6.2 Assisting Students with Setting Up and Solving Word Problems

Assisting Students with Word Problems

Word problems are one of the most challenging aspects of school mathematics. To solve them, students must combine reading comprehension, vocabulary decoding, logical reasoning, and algebraic translation with basic arithmetic skills. Many students experience "math anxiety" when faced with word problems, causing them to guess operations randomly.

Paraprofessionals play a vital role in helping students break down word problems. Rather than giving the answers or telling students which operations to use, paraprofessionals should teach students systematic strategies to decode, translate, solve, and verify their work.

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A Systematic Strategy: The CUBES Framework

To help students approach word problems methodically, paraprofessionals can model and encourage the use of structured frameworks. One widely used and effective method is the CUBES strategy:

• C — Circle the key numbers and units. (e.g., circle "12 pencils" and "3 friends")
• U — Underline the question. Identify exactly what needs to be solved. (e.g., "How many pencils does each friend get?")
• B — Box math action words. Look for clues that indicate operations. (e.g., box "share equally")
• E — Eliminate unnecessary information and evaluate. Cross out details that do not affect the math, and decide on a plan.
• S — Solve and check. Calculate the answer and verify if it makes sense.

By stepping through these letters, students slow down and analyze the text rather than rushing to perform calculations on the first numbers they see.

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Translating Words to Operations

Translating a narrative story into a mathematical equation is like translating a foreign language. Paraprofessionals should help students learn the "vocabulary" of math operations.

The Keyword Trap

Paraprofessionals must warn students that keywords are helpful clues, but they are not absolute rules. The overall context of the story always overrides keywords.

For instance, the word "each" is particularly notorious. Consider these two problems:

1. "Maria has 4 bags. Each bag has 5 marbles. How many marbles does she have total?" Here, "each" indicates multiplication (4 × 5 = 20).
2. "Maria has 20 marbles. She wants to put each marble into bags of 5. How many bags does she need?" Here, "each" indicates division (20 ÷ 5 = 4).

Paraprofessionals should guide students to visualize or draw the scenario to determine the correct action, rather than relying blindly on a single word.

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Checking Reasonableness and Estimation

A common mistake is for a student to perform a calculation, write down a number, and immediately move on, even if the answer is physically impossible. Paraprofessionals should teach students to check the reasonableness of their answers before finalizing them.

1. Estimation Strategies

Before performing exact calculations, students should estimate the answer. This establishes a "target range" or "ballpark."

• Rounding: Round multi-digit numbers to the nearest ten or hundred. For example, to solve 293 + 408, round to 300 + 400 = 700. If the final calculated answer is 601 or 891, the student knows they made a calculation error.
• Benchmark Numbers: For fractions or decimals, use familiar benchmarks like 0, 1/2, or 1. For instance, when adding 3/7 + 5/9, a student can recognize that both fractions are close to 1/2, so the sum should be very close to 1.

2. Real-World Constraints

Paraprofessionals should prompt students to ask: "Does this answer make sense in the real world?"

• If a problem asks: "How many school buses are needed to transport 95 students if each bus holds 30?" A student might compute 95 ÷ 30 = 3.16. In the real world, you cannot order 3.16 buses. The answer must be rounded up to 4 buses to accommodate everyone.
• If a subtraction problem asks for a person's age or height, it cannot be negative or ridiculously large (e.g., a child cannot be -4 years old or 180 feet tall).

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Worked Classroom Scenarios

Classroom Scenario 1 — Distractors (Irrelevant Information): Liam bought 3 notebooks for $2.00 each, 1 pack of pencils for $1.50, and a water bottle for $5.00. He is 9 years old and has $15.00. How much money did he spend on school supplies? The student is trying to add 3 + 2 + 1.50 + 5 + 9 + 15.

• Paraprofessional Intervention: The paraprofessional asks: "Let's read the question together: How much money did he spend on school supplies? Does his age (9) tell us about what he spent? Does the amount of money he started with ($15.00) tell us what he spent?"
• Action: The student crosses out "9 years old" and "$15.00".
• Resolution: The paraprofessional helps the student focus on the relevant costs: "Now, he bought 3 notebooks for $2.00 each. Let's draw that or write it: 3 × $2.00 = $6.00. And 1 pack of pencils for $1.50. Did he spend money on the water bottle? Is that a school supply? Yes. Let's add those up."

Classroom Scenario 2 — Prompting Self-Correction: A student calculates that a sweater originally priced at $50.00 is on sale for 20% off. The student subtracts $20.00 (confusing 20% with $20.00) and gets $30.00. In another problem, they add and get $60.00.

• Paraprofessional Intervention: "Let's think about this. If the sweater is on sale (20% off), should the new price be higher or lower than the original price of $50.00?"
• Student response: "Lower, because it is on sale."
• Prompt: "Right. Your answer of $60.00 is higher than $50.00. Let's look at how we calculate percent off to find the discount."