Mathematics - Term 1 - Week 10

Problem solving in mathematics involves identifying a problem, devising a plan, carrying out the plan, and reviewing the solution. This week, we will focus on breaking down problems into manageable steps. We will discuss different strategies such as drawing diagrams, creating tables, and using equations to represent problems. By understanding the problem thoroughly, we can choose the best approach to find a solution.

Imagine you have a basket containing apples and oranges. There are 12 fruits in total, and there are 4 more apples than oranges. To solve this, we can set up equations. Let 'x' be the number of oranges. Then, the number of apples is 'x + 4'. The equation becomes: x + (x + 4) = 12. Solving this gives us 2x + 4 = 12, leading to 2x = 8, so x = 4. Therefore, there are 4 oranges and 8 apples. This example shows how to translate a word problem into a mathematical equation.

Let's work together on this problem: Sarah has 3 times as many books as Tom. Together, they have 48 books. How many books does each person have? Start by letting 'y' represent the number of books Tom has. Then, Sarah has '3y' books. The equation is y + 3y = 48. Combine like terms to get 4y = 48, and solve for 'y'. What do you find? Discuss your process with a partner and share your findings with the class.

Now it's your turn to solve some problems on your own. Here are three problems to work on: 1) A rectangle has a length that is twice its width. If the perimeter is 36 cm, what are the dimensions of the rectangle? 2) A baker made 120 cookies and sold 3/5 of them. How many cookies are left? 3) If a car travels 60 km in 1 hour, how far will it travel in 3.5 hours? Show your working clearly for each problem.

• Review the solution
• Identify the problem
• Carry out the plan
• Devising a plan

Answer: Identify the problem

Identifying the problem is crucial as it sets the foundation for finding a solution.

• 10
• 13
• 8
• 15

Answer: 13

Substituting x with 5 gives 2(5) + 3 = 10 + 3 = 13.

Answer: I would calculate the time traveled (2 hours) and multiply it by the speed (80 km/h) to find the distance.

The distance can be found using the formula distance = speed × time.

• 30 cm
• 25 cm
• 50 cm
• 15 cm

Answer: 30 cm

The perimeter is calculated as 2(length + width) = 2(10 + 5) = 30 cm.

Answer: The area is 12 cm².

Area of a triangle = 1/2 × base × height = 1/2 × 6 × 4 = 12 cm².

• 8
• 16
• 12
• 20

Answer: 16

Giving away 1/3 of 24 means you give away 8 apples, leaving you with 24 - 8 = 16 apples.

Answer: The sum of the angles in a triangle is 180 degrees.

This is a fundamental property of triangles in Euclidean geometry.