To solve math problems effectively, here are some step-by-step strategies with examples:
- Draw a model or diagram: Visualizing the problem by drawing can help understand the relationships and make it easier to solve.
- Act it out: For some problems, especially word problems, physically acting out the scenario or using objects helps in understanding the math concept.
- Work backwards: Start from the solution and reverse the operations to find the unknown values, useful for multi-step problems.
- Write a number sentence: Translate the problem into a mathematical equation or expression to solve it.
- Use a formula: Use relevant formulas (e.g., area = length × width) directly when applicable.
Example:
Problem: John and Jivanti together have 45 marbles. Both lost 5 marbles each,
and the product of the marbles they now have is 124. How many marbles did they
have initially? Steps:
- Let John's marbles = xxx
- Jivanti's marbles = 45−x45-x45−x
- After losing 5 each: John's marbles = x−5x-5x−5, Jivanti's = 40−x40-x40−x
- Product equation: (x−5)(40−x)=124(x-5)(40-x)=124(x−5)(40−x)=124
- Expand: 40x−x2−200+5x=12440x-x^2-200+5x=12440x−x2−200+5x=124
- Simplify: −x2+45x−324=0-x^2+45x-324=0−x2+45x−324=0
- Multiply by -1: x2−45x+324=0x^2-45x+324=0x2−45x+324=0
- Factor: (x−36)(x−9)=0(x-36)(x-9)=0(x−36)(x−9)=0
- Solutions: x=36x=36x=36 or x=9x=9x=9
John had 36 marbles, Jivanti had 9 marbles or vice versa.
This combines writing the number sentence and solving the quadratic equation as a method to reach the solution. Similar detailed steps can be applied to various problems.
