4-Square Number Puzzles

Introduction

Students will have fun as they try to solve this challenging paper puzzle! The object is to fold the puzzle so that all four of the same number are displayed in a 4-square. Try to find all eight solutions.

Concepts

• Critical thinking
• Problem solving
• Scientific method

Materials

Safety Precautions

This activity is considered nonhazardous. Please follow all normal laboratory guidelines.

Disposal

The puzzles may be reused for several years.

Prelab Preparation

The first time the cards are used they need to be cut to size and folded.

1. Cut along the bold outline of the square (see Figure 1).
   {12655_Preparation_Figure_1}
2. The puzzle needs to be folded four times in order to form creases creating the “squares.” Fold the puzzle in half horizontally (see Figure 2).
   {12655_Preparation_Figure_2}
3. Keep the puzzle folded, and fold horizontally in half again, so that one row of numbers is displayed (see Figure 3).
   {12655_Preparation_Figure_3}
4. Unfold and flatten the paper back out (see Figure 4).
   {12655_Preparation_Figure_4}
5. Fold the puzzle in half vertically (see Figure 5).
   {12655_Preparation_Figure_5}
6. Keep the puzzle folded, and fold vertically in half again, so that one row of numbers is displayed (see Figure 6).
   {12655_Preparation_Figure_6}
7. Unfold and flatten out the puzzle. At this point the puzzle will have 16 squares on each side of the paper. The side of the card with three black lines should face upward.
8. Fold the puzzle again horizontally along the same crease created in step 2.
9. Cut along the three black lines. Do not cut any further than the end of the black line (see Figure 7).
   {12655_Preparation_Figure_7}
10. Unfold the puzzle. There should be three slits in the center spanning two squares.

Procedure

1. Show students how to maneuver the puzzle and explain that the object of the game is to achieve a 4-square of the same number (there are only four of each number on each card). Folds may only be made on the creases. No new creases can be made.
2. As a general rule, the solutions become harder as the numbers increase. Suggest that students start with 1 and work their way up to 8.
3. To get students started you may wish to show them the solution to the number 1 as an example (see Figures 8–12). The dotted arrows point at the creases to be folded and the solid arrows indicate the direction of the fold (assume that the section is folded behind the puzzle unless it is marked “forward”).
   {12655_Procedure_Figure_8}

Student Worksheet PDF

12655_Student1.pdf

Teacher Tips

• This kit includes a class set of 36, 4-Square Number Puzzles.
• As a time saver, instruct students on the procedure for cutting out and folding the puzzles.
• There may be other possible solutions to the puzzle than those shown.

Sample Data

Solution 2

Solution 7

References

Special thanks to Bob Becker, Kirkwood High School, Kirkwood, MO, for sharing this activity with Flinn Scientific.