Problem solving and revision (T1 W10)
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Problem solving in mathematics involves identifying a problem, devising a plan, carrying out the plan, and reviewing the solution. This week, we will explore different strategies such as drawing diagrams, using equations, and logical reasoning. Visual models, such as bar models and number lines, will help us visualize problems and find solutions more effectively.
Consider the problem: 'A farmer has 120 apples. He sells 30 apples and then buys 50 more. How many apples does he have now?' To solve this, we first subtract the apples sold from the total: 120 - 30 = 90. Then, we add the apples bought: 90 + 50 = 140. Therefore, the farmer has 140 apples now. This example illustrates the importance of breaking down the problem into manageable steps.
Let’s solve the following problem together: 'A school has 250 students. If 75 students are absent, how many students are present?' We can use a bar model to represent the total students and the absent students. First, draw a bar representing 250. Shade 75 to indicate the absent students. The remaining part of the bar represents the present students. Calculate 250 - 75 = 175. Therefore, 175 students are present. Work through this problem step-by-step with your partner.
Now, it's your turn to solve some problems on your own. Remember to show all your working clearly. Here are three problems: 1) A book costs R150. If you buy 3 books, how much do you spend? 2) If a car travels 60 km in 1 hour, how far will it travel in 3 hours? 3) There are 40 students in a class, and 10 are girls. How many boys are there? Solve these and be prepared to discuss your strategies.
Answer: Identify the problem
Identifying the problem is crucial as it sets the direction for the entire problem-solving process.
Answer: 150
Subtracting the apples given away (200 - 50) leaves you with 150 apples.
Answer: I would draw a diagram or model that represents the problem, breaking it down into parts to visualize the relationships.
Visual models help clarify the problem and make it easier to see how to solve it.
Answer: R400
The total cost is calculated by multiplying the number of books by the cost per book (5 x 80 = 400).
Answer: 60 km/h
Speed is calculated by dividing distance by time (120 km / 2 hours = 60 km/h).
Answer: Recalculate your answers
Recalculating helps ensure that your solution is accurate and that you haven't made any errors.
Answer: 42
Adding 15 and 27 gives a total of 42.
Answer: I might miscalculate a number, and I can correct it by double-checking my calculations.
Reviewing calculations helps identify and correct errors.