Different addition number sentences

This task is about finding the missing number in addition sentences.

Question 1Change answer

Write the missing number in each box in the following number sentences.

a)	9	+	8	=
b)	6	+		=	11
c)		+	12	=	19
d)	15	=		+	7
e)		=	3	+	9
f)	14	=	5	+

Teaching and learning:

Numbers of students become uncomfortable when they meet questions d)-f). These have the equals signs near the beginning of the equation rather than just before the "answer" (a = b + c). They may very well ask about these questions or state that they do not make sense. Encourage them to give the best answer they can.
Have a class (or group) discussion afterwards on what the equals sign means. Click on algebraic thinking: equality for more about this important idea. AL7112 gives a comprehensive guide on how a class discussion can be managed on mathematical classroom discourse.
The location of both the equals sign and the box for the missing number (called the unknown) is in corresponding positions. For example a) has it in the position generally used in number problems (a + b = ?), while b) is of similar form (a + ? = c).

Diagnostic and formative information:

	Common error	Likely misconception
a) b) c) d) e) f)	16 or 18 4 or 6 6 or 8 7 or 9 11 or 13 8 or 10	Counting on or counting back incorrectly Bolded numbers indicate 5 or more students in the sample responded this way, demonstrating that it is more common to be short by 1.
e) f)	6 or –6 19	Subtracting instead of adding: Incorrect use of the inverse operation Students use the incorrect operation on the two given numbers to get their answer, adding instead of subtracting or vice versa. Nearly 40% of students made this error in b)iv), and over 10% of students in a)v), a)vi).
d) e) f)	No answer given	Cannot understand the position of the equals sign Students do not know how to respond to the equals sign coming early in the number sentence or equation (? = b + c).

Next steps:

Counting on or counting back incorrectly
These students are likely to correctly understand the number sentence, and should be given credit for this. However, they are probably not solving the problems using the inverse operation, which is the more algebraic approach, and may need to either work on:

Part-whole strategies ( e.g., in b) saying 6 + 4 = 10, 10 + 1 = 11), or
improving their basic facts in addition or subtraction so the don't have to count on or back.

Click on the Basic facts concept map for more information.

Subtracting instead of adding: Incorrect use of the inverse operation
Students may have some realisation that they need to add the two numbers to get the answer, and may well be beginning to think algebraically. Other students may simply be performing addition because they can't think of what else to do.

Discuss with the students what they did and why.
Get them to check if the number sentence they get is true.
Discuss what they think the equals sign means. They may think it means "and the answers is" rather than "is the same as" (or more correctly "is the same amount as"). Click on Algebraic thinking: equality, which will take you to the algebraic thinking concept map.

Cannot understand the position of the equals sign
Students are used to the equals sign coming near the end of a number sentence. Question a) is of the form students usually meet,
i.e., 9 + 8 = ?
Students need to realise that the equals sign can come elsewhere in a number sentence or equation, and that equality is about the balance of numbers on both sides of the equals sign.
i.e., ? = 9 + 8 is a different way of asking the same question.

Location of the missing number
This affects how the student responds to the question.

a) is of the usual number form (9 + 8 = "what"?)
e) is closely related to this, but is harder for students.
The other questions place the box in a position where the number to be found is part of an expression, e.g., 6 + ?
Get students to say the problem out loud, and see if this makes sense,

e.g., 6 plus "what" equals 11;
"What" plus 12 equals 19;
15 = "what" plus 7.

Discuss the different strategies students use, both number types or algebraic types:

Examples: 6 + ? = 11

Numeric:

Algebraic:

"6, 7, 8, 9, 10, 11 so its 5"
"I know 6 + 5 = 11"
"6 + 4 = 10 and 10 + 1 = 11 so it is 5 (4+1)"
The answer must be 11 – 6

Counting on
Basic facts
Part-whole thinking
Additive inverse

Strategies
Students who used counting on incorrectly or subtracted instead of added had a significantly lower mean ability that students who got a correct answer. These students typically had a higher mean ability than those who got other wrong answers or did not answer the question, indicating that many of them had some level of understanding of the problem

		Y4 (06/2009)
a) b) c) d) e) f)	17 5 7 8 12 9	very easy very easy easy very easy easy easy

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Different addition number sentences

Different addition number sentences

Question 1Change answer