Mathematics - Term 1 - Week 10

Problem solving is a critical skill in mathematics that involves identifying a problem, devising a plan, carrying out the plan, and reviewing the solution. This week, we will explore various strategies to tackle problems effectively. We will use visual models, such as number lines and bar models, to represent problems visually, making them easier to understand and solve.

Let's solve the problem: What is 1/4 + 1/2? First, we need a common denominator. The least common denominator of 4 and 2 is 4. We can rewrite 1/2 as 2/4. Now, we add: 1/4 + 2/4 = 3/4. Therefore, the answer is 3/4. We used a visual model of a fraction bar to help us see the parts clearly.

Now, let's work together on the problem: 3 1/2 - 1 3/4. First, we convert the mixed numbers to improper fractions. 3 1/2 becomes 7/2 and 1 3/4 becomes 7/4. Next, we find a common denominator, which is 4. We convert 7/2 to 14/4. Now we can subtract: 14/4 - 7/4 = 7/4. Finally, we convert back to a mixed number: 7/4 = 1 3/4. Let's try another similar problem together.

Now it's your turn! Solve the following problems on your own. Remember to show all your working steps clearly. 1) 2/3 + 1/6, 2) 5 - 2 1/2, 3) 4 1/5 - 2 2/5. After you finish, we will review the answers together and discuss any mistakes.

• Review the solution
• Identify the problem
• Carry out the plan
• Write the answer

Answer: Identify the problem

The first step in problem solving is to clearly identify what the problem is before attempting to solve it.

• 1/2
• 2/6
• 1/6
• 1/3

Answer: 1/2

To add these fractions, find a common denominator (6), then convert 1/3 to 2/6. So, 2/6 + 1/6 = 3/6 = 1/2.

Answer: Showing working steps helps to track the thought process, makes it easier to find mistakes, and allows others to understand how the solution was reached.

This explanation emphasizes the value of transparency in problem-solving.

• 7
• 12
• 6
• 8

Answer: 12

The least common denominator is the smallest number that both denominators can divide into evenly, which is 12 for 3 and 4.

• 2 3/4
• 3 3/4
• 2 1/4
• 1 3/4

Answer: 2 3/4

First, convert 5 to 4 4/4. Then, subtract: 4 4/4 - 2 1/4 = 2 3/4.

Answer: I should review my steps, identify where I went wrong, and correct my calculations.

This shows the importance of reflection and correction in the learning process.

• Bar model
• Line graph
• Pie chart
• All of the above

Answer: All of the above

All these visual models can help represent fractions in different ways, aiding understanding.