A B C D E

Solutions for Session 10, Grades 6-8, Part E

See solutions for Problems: E1 | E2

Problem E1

 a. This problem shows the first three figures of a growing pattern, and requires students to find the number of tiles needed to make the 8th figure in the pattern. b. This problem uses a growing pattern, and the nth term uses n more tiles than the previous term. c. This problem can be used to help students learn to write a general rule for the nth term of a function. d. This problem could be extended to find the number of tiles needed for the 10th, 100th, and then the nth term. Ask students to describe how to build each term. Look for answers that relate each term to the previous term, and then relate the figure to its place in the pattern. For example, students might notice that the 1st term uses 1 tile, the 2nd term uses 1 + 2, or 3 tiles, the 3rd term uses 1 + 2 + 3, or 6 tiles, and so forth. The nth term uses 1 + 2 + 3 + ... + n tiles.

Problem E2

 a. This problem also shows the first three figures of a growing pattern. This problem not only requires students to find the number of dots needed to make the 6th figure in the pattern, however; it also requires students to determine whether it is possible for one of the terms to use 84 dots. b. This problem uses a growing pattern, and the nth term uses 2 more dots than the previous term. c. This problem can be used to help students learn to write a general rule for the nth term of a function. d. This problem asks students to find the number of dots needed for the 100th term, but could be further extended to ask for the number of dots needed for the nth term. Again ask students to describe how to build each term. Look for answers that relate each figure to its place in the pattern. For example, students might notice that the 1st term uses 1 dot + 1 pair of dots, the 2nd term uses 1 dot + 2 pairs of dots, the 3rd term uses 1 dot + 3 pairs of dots, and so forth. The nth term uses 1 dot + n pairs of dots, for a total of 2n + 1 dots.

 Session 10, Grades 6-8: Index | Notes | Solutions | Video