Math Detective Mission: Solving Grade 6 Word Problems
Materials Needed
- Pencil and paper or a whiteboard
- Colored pencils or highlighters
- Calculator for checking answers, if desired
- Timer or stopwatch
- Small objects for modeling, such as coins, blocks, or buttons
- Word Problem Detective Sheet, created from the questions below
Lesson Overview
Suggested age: 11 years old
Suggested time: 50–70 minutes
Focus: Understanding, planning, solving, and explaining grade 6 mathematical word problems
Learning Objectives
By the end of the lesson, the learner will be able to:
- Identify what a word problem is asking.
- Find important information and ignore information that is not needed.
- Choose an appropriate operation or combination of operations.
- Show work using numbers, drawings, tables, equations, or words.
- Check whether an answer is reasonable and includes the correct unit.
- Explain how they solved a problem using clear mathematical language.
Success Criteria
A successful solution will:
- Clearly state what the problem is asking.
- Underline or list the useful information.
- Show a sensible plan or equation.
- Include accurate calculations.
- Give an answer with a label, such as dollars, kilometers, or books.
- Include a quick check explaining why the answer makes sense.
Introduction: The Math Detective Challenge
Hook: Tell the learner: “You are a math detective. A word problem is a mystery. Your job is to find the clues, decide which clues matter, solve the mystery, and prove that your answer makes sense.”
Ask:
- “What makes a word problem different from a regular calculation?”
- “Why might a word problem include information that is not needed?”
- “How can you tell if an answer makes sense?”
Explain that today’s goal is not just to get an answer. The learner must show how they understood the problem and why their answer is reasonable.
Word Problem Detective Strategy
Teach this five-step strategy. The learner may remember it as CLUES:
- C — Clarify the question: What must you find?
- L — Locate the useful facts: Which numbers and details matter?
- U — Use a plan: Which operation or operations will help?
- E — Execute the plan: Solve carefully and show your work.
- S — Scan and check: Does the answer make sense? Does it have the right unit?
Body: I Do, We Do, You Do
Part 1: I Do — Teacher or Parent Models a Problem
Read this problem aloud:
Maya is planning a 3-day hiking trip. She wants to walk 8.5 kilometers on the first day, 6.75 kilometers on the second day, and 9.25 kilometers on the third day. How many kilometers will she walk altogether?
Model the thinking aloud:
- Clarify: The problem asks for the total distance.
- Locate: The useful numbers are 8.5, 6.75, and 9.25.
- Use a plan: “Altogether” means add.
- Execute: Align the decimal points and add:
8.50 + 6.75 + 9.25 = 24.50 - Scan and check: The answer should be a little more than 8 + 6 + 9, or 23. The answer of 24.5 kilometers is reasonable.
Answer: Maya will walk 24.5 kilometers altogether.
Point out that the phrase “3-day hiking trip” is helpful background information, but it is not used in the calculation because the three daily distances are already given.
Quick Check
Ask the learner:
- What was the question asking us to find?
- Why did we add instead of subtract?
- Why is it important to write “kilometers” in the answer?
Part 2: We Do — Solve Together
Work through the following problem with the learner. Ask the learner to explain each CLUES step before moving on.
A book has 240 pages. Jordan reads 35 pages on Monday, 42 pages on Tuesday, and 38 pages on Wednesday. How many pages are left to read?
Guide the learner with these questions:
- What are we trying to find?
- Which pages have already been read?
- What operation should we use first?
- What operation should we use next?
- Can you write an equation?
Possible equation:
240 − (35 + 42 + 38) = 125
Expected answer: Jordan has 125 pages left to read.
Think-Pair-Share or Explain-It-Aloud
If working with a parent or group, have the learner:
- Think silently about how to solve the problem.
- Explain the plan to a partner, parent, or stuffed animal.
- Compare the explanation with another method, such as drawing a bar model or using a number line.
Part 3: You Do — Independent Math Detective Mission
Ask the learner to solve each problem independently. For every problem, the learner should:
- Write what the problem is asking.
- Circle or list the useful facts.
- Write an equation or describe a plan.
- Solve and show work.
- Write a complete answer with a unit.
- Check whether the answer is reasonable.
Mission 1: School Carnival
A school carnival sells 6 packs of stickers. Each pack contains 24 stickers. The organizers give away 35 stickers as prizes. How many stickers are left?
Mission 2: Saving Money
Leo has saved $48. He earns $12.50 each week for helping with chores. He wants to buy a game that costs $86. How many more weeks must he work to have enough money?
