Mission 9 · Unit 4

Long Division

6.NS.B.2 · Unit 4
Today's objective: Fluently divide multi-digit numbers using the standard algorithm.
Need a hint?
Re-read the problem and underline the numbers and the question. Pick one representation (model, table, or equation), show your steps, and check that your answer makes sense for the situation.

The 6th-grade class is organizing a school field day. There are 438 students who need to be split into teams of exactly 16 for relay races. Any students left over will become referees. The PE teacher also has 1,254 water bottles to distribute equally among 24 water stations. Your team must figure out how many relay teams can be formed, how many referees there will be, and how many water bottles go to each station with none wasted.

Long Division 16 438 27 -32 118 -112 R 6 27 teams of 16 + 6 referees = 438 students Team 1 Team 2 Team 3 6 Referees (remainder) 1,254 bottles

Investigation

The Problem: (A) Divide 438 students into teams of 16. How many full teams? How many referees? (B) Divide 1,254 water bottles among 24 stations equally. How many bottles per station? How many are left over? (C) Interpret every quotient and remainder in the context of field day.

Visual Model: Division Steps Diagram

Step 1: Divide How many 16s in 43? 43 / 16 = 2 Write 2 above the 3 16 x 2 = 32 43 - 32 = 11 → Step 2: Bring Down Bring down the 8 11 → 118 How many 16s in 118? 118 / 16 = 7 16 x 7 = 112 → Step 3: Subtract 118 - 112 = 6 R = 6 6 is less than 16, so we are done! → Answer 27 R 6 27 full teams 6 referees Check: 27x16+6=438 Problem B: 1,254 / 24 = 52 R 6 → 52 bottles per station, 6 left over Quotient = number of equal groups 27 teams (Problem A) 52 bottles per station (Problem B) Remainder = what is left over 6 extra students become referees (A) 6 extra bottles kept in storage (B)

Step-by-Step Investigation Guide

  1. Set up the division. Write 438 inside the division bracket and 16 outside. Identify which is the dividend (total being split) and which is the divisor (group size). Which number is being split into groups? Which number tells you the group size?
  2. Estimate first. Round 438 to 440 and 16 to 20. What is 440 / 20? This estimate (22) helps you know if your final answer is reasonable. Why is estimating before dividing a smart strategy?
  3. Divide, multiply, subtract, bring down. Look at the first two digits (43). How many times does 16 fit into 43? Write that digit above. Multiply, subtract, bring down the next digit. Repeat. At each step, how do you know which digit to write in the quotient?
  4. Interpret the remainder. When you get a remainder of 6, ask: what does "6" mean in this story? Can you split 6 students into another team of 16? No — so they become referees. Does the remainder always mean the same thing? What if the problem were about cutting rope?
  5. Solve Problem B. Set up 1,254 / 24. Use the same steps: divide, multiply, subtract, bring down. Interpret the quotient and remainder for water bottles. Is the remainder handled the same way in both problems?
  6. Check with multiplication. For each problem: quotient x divisor + remainder = dividend. If it does not equal the original number, find your error. Why does quotient x divisor + remainder always equal the dividend?

Language Support: Key Vocabulary

dividend — the number being divided; the total you are splitting up (example: 438)
divisor — the number you divide by; the size of each group (example: 16)
quotient — the answer to a division; how many full groups (example: 27)
remainder — the amount left over that does not make a full group (example: 6)
estimate — a close guess that helps you check if an answer is reasonable
interpret — to explain what a number means in the real situation
regroup — to move value from one place to another when subtracting
equally — the same amount in every group; shared fairly

Sentence Frames

"When I divide _____ by _____, the quotient is _____ and the remainder is _____."

"The remainder of _____ means _____ because _____."

"I checked my answer: _____ times _____ plus _____ equals _____, which matches the dividend."

Multiple Representations

Standard Algorithm

Write the long division bracket. Divide digit by digit from left to right: divide, multiply, subtract, bring down. This is the most common method for large dividends.

Best for: getting an exact quotient and remainder step by step

Partial Quotients (Area Model)

Subtract friendly multiples of the divisor from the dividend:
438 - 160 (10 groups) = 278
278 - 160 (10 groups) = 118
118 - 112 (7 groups) = 6
Total: 10 + 10 + 7 = 27 R 6

Best for: students who prefer subtraction over the traditional algorithm

Multiplication Table Check

Build a quick table of 16s: 16, 32, 48, ... up to 16 x 30 = 480. Find where 438 fits between two multiples. 16 x 27 = 432, so the answer is 27 with 438 - 432 = 6 left.

