Two-Step Word Problems with a Letter for the Unknown
Print 3rd grade two-step word problem worksheets: write an equation with a letter, solve it, then check the answer with a rounded estimate. 12 versions.
Worksheet version 1 of 12. The answer key matches the current version.
Write one equation for each problem, using the letter for the number you need to find. Solve it. Then round each number of 10 or more to the nearest ten and work out an estimate. Is your answer close to the estimate?
Example: Leo has 4 bags with 6 marbles in each. He finds 12 more. How many marbles does he have?
Equation: 4 × 6 + 12 = n. Solve: 4 × 6 = 24, 24 + 12 = 36, so n = 36. Estimate: 4 × 6 + 10 = 34. 36 is close to 34, so the answer is reasonable.
a) The school library has 451 books. It gets 180 more, then lends out 55. How many books does it have now?
Equation: = s
s =
Estimate: =
b) Ruby has 15 green grapes and 21 purple grapes, and shares all of them equally between 4 plates. How many grapes does each plate get?
Equation: = b
b =
Estimate: =
c) Priya has 7 packs with 7 stickers in each. A friend gives Priya 31 more stickers. How many stickers does Priya have now?
Equation: = k
k =
Estimate: =
d) Zoe bakes 8 trays of 6 cookies. Then Zoe gives away 29 of them. How many cookies are left?
Equation: = t
t =
Estimate: =
e) Theo has 37 beads and uses 13 of them on a card. Theo shares the rest equally between 6 bracelets. How many beads go on each bracelet?
Equation: = n
n =
Estimate: =
f) Kai splits 90 children equally into 9 teams. Then 4 grown-ups join each team. How many people are in each team?
Equation: = p
p =
Estimate: =
About this worksheet
A two-step word problem needs two calculations, and the answer to the first is used in the second. Writing the whole problem as one equation, with a letter standing for the unknown, keeps both steps together. For "Maya has 4 boxes of 6 crayons and gets 12 more", the equation is 4 × 6 + 12 = n, so n = 36.
Multiplication and division come before addition and subtraction, and anything in brackets comes first. In (37 − 13) ÷ 6 the subtraction is done first because of the brackets: 24 ÷ 6 = 4. Each version mixes six of seven problem types: multiply then add, multiply then subtract, subtract then divide, add then subtract, divide then add, subtract a product, and add then divide. Products stay within 100, totals stay within 1,000 and every step gives a whole number.
The estimate is a quick check. Round every number of 10 or more to the nearest ten and keep one-digit numbers as they are, then work out the same equation. If 451 + 180 − 55 = 576 and the estimate is 450 + 180 − 60 = 570, the answer is reasonable. If the two are far apart, look for a mistake.
Practice aligned to CCSS 3.OA.D.8.
Before this: 2nd grade word problems within 100 and rounding on number lines. Also useful: unknown factors and fact families and division facts. More practice: multiplication worksheets and 3rd grade math worksheets.
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