Signal Words Teacher Guide Tier 2 Intervention • 1-on-1 Protocol Session Pacing: 15–20 Mins
Signal Words & Quantities
Lesson 1 • Teacher Facilitation Script
Target Skill
Translating operational key terms and verbal phrases into algebraic expressions.
9th Grade Focus
CCSS.MATH.CONTENT.HSA.CED.A.1, MP.1 (Making sense of problems), MP.4 (Modeling).
Materials Needed
Signal Words Practice Sheet, 2 colored highlighters (Yellow = number, Pink = operation).
15–20 Minute Tier 2 Instructional Framework
Step 1: Warm-Up
3 Minutes
Fluency & Symbol Match
Step 2: "I Do"
5 Minutes
Explicit Scripted Modeling
Step 3: "We Do"
6 Minutes
Coached Deconstruction
Step 4: "You Do"
4 Minutes
Check for Understanding
STEP 1: RAPID ACTIVATION (3 MINS) Say & Model
Teacher Script: "Today, we are going to crack the code of math word problems. Words are just clues that tell us what symbols to write. When you see 'increased by' , what symbol pops into your head? [Prompt student: (+)] . Exactly! We have four major operations: \(+\), \(-\), \(\times\), and \(\div\). Let's unlock the trickiest ones."
STEP 2: EXPLICIT TEACHER MODELING — "I DO" (5 MINS) Think-Aloud Script
Scenario Model: "Eight less than triple a mystery number is twenty-two."
Teacher Think-Aloud Script: 1. Identify the Unknown: "First, I ask: What do I not know? 'A mystery number.' I'll label it as variable \(n\)."2. Hunt for Operation Signals: "I see 'triple'. Triple means multiply by 3, so \(3n\). Next, I spot 'less than' . That's a Turn-Around Alert! When I say '8 less than something', I start with that quantity and subtract 8 at the end: \(3n - 8\)."3. Locate the Balance Point: "The word 'is' signals our equal sign (\(=\)). So my translated equation is \(3n - 8 = 22\)."
High-Yield 9th Grade Rule: "Turn-Around" Words
Phrases like "less than" , "subtracted from" , and "fewer than" reverse the written order.
Tier 2 Math Intervention • Equation Decoders Sequence Lesson 1: Signal Words • Page 1 of 2
Step-by-Step Guided Coaching & Error Protocols
Lesson 1 Guide
STEP 3: GUIDED COACHING — "WE DO" (6 MINS) Prompt & Check
Guided Task 1: "The quotient of a number and 4, increased by 7, is equal to 15."
Prompt 1: Variable
"What is our unknown quantity? Let's underline 'a number' and write \(x\)."
Prompt 2: Operations
"What does 'quotient' mean? (\(\div\) or fraction bar). 'Increased by'? (\(+ 7\))."
Prompt 3: Assembly
"Let's put it together: \(\frac{x}{4} + 7 = 15\). Let's read it back."
Guided Task 2: "Twelve subtracted from twice a number yields thirty."
Coaching Question: "Watch out! What phrase do you see? ('subtracted from'). Does 12 go first or last? (Last!). Write it down: \(2n - 12 = 30\)."
Diagnostic Error Correction Decision Tree
Student Error / Misconception Diagnostic Root Cause Targeted Teacher Script Translates "4 less than \(x\)" as \(4 - x\) Linear reading bias (translating word-for-word from left to right). "If you have $10 and I take $4 less than you, do you do 4 - 10 or 10 - 4? Start with what you have: \(x - 4\)." Misses the coefficient in "triple a number" Confusing addition with multiplication terms. "'Triple' means 3 groups of that number. Groups mean multiplication: \(3 \times x = 3x\)." Cannot identify what \(x\) represents Rushing directly to calculation without isolating the question. "Look at the question at the end. What are they asking us to find? Let's circle that and write '\(x =\)'."
STEP 4: INDEPENDENT EXIT DRILL (4 MINS) & FIDELITY Criteria for Mastery
Mastery Benchmark:
Student accurately translates 3 out of 3 exit items on the practice sheet.
