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Facilitation Cheatsheets

Print this packet and keep it on a clipboard. The front side covers the standard Challenge Block flow; the back side covers in-the-moment differentiation moves you can use while circulating. Moves marked ELL+ have added evidence for English language learners and students with limited math language exposure.

Standard Challenge Block Flow

Use this flow for most math-heavy sessions: formulas, worksheets, and dashboard work. Adjust minutes to match the daily schedule.

  1. 0–5 min
    Launch & connect
    Name the day's question in bot terms (for example, "How much does Speed really change goals?") and connect to yesterday's match or worksheet. One sentence, then into the task. ELL+: Post the key vocabulary term(s) for today on the board before students arrive — pre-teaching a word before it appears in context reduces language load during the math task itself.
  2. 5–10 min
    Introduce the formula or tool
    Write the formula on the board and work one full example with students, labeling each step in words. Think aloud — say every operation as you write it. Then ask students to translate the formula into a sentence aloud: for example, "y equals m times x plus b" said as "the output equals the rate times the input, plus a starting amount." Take one round of clarifying questions, then move on. ELL+: Leave the worked example visible on the board for the full work period.
  3. 10–45 min
    Team work: Challenge Block
    Teams work through three loadouts, three coordinate pairs, or the full worksheet using the formula. Write visible checkpoints on the board (for example, "Loadout 1 by 15, Loadout 2 by 30, Loadout 3 + trade-off by 40") and circulate with targeted prompts. ELL+: Allow students to work through calculations or discuss strategy in their home language first, then write their final answer in English — bilingual reasoning is a feature, not a shortcut.
  4. During work
    In-the-moment moves
    Use the differentiation tree on the back: Operations Quick Reference instead of reteaching, sentence frames for writing prompts, Checker/Verifier roles for students who are behind or finish early, and extra processing time where needed. For vocabulary gaps, point to the Math Vocabulary Wall — entries should include a visual, the precise definition, and an everyday synonym.
  5. 45–55 min
    Compare & interpret
    Do a whole-room share-out using a comparison surface (class table, scatter plot, or Team Comparison Table). Ask, "Which team changed the most? In which stat? In which direction? What does that mean in bot behavior?" ELL+: Post a sentence frame on the board for the share-out, for example: "Team __ changed the most because __ went from __ to __. That means the bot will __. "
  6. Last 5 min
    ENDS prompt & closing
    Have students write or speak a short ENDS response (evidence, nuance, decision, strategy) and preview how today's numbers feed into tomorrow's matches or rule decisions. ELL+: Accept a first-language response with a one-sentence English summary, or a labeled diagram in place of a full written explanation.
Protect if short on time: One worked example (with think-aloud), 20+ minutes of team calculation work, and a brief compare / interpret step with a sentence frame. Trim warm-up and number of share-out voices first.

In-the-Moment Differentiation Tree

Start with what you see at a table, then follow the move. Each move keeps the math at full rigor while removing barriers for that student. Profiles overlap — use multiple branches in the same session as needed.

ELL+ Language & math barriers together

Student is new or recent to English, hesitates on word problems even when arithmetic is solid, seems to understand more than they can express, or uses home language to explain their thinking to a peer.

  1. Reduce language load, not math rigor: Shorten the sentence structure of the prompt or cross out culturally loaded vocabulary in word problems that isn't mathematically necessary (for example, "school assembly," "dog groomer"). The math stays the same.
  2. Pre-teach and anchor vocabulary: Before the task, identify the two or three words that block entry. Teach them with a visual, the precise definition, and a cognate if one exists (Spanish examples: fracción/fraction, ecuación/equation, proporción/proportion). Post these on the board.
  3. Home language is a tool: Actively allow students to brainstorm, calculate, and discuss in their home language within the team. Ask for one sentence of explanation in English at the end. This is evidence-based, not a workaround.
  4. Multiple representation formats: Offer the same task in at least two formats — a diagram or matching activity alongside the word problem. Students can demonstrate math understanding before they can produce academic English.
  5. Avoid: Assuming math difficulty when the barrier is language. A student who explains the right answer to a peer in Spanish has the math. Scaffold the English output, not the math.

Stuck on arithmetic or operations

Pauses at 6 ÷ 20, adds instead of subtracting in parentheses, or avoids writing steps and only writes final answers.

  1. First move: Quietly point to the Operations Quick Reference at their station. Name the operation in one sentence (for example, "Six divided by twenty — put 6 on top, 20 on the bottom.") and move on.
  2. Concrete before abstract: If the reference card isn't enough, reach for a visual — a number line on the desk, a bar model sketched in 10 seconds, or algebra tiles if available. Research consistently shows moving from concrete → representational → abstract before jumping to procedures.
  3. If still stuck: Have a teammate explain one calculation aloud while the student writes every step. Keep them doing all three loadouts; do not reduce quantity.
  4. Avoid: Re-teaching all of division on the spot or letting a strong teammate do every calculation for them.

Math is fine, writing or vocabulary is blocked

Correct calculations but blank "write one sentence" prompts, copies a teammate's sentence, or points at the prompt asking, "What does this mean?"

  1. First move — sentence frame: Offer a frame that matches the prompt structure (for example, "When I doubled Speed from __ to __, the distance went from __ to __. That is / is not double because __."). Post it on the board so every student can use it, not just the one who needed it.
  2. Symbol-to-words technique: Ask the student to read the formula or equation aloud as a sentence before writing. For example, write y = 2x + 3 and say "y equals two times x plus three." This builds mathematical language and comprehension simultaneously.
  3. For vocabulary: Point to the term on the Math Vocabulary Wall (proportional, slope, budget). The wall entry should have three parts: the precise term, the "in your own words" definition, and a visual or symbol. Give one everyday synonym if needed ("steepness"), then step back.
  4. For journals / exhibition: Allow responses in a first language with a one-sentence English summary; accept labeled diagrams or sketches as valid mathematical writing.

Finishes well before the team

Completes calculations 10–15 minutes early, begins directing others, or shifts only to bot building or social roles.

  1. First move: Hand an extension prompt card tied to the same content (for example, "Find the Speed / Power combination that maximizes output subject to S + P = 14."). Present it as the next question, not extra credit.
  2. On match days: Assign Model Tracker or Math Verifier roles: they write the full prediction chain and check other teams' proposal math in real time.
  3. Avoid: Using them as a permanent tutor who does math for others; the goal is deeper math for them, not faster completion.

Understands ideas but cannot keep pace

Consistently last to finish even when correct, shuts down during timed checks, or drifts off mid-Challenge Block.

  1. First move: Make checkpoints visible on the board (for example, "Loadout 1 by minute 15, Loadout 2 by 30, Loadout 3 by 40"), and assign a Checker / Verifier role during team work.
  2. Timed events: During Cold Recall Checks, quietly allow an extra three minutes and collect their paper last. During Formula Relay, have them verify one card per round instead of racing to solve every card. Research supports timed fluency practice as a tool, not a test — shutdown means you're measuring anxiety, not knowledge.
  3. Digit reversal / transcription: Ask them to say the number aloud before writing. If they say "thirty-five" and write 53, point at the mismatch and have them correct it.
Reminder: Profiles overlap. A student may need a sentence frame, a vocabulary cognate, and an extension prompt in the same session. The ELL+ branch pairs with every other branch — language barriers and math barriers often co-occur and require simultaneous moves.