Operations and Algebraic Thinking: Solving Multistep Word Problems with Whole Numbers and Remainders (CCSS.4.OA.3)
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Common Core 4th Grade Math › Operations and Algebraic Thinking: Solving Multistep Word Problems with Whole Numbers and Remainders (CCSS.4.OA.3)
A soccer league has 7 teams coming to a party. Each team brings 13 players. Tables seat 8 people. How many players will not fit at full tables?
11 players
3 players
8 players
2 players
Explanation
Total players: 7 × 13 = 91. 91 ÷ 8 = 11 R 3, so 3 players won't fit at full tables. Let $r$ be the number of players without a seat. Equation: $91 = 8 \times 11 + r$, so $r = 3$. Estimate: 7 × 12 ≈ 84; 84 ÷ 8 = 10 with some left, so a small remainder like 3 is reasonable. The choice of 11 ignores the context and just reports the raw quotient.
The art club has 8 boxes of 12 markers each and finds 7 loose markers. They want to make sets of 15 markers for classroom art bins. How many markers will be left over?
13 markers
6 markers
15 markers
7 markers
Explanation
Total markers: 8 × 12 + 7 = 103. 103 ÷ 15 = 6 R 13, so 13 markers are left over. Let $r$ be the leftover markers. Equation: $103 = 15 \times 6 + r$, so $r = 13$. Estimate: about 100 ÷ 15 ≈ 6 with some left, so 13 leftover makes sense. The choice of 6 ignores the context and just reports the raw quotient.
Four 4th-grade classes are going on a field trip. Each class has 28 students, and 6 teachers are going too. Each bus holds 30 people. How many buses are needed?
3 buses
5 buses
4 buses
28 buses
Explanation
Total people: 28 × 4 + 6 = 118. 118 ÷ 30 = 3 R 28, so they need one more bus to carry everyone: 4 buses. Let $x$ be the number of buses. Equation: $30x \ge 118$; the least whole $x$ is 4. Estimate: 120 ÷ 30 ≈ 4, so 4 buses is reasonable. The choice of 3 ignores the context and just reports the raw quotient.
A lemonade stand earned 18 dollars on Saturday and 9 dollars on Sunday. Four friends will share the money equally. How much money does each friend get?
7 dollars
6 dollars
6 and 1/2 dollars
6 and 3/4 dollars
Explanation
Total money: 18 + 9 = 27 dollars. 27 ÷ 4 = 6 R 3, so each gets 6 and 3/4 dollars (since money can be shared as parts of a dollar). Let $x$ be the amount per friend. Equation: $4x = 27$, so $x = \frac{27}{4} = 6\tfrac{3}{4}$. Reasonableness: 4 × 6 = 24 (too low) and 4 × 7 = 28 (too high), so a little more than 6 is sensible. The choice of 6 ignores the remainder and just reports the raw quotient.