Collecting beads
Some students were collecting beads to make necklaces with.
Key competencies
This resource involves students reflecting on which arithmetic computations they found the easiest, and explaining the reasons for this. This relates to the Key Competency: Managing self and Using language, symbols and text.
For more information see https://nzcurriculum.tki.org.nz/Keycompetencies
Y6 (11/2013)  
a)  314  very easy 
b)  74  moderate 
c)  359  moderate 
Results based on an online sample of 56 Y6 students.
Student responses
Questions d) and e): Which calculations were easiest / hardest?
Question d): Which was easiest? 
Question e): Which was hardest? 

236 + 78 = ?  About 50%  About 10% 
253 + ? = 328  About 10%  About 15% 
? + 65 = 424  About 10%  About 60% 
All / none  About 30%  About 20% 
The most common responses are bolded,i.e., half of the students replied that 236 + 78 was the easiest, and over half said ? + 65 as the hardest.
Question d) and e): Typical reasons for items being easy or hard include:
Reasons for being easy (d)  Reasons for being hard (e)  Student examples 
Addition is easier than subtraction.  Subtraction is harder than addition. 
I like adding numbers together rather than subtracting. 
The numbers are small.  The numbers are big. 
Because its smaller numbers. 
The difference between the numbers is small (for 253 + ? = 328 or 236 + 78 = ?) 
The difference between the numbers is big (for ? + 65 = 424). 
Because you only had to add a little bit more. 
Comments on the location of the missing number (for ? + 65 = 424).  [Hard] because you had to find out how many beads he had before (for ? + 65 = 424).  
Descibes the strategy 
Add 230 and 70 = 300 then add the 14. 
Many students either gave a nonspecific answer, or did not give any reasons.
Results based on an online sample of 56 Y6 students.
 Using partitioning strategies when adding and multiplying using hundreds, tens and ones consistently using correct compensation (Year 7, Number Framework Stage 7 – Advanced multiplicative).

Partitioning using rounding and compensation to jump through tidy numbers or partitioning by rounding one number to a tidy number then compensation or
Using the vertical algorithm with understanding. (Year 6, Number Framework Stage 6).  Place value partitioning one number into hundreds, tens and ones then adding it on to the other in parts (Year 5, Number Framework Stage 6).
 Place value partitioning both numbers using hundreds, tens and ones with correct compensation (Year 4, Number Framework Stage 5).
 Counting strategies (Year 2, Number Framework Stage 14).
Common error  Likely reasons  Next steps  
b) c) 
582 489 
Student adds given numbers rather than subtracting them.  The student may have misread the question. They could reread the question carefully. 
b) c) 
134 or 34 341 or 441 
Student uses subtraction and takes away the bigger number from the smaller.
This happens with both place value partitioning and the vertical algorithm.

Students could do simpler subtractions where the strategy does not work (e.g., 65  57, which should be single digit). Get students to show their working on the number line. 
a)  214 or 304  The student does not " carry" tens to hundreds or ones to tens in addition.  Students could explore alternative strategies such place value partitioning [e.g., 200 + (30 + 70) + (6 + 8) = 200 + 100 + 14] 
b) c) 
174 or 274 369 
Student does not "rename" or "renames" incorrectly. 
Students could explore renaming using money ($100, $10 and $1 notes) or grouping the beads.

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