This activity is aligned to NCTM Standards - Grades 6-8: Number and Operations, Problem Solving, Reasoning and Proof, and Communication and to California Mathematics Standards Grade 7: Number Sense #1.2 and Mathematical Reasoning #1.1, 1.2, 2.4, 2.5, 2.6, 2.8, 3.2.

Glencoe's Interactive Mathematics text provides an activity (Units 7-12, p. 17) called "That's Sum Triangle."

Using a manipulative

Each group of 4 students is given two sets of the numbers and the triangle grid manipulative. Instruct the students to cut out the numbers so that they can place them in the triangles to help them figure out how to rearrange the numbers so that the sum of the four numbers in each of the three larger triangles is 46. Each pair of students can manipulate the puzzle as the group considers the answer.

As groups determine their answer, ask them to write down their process. What were they thinking?

Give time for the groups to work through the solution.

As the class discuss the answers use overhead transparencies of the triangle grid and numbers.

Processing the Activity

Assign the following writing prompt:

What discoveries or observations did your group make as you solved this problem?

Technology

The activity that the students have completed has to do with finding an arrangement of numbers that sum to the same number. Magic squares pose the same type of problem. Here is an interactive puzzle the students can try:

Magic Square Java Applet by Mike Morton, Math Forum.

Extensions/Links

Magic Squares
  A complete unit on magic squares.