Problem solving and revision (T3 W6)
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Problem solving in mathematics involves identifying a problem, devising a plan, carrying out the plan, and evaluating the solution. This week, we will explore various strategies such as drawing diagrams, using number lines, and breaking problems into smaller parts. These strategies help clarify the problem and make it easier to find a solution.
Consider the equation 5 + x = 12. To find the value of x, we can subtract 5 from both sides of the equation. This gives us x = 12 - 5, which simplifies to x = 7. We can visualize this on a number line, starting at 5 and moving 7 spaces to the right to reach 12.
If a book costs R45 and a pen costs R15, how much will it cost to buy 3 books and 2 pens? First, calculate the total cost of the books: 3 x R45 = R135. Then calculate the total cost of the pens: 2 x R15 = R30. Finally, add these two amounts together: R135 + R30 = R165. Show your working clearly to ensure you understand each step.
Now, try solving the following problems on your own. Remember to show all your working: 1) If a pizza costs R80 and you buy 4 pizzas, how much do you spend? 2) A bag contains 12 apples. If you eat 3 apples, how many are left? 3) Solve for y in the equation 3y + 6 = 21.
Answer: Identify the problem
The first step in problem solving is to clearly identify what the problem is.
Answer: 15
Adding 8 and 7 gives you 15.
Answer: 6
10 - 4 = 6, so you have 6 candies left.
Answer: A number line
A number line is a visual model that helps in understanding numerical relationships.
Answer: 4
Subtract 4 from both sides to get 2x = 8, then divide by 2 to find x = 4.
Answer: R100
5 notebooks at R20 each costs 5 x 20 = R100.
Answer: 10
15 - 5 = 10, so you have 10 marbles left.
Answer: Carry out the plan
After devising a plan, the next step is to implement that plan to find a solution.