Ms. Morales has a bag of beads.
• She gives Elena 5 beads.
• She gives Damian 8 more beads than Elena.
• She gives Trish 4 times as many beads as Damian.
Ms. Morales has 10 beads left in the bag.
Part A: How many beads did Damian and Trish each receive? Show or explain how you arrived at each answer.
Part B: How many beads were in Ms. Morales' bag before any beads were given to students?
Mr. Ruiz is starting a marching band at his school. He first does research and finds the following data about other local marching bands:
Number of brass instrument players: 123 (Band 1), 42 (Band 2), 150 (Band 3)
Number of percussion instrument players: 41 (Band 1), 14 (Band 2), 50 (band 3)
Part A: Mr. Ruiz realizes that there are how many brass instrument player(s) per percussion player?
Part B: Mr. Ruiz has 210 students who are interested in joining the marching band. He decides to have 80 percent of the band be made up of percussion and brass instruments. Use the unit rate you found in Part A to determine how many students should play brass instruments. Show or explain all your steps.
On Friday, three friends shared how much they read during the week.
• Barbara read the first 100 pages from a 320-page book in the last four days.
• Colleen read the first 54 pages from a 260-page book in the last three days.
• Nancy read the first 160 pages from a 480-page book in the last five days.
Part A: A person's average reading rate can be defined as the number of pages read divided by the number of days. Place three friends' reading rates in order from greatest to least by clicking on the names and dragging them to the appropriate boxes. Greatest rate (pages per day). Least rate (pages per day).
Part B: If the three friends continue to read every day at their rates, who will finish reading her book first? Second? Third?
Order the friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book. Click on the names and drag them to the appropriate boxes.Source: Partnership for Assessment of Readiness for College and Careers
Algebra I/Math II sample question
Michelle wanted to investigate the effect on the vertex of the graph of f(x)=xB+6x when f(x) is replaced by f(x+k). Michelle graphed functions of the form f(x+k) for k=1,2,3 and 4. For each of the functions she graphed, the x-coordinate of the vertex was negative and different for each value of k, but the y-coordinate of the vertex was the same for each value of k. Michelle made three conjectures based on her results.
1. The x-coordinate of the vertex depends on the value of k.
2. The x-coordinate of the vertex is negative for all values of k.
3. The y-coordinate of the vertex is independent of the value of k.
Determine if each of Michelle's three conjectures are true. Justify each answer.
Elena had 5 beads so Damian has 5+8=13 beads. Trish has 4x13=52. Altogether, there are 5+13+52=70 beads. I know that 80 is 10 more than 70, so there were 80 total beads.
Part A: 3
Part B: Explains or shows how to use the 80 percent. Explains or shows how to use the 3:1 ratio. Provides answer of 126.
Part A: Nancy (160/5= 32 pages per day); Barbara (100/4= 25 pages per day); Colleen (54/3= 18 pages per day)
Part B: Barbara (320−100/25= 8.8 days); Nancy (480−160/32= 10.0 days); Colleen (260−54/18= 11.4 days)
Algebra I/Math II
Students will earn one reasoning point for an adequate proof that conjecture 1 is correct. For example: As k increases, the vertex moves so I know that the x coordinate of the vertex will change as I change k.
Students will earn one reasoning point for an adequate proof that conjecture 2 is incorrect. For example: I figured that when k is much less than 1, then the vertex would be positive. I solved used k= -5 and found that f(x-5)=xB-4x-5=(x-2)B-9, and the vertex is at (2,-9).
For example: f(x+k)=(x-(-k-3))B-9. Therefore, when -k-3>0, i.e., when k<-3, the x-coordinate of the vertex is -k-3, which is positive. Students will earn one reasoning point for an adequate algebraic proof based on completing the square that conjecture 3 is correct