Candy Bar Math

Used during 6 th grade camp when I have to go but some of my students are left with a substitute in my absence. Original Smart Board versions of the days activities can be made available upon request via email – at

Monday

Purpose: To use a hands-on project to develop a better understanding of area and perimeter of rectangles, square numbers, prime vs. composite numbers, finding factors and making tables and charts. You will have to emphasize these terms throughout the activity of the kids will not realize how much math they are really doing.

Please turn on the overhead projector and click on the icon that says Monday Math and then just touch anywhere on the screen to get it to open the rest of the way.

Warm-up: Using the Smartboard. Please ask the students to list the Base, Height, Area and Perimeter for the two shapes while you take role using the seating chart. We have not officially covered Area and Perimeter but they are listed on a chart hanging up above the Smartboard. Please review the meanings of each with the class if they are needed and then call on students for the answers as you fill in the missing information.

Materials Needed: Rulers and blue ? inch grid sheets (one per student), can be found on the steps at the front of the room.

Launch: Hand each student a blue sheet of 1/2-inch grid paper. Introduce the “Willy Wonka Challenge”: To advance the Smartboard to the next screen, just press the green arrow at the upper left of the screen in the upper toolbar. Please read the following to the class while they read it for themselves from the board: Willy Wonka wants to introduce a new size of candy bar and he would really like you and your partner to come up with as many new sizes as you are able. The Oompa-loompas have been working hard at this and can wrap any size candy bar that you can come up with as long as the opposite sides of the figure are parallel. (Please make the hand motions like you are showing the sides of a rectangle) Which type of figures can we make using those requirements? (Please wait for the answers: squares and rectangles) Looking at your grid sheets what would the smallest new size of candy bar be if you had to follow along the lines? (Please wait for the answer: 1 square) Get them to say how they knew the terms to express the size of the candy bar. What would the biggest candy bar you make be? (130 squares) The sheets are 10 x 13. Again emphasize the terms needed to express size of a rectangle being in “square units”. A prize will be given to the team that is able to create the greatest number of different sized candy bars using just those two sheets of grid squares. You and your partner will want to organize to so that you do not make the same size twice, because I will only count it once, and you will want to start off with the smallest ones you can so that you can make more than if you started off with big ones. Please share: If one partner makes a 1 by 2 and the other partner makes a 2 by 1 – (hold them up) - and ask “aren’t those the same? (Hopefully they will agree that yes they are the same and will only count as one candy bar. (I have 2 jumbo size candy bars each period for the group that comes up with the most by the start of class Friday)

Explore: The students use pencils to outline the different sizes that they will be using. The teacher should roam around monitoring their progress and encouraging the students to work together so as not to copy the work of their partner because that would be a waste of paper and they need as many candy bars as possible. Ask if there are certain ways that the students are organizing the sizes so that they do not duplicate each other’s work.

Practice: After the pencil outlines have been completely created and the students know that theirs are not just copies of their partner’s, please have the students use the scissors to cut out their shapes. I have included paperclips and envelopes to help the kids keep track of small pieces.

I am not sure how fast they will be able to complete this task and have built in some flexibility should the students need more time. For example if it does not look like they will be finished with their drawings, hold off cutting until tomorrow. And skip the next part for now.

Summarize: Towards the end of class, please ask the students to put their candy bars into an organized pattern on their desk. Ask several students what techniques they might be using to help organize there candy bars. Ask the students if they know a quick way to find the size of the candy bar by looking at the base and the height instead of just counting the squares one at a time.

Closure/ Homework: Hand out the worksheet with the words base, height and area on it. For homework they are to use their candy bars to fill in the table as well as they can. Please tell them that they are to fill in only the ones that they or their partner have created and that it is okay if some are left blank for now, that you will not be collecting their work until Friday.

Tuesday

The kids will be eager to have you stamp their agendas to show that they have completed the work from last night, you may even ask a student that did the work correctly if they want to go around and stamp agendas – it would be a big treat for them. Please do not collect any work until Friday. (I only stamp agendas in math)

Warm-up: Please hand out the Candy Bar Table (the one with a bunch of the numbers already filled in) Using the Smartboard please show the first slide of “Tuesday Math” it should a table with the words base, height and area on it. Ask for volunteers to help fill out the first three boxes shown and then tell everyone to complete the rest of the worksheet.

Launch: As you did yesterday, please ask the students to put their candy bars into an organized pattern on their desk. Ask several students what techniques they might be using to help organize there candy bars. This time try to emphasize that some are missing and ask if the students would like to have an extra sheet of blue grid squares so that they could create the ones that are missing. Encourage them to keep thinking about what they still need to make and promise that you will give everyone one more sheet to work with.

Explore: After making your way around to each group as they lay out their organized pattern, hopefully you see several different layouts that will help students see what they are missing – there is no one correct answer to this and all patterns should be encouraged – please ask each group which pattern they see and have them explain it to you as you wander through the room. As they get them all laid out, please have the students put their names on the back of each one. Also have them write the area of each piece on its front as big as will fit.

Practice: Please give each person one more blue sheet so that they can continue to cut out any missing candy bars. They may use the pattern they just created or the lists from yesterday’s homework to help figure out which ones are missing.

