Number pairs
Y4 (11/07) | ||
a) |
Any unique number pairs that add to 8, i.e., (0, 8) or (8, 0); (7, 1) or (1, 7); (6, 2) or (2, 6); (5, 3) or (3, 5); (4, 4). |
4 correct – easy |
b) | Any unique number pairs that add to 17, i.e., (17, 0) or (0, 17); (16, 1) or (1, 16); (15, 2) or (2, 15); (14, 3) or (3, 14); (13, 4) or (4, 13); (12, 5) or (5, 12); (11, 6) or (6, 11); (10, 7) or (7, 10); (9, 8) or (8, 9). |
4 correct – moderate |
c) | Any two whole numbers that have a difference of 7. |
4 correct – moderate |
NOTE: While students generally used whole numbers for their answers, accept other numbers (e.g., fractions, decimals, etc.) that add or subtract to the given total.
Links to the Number Framework
This resource fits with the Grouping/Place Value aspect of the Advanced Counting stage (Stage 4) of the Number Framework and with Basic Facts in the Early-Additive stage (Stage 5).
Common response | Likely misconception | |
a) b) |
8 + 0 and 0 + 8 (for example) 10 + 7 and 7 + 10 (for example) |
Students repeat one or more of the number pairs, believing that having the numbers in a different order means it is a different number pair. |
c) | 3 and 4, 5 and 2, etc. | The numbers add to seven - the subtraction operator is ignored. |
c) | 0 – 7, 1 – 6, etc. | The smaller number is given before the larger number – students may believe that subtraction is commutative. |
If students have added, rather than subtracted, two numbers in part c), have them generate numbers that, when subtracted, give the answer of 7.
If students have reversed the order of the numbers in the subtraction equations, use materials to reinforce the need to record the larger number first and to emphasise that subtraction is not commutative. Alternatively, have students generate word problems to match their number sentences. See Algebraic Thinking Concept Map: Commutativity and Associativity for more information about commutativity and subtraction.
While many students were able to identify pairs of whole numbers successfully, using 0 as one of the numbers in their pair was less frequent than other numbers. There is an opportunity here to explore the additive identity with students and generate a rule about what happens to a number when it is added to zero or subtracted from zero. For more ideas and information about this concept, see the Algebraic Thinking Concept Map: Additive Identity.
If students have been able to generate four number pairs for each question, have them try to write as many number pairs for each as they think there are. Students could share their results and try to come up with as many answers as they can. (NOTE: There are an infinite number of combinations for part c) - students may need to be restricted to numbers below 50 or 100). Alternatively, give students another number to find totals for (e.g., 9, 12, and 20) and have them generate all possible number pairs.
The patterns of the number pairs can also be explored in an algebraic way too. Students can explore the relationship between the numbers by looking at what happens to each of the numbers in the number pair to turn it into another number pair. For example, use the number pairs (0, 8) and (1, 7). Encourage students to notice that when one is added to one number in the pair, i.e., 0 + 1 = 1, then the other number has one subtracted from it, i.e., 8 – 1 = 7. Students can use this relationship to help generate all the possible combinations of number pairs that add to a given number.
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