Best for: checking the answer and building number sense

Team Roles

Facilitator Keeps the group on track, watches the timer, makes sure everyone speaks. Mission 9 task: Make sure the team completes BOTH division problems and interprets BOTH remainders in context.
Model Builder Creates the long division work and any alternative models (partial quotients, tables). Mission 9 task: Write the long division for 438/16 step by step AND show at least one alternative method for 1,254/24.
Precision Checker Checks each subtraction, verifies with multiplication, and confirms the answer is reasonable. Mission 9 task: Use the check (quotient x divisor + remainder = dividend) for both problems. Compare to the estimates.
Reporter Prepares the defense: claim, evidence, and one mistake the team caught. Mission 9 task: Explain what BOTH remainders mean in the field day context. Why can you not just ignore them?

Timed Lab Phases

Ready
Click a phase, then press Start.
03:00

Read the scenario out loud. Assign roles. Circle the two division problems: 438/16 and 1,254/24.

  • Which number is the dividend in each problem? Which is the divisor?
  • Estimate each answer by rounding: 440/20 and 1,260/25.
  • What will the remainder mean in each situation?
Checkpoint: Every teammate can identify the dividend, divisor, and estimated quotient for both problems.

Set up and solve 438 / 16 using long division. Write every step: divide, multiply, subtract, bring down.

  • How many 16s fit in 43? Write the first partial quotient.
  • Multiply and subtract. Bring down the 8.
  • How many 16s fit in 118? Complete the division.
  • Record the quotient and remainder.
Checkpoint: The team has a quotient of 27 R 6 with every step shown.

Solve 1,254 / 24. Then check BOTH answers using multiplication.

  • Set up the long division for 1,254 / 24.
  • Work through each step carefully.
  • Check: 27 x 16 + 6 = ? Does it equal 438?
  • Check: quotient x 24 + remainder = ? Does it equal 1,254?
  • Write what each remainder means in the field day story.
Checkpoint: Both divisions are complete with multiplication checks that balance.

Prepare your presentation. Write a claim about each problem. Show evidence. Explain one correction.

  • State both answers with their real-world meanings.
  • Point to the specific step in long division as evidence.
  • Explain why interpreting the remainder matters (you cannot have half a team).
  • Share one error your team found and fixed.
Checkpoint: The Reporter can present both answers with context in under 60 seconds.

Challenge Zone

Extension: The PE teacher changes the relay team size to 18 students instead of 16. Now how many teams and how many referees? Does a larger team size always mean fewer leftover students? Prove it.
What If? What if 12 more students sign up for field day (making 450 total)? Recalculate 450/16. Compare the new remainder to the original remainder. Is it possible to get a remainder of 0?
Real-Life Connection: A bakery makes 875 cookies and packs them in boxes of 12. How many full boxes? How many loose cookies? Should the bakery give the extras away, eat them, or start another box? The remainder changes meaning based on the situation.

Defense Preparation

Questions Your Team Must Answer

  1. Walk us through your long division for 438/16. What happens at each step?
  2. What does the quotient of 27 mean in this story? What does the remainder of 6 mean?
  3. How did you check your answer using multiplication?
  4. For 1,254/24, is the remainder handled the same way? Why or why not?
  5. How close was your estimate to the actual answer? What does that tell you?

Sentence Starters for Your Defense

"438 divided by 16 equals 27 with a remainder of 6, which means _____."

"We checked our answer by multiplying: 27 times 16 equals 432, plus 6 equals 438."

"The remainder of _____ cannot form another full group because _____."

"Our estimate of _____ was close to the actual answer of _____, so we know our answer is reasonable."

Accuracy (4 pts) Both divisions are correct with correct remainders. Multiplication checks balance.
Process (4 pts) Every step of long division is shown: divide, multiply, subtract, bring down.
Interpretation (4 pts) Both remainders are explained in the real-world context. Team explains why remainders matter.
Communication (4 pts) Reporter uses vocabulary (dividend, divisor, quotient, remainder) and all teammates can explain.

Exit Product

Deliver: Field Day Planning Report

Your team submits a one-page report that includes:

  • Long division work for 438 / 16 with every step shown
  • Long division work for 1,254 / 24 with every step shown
  • Multiplication checks for both problems
  • A sentence explaining what each remainder means in context
  • An estimate for each problem and how close it was
  • A 3-sentence defense: claim, evidence, and reasonableness check

Self-Assessment

  • I can set up and solve a long division problem with a 2-digit divisor.
  • I checked my answer using multiplication: quotient x divisor + remainder = dividend.
  • I can explain what the remainder means in a real situation.
  • I used math vocabulary (dividend, divisor, quotient, remainder) correctly.

Student Work Space

Problem A: 438 / 16 (Long Division)

Multiplication Check for Problem A:

Problem B: 1,254 / 24 (Long Division)

Multiplication Check for Problem B:

Remainder Interpretations:

Defense (Claim, Evidence, Reasonableness):