# Mathematics   >>   Problem Solving   >>   Elementary

Book Resource—Get It Together

Resource
Get It Together
Erickson, T.
Berkley, CA: Equals Lawrence Hall of Science
1989
This group problem-solving resource is written for students in grades 4-12.
Problem Solving
Get It Together is a supplemental mathematics problem-solving resource that contains a collection of group problem-solving activities. The problems span a wide range of mathematics topics. Students are challenged to use critical thinking and reasoning skills as they work together to arrive at a solution.
Description
The problems presented in Get It Together cover a number of mathematics topics: logic, number, geometry, algebra, probability, measurement, and functions. The problems are organized in “families” and each family of problems either have similar types of solutions, involve a specific subject, or are appropriate for a particular grade level. A topics grid, located at the back of the book, offers an “at a glance” view of the math topics and grade levels that relate to each family of problems. Generally, problems at the beginning of a family are considered easier, and problems towards the end are considered more difficult. Problems in this series are presented in the same format. Every problem has 4 to 6 clue cards written on a single reproducible page. Students begin working on the problems by passing out clue cards to each member of the group. Members take turns reading their own clue to the group, without showing the clue to another member. Since each member’s information is important, the group must work together to solve the problem. Some problems contain a question that has more than one solution. Other problems require the group to answer more than one question, and the questions are distributed among several clues in the given problem.
Appeal and User Friendliness
The wide range of grade levels and topics present good opportunities for differentiation. The teacher notes found at the beginning of each family of problems list key vocabulary and provide wonderful debriefing questions to help stimulate class discussions that focus on student strategies and understandings gleaned from the activities. The comments also provide excellent rationale and background information concerning the mathematical skills and concepts that relate to the problems. Helpful tips for facilitating cooperative groups and assessing student work are also given. It is recommended that teachers attempt the problems before assigning them to students. Teachers may want to limit the group size to two students, rather than four, to encourage full participation from each member in the group.
Sample Problem
Four Kids with Beans, page 30.

Web Resource—AIMS

Varies, 3rd-5th enrichment specifically
Problem Solving
The problems are all different, creative, authentic puzzles. Some are open ended with more than one solution, while others are trick problems requiring divergent thinking that can stump people of all ages. Most problems have a spatial visualization component. The problems are interesting and involve higher order thinking.
Description
This site is organized by the months of the year. Each month displays a new problem and the answer to the puzzles can be found in the following month. To gain access to the solution archive, you must solve a riddle. This prevents people who have not tried the problems from accessing the answers. An example of the riddle is: Which phase of the moon is always in the opposite part of the sky to the sun?

This site is devised for teachers to use. Each problem has a background page with ideas on how the problems can be used in the classrooms with the students. From this page there are links to student worksheets that can be printed out. Previous years puzzles from 1995 to the present are also accessible.
Appeal and User Friendliness
This site is designed for teachers and is not as catchy as others. However, the worksheets that are provided for the children do offer pictures and attractive fonts. This site is very easy to use. The months are each displayed on a puzzle piece and you just have to click on that to access the background and worksheets for the puzzle. You may need Acrobat Adobe to open some materials.

These puzzles are not categorized by subject or grade level. Because of this, it may take time to search for an appropriate puzzle for your students. The puzzles are produced by different authors and thus focus on different types of problem solving.
Sample Problem
TRICK QUESTION. Use divergent thinking.
Juanita’s grandmother is only five years older than her mother is. How is this possible?

OPEN ENDED/CREATIVE PROBLEM
Toothpick Triangle Challenges
Can you make all of the triangles below? If you can’t make one, explain why.

• one equilateral triangle with 6 toothpicks
• two equilateral triangles with 6 toothpicks
• three equilateral triangles with 6 toothpicks
• four equilateral triangles with 6 toothpicks.

Web Resource—Aunty Math

K-5, geared towards grades 2-4 enrichment
Problem Solving
These problems are creative and very attractive to young children. They involve higher order thinking skills and some include extensions to increase the challenge. Most of the problems offer only one solution but include multiple ways to find that solution and also include follow-up questions to increase the challenge.
Description
This site is very effective since it is geared towards students with a problem to try every other week and also has a background link for teachers or parents. It offers problem solving strategies (drawing pictures, looking for patterns, using objects, etc.) and ways that each problem can be modified or extended. One link groups the problems according to the NCTM standards looking at content and process and describes what math topics are involved in each problem. However, the problems are not categorized by grade level.
Appeal and User Friendliness
This site is very attractive, includes pictures and colors and is easy for students to read (Aunty Math talks directly to children). It includes many links to other sites and can be used by children, parents, and teachers. The children can also send their answers directly to Aunty Math on the site and their solutions will be posted with a letter back from Aunty. This is very motivational for students.
Sample Problem
Would you like to know how old I am? Here are some clues:

• I am older than 50 but younger than 60.
• When you add the digits of my age, you get an even number.
• Both the digits in my age are odd.
• When you add the digits in my age you get a 2-digit number with consecutive odd digits.
Website
web.archive.org/web/20081005022248/http://www.dupagechildrensmuseum.org/aunty/index.html (website no longer active) [Aunty Math has Retired. The listed website is an archive form 2008 and before.]

