Multi-Digit Division

1. Identify a possible rule of a growing number pattern (MP.7, MP.8).
2. Use the rule of a growing number pattern to extend it to subsequent term (MP.8).
3. Use the rule of a growing number pattern to find its $${n^{\mathrm{th}}}$$ term (MP.8).
4. Identify features of a number pattern that aren’t explicit in the rule itself (such as, in a pattern that starts with 2 and the rule is “add 4,” all of the terms in the pattern are even) (MP.7, MP.8).
5. Explain why those embedded features are true (e.g., all of the terms in the sequence are even in the above pattern because the starting number is even and the rule is to add an even number, and an even number plus an even number is even, so all of the subsequent terms will be even) (MP.3, MP.7, MP.8).
6. Determine whether a given number is a term in a given pattern and explain why or why not (MP.3).

Note that whenever students are given the first few terms in a pattern and asked to identify the rule or to continue the pattern, there are many possible correct answers. For example, say "students are asked to continue the pattern 2, 4, 6, 8, ... Here are some legitimate responses:

• Cody: I am thinking of a “plus 2 pattern,” so it continues 10, 12, 14, 16, . . . 
• Ali: I am thinking of a repeating pattern, so it continues 2, 4, 6, 8, 2, 4, 6, 8, . . . 
• Suri: I am thinking of the units digit in the multiples of 2, so it continues 0, 2, 4, 6, 8, 0, 2, . . .”, among others (CC to RP Progression, p. 40). 

Thus, if students are not told the rule but asked to infer it or to extend a pattern, consider that there may be more than one correct answer, and validate any reasonable response. 

• Problem Set

• Problem Set Answer Key