standard_description: Construct a tangent line from a point outside a given circle to the circle.
problem_activity: Narrative
The purpose of this Choral Count is to invite students to practice counting by
\(\frac{1}{2}\)
and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students recognize and generate equivalent fractions. In the synthesis, students have the opportunity to notice that
\(\frac{2}{2}\)
and
\(\frac{4}{4}\)
are both equal to 1 whole.
Required Preparation
Have recording of choral count by one-fourth available, from a previous lesson.
Launch
“Count by
\(\frac{1}{2}\)
, starting at
\(\frac{1}{2}\)
.”
Record as students count. Record 2 fractions in each row, then start a new row. There will be 4 rows.
Stop counting and recording at
\(\frac{8}{2}\)
.
Activity
“What patterns do you see?”
1–2 minutes: quiet think time
Record responses.
Student Response
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Activity Synthesis
Display count by
\(\frac{1}{4}\)
from the previous lesson. There should be 4 rows and 4 fractions in each row with the count ending at
\(\frac{16}{4}\)
.
“How are these two counts the same? How are they different?” (The denominator stays the same in both counts—4 for the last count, and 2 for today’s count. The numerators change in the same way because they both count by one. They start a new line at
\(\frac{2}{2}\)
and
\(\frac{4}{4}\)
, which are both whole numbers.)
Consider asking:
“Who can restate the pattern in different words?”
“Does anyone want to add an observation as to why that pattern is happening here?”
“Do you agree or disagree? Why?”


aligns: no