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Problem solving and word problem resources online

Find here an annotated list of problem solving websites and books, and a list of math contests. There are many fine resources for word problems on the net! have personally checked & reviewed each website, to make sure it is truly useful.

Websites   Books   Contests   Math Projects  

General

Scales Problems
A video lesson that shows the solution to 14 different balance problems, starting from the most simple and advancing to some that have double scales.
www.homeschoolmath.net/teaching/md/scales_problems_video.php

The do's and don'ts of teaching problem solving
Why do most students have so much trouble with word problems? Is the reason related to one-step word problems in math textbooks?
www.homeschoolmath.net/teaching/problem_solving.php

Growth mindset and the value of mistakes in math learning
This article discusses brain plasticity -- or the huge potential for our brains to grow -- which means that EVERY student CAN learn math. Students need to have a growth mindset where they value mistakes and see them as opportunities for brain growth and learning.
www.mathmammoth.com/lessons/value_of_mistakes.php


Problem solving websites

Word Problems for Kids
A great selection of word problems for grades 5-12.  A hint and a complete solution available for each problem.
people.stfx.ca/rtmacdon/mathproblems

Problem Solving Decks from North Carolina Public Schools
Includes a deck of problem cards for grades 1-8, student sheets, and solutions. Many of these problems are best solved with calculators. All of these problems lend themselves to students telling and writing about their thinking.
mathlearnnc.sharpschool.com/cms/One.aspx?portalId=4507283&pageId=5856325

Math Stars Problem Solving Newsletter (grades 1-8)
These newsletters are a fantastic, printable resource for problesm solve and their solutions.
mathlearnnc.sharpschool.com/cms/One.aspx?portalId=4507283&pageId=5856332

Variations of Sudoku from Nrich
Fun, puzzling, and engaging variations on Sudoku. For example, you are given products, differences, equations, ratios, and so on as clues to complete the Sudoku.
nrich.maths.org/public/search.php?search=SUDOKU&page=0

Word Problem Worksheets from DadsWorksheets.com
Very simple, mostly one-operation word problem worksheets for grades 1-4. Some worksheets have problems for two different operations.
www.dadsworksheets.com/v1/Worksheets/Word Problems.html

MathCounts School Handbook
This handbook contains 300 creative problems for grades 6-8. All problems are mapped according to topic, to difficulty level, and to the Common Core State Standards.
mathcounts.org/resources/school-handbook

Enriching Mathematics
Open-ended, rich, and investigative math challenges & activities for all levels.
nrich.maths.org

Maths Problem Solving
A collection of math problems in two levels.
www.mathsproblemsolving.com/

Virtual Math Club
Problem sets & puzzles similar to those found on math contests such as the AMC 8, AMC 10, MATHCOUNTS, or the middle school math olympiads, including answers and video solutions posted a week later. For middle school/early high school level.
virtualmathclub.wordpress.com

Open-Ended Math Problems
Collection of problems that lend themselves to more than one way of solving.
fi.edu/school/math2/

Thinking Blocks
Learn to model or make visual representations of word problems with this interactive program.
www.thinkingblocks.com

Math Circle Presentations
Math circle presentations for grades 6-12 from University of Waterloo and their related student exercises, available as PDF files. These can be used as enrichment, as challenging word problems or as review of certain topics.
cemc.math.uwaterloo.ca/events/mathcircle_presentations.html

Figure This! Math Challenges for Families
Word problems related to real life. They don't always have all the information but you have to estimate and think. For each problem, there is a hint, other related problems, and interesting trivia. Website supported by National Council of Teachers of Mathematics.
www.figurethis.org

Problem Solving Skills tutorial
This is an overview of problem solving skills that you can use to attack problems in many areas of life. Includes tips and ideas such as: ask the right questions, slow down, make sure you're solving the right problem, assessing the situation, and so on.
ryanstutorials.net/problem-solving-skills

Maths Problem Solving
A collection of math problems in two levels.
www.mathsproblemsolving.com/

Learn to Solve Word Problems
A collection of school algebra word problem solvers that solve your problems and help you understand the solutions. All problems are customizable, meaning that you can change all parameters.
www.algebra.com/algebra/homework/word

Math Word Problems for Children - MathStories.com
Over 12,000 interactive and non-interactive NCTM compliant math word problems, available in both English and Spanish. Helps elementary and middle school children boost their math problem solving and critical-thinking skills. Need to pay for membership. 
www.mathstories.com

Massachusetts Tests for Educator Licensure, Mathematics Subtest
This is a downloadable math practice test for prospective elementary school teachers, and it contains a lot of good problems for problem solving practice, mostly in the middle school, some in the high school level.
www.mtel.nesinc.com/PDFs/MA_FLD003_SubtestII_PRACTICE_TEST.pdf

See also:

Math Word Problems Worksheets
Free worksheets from About.com for various grades in PDF form.
math.about.com/od/wordproblem1/

Problem Makeovers by Dan Meyer
Textbook problems that have been changed to be more open and inviting for student exploration.
blog.mrmeyer.com/?cat=104


Primary Grade Challenge Math cover

Primary Grade Challenge Math by Edward Zaccaro

A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.


