Problem Solving: Remainders in Division

Top of the Morning to You!

This problem challenges students to identify the 100th and 1000th letter that will be printed on the electronic signboard. To solve this, students will grapple with a division problem, figuring out how many letters are in the message and how many times the message will repeat to identify the 100th letter.  This is a good introductory problem because there are no remainders, making this a straightforward division problem. Nonetheless, students must explain their thinking and the process they used to solve the problem, so it's effective practice for state testing.

•  Download the  Top of the Morning problem set with possible solution.

Problem Solving: Remainders in Division

Snow Day Signboard and School Closed Signboard encourage students to look for patterns in repeating letters to figure out which letter will be the 100th letter to be repeated on the signboard.   Students may use division and remainders, skip counting or repeated addition to solve the problems, making them accessible to students in many grades.

Each problem includes a challenge to extend the problem-solving experience and a possible solution. 

• Download Snow Day Signboard.
• Download School Closed Signboard.

Pumpkin Problem Solving

Take advantage of the seasonal preoccupation with pumpkins to include some problem solving activities.  These seasonal activities include the student handout and a detailed possible solution, both in PDF format for easy downloading and printing.

• Pascal's Pumpkins is an activity from the Rutger's Discrete Math collection, revised by Mathwire, that challenges students to analyze the patterns in order to complete the array. The file contains the student handout as well as an explanation of the different patterns students may find and the solution.
• Pumpkin Picking challenges students to solve a pattern problem. The solution provided details how students might use a table to organize the data and easily identify the correct answer to this problem.
• Pumpkin Farm is a sneaky way to get students to analyze the meaning of remainders in long division. Students must figure out which character will be the 100th to be printed on a neon signboard. The file contains the student handout as well as a detailed possible solution.
• Jack-o-Lantern Combinations challenges students to figure out how many different pumpkins may be made, given the assortment of eyes, noses and mouths. This problem provides an opportunity to expose students to the concept of orderly counting where they exhaust all possibilities for one component before moving to the next, so that they exhaust all possibilities without duplication.

Be sure to check out more fall math activities on Mathwire.com.