Problem solving and revision (T2 W8)
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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 tables, and working backward. Visual models can help clarify complex problems and make abstract concepts more tangible. We will also discuss the importance of reviewing mistakes to improve our understanding and approach.
Consider a triangle with a base of 10 cm and a height of 5 cm. To find the area, we use the formula: Area = 1/2 × base × height. Substituting the values, we have Area = 1/2 × 10 × 5 = 25 cm². This example illustrates how to apply a formula step-by-step, ensuring we show all working clearly.
Let's solve a word problem together: 'A farmer has 120 apples. He wants to pack them into boxes that hold 8 apples each. How many boxes does he need?' First, we divide the total number of apples by the number of apples per box: 120 ÷ 8 = 15. Therefore, the farmer needs 15 boxes. As we work through this, remember to write down each step to keep track of our process.
Now it's your turn! Solve the following problems independently. Remember to show all your working: 1) A rectangle has a length of 12 cm and a width of 4 cm. What is its perimeter? 2) If a book costs R150 and you have R600, how many books can you buy? 3) A train travels 60 km in 1 hour. How far will it travel in 3 hours? Write down your answers and be prepared to discuss your strategies.
Answer: Area = length × width
The area of a rectangle is calculated by multiplying its length by its width.
Answer: 12 cm²
Using the formula Area = 1/2 × base × height, we calculate Area = 1/2 × 8 × 3 = 12 cm².
Answer: 6
A hexagon is defined as a polygon with six sides.
Answer: 20 cm
The perimeter of a square is calculated as 4 times the side length: 4 × 5 = 20 cm.
Answer: 30
To find 15% of 200, multiply 200 by 0.15, which equals 30.
Answer: R350
Subtracting the amount spent from the total gives R500 - R150 = R350.
Answer: 7
A prime number is only divisible by 1 and itself; 7 meets this criterion.
Answer: 4
To solve for x, subtract 3 from both sides to get 2x = 8, then divide by 2 to find x = 4.