Student correctly identifies turn-around phrases without prompt.
If <2 correct: Re-teach Step 2 using colored highlighter cues.
Tier 2 Intervention Fidelity Check:
Scripted think-aloud delivered verbatim. Highlighters used for visual segregation. Corrective feedback provided within 3 seconds.
Tier 2 Math Intervention • Equation Decoders Sequence Lesson 1: Signal Words • Page 2 of 2
Signal Words Practice Sheet Tier 2 Math Practice
Signal Words & Quantities
Lesson 1: Practice Sheet
Deconstructing Verbal Expressions
Student:
Date:
Interventionist:
Equation Decoder: The 4 Operational Clue Banks
Addition (+) +
Sum, plus, increased by, more than, combined, total, added to
Subtraction (−) −
Difference, decreased by, minus, less than* , subtracted from*
Multiplication (×) ×
Product, times, double (2x), triple (3x), each, per, of
Division (÷) ÷
Quotient, divided by, split into, ratio, half (\(\frac{1}{2}\)), per
*Turn-Around Alert: "Less than" & "subtracted from" switch the order! "7 less than \(y\)" \(\rightarrow\) \(y - 7\).
PART 1: SIGNAL WORD DRILL Circle the signal word & write the math operation symbol (+, −, ×, ÷)
1. The quotient of 18 and 3
2. 14 decreased by 6
3. The product of 7 and \(m\)
4. 9 less than a number \(k\)
5. The sum of 25 and \(x\)
6. Triple the amount of \(p\)
PART 2: GUIDED TRANSLATION FRAMES Break down the phrase and write the algebraic expression
A. "Five more than double a number \(x\) is equal to twenty-one." Guided Model
1. Identify Variable: \(x\)
2. Signal Words: double (\(2x\)), more than (\(+5\))
3. Final Equation: \(2x + 5 = 21\)
B. "The difference of triple a number \(y\) and twelve is forty-eight."
1. Unknown Variable:
2. Operation Clues:
3. Translated Equation:
C. "Nine less than the quotient of a number \(w\) and six yields ten."
1. Unknown Variable:
2. Turn-Around Clue? (Y/N):
3. Translated Equation:
Tier 2 Math Intervention • Equation Decoders Page 1 of 2
Real-World Deconstruction & Error Analysis
Lesson 1: Practice
PART 3: REAL-WORLD SCENARIO DECONSTRUCTION Underline quantities, circle keywords, write the equation
Scenario 1: Music Streaming Subscription
Flat Fee + Rate
Marcus pays a flat subscription fee of $10 per month plus $2 for every premium album download. Last month, his total bill was
Equation Builders Teacher Guide Tier 2 Intervention • Two-Step Equations Session Pacing: 15–20 Mins
Equation Builders Routine
Lesson 2 • Teacher Facilitation Script
Target Skill
Deconstructing 2-step real-world scenarios into \(mx + b = y\) and executing inverse calculations.
High School Standards
CCSS.MATH.CONTENT.HSA.REI.B.3, HSA.CED.A.1, MP.1, MP.2 (Reasoning quantitatively).
Materials & Tools
Equation Builders Practice Sheet, Calculator (for calculation verification check).
The 4-Step Problem-Solving Decoder Frame
1. READ & HUNT
Underline the question. Define the variable \(x\).
2. MAP STRUCTURE
Find the Flat Fee (b), Rate (m), and Total (y).
3. SOLVE STEP-BY-STEP
Inverse operations: Undo \(+\)/\(-\), then \(\times\)/\(\div\).
4. CHECK & UNIT
Substitute back into context & label units.
EXPLICIT TEACHER MODELING — "I DO" (6 MINS) Scripted Think-Aloud
Exemplar Problem: "An arcade charges a $15 admission fee plus $1.50 per game token. Maya spent a total of $33. How many tokens did Maya buy?"
1. Define the Unknown: "I read the final sentence. 'How many tokens did Maya buy?' I define my variable: Let \(t =\) number of tokens."
