Estimating worksheet for students to practice estimating quantities and solving real-world math problems.

I will solve the estimation problems presented in the image. The task is to estimate the answers for several word problems and then provide a "Sanity Check" or "About how much..." answer for each.

Let me go through each problem one by one, providing an estimated solution and explanation.

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Problem 1: Apples

Question: One crate of apples sells for between $8 and $12. If Sam sold 32 crates of apples, about how much did he earn?

Estimation:
To estimate, I can use the midpoint of the price range, which is $10 per crate.
- Estimated earnings = 32 crates × $10/crate = $320

Sanity Check:
The actual amount must be between:
- Minimum: 32 × $8 = $256
- Maximum: 32 × $12 = $384

So, earning about $300 is a reasonable estimate that falls within this range.

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Problem 2: Field Trip

Question: The first ferry makes 5 trips a day. There are between 62 and 82 people on each trip. About how many people ride the ferry every day?

Estimation:
I'll use the midpoint of the passenger range, which is approximately 72 people per trip.
- Estimated riders = 5 trips × 72 people = 360 people

Sanity Check:
The actual number must be between:
- Minimum: 5 × 62 = 310 people
- Maximum: 5 × 82 = 410 people

An estimate of 350 is a good round number that fits well within this range.

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Problem 3: Garden Plants

Question: There are 94 bean plants in the garden. Each plant produces 3 to 5 sprouts of beans. About how many sprouts of beans will there be?

Estimation:
I'll use the midpoint of the sprout range, which is 4 sprouts per plant.
- Estimated sprouts = 94 plants × 4 sprouts = 376 sprouts

Sanity Check:
The actual number must be between:
- Minimum: 94 × 3 = 282 sprouts
- Maximum: 94 × 5 = 470 sprouts

Rounding 376 to the nearest hundred gives us 400, which is a good, simple estimate.

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Problem 4: Movie Theater

Question: Movie tickets cost between $6 and $10. If the theater holds 120 people, about how much money is made in ticket sales when the theater is full?

Estimation:
I'll use the midpoint of the ticket price, which is $8.
- Estimated revenue = 120 people × $8 = $960

Sanity Check:
The actual revenue must be between:
- Minimum: 120 × $6 = $720
- Maximum: 120 × $10 = $1,200

An estimate of $1,000 is a very reasonable round number for this range.

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Problem 5: Storage Bin

Question: Let’s say between 300 and 500 books in a storage bin. If the bin is 12 bags, about how many books will she be able to put in each bag?

Estimation:
I'll use the midpoint of the book range, which is 400 books.
- Estimated books per bag = 400 books ÷ 12 bags ≈ 33 books per bag

Sanity Check:
The actual number per bag must be between:
- Minimum: 300 ÷ 12 = 25 books per bag
- Maximum: 500 ÷ 12 ≈ 41.67 books per bag

An estimate of 30 books per bag is a good, easy-to-understand number that falls within this range.

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Problem 6: Bike Ride

Question: Abigail rides her bike 12 to 20 miles a day. About how many miles does she ride in a week?

Estimation:
I'll use the midpoint of the daily distance, which is 16 miles.
- Estimated weekly miles = 16 miles/day × 7 days = 112 miles

Sanity Check:
The actual weekly mileage must be between:
- Minimum: 12 × 7 = 84 miles
- Maximum: 20 × 7 = 140 miles

An estimate of 100 miles is a good, round number that represents the lower end of the possible range, which is often a safe conservative estimate.

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Final Answers Summary:

1. Apples: About $300
2. Ferry: About 350 people
3. Beans: About 400 sprouts
4. Movie Theater: About $1,000
5. Storage Bin: About 30 books per bag
6. Bike Ride: About 100 miles

These estimates are all reasonable approximations based on using midpoints and rounding to make the numbers easy to understand while staying within the given ranges.