The purpose of this Warm-up is to elicit the idea that the values in the table have a predictable pattern, which will be useful when students consider the context of a falling object in a later activity. While students may notice and wonder many things about this table, the patterns are the important discussion points, rather than trying to find a rule for the function. Because the rule is not easy to uncover, studying the numbers ahead of time should prove helpful as students analyze the function later.
This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is that all the y values are multiples of 16 and perfect squares. Some may notice that the pattern is not linear and wonder whether it is quadratic.
Study the table. What do you notice? What do you wonder?
| x | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| y | 0 | 16 | 64 | 144 | 256 | 400 |
Students may notice:
Students may wonder:
Ask students to share the things they noticed and wondered about. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the table. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If the patterns for the values do not come up during the conversation, ask students to discuss this idea.
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The purpose of this Warm-up is to elicit the idea that the values in the table have a predictable pattern, which will be useful when students consider the context of a falling object in a later activity. While students may notice and wonder many things about this table, the patterns are the important discussion points, rather than trying to find a rule for the function. Because the rule is not easy to uncover, studying the numbers ahead of time should prove helpful as students analyze the function later.
This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is that all the y values are multiples of 16 and perfect squares. Some may notice that the pattern is not linear and wonder whether it is quadratic.
Study the table. What do you notice? What do you wonder?
| x | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| y | 0 | 16 | 64 | 144 | 256 | 400 |
Students may notice:
Students may wonder:
Ask students to share the things they noticed and wondered about. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the table. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If the patterns for the values do not come up during the conversation, ask students to discuss this idea.