standard_description: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
problem_activity: Narrative
The purpose of this activity is for students to find quotients and represent their thinking with base-ten blocks. The numbers in the expressions are designed to encourage students to think about when the base-ten blocks may be helpful and when they become cumbersome. In future lessons, students will be asked to interpret base-ten representations but may use any method or representation that makes sense to them.
Representation: Develop Language and Symbols.
Synthesis: Use gestures or annotations such as labels or arrows to make connections between representations visible on displayed student work.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
“You are going to solve some problems on your own. Use base-ten blocks and represent your thinking in your book.”
Activity
5–6 minutes: independent work time
2 minutes: partner discussion
Monitor for students who draw base-ten representations using small and large squares and rectangles labeled with numbers, to share in the lesson synthesis.
Student Facing
Find the value of each expression. Explain or show how you used base-ten blocks to find the value.
\(96\div4\)
\(86\div2\)
\(108\div9\)
Student Response
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Advancing Student Thinking
Students may use mental math to solve problems. Consider asking: “How might your use the blocks to check your mental math?”
Activity Synthesis
See lesson synthesis.


aligns: no