Mathematics
Grade 5
15 min
Estimate sums and differences: word problems
Estimate sums and differences: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Identify situations in word problems where estimation is appropriate.
Round multi-digit whole numbers to the nearest ten, hundred, or thousand.
Round decimal numbers to the nearest whole number.
Estimate sums of whole numbers and decimals by rounding before adding.
Estimate differences of whole numbers and decimals by rounding before subtracting.
Solve word problems requiring the estimation of sums and differences.
Explain the reasonableness of an estimated answer in context.
Ever been to a store and quickly wanted to know if you have enough money for a few items? 💰 Or wondered approximately how many steps you've walked today?
In this lesson, you'll learn a super useful skill: how to quickly estimate sums and differences in word problems. Th...
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Key Concepts & Vocabulary
TermDefinitionExample
EstimateAn approximate answer or calculation that is close to the exact answer, but not necessarily precise.If you have $10 and want to buy items costing $3.85 and $5.10, you can estimate you'll spend about $4 + $5 = $9.
RoundingThe process of replacing a number with an approximate value that is easier to use, often ending in zero.Rounding 27 to the nearest ten gives you 30. Rounding 143 to the nearest hundred gives you 100.
SumThe result obtained when two or more numbers are added together.The sum of 15 and 20 is 35.
DifferenceThe result obtained when one number is subtracted from another.The difference between 50 and 12 is 38.
Place ValueThe value of a digit based on its position in a number (e.g., ones, tens, hundreds, tenths, hundredths).In the number 345, t...
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Core Formulas
Rounding Rule
1. Identify the place value you are rounding to. 2. Look at the digit immediately to the right of that place value. 3. If this digit is 5 or greater (5, 6, 7, 8, 9), round up: add 1 to the digit in the rounding place, and change all digits to its right to zero. 4. If this digit is less than 5 (0, 1, 2, 3, 4), round down: keep the digit in the rounding place the same, and change all digits to its right to zero.
Use this rule to simplify numbers before performing operations. For decimals, when rounding to the nearest whole number, look at the tenths digit.
Estimating Sums
\text{Estimated Sum} \approx \text{Rounded Number 1} + \text{Rounded Number 2}
To estimate a sum, first round each number in the problem to a chosen or specified place value (e.g., nearest ten,...
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Challenging
A rectangular garden is 24.6 meters long and 9.8 meters wide. To estimate the perimeter (2 × length + 2 × width), Student A rounds to the nearest whole number first, and Student B rounds to the nearest ten first. Which statement is true?
A.Both students will get the same estimated perimeter.
B.Student A's estimate will be more accurate.
C.Student B's estimate will be more accurate.
D.Estimation is not appropriate for this problem.
Challenging
To estimate the difference between 5,109 and 2,988, Sam calculated the exact answer (2,121) and then rounded it to 2,000. Why is Sam's method not the correct way to estimate?
A.His final answer is wrong; the estimate should be 3,000.
B.He should have rounded to the nearest hundred for a better estimate.
C.The purpose of estimation is to simplify the calculation *before* computing, which he did not do.
D.He correctly estimated the difference.
Challenging
Leo has $50. He wants to buy a book for $12.85, a notebook for $4.25, and a calculator for $28.99. Which statement best explains if he can afford the items based on estimation?
A.Yes, because $12 + $4 + $28 = $44, which is less than $50.
B.No, because $13 + $4 + $29 = $46, but the exact cost might be over $50.
C.Yes, because $13 + $4 + $29 = $46, which is less than $50.
D.No, because $10 + $0 + $30 = $40, which is too rough an estimate.
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