Lesson Brief

Operations — Problem 2, Part 2

Generated March 24, 2026

Standard: 3.OA.D.8 — Solve two-step word problems using the four operations

Submissions: 9 | Class Average: 56%

Gap Summary: 5 of 9 students skipped the doubling step on question c, writing 55 + 8 = 63 instead of 55 + 55 = 110, then 110 + 8 = 118

Misconception: Students treat "Double 55 then add 8" as a single addition (55 + 8 = 63). They do not recognize that "double 55" is a complete first operation producing 110, and that "then add 8" applies to that intermediate result — not to the original 55.

Comparison Type: Contrast Type B (correct vs. common error) — 56% error rate on Qc, above the 30% threshold

Teaching Point: Each step in a multi-step problem uses the answer from the step before it. "Double 55" means 55 + 55 = 110 first — then you add 8 to that 110, not to 55.

Rationale: Students already demonstrate multi-step computation skills on question f (eight of nine correct), so the doubling error is not an arithmetic issue — it is a comprehension issue about how operation sequences work.

Student Monitoring Table

Student%StatusLookfor During IP
Amelia20%🔴Check: does she execute the doubling as a separate first step? She added instead of subtracting on multiple questions too — watch operation signs.
Emma100%🟢Extend: can she explain WHY the order of steps matters using her own words?
Liam ⭐100%🟢Extend: can he write his own multi-step instruction that equals a target number?
Lucas20%🔴Check: can he write out step one and step two separately? He has major arithmetic errors — may need scaffolded number line.
Mateo20%🔴Check: does he double before moving to the next operation? He confused add/subtract directions too — watch operation signs closely.
Mia40%🔴Check: does she complete ALL steps? She understood doubling on Qc but made arithmetic errors on Qd and Qf — watch computation accuracy.
Noah ⭐60%🔴Check: does he execute the doubling step? He has strong skills (got Qd, Qe, Qf right) — this specific fix should click quickly.
Olivia100%🟢Extend: can she write a multi-step instruction using "triple" instead of "double"?
Sophia40%🔴Check: does she identify the correct starting number and operation? She used wrong numbers on Qd (started with 55 instead of 58).

⭐ = Work displayed in Guided Slides (anonymized as Student 1 / Student 2)

Presenter Notes (Slide-by-Slide)

Slide 1: Shout-Out

  • Praise Qf strategy variety: 8 of 9 solved it correctly.
  • Highlight Emma's clean stacked column (100+5+8=113) and Noah's top-down approach (started with 100).
  • Max 2 student names mentioned. Keep to strategy observations, not individual answers.
  • Key message: the class CAN do multi-step computation — that's the foundation for the lesson.

Slide 2: Frame the Task

  • Display Qc verbatim: "Double 55 then add 8."
  • Performance split: 4 of 9 got this one.
  • Cold call: Olivia reads Qc aloud. Why Olivia: She mastered all five questions and writes fluent explanations — confident, fluent reader. She reads from the beginning: "Double fifty-five then add eight."

Slide 3: Side-by-Side Display + Think Time

  • Student 1 (left) = Liam's Qc work (page-02.jpg): Two-step vertical computation — 55+55=110, then 110+8=118.
  • Student 2 (right) = Noah's Qc work (page-04.jpg): Single-step — 55+8=63, marked X.
  • Display original photographs (math notation and spatial layout matter).
  • Observational prompt: "As you read their work, pay attention to how many steps each student took. Count the calculations you see."
  • 30-second silent think time.

Slide 4: Finger Check

  • "Which student followed the directions correctly — Student 1 or Student 2?"
  • Expected: Most will say Student 1. Students who made the same error on their own work may hesitate or pick Student 2.
  • Watch for students who hesitate — they may be rethinking their own Qc work.