Web Resource—Figure This

Elementary (3-5) enrichment; encourages family participation
Problem Solving
The problems are creative and real world to attract the students’ interests and highlight math applications. Most of the problems have single solutions but pose a variety of challenging questions that are extensions. They also offer hints to get the children thinking in different ways. The development of each problem with extensions and resources is excellent.
Description
Each challenge features:
A description of the important math involved, a note on where the math is used in the real world, a hint to get started, complete solutions, a “Try This” section with additional related problems with answers, excellent extension questions, fun facts related to the math, and resources for further exploration.

The problems are listed in order in which they are added to the site. There is also a math index which categorizes the problems according to the following standards: algebra, geometry, measurement, number, and statistics & probability. Each of these standards is further broken down into subtopics. This is convenient for teachers or parents to follow.

The family corner provides resources and information linking home and school such as good books to read at home that connect mathematics and literature. It is available in English and Spanish.
Appeal and User Friendliness
This site is very attractive for children, easy to use, and has plenty of animation with different creatures and colors. The site has 80 problems that are listed in numerical order. They are not categorized by age level, but are categorized according to topic in the math index. Each month three to four new ones are posted.
Sample Problem
If you started counting your heartbeats at midnight on January 1, 2002, when would you count the millionth beat? How about the billionth beat?

This problem is listed under the Measurement standard, specifically the sub-categories of both estimation and rates & velocity. It is also listed under the Number standard within the large numbers & notation category.

If you had one million drops of water, would you be more likely to drink it, take a bath in it, or swim in it?

Web Resource—Houghton-Mifflin Brainteasers

Middle School 3-4:5-6
Problem Solving
Students are presented with weekly brainteasers. Challenges include visual spatial reasoning, numeric computation, as well as higher-level evaluation.
Description
This site offers varied levels of brainteasers, allowing more advanced students to investigate more challenging questions. Each week (posted on each Wednesday), new sets of brainteasers are added and the previous stored in the archives (only for the last 3 weeks). For each archived problem, a solution is included. The current weekly questions do not supply answers until the following week. These brainteasers come from the mathematical section of the Houghton-Mifflin website. Other subject areas can be explored through the remaining website.

This site is easy to navigate and students can begin to explore problems all on their own without teacher assistance. “Helpful Hints” are provided on each question to aid students in the right direction.
Appeal and User Friendliness
Bright colors and characters make this site great to start with. Questions are varied for ability, allowing advanced students to explore higher-level problems. Answers to the brainteasers are provided a week after a problem is presented. Problems are changed every Wednesday, allowing students to begin working on a new problem throughout the weekend. Only the last 3 weeks of problems are saved in the archives. Problems past 3 weeks are not accessible or printable. This means both students and teachers must check the answers before the question is taken off the website.

Web Resource—Math Forum

Grades 1-4 enrichment. This site also has problems for middle and high school students that may be appropriate for your most advanced students.
Problem Solving
There are a wide variety of problems at this site. They are creative and authentic, attractive to children’s interest, and foster higher order thinking.
Description
This site allows you to pick an age group, content area (based on NCTM standards) and type of story problem and then offers many problems under each one. The site also offers links for teachers such as a rubric for coding the problem difficulty, a chance to read what other teachers say about how they use the problems in their class, and a link to look at student solutions. The students have an opportunity to send solutions to the site and mentors from high school math classes across the country will respond to the solutions and communicate with the students working on the problems. If the problem is solved correctly, the students will be recognized on the site.

The problems of the week are categorized into the areas of elementary, middle, geometry, algebra, discrete math, and trigonometry & calculus. Under these headings they are further broken down into different areas. For elementary there are topics such as algebraic reasoning, patterns, logic, probability and statistics. Under story problems, topics include age, animals, food, travel/geography, holiday, sports, and money. Each problem is also rated on a difficulty level of 1-5 according to the NCTM standards.
Appeal and User Friendliness
This site does not have the “bells and whistles” such as animation and graphics that other sites have but is very well organized and easy to use. The links described above are rarely found in other sites. These are useful for differentiating instruction within the regular classroom and for providing additional challenge to bright students.
Sample Problem
This problem was found under elementary (3-5) algebraic reasoning with a difficulty level of 3.

A man purchased what he thought were 6 barrels of soda, only to find out that one of the barrels contained apple juice. (He loved apple juice!) The barrels held 15 liters, 19 liters, 20 liters, 16 liters, 31 liters, and 18 liters. He sold some of the barrels to Randy and some to Rachel. Randy purchased twice as many liters as Rachel did. Being very fond of apple juice the man kept this barrel for himself.

The problem is to figure out which barrel (in liters) contained the apple juice. Of course the man sold the barrels as he bought them, without taking a drink from any of them, so tasting didn’t help him figure this one out.