Problem Solving in Math

By Darla Milford, Instructional Coach
Running Record, CRC Session with Dr.Nicki Newton

Real World Connection:

Problem solving in math should not be taught separately from the mathematical skills, processes, and understanding.  In fact, according to Dr. Nicki Newton, everything ‘math’, should be attached to the real world with a story attached to it.   In order to intellectually engage our students in math, it is essential we approach problem solving from a real world context with personalization being key.  

On Dr. Newton’s Guided Math Blog, she quotes Bailey saying students “don’t care how many apples
Bob gave to Suzy. They’re much more interested in things like music, video games, movies, trading
cards, money, and friends” (Bailey, 2002, p. 61) so make it personal!!!

Here are some sites with engaging problems ready to use with your own students:

*Greg Tang Math

*South Dakota Counts

*Math Playground Story Math

Cue Words/Keywords

We often fall into the trap of teaching our students to pick out ‘cue words’ or ‘keywords’ within a
problem to figure out the answer.  Some of these words may include ‘how many in all’ referring to
addition or ‘what is the difference’ suggesting subtraction. This strategy is essentially a quick ‘trick’
to help students solve the problem but it is important not to focus entirely on keywords without
considering the contextual information within the problem.  Focusing on words alone takes away
from the mathematical reasoning and understanding that is required in higher level or multi-step
problems students will encounter as they move forward in math.

Here’s an example:

Joe has 8 marbles, which is 2 times more than his brother. How many marbles do they have
altogether?

If kids focus primarily on key mathematical vocabulary, it may lead to a misunderstanding that the
term ‘times’ means that we multiply 8 X 2, when, in fact, if you read the problem in context you will
figure out that you already know that Joe has 8 marbles but you need to figure how many marbles
Joe’s brother had before adding these numbers together to get our answer.

Joe-8 marbles

Brother-½ of Joe’s 8 marbles = 4

So,

8+4=12 marbles altogether

Open-Ended Problem Solving

Dr. Nicki Newton emphasizes that math is best learned in contextual situations and that it is
important to provide opportunities for kids to demonstrate their mathematical understanding through
the use of ‘Open’ word problems.  ‘Open’ word problems are just that, open-ended, with a variety
of questions that could be asked as well as proven.  She suggested using a ‘3 Reads Protocol’
reading strategy to help make the problem more about the math than the reading  component.

Here’s an ‘Open’ problem example using the ‘3 Reads Protocol’ Reading Strategy.

The Smith Family Vacation Problem

The Smith family went on vacation. They drove 201 km on Monday, 177 km on Tuesday and 99 km
on Wednesday.

Write a story problem that includes the information given with an answer that makes sense.

When using this strategy, which can be used for whole group or guided math instruction there are 3
steps:

1. Begin by reading the problem altogether out loud.

     2) Reread the problem altogether again, this time, unpacking the math.

     3) Read the problem a 3rd time and have students create possible problems linked to the  
information and have them figure out the answer.

Here is an interesting article about open-ended questions and the value in having students write their
own problems to increase engagement and metacognition.  

The Answer is 20 Cookies

Dr. Nicki Newton’s authentic approach to teaching math problem solving in real world contexts makes
sense.  When students are connected to their learning and they can see the implications in the world
around them, they become much more invested.  Make sure you check out Dr. Nicki’s blog and if you
have any questions about her material, be in touch with the Instructional Coach in your building!