2. Map the Components into Equation Structure: Total Amount: $33 \(\rightarrow\) This goes on one side of the equal sign: \(= 33\).Starting Value (Flat / Fixed Cost): $15 admission fee \(\rightarrow\) Happens once, no variable attached.Rate of Change (Recurring Cost): $1.50 per token \(\rightarrow\) Key word 'per' attaches to \(t\): \(1.50t\).Construct the Equation: \(\mathbf{1.50t + 15 = 33}\).
3. Solve Using Inverse Operations: Step 1 (Undo the constant): Subtract 15 from both sides \(\rightarrow 1.50t = 18\).Step 2 (Undo the coefficient): Divide both sides by 1.50 \(\rightarrow t = 12\).
4. Verify & Label: "\(1.50(12) + 15 = 18 + 15 = 33\). Correct! Maya bought 12 game tokens ."
Instructional Anchor: The "Starting Value vs. Rate" Rule
Teach students to ask: "Does this number happen over and over (Rate \(\rightarrow\) variable), or does it happen just once (Constant \(\rightarrow\) standalone number)?"
Tier 2 Math Intervention • Equation Decoders Sequence Lesson 2: Equation Builders • Page 1 of 2
Equation Builders Practice Sheet Tier 2 Math Practice
Equation Builders Practice
Lesson 2: Student Sheet
Deconstructing Two-Step Scenarios
Student:
Date:
Interventionist:
THE 4-STEP STRATEGY:
1. READ: Identify Unknown (\(x\)) 2. MAP: Rate (\(m\)) & Flat Fee (\(b\)) 3. SOLVE: Undo \(+\)/\(-\), then \(\times\)/\(\div\) 4. CHECK: Plug in & Label
PROBLEM 1 (GUIDED): The Gym Membership Guided Frame
A fitness gym charges a $35 one-time registration fee plus a monthly fee of $20 per month . Jordan has spent a total of $155 at the gym. How many months has Jordan been a member?
Step 1: Define \(m\) What are we finding?
Step 2: Map Values Rate, Start, Total
Step 3: Equation Set up \(20m + 35 = 155\)
Step 4: Solve & Unit Show 2-step solution
PROBLEM 2: Smartphone Screen Repair Structured Frame
A phone repair shop charges $45 for replacement parts and $25 per hour of technician labor. The final repair invoice came out to $120 . How many hours did the technician work on the phone?
A. Map & Write Equation:
• Variable: Let \(h =\) hours worked
• Flat Parts Fee = $____ | Rate per Hour = $____
B. Show Inverse Steps & Answer:
Tier 2 Math Intervention • Equation Decoders Lesson 2: Equation Builders • Page 1 of 2
Independent Problem Solving & Verification
Lesson 2: Independent Practice
PROBLEM 3: Moving Van Rental Real-World Application
A rental company charges $30 base fee to rent a truck plus $0.50 per mile driven . Sam paid a total of $62 when he returned the truck. How many miles did Sam drive?
1. Define Variable & Write Equation:
2. Show 2-Step Calculations & Final Answer:
PROBLEM 4: Saving for a Game Console Savings Accumulation
Devon already has $80 in savings . He earns $15 per week doing weekend chores. If the video game console costs $275 , how many weeks must Devon work to save enough money?
1. Define Variable & Write Equation:
2. Show 2-Step Calculations & Final Answer:
STEP 4 VERIFICATION MAT: DID YOU CHECK YOUR WORK? Substitute your answer back into Problem 4
Weekly Word Probes Tracker Tier 2 RTI Assessment
Weekly Progress Monitoring Probes
Probes 1 & 2
Standardized 5-Minute Probes
Student:
Grade: 9th Grade
Pacing: 5 Mins / Probe
Score Scale: /6 Points
STANDARD PROBE SCORING (2 Pts Per Item = 6 Pts Total): • 1 pt: Correct equation setup with variable defined. • 1 pt: Accurate calculation & units labeled.
