Mathematics - Term 3 - Week 6

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, will help us visualize the 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: 120 - 30 = 90. Then, we add the apples bought: 90 + 50 = 140. Thus, the farmer has 140 apples now. This example illustrates the importance of following a clear sequence in problem-solving.

Let's work through a problem together: 'There are 45 students in a class. If 18 are boys, how many are girls?' We can use a bar model to represent the total number of students and the boys. Draw a bar of 45 and shade 18 for the boys. The remaining part of the bar represents the girls. To find the number of girls, we calculate 45 - 18 = 27. This visual representation helps us understand the problem better.

Now it's your turn to solve some problems on your own. Remember to show your working clearly. Here are three problems: 1) A book costs R80. If you buy 3 books, how much do you spend? 2) A box contains 60 chocolates. If 15 are eaten, how many are left? 3) If a car travels 120 km in 2 hours, what is its speed in km/h? Take your time and apply the strategies we've discussed.

• Finding a solution
• Identifying the problem
• Reviewing the solution
• Implementing the plan

Answer: Identifying the problem

The first step in problem solving is to clearly identify what the problem is.

• 15 cm²
• 50 cm²
• 25 cm²
• 30 cm²

Answer: 50 cm²

The area of a rectangle is calculated by multiplying length by width: 10 cm * 5 cm = 50 cm².

Answer: 125

First, subtract 45 from 150 to get 105, then add 20 to get 125.

• A number line
• An equation
• A word problem
• A graph

Answer: A number line

A number line is a visual representation that helps in understanding numerical relationships.

Answer: 56

Multiplying 8 by 7 gives 56.

• 8 apples
• 7 apples
• 6 apples
• 5 apples

Answer: 8 apples

Adding 3 apples to 5 apples results in a total of 8 apples.

Answer: 16 cm

The perimeter of a square is calculated as 4 times the side length: 4 cm * 4 = 16 cm.

• Addition
• Subtraction
• Multiplication
• Division

Answer: Multiplication