MathsChallenge.net
Search for number, geometry, probability etc. word problems and challenges. Includes solutions.
mathschallenge.net

Noetic Learning Challenge Math
This is a program with weekly assignemts, designed to hone young students' mathematical problem solving skills and logical reasoning skills. The problems are non-routine problem solving questions that are adapted to many math competitions. Price is about $20 for a semester.
http://www.noetic-learning.com/gifted/index.jsp

Archive for the Handley Math Page Problems of the Week
From 1998 till 2005 - lots of good problems with solutions.
www.pleacher.com/handley/probweek/probarch.html

Best Articles about Solving Word Problems from Let's Play Math
A collection of the best problem solving articles from Let's Play Math blog. Many of these explain and use the bar diagram method also found in Singapore Math books.
letsplaymath.net/2010/05/24/best-articles-about-solving-word-problems

Smart Skies - Distance Rate Time problems
Six Air Traffic Control (ATC) Problems, with downloadable curriculum materials and teacher guide. For grades 5-9.
quest.nasa.gov/projects/smart_skies

Ms. Lindquist: the Tutor
An intelligent tutoring system for algebra for tutoring students in writing expressions for algebra word problems.
www.cs.cmu.edu/~neil



Books


Ratios, Proportions, and Problem Solving
A self-teaching worktext for 6th-7th grades that covers ratios, proportions, aspect ratio, scaling, and includes many lessons on problem solving and the usage of the bar model (Singapore math style). Available both as a download and as a printed copy.
www.mathmammoth.com/ratios_proportions_problem_solving.php


Primary Grade Challenge Math cover Primary Grade Challenge Math by Edward Zaccaro
A very good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.
 
Challenge Math cover Challenge Math For the Elementary and Middle School Student by Edward Zaccaro
Another problem-solving book by Zaccaro, for middle school levels. It contains both lessons and exercises for problem solving with three levels of questions.

Evan-Moore Daily Word Problems, grades 1-6
Browse Amazon's collection of Evan-Moore Daily Word Problem books for grades 1-6, which can be used to supplement any math curriculum. The problems are realistic, often challenging, and cover a good variety of topics for the given grade level.
www.amazon.com

Ray's Arithmetic (free download)
This old arithmetic book bases its instruction on word problems, starting with 1st grade addition and subtraction problems, and advancing through the topics until percentage. One could use it to help children solve word problems, since it starts from the simplest kind of word problems, and gradually advances. Read online or download for free; the links are in the left sidebar.
www.archive.org/details/raysarithmeticse00rayjrich

A Middle School Math Workbook: Pre-Algebra, Algebra I, and Geometry by Qishen Huang
This book contains challenging problems that will help your child gain math skills at an internationally competitive level.
www.amazon.com/gp/product/0981907245

A High School Math Workbook: Algebra, Geometry & Precalculus by Qishen Huang
This book contains challenging problems that will help your child gain math skills at an internationally competitive level.
www.amazon.com/High-School-Math-Workbook-Precalculus/dp/0981907253

 

Contests and similar

"Problem of the Week" (POWs)
Problem of the week contests are excellent for finding challenging problems and for motivation. There exist several:

Mathathlon
Mathlathon is a monthly online math contest for students in grades 3-10. It is free if you have a subscription to Math Buddy; otherwise it costs $9.99 a year. I have checked the free sample contest for grade 6 and liked it really well! The questions are designed to foster intuition and problem solving skills.
www.mathbuddyonline.com/mathlathon

Math League Contests
Get access to a vast online practice area and enroll in the official 2014-2015 Online Math League competitions. Contests are available from grade 2 through algebra. Involves a registration fee.
www.onlinemathleague.com

National Math Bee
Online math tournament in which students in grades one through six compete in any or all of the four basic operations: addition, subtraction, multiplication, and division.
www.nationalmathbee.org

 

Math projects or investigations

Mixing in Math
A list of activities that mix math in to sports, snack time, arts and crafts, playground games etc. Easy to prepare and lead, and free.
mixinginmath.terc.edu

Yummy Math
Quality math activities from real life, organized into categories such as math and social studies, geometry, data and probability, holidays and annual events, food, sports, number sense, etc. Available as PDF and DOC files. The activities are free but answers are available only to subscribers.
www.yummymath.com

Make It Real Learning
Math projects or activitity worksheets of real-life applications, focused on answering the question, "When am I ever going to use this?" Free samples available.
www.mathmammoth.com/worksheets/mirl

MathNotations
A blog with quality math investigations and projects for middle and high school level.
mathnotations.blogspot.com

Math Projects.com (MPJ)
Powerful and innovative math projects, lesson plans, and thought-provoking articles, from pre-algebra through geometry.
www.mathprojects.com

Middle School Math Projects
Quality math projects, spanning from number sense, geometry, statistics, probability, algebra, to special math events. Pricing $7 on up.
www.digitallesson.com

the Math Academy
Downloadable booklets that include hands-on activities about real-life applications of mathematics. Includes probability, fractions & percents, statistics, combinatorics, and patterns & functions.
www.actuarialfoundation.org/programs/youth/math_academy.shtml

Real-Life Math Vol. 1 PDF download
A collection of activities for grades 6-8 of how math is used in real life. All twelve lessons include a teacher's guide that explains how to conduct the activity and a student worksheet that guides the student and poses problems. Price: $9.99. Free example pages included.
makemathmore.com/real-life-math

Math Activities and Games at Education.com
A huge list of free math activities, organized by grade level from kindergarten through high school.
www.education.com/activity/math

Mathwire.com
Innovative and creative board games, activities and worksheets for elementary and middle school math topics.
www.mathwire.com

Hands-on Manipulative Instructions
Print, cut out, and color & glue - various blocks, tiles, graph paper.
mason.gmu.edu/~mmankus/Handson/manipulatives.htm



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