Mathematics - Term 1 - Week 10

Problem solving in mathematics involves identifying a problem, devising a plan, carrying out the plan, and reviewing the solution. It is essential to break down complex problems into manageable steps. Visual models, such as diagrams or charts, can help illustrate relationships and clarify the problem. Number talks encourage students to verbalize their thought processes, allowing them to explore different strategies and solutions collaboratively.

Consider the equation 2x + 3 = 11. To solve for x, first subtract 3 from both sides, yielding 2x = 8. Next, divide both sides by 2 to find x = 4. This example demonstrates the importance of isolating the variable step by step, ensuring clarity in each operation.

Let's find the area of a triangle with a base of 10 cm and a height of 5 cm. The formula for the area of a triangle is A = 1/2 × base × height. Substituting the values, we have A = 1/2 × 10 × 5 = 25 cm². Work through this problem as a class, discussing each step and the reasoning behind it.

Now, solve the following problems independently. Make sure to show all your working steps clearly. 1) Solve for y in the equation 3y - 4 = 11. 2) Calculate the perimeter of a rectangle with length 8 cm and width 3 cm. 3) If a book costs R120 and is on sale for 25% off, what is the sale price? Remember to check your answers and review any mistakes.

• Multiply both sides by 5
• Add 2 to both sides
• Subtract 5 from both sides
• Divide both sides by 5

Answer: Add 2 to both sides

To isolate the term with x, you first need to eliminate the constant term on the left side.

Answer: 48 cm²

Area is calculated using the formula A = length × width, so A = 12 × 4 = 48 cm².

• A number line
• A pie chart
• A bar graph
• All of the above

Answer: All of the above

All these visual models can help represent mathematical concepts and aid in problem-solving.

Answer: 8 apples

You subtract the number of apples given away from the total: 15 - 7 = 8.

• 10 cm
• 15 cm
• 20 cm
• 25 cm

Answer: 20 cm

The perimeter of a square is calculated as P = 4 × side length, so P = 4 × 5 = 20 cm.

Answer: x = 6

First, subtract 6 from both sides to get 4x = 24, then divide by 4 to find x = 6.

• Ignore the answer
• Re-solve the problem
• Ask a friend
• All of the above

Answer: Re-solve the problem

Re-solving the problem helps verify that the solution is correct and that no mistakes were made.

Answer: R50