Computation and Operations - Solving Multi-step Word Problems

Identify Key Information (CUBES Method): To solve multi-step problems, start by circling numbers and underlining the question. Imagine a 'CUBES' checklist in your mind: Circle numbers, Underline the question, Box keywords, Evaluate steps, and Solve. This helps break down complex paragraphs into manageable math tasks.

Keywords for Operations: Recognize words that signal which operation to use. 'Total', 'sum', and 'altogether' usually mean addition ($+$); 'Difference', 'how many more', or 'left' usually mean subtraction ($-$). 'Each' or 'product' often signals multiplication ($\times$), while 'share', 'divided equally', or 'split' signal division ($\div$).

Visualizing with Bar Models: Use bar models to 'see' the problem. A Part-Whole Bar Model shows a long rectangle (the total) divided into smaller sections (the parts). If you have two parts and need the total, you add ($P_1 + P_2 = T$). If you have the total and one part, you subtract to find the missing piece ($T - P_1 = P_2$).

Comparison Bar Models: For 'more than' or 'less than' problems, draw two bars of different lengths stacked vertically. The difference between the lengths of the two bars represents the value you are trying to find ($Large - Small = Difference$). Visualizing these side-by-side helps determine which value is the 'base' and which is the 'extra'.

Order of Steps: Multi-step problems are solved like a sequence or a chain. You must find the 'hidden' question first. For example, if you buy 3 shirts and pay with a $\$50$ bill, the hidden step is calculating the total cost of the 3 shirts ($3 \times price$) before you can subtract that from $\$50$.

Interpreting Remainders: In division steps, the remainder ($r$) must be handled based on context. Imagine you have $13$ students and each car fits $4$. $13 \div 4 = 3 \text{ R } 1$. In this case, you need $4$ cars (rounding up) because that last student cannot be left behind.

Reasonableness and Estimation: After solving, round your numbers to the nearest $10$ or $100$ to see if your answer makes sense. If your exact calculation is $452$ but your estimate is $800$, you should re-read the problem to ensure you used the correct operations.