These results are based on a trial set of 149 Y5 students.
Teaching and learning:
Students could solve these equations in a number of ways - by counting on, counting back (Stage 4: Advanced counting - strategy, from The Number framework, book 1, 2004) or by simply recalling them as addition and subtraction facts (addition facts to 10 is at Stage 4: Advanced counting - knowledge).
Diagnostic and formative information:
Common error
Likely calculation
Likely misconception
b) i)
b) iv)
6
7
4 + 2 = 6
4 + 3 = 7
Adds the numbers given rather than seeking a solution that adds to 10.
b) iii)
b) v)
4
3
6 + 4 = 10
3 + 7 = 10
Ignores '3 +' or '1 + '.
Next steps:
Once students are comfortable and confident with equations that total to ten and are calculating without materials or pictures, get them to solve similar problems that total to twenty.
Give students problems similar to those in part b) but with two missing numbers, for example
4 + + = 10
Encourage students to explore the relationships between the numbers by getting them to find all the possible combinations of numbers that would correctly solve the problem (including 0).