PROBE 1 Week 1 (Baseline Assessment)
Date: _______ | Score: ____ / 6
1. Six more than double a number \(n\) is 28. What is \(n\)?
2. A rideshare charges $4 base fee plus $3 per mile. Total cost was $22. How many miles?
3. Maya had $50. She bought 3 identical shirts and has $14 left. How much was 1 shirt?
PROBE 2 Week 2 (Formative Progress Check)
Date: _______ | Score: ____ / 6
1. Five less than triple a mystery number \(x\) equals 31. What is \(x\)?
2. An internet plan costs $40/month plus $5 per extra gigabyte. The bill was $65. How many extra GB?
3. Lucas saved $95. He bought a skateboard for $35 and 4 packs of bearings. Each pack cost?
Tier 2 Math Intervention • RTI Progress Monitoring Probes Page 1 of 2
Weekly Progress Probes 3 & 4 (Mastery Checks)
Probes 3 & 4
PROBE 3 Week 3 (Mid-Intervention Check)
Date: _______ | Score: ____ / 6
1. Eight subtracted from the product of 5 and \(y\) is 32. Find \(y\).
2. A bowling alley charges $6 for shoe rental and $4.50 per game. Jada paid $24. Games bowled?
3. A teacher has 80 pencils. She keeps 20 and divides the rest among 5 caddies. Pencils per caddy?
PROBE 4 Week 4 (Post-Intervention Mastery Probe)
Date: _______ | Score: ____ / 6
1. Fourteen more than the quotient of \(k\) and 3 equals 22. Find \(k\).
2. An electrician charges $60 service visit plus $40 per hour. Total invoice: $180. Hours worked?
3. Tyler needs $200 for camp. He saved $50 and will earn $25/lawn. How many lawns must he mow?
Mastery Answer Key & Equation Reference
Probe # Problem 1 (Setup & Sol) Problem 2 (Setup & Sol) Problem 3 (Setup & Sol) Mastery Target Probe 1 2n + 6 = 28 \(\rightarrow\) n = 11 3m + 4 = 22 \(\rightarrow\) m = 6 mi 3s + 14 = 50 \(\rightarrow\) s = $12 5 / 6 (83%)
Tier Two Tracking Log Tier 2 RTI Documentation
Tier 2 Intervention Tracking Log
Student Profile & Data
1-on-1 Intervention Record
Student Name:
Student ID / Grade:
9th Grade
Interventionist:
Intervention Period:
4 Weeks (2x / wk)
SMART INTERVENTION GOAL & AIMLINE TARGET Target: 83%+ (5/6 pts) on 3 consecutive probes
Target Goal Statement: In 4 weeks, when presented with a 2-step algebraic word scenario, student will accurately translate the verbal text into an equation (\(mx + b = y\)) and calculate the correct solution with appropriate units with at least 83% accuracy (5/6 points) across 3 consecutive weekly probes.
Baseline
___ / 6
Week 0
Week 1 Probe
___ / 6
Signal Words
Week 2 Probe
___ / 6
Formative 1
Week 3 Probe
___ / 6
Mid-Check
Week 4 Mastery
___ / 6
Goal: \(\ge 5\)
INTERVENTION IMPLEMENTATION & FIDELITY LOG Document each 15–20 min 1-on-1 session
Session / Date Minutes Focus Topic / Material Used Accommodations & Highlighters Fidelity (Y/N) Initials Session 1: __/__ ___ min Lesson 1: Signal Words & Quantities Color highlighters (Pink/Yellow) [ ] Y [ ] N _____ Session 2: __/__ ___ min Lesson 1: Turn-Around Words & Expressions Cue card + Turn-Around Alert [ ] Y [ ] N _____ Session 3: __/__ ___ min Lesson 2: Equation Builders (Read-Map) 4-Step Decoder Organizer [ ] Y [ ] N _____ Session 4: __/__ ___ min Lesson 2: Two-Step Solving & Inverse Ops SADMEP Ladder & Calculator check [ ] Y [ ] N _____ Session 5: __/__ ___ min Review: Multi-Step Scenarios & Check Mat Self-Check Mat + Verification [ ] Y [ ] N _____ Session 6: __/__ ___ min Post-Assessment: Probe 4 Mastery Check
