For this warm up I review measuring in centimeters and millimeters since this is necessary for the concept development of this lesson
Each student measures the length of their pencil to the nearest centimeter and to the nearest millimeter. I model measuring a pencil to the nearest centimeter and millimeter under the document camera and emphasize being precise and accurate in my measurements. CCSS Math Practice Standard 6 is all about precision. Students must calculate accurately and efficiently and express numerical answers with a degree of precision appropriate for the problem context.
I begin this lesson by giving each student a bead plan sheet and a long piece of string. Their first task is to work with their learning partner and measure their wrist in millimeters. This is easily accomplished by wrapping a piece of string around the wrist, cutting the string, then measuring it with a ruler. I modeled on my wrist to show why students wouldn't want to make the string too tight or too loose. Then I modeled adding 30 millimeters onto the wrist length to accommodate for the beads and allowing room to tie the ends together. (I am using thread for these bracelets. You could use stretchy bands/string or more specific jewelery wire. For this projects bead cost, I decided thread would work just as well)
Students then record their wrist or bracelet length information on their bead plan worksheets. Next, I tell students they have three colors of beads to choose from. Using three colors, they need to decide on a pattern. I tell them all the colors I have; red, yellow, orange, white, clear, black, purple, green, blue, teal, pink, dark pink, and brown.
I then allow students to plan their patterns and to test patterns they like by using crayons and the back of their worksheet. I try to limit this time to about 7 minutes in order to continue planning the bracelet. When students have chosen the pattern they wish to work with they record that on their bead planning sheet. (ie. AABC, ABC, ABBC, AABBC, etc)
Then, together using the document camera so we can enlarge the bead as big as I can, we determine the width of one bead. I chose to use the document camera and a whole class activity because I want to stress the importance of being precise. I remind student that if we were working with gold or silver, being precise would be really important because of their monetary value. Jewelery makers wouldn't want to lose money, so being precise is an important skill. When the bead is zoomed in on next to a millimeter side of the ruler, it's easy to see that each bead is 8 millimeters wide. Before I zoomed in, students were quick to say that they bead was 5 millimeters. They were surprised that when we took our time, found an appropriate magnification tool, the bead was actually 8 millimeters. I remind them that as mathematicians, it is important we are precise in communicating our information.
Once we discovered the bead was 8 millimeters wide, I ask students what the length of their pattern would be. Many students understood right away that they could multiply 8 with the number of beads in their pattern to get the total length of the pattern. A few students had trouble understanding that their was enough information to answer that question. They were sure they would have to build it and then measure. I guided their thinking by asking questions like this:
Would someone who builds houses know how long the wall was going to be before they built it? How would they know that? Would a jeweler order some gold and then measure how much he/she had, or would she/he determine how much gold was needed for the project? If I gave you a pile of blocks and asked you to stack them up, could you figure out the height before you made the tower?
Then, the next question on the bead sheet asks students how many times their pattern will repeat for the bracelet. This is where more students became less sure of what to do. Since students were sitting in their table groups, peer learning was happening at several tables in the room. For students that were struggling, I modeled how I would draw what was happening. Most students understood that to figure out the number of times their pattern would be repeated they had to take their pattern length times some number that would equal or come close to equaling their bracelet length. I wrote an equation on the board to model the situation. I modeled an equation for an ABC pattern with a bracelet length of 162 mm. 24 x r = 162
Next, some students calculated how many beads they would need for the entire bracelet. Many students did not reach this step.
I collected the bead planning sheets so we can continue with the project tomorrow.
This video shows a student trying to determine how many times his pattern will repeat on the bracelet.