Handoff Sheet: Workshop & Independent Hour

Session 11 | Week 6, Tuesday, March 18, 2026
Assisting Teacher Briefing | MATH 102 Stream C

Your Role This Session

You are the primary instructor during the 60-min workshop and 30-min independent hour (2:00-3:30 PM). The main instructor leads the 30-min Socratic review (1:30-2:00), then hands off to you.

Your mission: Help students practice polynomial operations (adding, subtracting, multiplying), work through FOIL problems, and apply polynomials to real-world contexts. Focus on building fluency with like terms, distributing negatives, and special products.

Session Structure You're Managing

Your Responsibilities (2:00-3:30 PM)
Time	Activity	Your Role
2:00-2:20	Part A-B: Terminology and Adding/Subtracting (Problems 1-6) Students work individually or in pairs on polynomial terminology, then adding and subtracting polynomials.	Circulate. Watch for sign errors when distributing negatives. Encourage showing work and writing answers in standard form.
2:20-2:45	Part C: FOIL and Multiplying Binomials (Problems 7-10) Students practice FOIL, special products (difference of squares, perfect square trinomials), and area models.	Help students set up FOIL correctly. Watch for the common error of forgetting to combine middle terms. Use area model as a visual backup for students who struggle with FOIL.
2:45-3:00	Part D: Real-World Applications (Problems 11-14) Coast Salish garden area, Tlingit cedar plank, projectile motion, and perimeter/area problems.	Help students set up the polynomial expressions from word problems. Remind them to include units and interpret answers in context.
3:00-3:30	Reflection and Independent Hour (Problem 15) Students write their weekly reflection, then finalize and submit the worksheet.	Spot check progress. Encourage students to use math vocabulary in their reflection. Answer questions. Document who needs follow-up.

Critical Moves During Phases

Phase 1: Terminology and Adding/Subtracting (20 min)

Circulation Strategy:

Start with students who typically need support. Help them get unblocked on terminology first.
Ask: "Walk me through your thinking on Problem 3. How did you rewrite this in standard form?"
If a student is confused, probe before giving the answer: "What does 'like terms' mean again? Can you point to two like terms in this expression?"
If work is careless, gently push: "Show me your steps. Did you distribute the negative to every term in the second polynomial?"

Watch for these misconceptions:

Adding exponents: Students may write 3x² + 2x = 5x³. Remind them: you can only combine like terms (same variable AND same exponent).
Distributing negatives: -(3x + 5) should be -3x - 5, not -3x + 5. This is the most common error in subtraction problems.
FOIL middle terms: Students may forget to combine the Outer and Inner products. Walk them through each step.
Special products shortcuts: (x+5)² is NOT x² + 25. It is x² + 10x + 25. The middle term is critical.

Affirmation moves: When a student gets something right, ask them to explain it to a neighbor. This builds confidence and deepens understanding.

Phase 2: FOIL and Multiplying Binomials (25 min)

Teaching Tips for FOIL:

Start simple: Have students label F, O, I, L on each problem before computing.
Show the area model: For visual learners, draw a 2x2 grid. Label the top with one binomial and the side with the other. Fill in each cell.
Emphasize combining: After getting four terms, always check if the two middle terms can combine.
Special products: Point out the patterns. Difference of squares always cancels the middle term. Perfect squares always double the middle term.

Common Struggles to Address:

Student gets four terms but forgets to combine like terms. Prompt: "Are there any terms you can still simplify?"
Student writes (x+3)² = x² + 9. Ask: "What does squaring mean? Can you rewrite this as (x+3)(x+3) and FOIL it?"
Student rushes through and gets wrong answers. Ask: "Can you slow down and show me each FOIL step? Label F, O, I, L."
Student confuses adding polynomials with multiplying. Remind: "When we add, we combine like terms. When we multiply, we use FOIL or distribution."

Tone Tip: Polynomial operations involve a lot of moving parts. Normalize that it takes practice. Celebrate when students catch their own sign errors.

