Now that the floor plan design has been decided on, our fictional Rosada family is having their restaurant painted before its grand opening. They have consulted with the painters and know that their budget enables them to use four colors At the initial meeting, the painters brought samples in five colors -red, green, blue, yellow and orange. The Rosadas have asked you what four-color combinations are possible with these five colors. The boys dutifully colored in blocks and figured out that there were five possible combinations.
Now add one more color, purple. How many distinct four-color combinations can be made now?
When I asked this question, James immediately said, "Well, it would by five plus five plus five; fifteen combinations." He did not need to do any paperwork to figure out the solution, but he has always been mathematically minded. By contrast, Quentin, struggled with keeping the colors straight, even using paper to work them out. I showed him that he could keep them straight by using some alternative methods for systematically arranging the colors. I told him, for the four-color combinations, to try recording the first three colors red, green, blue) and then, keeping those three colors constant, record the two possible combinations (red, green, blue, yellow and red, green, blue, orange.) Next, following the same orderly procession, link together the next combinations. He quickly found the five combinations and was able to apply
We talked about the impact of one additional color on the number of combinations.
In a math journal, students can write about what strategies they used to solve this problem, using illustrations, diagrams or charts to illustrate and support the explanations.
- La Tostada Sabrosa
- Money Matters: Tostada Cost Analysis
- Money Matters: Setting Tostada Prices
- Combination Platters: Making Combo Plates