Numbers and Algebra - Patterns and Algebra - Quiz 10

In Anytown ISD, 13 out of every 20 students ride the bus. Which ratio compares the number or students who ride the bus to those who do not?

13:7 This is the ratio that compares riders to non-riders. 13 out of 20 ride the bus. This means that the complement of this relationship, those who do not ride the bus, is 20 - 13 = 7. So, the ratio of those who ride the bus to those who do not ride the bus is 13:7. When writing ratios, remember that order is important and matters. 13:7 is not the same as 7:13.

If the pattern below is continued, how many blocks will be in the 7th term?

36 The first model is made with three blocks, 1 in column 1, and 2 in column 2; the second term is made of 1 block in column 1, 2 blocks in column 2, and 3 blocks in column 3. So, term #1 = 1 + 2 blocks; term #2 = 1 + 2 + 3 blocks; term #3 = 1 + 2 + 3 + 4 blocks. Each term, n, is the sum of the numbers from 1 to (n + 1); the sum of the consecutive integers from 1 to (n + 1). So, the 7th term would be: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 or 36 blocks. This is a small enough number that you could actually sketch the model and count the blocks.

Mrs. Fields' science class takes care of a plant at school. The class is responsible for watering the plant and measuring its growth. The students' measurements are charted in the table. Number of Months (m) Height of the Plant (h) in inches 1 8 2 13 3 18 4 23 Which of the following equations relates the height of the plant, h, and the number of months, m, assuming a constant rate of growth?

5m + 3 = h The difference between the growth of each month is 5 inches; looking at the growth of each month, the plant's height increases 5 inches each month. If the rate of growth is constant, then the beginning height of the plant is 3 inches; the height at the first month (8 inches) minus the growth of that month (5 inches) would equal 3 inches. If the growth of each month is 5 inches, then one can find the height of the plant by the growth of each month (5 inches) multiplied by the month (m) and then add 3 inches to account for the initial height. 5m + 3 = h.

Anthony sold x boxes of popcorn for $6.00 per box for his Cub Scout troop. Which expression will help him determine the amount of money he earned for his troop?

6x He needs to multiply the number of boxes by the cost of each box to determine the total earned.

John's car can drive 50 miles per gallon of gas, he wants to take a trip that is 750 miles. Gas currently costs $3.45 per gallon. He drives an average of 60 miles per hour during the trip. Which of the following expressions can solve for how many gallons of gas must he purchase for the trip?

750 \div÷ 50 750 \div÷ 50 represents the 750 miles traveled divided by the 50 miles per gallon his car can travel. The answer would provide the number of gallons needed.

Mrs. Dobbs is teaching students to skip-count by 2s, 5s, and 10s in her second-grade class. Earlier in the year, she evaluated her students learning style and assigns them one task based on this evaluation. Visual learners have been given a number line and they are to draw the hops across the top. Auditory learners have been given a list of the even number to 20, numbers divisible by 5 to 50 and numbers ending in 0 up to 100. They are told to say them over and over aloud to memorize the skips. Kinesthetic learners have been given a large number line on the floor. They are jumping to the next number as they skip-count. What can Mrs. Dobbs do to improve her teaching?

Allow all students to participate in all three activities by rotating through them. This encourages students to exercise different parts of their brain and strengthen different learning styles.

Peter babysits in the evenings for neighborhood children. He charges a flat rate of $12 per evening plus $7 for each hour he sits. If E represents his total earnings for an evening of babysitting and t is the number of hours that Peter babysits that evening, which of the following equations represent the relationship between the amount of time he babysits and his total earnings?

E=7t+12 Multiply $7 by the number of hours Peter babysits and add the $12 additional flat rate. The number of hours is represented by t and his earnings are represented by E=7t + 12E=7t+12.

What type of sequence is the following number sequence? 4, 12, 20, 28, 36, 44...

It is an arithmetic sequence; you add 8 every time to get the next term. Arithmetic sequences have a common difference. This sequence has a common difference of 8 (12-4=8; 30-12=8; 28-20=8;36-28=8; 44-36=8).

A student-athlete can run 10 yards in 6 seconds. Which equation shows the number of yards that can be run in s seconds?

s/0.6 If 10 yards can be run in 6 seconds, 1 yard can be run in 0.6 seconds. Therefore, the total number of seconds divided by 0.6 will give the number of yards run.

Which of the following equations satisfies the data table? x y -1 1 0 0 2 4

y = x2 This equation works for all sets of numbers. 1 = (-1)2 = 1 0 = (0)2 = 0 4 = (2)2 = 4