Make a Table: Homework

When a problem gets too tangled to do in your head, make a table. Each row is one step, and the pattern shows up on its own.

Part A — Build a Table / 8

Every problem here is made up for practice. Draw a table on scrap paper for each one, label the columns, and fill it in row by row.

1.
You save $3 in week 1, and each week you save $2 more than the week before. How much have you saved in all after 5 weeks?Answer
2.
Five people each shake hands once with every other person. How many handshakes?Answer
3.
A snail at the bottom of a 10 foot well climbs 3 feet each day and slips back 1 foot each night. On which day does it get out?Answer
4.
How many ways can you make exactly 30 cents using only nickels and dimes?Answer
5.
One bacterium splits into two every 20 minutes, and every new one splits too. How many are there after 2 hours?Answer
6.
A bike rental costs $5 plus $2.50 for every hour. Make a table for 1 to 6 hours. What does 6 hours cost?Answer
7.
A theater's first row has 8 seats, and each row after it has 2 more. How many seats are in the first 6 rows?Answer
8.
Which skill? You are told a pizza shop's sales for each month in a finished graph, and asked which month was best. Then you are given a pile of 25 test scores in the order they were handed in and asked how many were above 80. For each, say whether you read a graph (U3-L1) or make a table (U3-L2), and why.Answer

Part B — How Far Away Is the Storm? / 5

Real science. Sound travels about 343 meters each second in air. Light arrives almost instantly, so the seconds between the flash and the thunder tell you the distance.

1.
Make a table with the seconds 1, 2, 3, 4, 5 in one column and how far sound has traveled in meters in the other. Then use it:
a. How far does sound travel in 5 seconds?Answer
b. About how many seconds does sound take to travel one kilometer (1,000 meters)? Extend your table to see.Answer
c. You see lightning and hear thunder 9 seconds later. How far away is the strike?Answer
d. You hear thunder 6 seconds after the flash. Is the storm closer than 2 kilometers?Answer
e. People use a rule: divide the seconds by 3 to get the kilometers. Use the rule for a 12 second gap, then check it against the table rule.Answer

Part C — Critical Thinking / 2

Think it through, then write your answer and one sentence about how you knew.

1.
A table shows step 1 gives 4, step 2 gives 7, step 3 gives 10, step 4 gives 13. Find the rule, then find the value at step 8.Answer
2.
In the snail problem, you stop making the table at day 5. Why is that the right place to stop, and what would go wrong if you kept going?Answer

Part D — Make Up a Problem / 1

Write your own, then solve it yourself.

1.
Write a problem that is easiest to solve by making a table. Then give the first four rows of your table and the answer.Answer

Total / 16

Graded by

Notes

Answer key

Part A — the answer.

$35. The weeks are 3, 5, 7, 9 and 11.
10. The first person has 4 handshakes, the next has 3 new ones, then 2, then 1.
Day 5. After each night it is at 2, 4, 6 and 8, so on day 5 it climbs from 8 to 11 and is out before it can slip.
4 ways: 6 nickels; 1 dime and 4 nickels; 2 dimes and 2 nickels; 3 dimes.
64. The counts are 2, 4, 8, 16, 32 and 64, six splits in two hours.
$20
78. The rows have 8, 10, 12, 14, 16 and 18 seats.
The first is reading a graph (U3-L1), because the data is already drawn and you find the tallest bar. The second is making a table (U3-L2), because the data is a loose list. Sort the scores into groups and count.

Part B — the answers.

a. 1,715 meters b. 3 seconds. In 3 seconds it travels 1,029 meters. c. 3,087 meters d. 2,058 meters, which is just over 2 kilometers, so no, it is not closer than 2 km. e. about 4 km. The exact distance is 343 × 12 = 4,116 meters.

Part C — one correct answer, and what a good explanation says.

25. The values go up by 3 each step, so the rule is 3 × step + 1, and 3 × 8 + 1 = 25.
The snail is out on day 5, so the question is answered. Rows after that would describe a snail that is no longer in the well, and the numbers would mean nothing.

Part D — what a good problem looks like.

Answers vary. A good one grows by a pattern, such as a plant that doubles its leaves every week, with rows 1 leaf, 2, 4, 8, and a question about week 6, which is 32.