standard_description: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
problem_activity: Warm-up
The purpose of this warm-up is to review factors and multiples while eliciting ideas on common factors and common multiples that will be useful in the activities of this lesson. While students may notice and wonder many things about the numbers they have circled, it is important for students to notice the multiples 4 and 6 have in common and wonder what other multiples they would have in common if the counting sequence continued.
Launch
Arrange students in groups of 2. Tell students 10 is a multiple of 5 because
\(10 = 5 \boldcdot 2\)
. One way you can find multiples of a number is by skip counting. For example, the multiples of 5 are 5, 10, 15, 20. . . and so on. Give students 1 minute of quiet work time to circle the multiples of 4 and 6. Give students 1 minute to discuss the things they notice and wonder with a partner, followed by a whole-class discussion.
Student Facing
Circle all the multiples of 4 in this list.
1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26
Circle all the multiples of 6 in this list.
1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26
What do you notice? What do you wonder?
Student Response
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Activity Synthesis
Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image. After each response, ask the class if they agree or disagree and to explain alternative ways of thinking, referring back to the images each time. If there is time, ask students what other multiples 4 and 6 would have in common if the counting sequence continued. Ask them to explain their reasoning. Record and display their responses for all to see.


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