I have three questions...

Okay think of a 1-9 multiplication table.

1. Are there more odd or even products? How can you determine the answer without counting?

2. Is this different from a 1-9 addition facts table? Explain.

And for the last one don't use the table or anything else.

3. Explain why it is helpful to use a plan to solve problems. Include an explanation of the importance of performing each step of the four-step plan
(Four-step problem solving plan: Explore. Plan. Solve. Check)

I just can come up with the answers! Can you help?!

Of course, I can help you with your questions!

1. To determine if there are more odd or even products in a 1-9 multiplication table without counting, you can use a logical reasoning approach.

In the multiplication table, you have nine numbers to multiply with nine other numbers. In each multiplication operation, one number is odd (1, 3, 5, 7, or 9), and the other is even (2, 4, 6, or 8).

When you multiply an odd number by an even number, the product is always an even number. This is because whenever you multiply an odd number by any number, the result will always have the same parity (odd or even) as the other number.

Since you have an equal number of odd and even numbers in the multiplication table, and in each multiplication operation, an odd number is multiplied by an even number, it follows that there will be an equal number of odd and even products.

2. Yes, a 1-9 multiplication table is different from a 1-9 addition facts table. Here's an explanation:

In a multiplication table, each cell contains the product of multiplying the corresponding row and column numbers. It shows the result of combining two numbers through multiplication. On the other hand, an addition facts table shows the sum of adding the corresponding row and column numbers. It represents the outcome of combining two numbers through addition.

For example, in a multiplication table, the number in the cell where the row number is 3 and the column number is 4 would be the product of 3 multiplied by 4, which is 12. In an addition facts table, the number in the same cell would be the sum of 3 and 4, which is 7.

In summary, a multiplication table reflects the results of multiplication operations, while an addition facts table reflects the results of addition operations. The operations and outcomes are different for each table.

3. It is helpful to use a plan to solve problems because it provides a structured approach that increases the chances of finding a correct solution. The four-step problem-solving plan (Explore, Plan, Solve, Check) is one such method that helps organize your thoughts and actions. Here's an explanation of each step:

- Explore: In this step, you gather all the necessary information about the problem, identify what is given, and understand what is being asked. This helps you define the problem clearly and ensures you have all the relevant information at hand.

- Plan: Once you understand the problem, you need to develop a plan or strategy to solve it. This involves breaking the problem down into smaller, manageable parts, identifying the appropriate formulas or techniques to use, and considering potential obstacles or challenges.

- Solve: This step involves carrying out the plan you developed in the previous step. You perform the necessary calculations, apply the identified methods, and follow the logical steps to reach a solution.

- Check: After finding a solution, it is important to check its validity and accuracy. You review your solution, ensure that it makes sense within the context of the problem, and verify that all steps were correctly executed. This helps you catch any errors and provides confidence in your solution.

By following this four-step problem-solving plan, you establish a systematic and organized approach to problem-solving. It helps you avoid mistakes, improve efficiency, and build problem-solving skills that can be applied to future challenges. Each step plays a vital role in ensuring a comprehensive and accurate solution.

In such a table, without zeroes, there are 9 x 9 = 81 entries. 5 x 5 = 25 are odd-odd products (and therefore odd); 4x4 = 16 are even-even products (and therefore even) and 2x4x5= 40 are even-odd products (and therefore even).

Only 25 of the 81 entries are therefore odd.

The results will be different for a 1-9 addition table, because you need odd + even to get odd. Other combinations are even.

Use your own words to answer 3.

12x whenx=5