Mai, Clare, and Noah are making signs to advertise the school dance. It takes Mai 6 minutes to complete a sign, it takes Clare 8 minutes to complete a sign, and it takes Noah 5 minutes to complete a sign. They keep working at the same rate for a half hour.

1. Will Mai and Clare complete a sign at the same time? Explain your reasoning.

2. Will Mai and Noah complete a sign at the same time? Explain your reasoning.

3. Will Clare and Noah complete a sign at the same time? Explain your reasoning.

4. Will all three students complete a sign at the same time? Explain your reasoning

Diego has 48 purple beads, 64 blue beads, and 100 orange beads to make a bracelet. He wants to make bracelets that have all three colors and the same number of each color per bracelet.

1. How many bracelets can he make without having any beads left over?
2. Find another solution to this problem.

1. Find the product of 12 and 8.

2. Find the greatest common factor of 12 and 8.

3. Find the least common multiple of 12 and 8.

4. Find the product of the greatest common factor and the least common multiple of 12 and 8.

5. What do you notice about the answers to question 1 and question 4?
6. Choose 2 other numbers, and repeat the previous steps. Do you get the same results?

1. Given the point \((5.5, \text-4)\), name a second point so that the two points form a vertical segment. What is the length of the segment?
2. Given the point \((3, 3.5)\), name a second point so that the two points form a horizontal segment. What is the length of the segment?

Find the value of each expression mentally.

1. \(\frac12\boldcdot 37-\frac12 \boldcdot 7\)
2. \(3.5\boldcdot 40+3.5\boldcdot 60\)
3. \(999\boldcdot 5\)