Unit 1, Lesson 11
Adding Up
Algebra 2
11.1
Warm-up
5 mins
Math Talk: Adding Terms
Standards Alignment
Building On
Addressing
Building Toward
HSA-SSE.B.4
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.
Materials
None
Activity Narrative
The purpose of this Math Talk is to elicit strategies and understandings students have for adding fractions. It encourages students to think about common denominators and to rely on what they know about factors of numbers to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students add and subtract fractions.
Students look for and make use of structure (MP7) when they use the previous answer when they solve the next step.
Launch
Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:
- Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
- Invite students to share their strategies, and record and display their responses for all to see.
- Use the questions in the Activity Synthesis to involve more students in the conversation before moving to the next problem.
Keep all previous problems and work displayed throughout the talk.
Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization
Supports accessibility for: Memory, Organization
Activity
NoneStudent Task Statement
Evaluate mentally.
Activity Synthesis
The goal of this discussion is to review students’ strategies for adding fractions that do not have common denominators.
To involve more students in the conversation, consider asking:
- “Who can restate
’s reasoning in a different way?” - “Did anyone use the same strategy but would explain it differently?”
- “Did anyone solve the problem in a different way?”
- “Does anyone want to add on to
’s strategy?” - “Do you agree or disagree? Why?”
- “What connections to previous problems do you see?”
MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. Examples:
Advances: Speaking, Representing
- “First, I
because .” - “I noticed
, so I .”
Advances: Speaking, Representing
11.2
Activity
15 mins
11.3
Activity
15 mins
A Threefold Design
Instructional Routines
Materials
None
Activity Narrative
This activity is an opportunity to contrast when it does and does not make sense to sum a sequence. This task is relatively unscaffolded compared to previous lessons, giving students opportunities to make sense of the problem by, for example, drawing Step 2 or organizing the data in a table (MP1).
If you wish, share with students that this shape is known in mathematics as the Koch (pronounced “coke”) Snowflake.
Lesson Synthesis
Ask students to consider what it would mean to find the sum of the sequence defined by
Student Lesson Summary
The sum of a sequence is the sum of its terms.
For example, suppose you were given $1 on the first day, then $2 the second day, then $4 the third day, and it doubled each day for seven days. After finding each term of the sequence, you can find the sum:
For these seven days, the total amount of money is $127. In a later unit, you will learn a method to find the sum of a geometric sequence more efficiently.
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