Solving Problems
What is Problem Solving?
Problem solving is a critical skill in mathematics and in everyday life. It involves the ability to analyze a situation, identify the problem, develop a plan or strategy to solve it, and then apply the appropriate techniques to arrive at a solution.Steps for Problem Solving:
- Understand the Problem: Read the problem carefully and make sure you understand what is being asked.
- Devise a Plan: Think about the different strategies or methods you could use to solve the problem. This might involve drawing a diagram, making a table, or using algebraic equations.
- Carry Out the Plan: Implement the plan you devised in step 2. Use the appropriate mathematical operations or techniques to work through the problem.
- Check Your Answer: Once you have a solution, go back and check your work to ensure that it is accurate and makes sense in the context of the problem.
Types of Problems:
- Word Problems: These problems require translating a real-world situation into mathematical expressions and equations.
- Number Problems: These problems involve working with numerical quantities and operations.
- Geometry Problems: These problems relate to the properties and measurements of shapes and figures.
- Algebraic Problems: These problems involve using variables and algebraic expressions to solve equations and inequalities.
Study Guide for Solving Problems:
- Practice identifying key information in word problems and translating it into mathematical expressions.
- Review different problem-solving strategies such as drawing diagrams, making tables, using algebraic formulas, and working through step-by-step solutions.
- Work on developing your critical thinking and logical reasoning skills, as these are essential for problem solving.
- Seek out challenging problems and practice solving them to enhance your problem-solving abilities.
- Collaborate with peers and discuss problem-solving approaches to gain different perspectives and insights.
◂Math Worksheets and Study Guides Sixth Grade. Ratio
The resources above cover the following skills:
Number and Operations (NCTM)
Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
Understand and use ratios and proportions to represent quantitative relationships.
Compute fluently and make reasonable estimates.
Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.
Grade 6 Curriculum Focal Points (NCTM)
Number and Operations: Connecting ratio and rate to multiplication and division
Students use simple reasoning about multiplication and division to solve ratio and rate problems (e.g., 'If 5 items cost $3.75 and all items are the same price, then I can find the cost of 12 items by first dividing $3.75 by 5 to find out how much one item costs and then multiplying the cost of a single item by 12'). By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative sizes of quantities, students extend whole number multiplication and division to ratios and rates. Thus, they expand the repertoire of problems that they can solve by using multiplication and division, and they build on their understanding of fractions to understand ratios. Students solve a wide variety of problems involving ratios and rates.