Slide 5: Compare — Turn & Talk + Debrief

  • Discussion questions:
    1. "What number did both students start with?" (display) / "Both students started with the number 55 from the problem. Look at their very first step — what number did both students write down first?" (full)
    2. "What did Student 1 do with the word 'double' that Student 2 skipped?" (display) / "Student 1 wrote 55 + 55 as the first step. Student 2 wrote 55 + 8. The problem says 'Double 55 then add 8.' What did Student 1 do with the word 'double' that Student 2 missed?" (full)
  • 90-second partner talk.
  • Cold call for Q1 (same): Noah. Why: He got Qc wrong but has strong skills (Qd, Qe, Qf correct). Identifying that both students started with 55 is within his ZPD — low-risk entry point. Exemplar: "Both students started with 55." Scaffold if stuck: "Look at the top of each student's work. What number do you see first?"
  • Teacher call for Q2 (different): Mr. Bravo selects. Why: This is the key conceptual moment — the teacher can pick a student who's making the connection. Exemplar: "Student 1 doubled 55 — they wrote 55 + 55 = 110. Then they added 8 to 110. Student 2 just added 55 + 8 because they skipped the doubling." Scaffold if stuck: "What does 'double' mean? If I double 55, what math do I do?"

Slide 6: Takeaway Stamp

  • Teacher call: Mr. Bravo calls on 1-2 students for the big idea.
  • Teaching point appears: "Each step in a multi-step problem uses the answer from the step before it. 'Double 55' means 55 + 55 = 110 first — then you add 8 to that 110, not to 55."
  • Visual: Step-by-step flow diagram showing Step 1 (55+55=110) flowing into Step 2 (110+8=118), with the wrong path (55+8=63) crossed out below.
  • Talk track stamps the concept clearly: each step feeds the next.

Slide 7: Release to IP

  • Worksheet A (needs teaching point): Amelia, Lucas, Mateo, Mia, Noah, Sophia
  • Worksheet B (mastery): Emma, Liam, Olivia
  • Primary lookfor: Is the student executing the doubling (or first operation) as a separate step BEFORE moving to the next operation? Look for two distinct calculations, not one.
  • Walk the room using the Student Monitoring Table above for per-student lookfors.

Answer Keys

Worksheet A (Needs Teaching Point) — Multi-Step Operations Practice

Q1: Double 30 then add 7.

  • Step 1: 30 + 30 = 60
  • Step 2: 60 + 7 = 67
  • Answer: 67

Q2: Double 45 then subtract 10.

  • Step 1: 45 + 45 = 90
  • Step 2: 90 - 10 = 80
  • Answer: 80

Q3: Emma says "Double 25 then add 3" equals 28 because 25 + 3 = 28. What step did Emma skip? Fix her work.

  • Emma skipped the doubling step. "Double 25" means 25 + 25 = 50. Then add 3: 50 + 3 = 53. The correct answer is 53, not 28.

Finished Early: Triple 20 then subtract 5. ("Triple" means three groups of 20: 20+20+20=60. Then 60-5=55.)

Worksheet B (Demonstrated Mastery) — Multi-Step Operations Challenge

Q1: Write your own instruction that makes exactly 200. Your instruction must use "double" and at least one more step.

  • Sample answer: Double 95 then add 10. (95+95=190, 190+10=200.) Many correct answers possible.

Q2: Does "Double 55 then add 8" give the same answer as "Add 8 to 55 then double the result"? Prove it.

  • Way 1 — "Double 55 then add 8": 55+55=110, 110+8=118.
  • Way 2 — "Add 8 to 55 then double the result": 55+8=63, 63+63=126.
  • They are NOT the same (118 vs. 126). The order matters because doubling a bigger number (110) and then adding 8 gives a different result than adding 8 first (to get 63) and then doubling.

Q3: [Classmate] wrote a three-step instruction: "Start with 40, double it, then subtract 12." What is the final answer? Write your OWN three-step instruction that gives the same final answer.

  • Step 1: Start with 40.
  • Step 2: Double it: 40+40=80.
  • Step 3: Subtract 12: 80-12=68.
  • Answer: 68. Many valid instructions possible (e.g., "Start with 50, add 25, subtract 7" = 68).

Finished Early: Can you write an instruction using "double" where the answer is exactly 100? How many different ways can you find?

  • Double 50 = 100. Double 45 then add 10 = 100. Double 30 then add 40 = 100. Many solutions.