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If students can develop a mental image of the problem in their head, then they likely have a solid understanding of what the problem is asking. To solve math problems like this one, there are a multitude of strategies involved. This is a great example to use with children to model thinking out-loud about the steps required to solve this and how to draw models to show their thinking. What helper facts could you use to solve these problems: 9 21, 4 x 5, 7 x 3, and 6 6? I made it up on the spot with my class of second graders to demonstrate how to use Polya's Problem Solving Steps. Two bars could be drawn: 1 representing 20, and the other in half. How many red books do we need to balance the scale?
Exercises are chosen with the goal of either teaching a strategy or practicing a technique to mastery. Decide if there are multiple steps that will need to be taken to arrive at the final answer.
We also want to engage our students in real-life mathematical situations (problems they likely will encounter in everyday situations). Determine what the question is asking you to actually do. Is there another way to solve the problem or show your answer differently? In order to understand it, we have to realize that the herd is much larger than at the beginning of the problem.
Could you imagine a more accessible related problem?
" "Understand the problem" is often neglected as being obvious and is not even mentioned in many mathematics classes.
This step is usually easier than devising the plan.
In general, all you need is care and patience, given that you have the necessary skills. If it continues not to work, discard it and choose another.
A teacher should support students with devising their own plan with a question method that goes from the most general questions to more particular questions, with the goal that the last step to having a plan is made by the student.
He maintains that just showing students a plan, no matter how good it is, does not help them.
How will your students pull all of it together to answer the final question?
I am thinking of 2 numbers with a sum of 12 and a difference of 2.