Summarize: While the kids clean-up and get their candy bars packed carefully away remind them that if they lose one of their candy bars and another group picks it up the other group can add it to their collection. One more time, remind them to label their candy bars by putting their names on the back and the area of each candy bar on the front.

Closure/ Homework: Finish cutting out and labeling all of your candy bars and make sure to bring them back for class tomorrow.

Wednesday

While the students complete their warm-up, please go around and stamp. Or have a student stamp the kids agendas.

Warm-up: (Written on Smartboard) Get out all of your Candy Bars and quickly lay them out so you can see them all.

Launch: Using the second slide, please demonstrate how the students are supposed to fill in the Candy Bar Math Results Chart (the one with the black dot in the upper left hand corner). Tell the class that you would like to make a list of all the different sizes of candy bars that the class came up with and that you would like the class to work together as one big group to complete this task. Discuss the procedure for filling in the charts. Start by using a red or blue pen to outline a 2 by 1 rectangle starting from the dot in the upper corner as the corner of your rectangle. Ask, “What is the area of this rectangle?” and then write a “2” in the second box to the right. Without erasing, draw another rectangle using a different color but this time make it a 1 by 2 Ask “What is the area of this rectangle?” and then write a “2” in the second box from the top. Demonstrate that the 1 x 2 and the 2 x 1, both give you an area of 2, but they place them in different places and both are okay. Display the same thing using the 3 x 5 and the 5 x 3 this time asking a student to explain the technique. Placing two “15’s”

Explore: Working as one big group, (using pencil) the students must fill in their charts as much as they can using their own candy bars and then they must find other groups that may have the candy bars needed to fill in their missing spots.

Practice: Once the students realize they are filling in a multiplication chart, have the students correct any mistakes that they may have made, and use their multiplication knowledge to complete the rest of the chart.

Summarize: Ask for students to help you fill in the area for rectangles that are 6 x 8, 7 x 8, 7 x 9 and 11 x 12. Even though the students were not able to create a rectangle that was 11 x 12, emphasize that these are the most commonly missed multiplication problems for students their age.

If you get done too quickly – you may want to hand out another blue grid sheet to each student and ask them to go back and create any candy bars that they know they are missing.

If there is time to spare - Quick Multiplication Timed Test I, 3 minutes 10 x 10 chart (AR-13). The students may use their Candy Bar Math Results Chart if they would like.

Closure/ Homework: Finish filling in their Candy Bar Math Results Chart and correct/complete their multiplication timed test.

Thursday

Warm-up: Quick Multiplication Timed Test II (AR-22), please allow 3 minutes. The students may use their Candy Bar Math Results Chart if they would like. Once the 3 minutes is up, please discuss with the class which ones they found most difficult. Write them on the board and have the class repeat them out loud 3-times each. Then have them complete/correct any that they may have missed using the chart on the Smartboard that has been completed already. Have them say “seven times eight is fifty-six”, “seven times eight is fifty-six”, “seven times eight is fifty-six”. I have found that repetition helps some of them remember when it comes up again. After a few second wait, you can then ask “And, what was seven times eight again?”

Launch: Please find the chart paper with many of the “candy bars” already glued into place; a 1 x 1, 1 x 2, 1 x 3, and a 1 x 4 in a straight line along the left side of the chart. It is on the easel that gives the class instructions about staying on task. Ask the students if they can figure out what technique I was using to organize my chart. Allow for a few explanations and then point out that there is a 2 x 2 to the far right side of the 1 x 4. Ask if anyone knows why I put it there. Also ask if they know what Candy bar size (area) and shape would go next.

Explore: Continue pointing out a few more shapes on the chart emphasizing any square figures that come up. After you get to 4 x 4 stop and ask if anyone knows what the next “square number” would be. Discuss techniques for finding square numbers. Have the students make a list of square numbers even though they may not have made an actual candy bar that size. What would the biggest square number have been if I had another grid sheet to cut it from? Stop your lists at that size. (10 x 10)

Looking at the table we have made, lead a discovery of how the numbers were grouped according to their height. See if a student recognizes the grouping as an application of divisibility rules previously covered and guide the discussion towards the prime and composite numbers. Prime numbers will be the ones that are a “1 by”, while the composite numbers will have multiple ways of making them.

Practice: Working with their partners, have students create a list of prime numbers up to 100 using there candy bar math results chart from yesterday and the divisibility rules. (a 100’s chart with the prime numbers in red is at the front of the room)

Summarize: Ask for the student to write their list on the board leaving a space between each number. Ask for other students to review the list and fill in any of the spaces that may be missing a prime, or erase and explain why a number should not be on the list if a composite number has been written.

Closure/ Homework: Make a list of all the composite numbers from 1 – 100

Friday

Warm-up: Quick Multiplication Timed Test III (AR-40), this time please allow 5 minutes. See if the students can do it without using their candy bar results chart. Once the 5 minutes is up, have the students switch papers with a partner and then have the partners circle any incorrect answers. The answers grid is again on the Smartboard. This time when the original person gets their paper back, they have to write out any missed / incorrect problems 3 times each on a lined piece of paper.

The following activities are filler –just in case- and all or most of today may be used as cushion to allow the kids more time to finish anything they may need more time for –Please collect everything towards the end of the class.