November 2005

Featured Topic: Problem Solving

This Mathwire.com webpage continues to grow with the addition of many open-ended problems that link to Everyday Math units in Grades 3 - 4. These open-ended assessments require students to analyze patterns and explain solutions.

New problems for Grades 5-8 address number patterns in factors and exponents. Thirteen Ways challenges students' spatial sense as they try to find all 13 ways to show 1/2 of the given figure.

Be sure to visit this page often as open-ended problems and links to problem-solving sites are added to the collection.

See Problem Solving webpage for problems and links to problems for students in Grades K-8.
See Fall into Math webpage for fall problems including discrete math topics.
See Winter Math Activities webpage for winter problem solving activities and additional discrete math problems.

New Problems for Grades 3-4:

Download Ants Marching for sample open-ended problem designed to assess student understanding of the concept of multiplication as arrays.
Download Third Grade Parade for another sample open-ended problem that assesses student understanding of the concept of multiplication as arrays.
Download Marathon Training, a pattern problem that encourages students to use an input/output table to organize the data and the solution.
Download Pumpkin Picking, another pattern problem that can be solved using a picture or an input/output table. [Contributed by Shannon Collier, Joseph C. Caruso School, Keansburg, NJ]
Download Baseball Season for a pattern problem that is easily solved using a table of values.
Download Anthony's Allowance for additional pattern practice.

New Problems for Grades 5-8:

Download Bake Sale which requires students to work backward to solve the problem. (Grades 5-8)
Download Monkey Business which also requires students to work backward to figure out how many coconuts there were before each monkey ate one and took a third of what was left. (Grades 5-8)
Download Reading Challenge which requires students to figure out what page a student read last, given only the product of the last two pages. (Grades 5-8)
Download Factor Investigation which challenges students to list all factors of the numbers 1-25 and identify the numbers as abundant, deficient, perfect, prime. Students can refer to this list when playing Factor Blaster or Factor Game. (Grades 5-8)
Download Investigating Exponents which challenges students to identify the different patterns found in the units digits of numbers raised to different powers. (Grades 5-8)
Download Thirteen Ways Recording Sheet so students can record the thirteen ways to shade the diagram to represent 1/2 as found on the PBS Cyberchase website listed on the Recording sheet. (Grades 5-8)

Recent Additions to Mathwire.com

Check the New on Mathwire.com webpage to see what's new on the site.

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Turkey Glyphs

Students in Mrs. Bestle's first grade created turkey glyphs that tell a story about how they celebrate Thanksgiving and what foods they like to eat on that special day.

Online directions for creating a Turkey Glyph
Get more information on the Super Graphs, Venns and Glyphs Resource Book from which the Turkey Glyph activity was taken.
See more examples of glyphs.

Fall into Math

Seasonal Math Activities: Check out the Fall into Math page for these math activities:

Measurement Man is a great hands-on activity as students assemble the pieces which build on student experience with cut-paper fractions. Students are able to visualize the relationship among these different units of capacity as they cut and assemble the figure. Consider adding a pointed cap and some raffia straw to create a field of scarecrows, just perfect for fall.
- Measurement Man Directions
- Pictures of Student Measurement Scarecrows

Pascal's Pumpkins encourages students to look for patterns in Pascal's Triangle. The handout develops awareness of this important mathematical pattern through this timely seasonal activity. Students who take higher math courses will meet Pascal again in many different applications, including probability. This handout is an outgrowth of the Rutgers Discrete Math Institute.
- Download Pascal's Pumpkins problem and answer key.
Use Pascal's Penguins from the Winter Math Activities to revisit this pattern in a winter motif. See the picture below. Two versions are available to download.

Winter Math Activities

Math activities on this Mathwire.com Seasonal Math web page include:

Koch Snowflake
Penguin Math
Snowflake Activities
Snowman Problem Solving
Literature Connections
Winter Glyphs
Winter Data Collection
Gingerbread Math Activities
Winter Coordinate Graphing
Holiday Problem Solving
Student Work: Winter Math Activities

See Winter Math Activities for more details on these activities.

Featured Link: Do You SuDoku?

The Sudoku Puzzles have become very popular with adults. The challenge is to place each of the digits 1-4 or 1-6 or 1-9 in each box within the larger puzzle box so that no digit appears twice in any row or column. The puzzles require logic to reason through the placement of specific digits and the ability to scan the entire puzzle for starting clues. Now teachers can also use this popular format with students, thanks to this SuDoku for Kids website.

Daily SuDoku for Kids presents easier versions of the SuDoku puzzles especially designed for younger students. Each SuDoku is rated as easy, medium or hard so that teachers can select the most appropriate versions for their students. An archive of past SuDoku problems and answers are available and are easily printed for use with students. Consider introducing this problem-solving activity as an enrichment or center activity for interested students. Solving the problems requires logic, methodical approach and persistence.
Download the SuDoku Templates to use as a reusable overhead or place the templates in sheet protectors so that students can use dry erase markers to solve the posted SuDoku problems and then reuse the templates for future problems. Both 4x4 and 6x6 SuDoku problem grids are included so that teachers are able to differentiate problems for students in their classes.

Browse Other Activities on Mathwire.com

Visit this page for links to activities organized by math topics.

Browse Math Topics on Mathwire.com

You can click on the file icon to the left or access this link at the top right of any page on the website.

About Mathwire.com

Mathwire.com is designed to provide activities and appropriate worksheets for teachers to use in their classrooms. All activities and worksheets support the constructivist approach to learning mathematics and the NCTM Standards.

Activities: The activities on this site were developed by Terry Kawas and the teachers in districts where she has worked as a math consultant and coach or with students she has taught in college math-methods courses. The activities are classroom-tested by teachers and appropriate modifications have been made to reflect this field-testing. These activities are posted online in an effort to share quality activities and routines within the mathematics community.

Terms of Use: Teachers are welcome to download any of the activities for free use in their classrooms. No activities may be copied for use on other websites or included in commercial products without permission in writing from Terry Kawas, webmaster. Contact Terry Kawas