students:
(i) Standard place value with tidy numbers and compensation
Example: 63 – 29 as 63 – 30 + 1.
(ii) Reversibility
Example: 53 – 26 = □ as 26 + □ = 53. 26 + (4 + 20 + 3) = 53, so 53 – 26 = 27.
Advanced Additive students also use addition strategies to derive multiplication facts. Their strategies usually involve partitioning factors additively.
Here are two examples of such strategies:
(i) DoublingExample: 3 x 8 = 24, so 6 x 8 = 24 + 24 = 48.
(ii) CompensationExample: 5 x 3 = 15, so 6 x 3 = 18 (three more).
Greedy Pig
This is a warm up activity using addition, subtraction and probability.
