Mathematical Processes and Problem Solving
What you must understand
Problem solving in Grade 5 means selecting and applying strategies: drawing a diagram, making a table or organized list, working backward, guessing and checking, finding a pattern, and breaking a problem into parts. You must explain your reasoning in words, show the steps, and judge whether an answer is reasonable. Multi-step problems require identifying what is asked, what is given, and which operations connect them. Communication matters: use correct mathematical vocabulary, label units, and justify each step.
Traps to watch
- Answering only the first step of a two-step problem and stopping.
- Ignoring the question's actual demand: "how many are left" versus "how many in all".
- Forgetting to check whether the answer makes sense in context, such as a fractional number of people.
- Losing track of units or mislabeling the final answer.
- Giving only a number when the question asks for an explanation.
Worked example
A class of 28 students is going on a trip in vans that hold 6 students each. How many vans are needed? Divide: 28 ÷ 6 = 4 remainder 4. Four vans hold 24 students, leaving 4, so a fifth van is needed. Answer: 5 vans. Working backward also helps: 5 vans hold 30 seats, which is enough for 28.
Rule of thumb
After solving, reread the question, confirm every part is answered, check the units, and ask whether the result is reasonable in the real situation.