## Solving Word Problems

##### Pre-kindergarten

##### Kindergarten through 2nd grade

At the end of 2nd grade, Tiffany should be able to solve this problem:

I am thinking of a number. My number has 3 digits. It is between 110 and 130. The sum of its digits is 9. My number is even. What is my number?

##### 3rd grade through 5th grade

The Common Core State Standards for Mathematics states that teachers (and parents) should seek to develop basic mathematical practices in each student. These practices rest on important “process and proficiencies” in mathematical education. These practices are as follows:

Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision Look for and make use of structure. Look for and express regularity in repeated reasoning. At the end of 5th grade, Tiffany should be able to solve this problem:

When she arrived at the airport, Kerry checked her watch. She noted that she had one hour to wait until her scheduled flight time. As soon as she looked at her watch, she heard an announcement that her flight would be delayed by two hours. Later, an additional one and one half hour delay was announced. Kerry’s plane finally took off at 9:00 pm. At what time had Kerry arrived at the airport?

##### 6th grade through 8th grade

So that Tiffany does not have to endure that same trying experience, it is crucial that her math education focus on allowing her the room to find the solutions to complex math problems on her own. This may be the most important time in Tiffany’s math education, since the math found in many careers is the math learned in an 8th grade curriculum. With a strong foundation in necessary algorithms and complex problem solving, Tiffany will have the skills she needs to advance and succeed, not only in math, but in every aspect of her life. As Rusczyk says,

Problem solving is crucial in mathematics education because it transcends mathematics. By developing problem solving skills, we learn not only how to tackle math problems, but also how to logically work our way through any problems we may face. The memorizer can only solve problems he has encountered already, but the problem solver can solve problems she’s never seen before. (https://www.artofproblemsolving.com/Resources/articles.php?page=problemsolving)

At the end of 8th grade, Tiffany should be able to solve this problem:

Ashrita Furman, who holds 19 Guinness World Records, walked 80.96 miles in about 24 hours carrying a bottle of milk on his head. He also bounced about 23 miles on a pogo stick in 12.5 hours. What is the difference in rate per hour in these two feats?