This is a level 2 algebra strand activity from the Figure It Out series.
A PDF of the student activity is included.
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find the rule connecting members in a pattern
Activities One and Two
Although students are not asked to draw graphs in these activities, you may wish to ask your students to do so. The important concept being developed is that of a relation: how the value of one variable (the number on the left) maps onto the values of another variable (the numbers on the right).
For example, in Activity One, question 3, 4 maps onto 8, 5 maps onto 10, and 6 maps onto 12, which suggests that students need to double the numbers on the left to map them onto the numbers on the right. This could be graphed as:
You can ask students to look for a pattern in the points on a graph and use this pattern to predict other values.
Students will probably use informal rules about the operations, such as “the numbers on the right are larger than the numbers on the left, so either addition or multiplication is used”. Although these informal rules are useful in some problems, they can prove troublesome in later study. For example, adding a negative integer gives an answer less than the starting addend, as does multiplication by a fraction less than one.
Answers to Activities