Counting

Pre - Requisite
Standard / 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems.
7.EE.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
CC Lesson / Lesson 7.4.18
Student Learning Goal /
  • Students solve counting problems related to computing percents.

Media
HW / #94
Spiral Review #25
WKSP

You are about to switch out your books from your locker but forget the order of your locker combination. You know that your locker combination has a 2, 5, and 7 in some order. What is the percent of locker combinations that start with 2?

Possibilities

Exercise

1. / All of the 3-letter passwords that can be formed using the letters ‘A’ and ‘B’ are as follows: AAA BAA
AABBAB
ABABBA
ABBBBB
What percent of passwords contain:
  1. no A’s:b. exactly one A:c. exactly two A’s:
  1. three A’s:e. at least two B’s:f. the same number of A’s B’s:

2. / Fridays are selected to show Jane’s school pride. The colors of Jane’s school are orange, blue, and white. Jane can show her spirit by earing a top, a bottom, and an accessory with the colors of her school. During lunch, 11 students are chosen to play for a prize on stage. The table charts what the students wore:

What is the percent of outfits that are one color?
What is the percent of outfits that include orange accessories?
3. / Look at the 36 points on the coordinate plane with whole number coordinates between 1 and 6:

a. What percent of the 36 points have a coordinate sum of 7?
b. What percent of the 36 points have a coordinate sum of 5 or less?
c. What percent of the 36 points have a coordinate sum of 4 or 10?

Name: ______Date: ______

Pre-AlgebraExit Ticket

Using three different keys on a piano, a songwriter makes the beginning of his melody with three notes, C, E and G:

CCC
CCE
CCG
CEE
CEG
CGC
CGE / ECC
ECG
EEC
EEE
EGC
EGE
EGG / GCE
GCG
GEC
GEE
GEG
GGE
GGG
  1. From the list above, what is the percent of melodies with all three notes that are different?
  1. From the list above, what is the percent of melodies that have three of the same notes?

Name: ______Date: ______

Pre-AlgebraExit Ticket

Using three different keys on a piano, a songwriter makes the beginning of his melody with three notes, C, E and G:

CCC
CCE
CCG
CEE
CEG
CGC
CGE / ECC
ECG
EEC
EEE
EGC
EGE
EGG / GCE
GCG
GEC
GEE
GEG
GGE
GGG
  1. From the list above, what is the percent of melodies with all three notes that are different?
  1. From the list above, what is the percent of melodies that have three of the same notes?


Name: ______Date: _____

Pre-AlgebraHW #94

1. / Ina a set of 3-letter passwords, 40% of the passwords contain the letter B and two of another. Which of the two sets below meet the criteria? Explain (use words) how you arrived at your answer.

2. / There are a van and a bus transporting students on a student camping trip. Arriving at the site, there are 3 parking spots. Let v represent the van and b represent the bus. The chart shows the different ways the vehicles can park.
In what percent of the arrangements are the vehicles separated by an empty parking space?
In what percent of the arrangements are the vehicles parked next to each other?
In what percent of arrangements does the left or right parking space remain vacant?

over

Review:

3. / Ms. Graves gave her class 12 minutes to read. Carrie read pages in that time. At what rate, in pages per hour, did Carrie read?
a. 1b. 22c. d. 66
4. / The relationship between the length of one side of a square, x, and the perimeter of the square, y, can be represented in anxy-plane by a straight line. Which of the points with coordinates (x, y) lie on the line?
a. (2, 6)b. (2, 8)c. (6, 2)d. (8, 2)