Problem solving and revision (T2 W8)
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Move from lesson study to exam practice in Mathematics.
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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 various strategies such as drawing diagrams, using equations, and breaking problems into smaller parts. Visual models, like bar models and number lines, can help clarify complex problems and make them easier to solve.
Suppose you want to buy 3 notebooks that cost R15 each and 2 pens that cost R5 each. To find the total cost, first calculate the cost of the notebooks: 3 x R15 = R45. Next, calculate the cost of the pens: 2 x R5 = R10. Finally, add the two amounts together: R45 + R10 = R55. Therefore, the total cost is R55.
You have 24 candies and want to share them equally among 6 friends. To find out how many candies each friend gets, divide the total number of candies by the number of friends: 24 ÷ 6 = 4. Each friend receives 4 candies. Now, let's try another similar problem together: If you have 30 candies and share them among 5 friends, how many does each friend get?
Now it's your turn to solve some problems on your own. Solve the following: 1) If a book costs R80 and you buy 4 books, what is the total cost? 2) You have 50 marbles and want to put them into bags of 10. How many bags do you need? Show your working clearly for each problem.
Answer: Identify the problem
Identifying the problem is crucial as it sets the direction for the entire problem-solving process.
Answer: R15
The total cost is calculated by multiplying the number of apples by the cost per apple: 5 x R3 = R15.
Answer: To find the area of a rectangle, multiply its length by its width.
The area is calculated using the formula A = length x width.
Answer: 8
Dividing 48 by 6 gives you 8, as 6 goes into 48 exactly 8 times.
Answer: Bar model
A bar model visually represents quantities, making it easier to understand addition.
Answer: Review your steps and correct the mistake.
It's important to go back through your work to identify where you went wrong and fix it.
Answer: 75
Subtracting the number of stickers given away from the total gives you 100 - 25 = 75.
Answer: It helps to understand the process and allows for easier correction of mistakes.
Showing your working provides clarity and helps identify errors in your reasoning.