Mathematics - Term 2 - Week 8

Problem solving in mathematics involves identifying a problem, devising a plan, carrying out the plan, and reviewing the solution. This process helps students to think critically and apply their mathematical knowledge to real-world situations. We will explore various strategies such as drawing diagrams, creating tables, and using equations to solve problems effectively.

Let's consider a rectangle with a length of 8 cm and a width of 5 cm. To find the area, we use the formula Area = Length × Width. Thus, Area = 8 cm × 5 cm = 40 cm². This example illustrates how to apply a formula to solve a problem. Notice how we clearly show our working steps to ensure understanding.

Now, let's solve a problem together. If 3x + 5 = 20, what is the value of x? First, we subtract 5 from both sides to get 3x = 15. Next, we divide both sides by 3, resulting in x = 5. This step-by-step approach helps clarify each part of the solution process.

Students will now work on the following problems independently: 1) Solve for y in the equation 2y + 4 = 12. 2) Calculate the perimeter of a triangle with sides measuring 7 cm, 5 cm, and 3 cm. Remember to show all your working clearly. After completing the problems, we will review the answers together.

• Add 7 to both sides
• Subtract 4 from both sides
• Multiply both sides by 4
• Divide both sides by 4

Answer: Add 7 to both sides

To isolate the term with x, we first need to eliminate the -7 by adding 7 to both sides.

Answer: 25 cm²

The area of a triangle is calculated using the formula Area = 1/2 × base × height, which gives us 1/2 × 10 cm × 5 cm = 25 cm².

• A graph
• A table
• A diagram
• All of the above

Answer: All of the above

All these options are valid visual models that can help in understanding and solving mathematical problems.

Answer: 9

To find y, divide both sides by 5: y = 45 / 5 = 9.

• 20 cm
• 24 cm
• 10 cm
• 12 cm

Answer: 20 cm

The perimeter of a rectangle is calculated as P = 2(length + width) = 2(6 cm + 4 cm) = 20 cm.

Answer: 36

To solve for x, multiply both sides by 3: x = 12 × 3 = 36.

• Substituting the value back into the original equation
• Ignoring the original equation
• Changing the equation completely
• None of the above

Answer: Substituting the value back into the original equation

Substituting the found value back into the original equation verifies if the solution is correct.