Domino Problem Solving

Students will have to really think about dominoes as they solve Garage Sale Dominoes.  A sample solution using an orderly list is included in the pdf file.


After students have solved Garage Sale Dominoes, challenge them to solve More Garage Sale Dominoes in which they must figure out how many different dominoes there are in a complete double-nine set.  A sample solution using an orderly list is included in the pdf file.

Enrichment on the Internet:

• Challenge students to solve Math Forum's Domino Activities.
• Amaze students with your psychic abilities using the Domino Trick.
• Challenge students to solve the Domino Maze from Games magazine.
• Check out examples of Domino Artwork.

Hundred Board Logic Problems

These original Mathwire Hundred Board Logic problems are designed to help students use a hundred board to solve problems.  Students read each clue, then eliminate numbers on the hundred board that do not fit the clue.  After reading through all clues, students should be left with only one solution.  They should check their solution by rereading each clue to be sure their solution fits.  These problems were field-tested in Grades 3-8 classrooms and students loved the experience because the step-by-step process enabled them to be successful at solving these problems.

Enrichment:  After students have solved several of these problems, they may be challenged to create their own original problems.  Provide blank 100 board and logic problem templates.  Students should start by circling their target solution.  They then write clues that will eliminate all other numbers.  Finally, students should exchange problems and use peer review to edit their problems, clarifying and modifying clues to eliminate any confusion.

Creating original problems is a higher-order thinking skill (Synthesis on Bloom's Taxonomy) that extends students' problem solving ability and requires flexible thinking about mathematical concepts, skills and vocabulary terms.  Student-created problems may be added to the classroom math center and used on game days as a problem-solving center.  Additionally, these problems may be used in the initial lesson in subsequent years.  Consider publishing the problems with the author's name and copyright year.  Students love seeing their names in print!

Materials:

• Read more about Hundred Board Logic Problems including classroom management suggestions and ideas for a cooperative learning lesson.  The discussion includes PDF documents for all problems and templates needed for this lesson.

Two of Everything

Use the book Two of Everything to introduce students to the doubling pattern.  Students will enjoy the story and predict what will happen each time something is put into the magic pot.

Make the math connection even more concrete by using a pot and linking cubes to illustrate the story.  Students may use a Magic Pot Workmat to record the input and output, then write a rule.

Extension:  Extend the activity by using the magic pot and simple rules to create data sets.  Students should guess the rule by giving an input number and telling the output that would result.  By not stating the rule, students provide more time for other class members to generalize the rule.  Each guess simply provides another data set for students to enter in their table.

Enrichment:  After reading Two of Everything, challenge students to solve NCTM's 5 Coins problem:  Would you rather have 1000 coins or 5 coins and a Magic Doubling Pot that works 10 times?  Students might work in pairs and use in/out charts to record their solutions.

Game Day

Many teachers have instituted a weekly game day. On this day, students rotate in small groups through various math centers. Students play games, practice math facts, finish up projects, meet with the teacher, or work on enrichment activities. A simple work chart and a timer are all that are needed to keep the activities rolling.

Teachers who plan this day find that they are better able to differentiate instruction to meet both the need for reteaching and the need for enrichment. While students play games to practice math facts or math skills (e.g. place value), the teacher is free to meet with small groups of students to reteach a concept/skill, provide additional guided practice, conduct oral assessment, introduce problem solving tasks or provide enrichment to more talented students. Each group may rotate to the teacher station for varied purposes.

While at first, it may seem tough to carve out this time in an already demanding schedule, teachers find that it is incredibly successful and very effective in keeping the class on the pacing schedule. This day provides dedicated time to meet varied needs, catch up on workbook correction, practice open-ended problem solving skills and/or conduct one-on-one or small group oral assessment. Grade level teams may coordinate to effectively plan activities for these weekly sessions.

Read more about setting up a Game Day on Mathwire: http://www.mathwire.com/archives/june09.html
Try it -- you just might like the practice!