Phase 3: Real-World Applications (15 min)

Helping with Story Problems:

Help students translate the word problem into a polynomial expression first, before computing.
Garden area (Problem 11): "What is the formula for area of a rectangle? Now substitute the polynomial expressions for length and width."
Cedar plank (Problem 12): "Set up the area first, then subtract the removed piece. Watch your signs."
Projectile motion (Problem 13): "This one is about evaluating. Plug in the time value and compute carefully."
Perimeter (Problem 14): "Perimeter means adding, not multiplying. Use P = 2L + 2W."

Sample Conversation (Problem 11):

You: "What are the dimensions of the garden?"
Student: "(x - 1) meters long and (x + 2) meters wide."
You: "Good. Area equals length times width. Can you set that up?"
Student: "(x - 1)(x + 2)... so I FOIL it?"
You: "Exactly. Show me each step."
Student: "x times x is x², x times 2 is 2x, -1 times x is -x, -1 times 2 is -2. So x² + 2x - x - 2 = x² + x - 2."
You: "That is correct. Now evaluate at x = 5. What do you get?"

Phase 4: Reflection and Independent Hour (30 min)

Your Presence (Not Lecturing):

Be available but not hovering. Students should attempt work independently first.
If a student raises their hand, ask: "What did you try? Where did you get stuck?"
Offer hints, not full answers. "You are on the right track. Try setting up the FOIL just like Problem 7, but with these new binomials."
Check in 1-on-1 with any students who seemed lost during the workshop.
Note who finishes early. They can peer-tutor or review the answer key.

Documentation (For Instructor Handoff):
Before the instructor returns, jot down:

Whole-class themes: "Most students struggled with distributing negatives in subtraction." "FOIL is clicking for most."
Students needing follow-up: Names and specific gaps (e.g., "Maya - still confusing adding and multiplying polynomials; needs extra practice").
Strong performers: Who finished early and helped others? (These students can be peer mentors.)
Worksheets submitted: Track who turned in complete work vs. who needs more time.

Materials & Setup

Worksheet - Polynomial Operations.html (printed or share on screen)
Answer Key - Polynomial Operations.html (for your reference; don't show yet)
Work collection (Google Drive link or Canvas): Students need access to review their work from Weeks 1-5.
Zoom with breakout rooms (optional): If you break into 1-on-1 conversations, use breakout rooms so students can stay organized.
Scratch paper: Students may work on paper and then upload later, or use a shared Google Doc for live collaboration.
Stopwatch/timer: Keep an eye on time. 20 min practice goes faster than expected.

Key Outcomes of This Handoff

By end of independent hour (3:30 PM), students should have:

Completed the Polynomial Operations worksheet (15 problems covering terminology, adding/subtracting, FOIL, and real-world applications).
Demonstrated ability to identify polynomial degree, leading coefficient, and standard form.
Practiced adding, subtracting, and multiplying polynomials with correct sign handling.
Applied FOIL and recognized special products (difference of squares, perfect square trinomials).
Submitted or finalized the worksheet for grading.

By the time you hand off back to the main instructor (3:30 PM), you should have:

✓ Graded or spot-checked worksheets.
✓ Identified students who scored below 25/35 (eligible for resubmission).
✓ Noted whole-class misconceptions or themes.
✓ Documented students needing follow-up support.
✓ Left brief notes on the "Handoff" (this document) or a separate log for the instructor.

Tone & Mindset

This is a support session, not a high-stakes assessment. Students may feel behind, anxious, or discouraged. Your role is to:

Affirm effort: "You're thinking about this deeply. That's good."
Normalize struggle: "Distributing negatives trips up a lot of people. Let's untangle it together."
Empower agency: "You just FOILed that correctly. That means you can multiply any two binomials."
Show confidence: "Polynomial operations are the building blocks for everything we do next. You are building a strong foundation."

Celebrate small wins. If a student solves a problem correctly or catches their own sign error, notice it. "You caught that negative sign on your own. That attention to detail is exactly what polynomial work requires."

Questions Before You Start?

Connect with the main instructor before 2:00 PM if you need clarity on:

How the Socratic session went. Did students seem comfortable with polynomial terminology?
Any specific students who may need extra patience or scaffolding.
Whether resubmissions for students below 26/35 are accepted or if that's handled later.
How to share notes back (document, email, etc.).

Thank you for being here. Your presence, questions, and affirmation make a real difference as students build fluency with polynomial operations.