The purpose of this Warm-up is to remind students that two different numbers can have the same square. This is an example of two inputs having the same output for a given rule—in this case, the rule is “Square the number.” Later activities in the lesson explore rules that have multiple outputs for the same input.
Give students 1–2 minutes of quiet work time, and follow with a whole-class discussion.
Here are some numbers in a list:
The focus of this discussion should be on the final question, which, even though the language isn't used in the problem, helps prepare students for thinking about the collection of values that make up the inputs and outputs for given rules. Here, the input is a list of 7 unique values, while the output has only 5 unique values.
Invite students to share their responses to the second problem, and display this new list of numbers along with the original list for all to see. Next, invite different students to share their explanations from the forth problem. Emphasize the idea that when we square a negative number, we get a positive number. This means two different numbers can have the same square, or using the language of inputs and outputs, two different inputs can have the same output for a rule.
If time allows, ask, “Can you think of other rules where different inputs can have the same output?” After 30 seconds of quiet think time, select students to share their rules. They may recall the previous lesson where they encountered the rule “Write 7,” which has only 1 output for all inputs, and the rule “Name the digit in the tenths place,” which has only 10 unique outputs for all inputs.
All skills for this lesson
No KCs tagged for this lesson
The purpose of this Warm-up is to remind students that two different numbers can have the same square. This is an example of two inputs having the same output for a given rule—in this case, the rule is “Square the number.” Later activities in the lesson explore rules that have multiple outputs for the same input.
Give students 1–2 minutes of quiet work time, and follow with a whole-class discussion.
Here are some numbers in a list:
The focus of this discussion should be on the final question, which, even though the language isn't used in the problem, helps prepare students for thinking about the collection of values that make up the inputs and outputs for given rules. Here, the input is a list of 7 unique values, while the output has only 5 unique values.
Invite students to share their responses to the second problem, and display this new list of numbers along with the original list for all to see. Next, invite different students to share their explanations from the forth problem. Emphasize the idea that when we square a negative number, we get a positive number. This means two different numbers can have the same square, or using the language of inputs and outputs, two different inputs can have the same output for a rule.
If time allows, ask, “Can you think of other rules where different inputs can have the same output?” After 30 seconds of quiet think time, select students to share their rules. They may recall the previous lesson where they encountered the rule “Write 7,” which has only 1 output for all inputs, and the rule “Name the digit in the tenths place,” which has only 10 unique outputs for all inputs.