Mission 3: Sharing Pizza
Three pizzas are each cut into 8 equal slices. During a party, 17 slices are eaten. What fraction of the total slices is left? Give your answer in simplest form.
Mission 4: Bicycle Trip
A cyclist travels 7.5 miles in the morning and 8.25 miles in the afternoon. She takes a 1.5-mile shortcut on the way home. How many miles does she travel altogether?
Mission 5: Garden Planning
A rectangular garden is 12 meters long and 7 meters wide. A fence will go around the entire garden. How many meters of fencing are needed?
Mission 6: Recipe Challenge
A recipe uses 2.5 cups of flour to make 10 muffins. If the recipe is increased to make 30 muffins, how many cups of flour are needed?
Creative Application: Design Your Own Word Problem
Invite the learner to choose one setting:
- A space mission
- A sports tournament
- A pet-care business
- A video game adventure
- A camping trip
- A shopping trip
The learner should create a word problem that includes:
- At least three useful facts
- One piece of extra information that is not needed
- At least one grade 6 skill, such as decimals, fractions, ratios, area, or multiple operations
- A question with a clear answer
Then have the learner solve their own problem and trade it with a parent, sibling, or teacher to solve.
Formative Assessment During the Lesson
Use these checks while the learner works:
- Question check: “Tell me what you are trying to find without solving yet.”
- Operation check: “What words or clues helped you choose that operation?”
- Reasonableness check: “Should the answer be larger or smaller than the numbers in the problem?”
- Unit check: “What should the answer be measured in?”
- Explanation check: “Could someone else follow your work?”
Summative Assessment
Use Missions 1–6 as the assessment. Score each problem using the following rubric.
| Skill | 2 Points | 1 Point | 0 Points |
|---|---|---|---|
| Understanding the question | Clearly identifies what must be found | Partly identifies the question | Does not identify the question |
| Choosing a plan | Chooses the correct operation or operations | Plan is partly correct or needs help | Chooses an unrelated plan |
| Calculating | Calculations are accurate | Minor calculation error | Calculations are mostly incorrect or missing |
| Showing work | Shows an equation, model, table, or clear steps | Shows some work | Shows no work |
| Explaining and checking | Uses a complete answer, correct unit, and reasonable check | Includes only part of an explanation or check | Does not explain or check |
There are 10 possible points per problem and 60 points total.
- 50–60 points: Strong understanding of grade 6 word-problem skills
- 38–49 points: Developing understanding; review one or two areas
- 0–37 points: Needs additional modeling and guided practice
Differentiation and Support
For a Learner Who Needs Support
- Read each problem aloud and allow the learner to retell it in their own words.
- Cover extra information at first, then reveal it later.
- Use colored pencils: one color for the question, one for useful numbers, and one for operation clues.
- Provide a sentence frame: “I need to find ____. I know ____. I will ____ because ____.”
- Allow drawings, counters, number lines, tables, or calculators for checking.
- Work on Missions 1–3 first and complete the remaining problems another day.
For a Learner Ready for More Challenge
- Ask the learner to solve a problem in two different ways.
- Ask the learner to change one number and explain how the answer changes.
- Have the learner write a problem with two possible interpretations and explain which interpretation is best.
- Ask the learner to identify whether the answer is exact or an estimate.
- Challenge the learner to create a problem with a misleading but unnecessary fact.
Answer Key
- Mission 1: 6 × 24 = 144; 144 − 35 = 109 stickers.
- Mission 2: $86 − $48 = $38; $38 ÷ $12.50 = 3.04 weeks, so Leo needs 4 more weeks to have enough money.
- Mission 3: 3 × 8 = 24 total slices; 24 − 17 = 7 slices left; the fraction is 7/24.
- Mission 4: 7.5 + 8.25 − 1.5 = 14.25 miles.
- Mission 5: Perimeter = 2 × 12 + 2 × 7 = 38 meters.
- Mission 6: 30 is 3 times 10; 2.5 × 3 = 7.5 cups of flour.
Conclusion: Case Closed
Ask the learner to complete these statements:
- “The first thing I should do when I read a word problem is…”
- “A useful way to choose an operation is…”
- “One way to check my answer is…”
- “The word problem strategy that helped me most was…”
Finish by asking the learner to give a “case report”:
“I solved a problem by ____. My answer was ____. I know it makes sense because ____.”
Reinforce the main takeaway: Strong mathematicians do more than calculate. They understand the question, choose a plan, show their thinking, and check their answer.