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Use inductive reasoning to predict the next three numbers or figures in the pattern.

3, 8, 13, 18, …

Use inductive reasoning to predict the next three numbers or figures in the pattern.

28, 25, 22, 19, …

Use inductive reasoning to predict the next three numbers or figures in the pattern.

4, -8, 16, -32,…

Use inductive reasoning to predict the next three numbers or figures in the pattern.

5, 7, 10, 14, 19,. . . 

Use inductive reasoning to predict the next three numbers or figures in the pattern.

25, 24, 22, 19, 15,. . . 

Use inductive reasoning to predict the next three numbers or figures in the pattern.

6, 3, 3/2, 3/4 , . . . 

Use inductive reasoning to predict the next three numbers or figures in the pattern.

Use inductive reasoning to predict the next three numbers or figures in the pattern.

Examine the grid above and to the right for a pattern and then select the answer which completes the pattern. (Hint: Think about rotating groups of four squares at a time.)

Pick any number and multiply the number by 10. Add 5 to the product. Divide the sum by 5. Subtract 1 from the quotient. 

(a) What is the relationship between the number you started with and the final number?

(b) Arbitrarily select some different numbers and repeat the process. Record the original number and the results.

(c) Make a conjecture about the original number and the final number. The final number is twice the original number.

(d) Prove, using deductive reasoning, the conjecture you made in part (c)

Pick any number between 1 and 20. Add 5 to the number. Multiply the sum by 6. Subtract 12 from the product. Divide the difference by 2. Divide the quotient by 3. Subtract the number you started with from the quotient. What is your answer? Try this process with a different number. Make a conjecture as to what your final answer will always be.

Find a counterexample to the statement “The sum of two squares is an even number."

Estimate the answer. 

205, 123  x 4002

Estimate the answer. 

215.9 + 128.752 + 3.6 + 861 + 792

Estimate the answer. 

21% of 2095

Estimate the answer. 

Cost Estimate the cost of 48 decorative bricks if one brick costs $3.97.

Estimate the answer.

Estimate the sales tax on a boat that costs $21,000 if the sales tax rate is 8%.

Estimate the answer. 

Estimate your average walking speed in miles per hour if you walked 1.1 mi in 22 min.

Estimate the answer. 

Estimate the total cost of six grocery items that cost $2.49, $0.79, $1.89, $0.10, $2.19, and $6.75.

Estimate the answer. 

The scale of the map is 1/4 = 0.11 mi. Estimate the distance of the walking path indicated in red.

Refer to the following graph, which illustrates the number of registered nurses (RNs) needed (demand) and the number of RNs available (supply) from 2000 to 2014. The graph also illustrates the projected number of RNs needed and the projected number of RNs available from 2015 to 2020.


Estimate the difference in the number of RNs needed and the number of RNs available in 2014

Estimate the difference in the projected number of RNs needed and the projected number of RNs available in 2020.


Refer to the following graph, which illustrates the number of registered nurses (RNs) needed (demand) and the number of RNs available (supply) from 2000 to 2014. The graph also illustrates the projected number of RNs needed and the projected number of RNs available from 2015 to 2020.


If each square represents one square unit, estimate the size of the shaded area.

The scale of a model railroad is 1 in. = 12.5 ft.Estimate the size of an actual box car if this drawing is the same size as the model box car.

David can buy a copier from Staples for $500 that prints, copies, and scans. He can either pay the total amount at the time of purchase, or he can agree to pay the store $50 down and $40 a month for 12 months. How much money can he save by paying the total amount at the time of purchase?

A six-pack of bottled water costs $1.99. A case of 4 six-packs costs $4.99. How much will be saved by purchasing the case rather than 4 individual six-packs?

The rental cost of a jet ski from Freemac Marina is $15 for 15 minutes and the cost from Silvan Rental is $25 per half-hour. If you plan to rent the jet ski for 2 hours, which is the better deal and by how much?

Sam and four of his friends want to schedule a 6-hour fishing trip on Lake Ontario with Reel Easy Sport Fishing. The cost for five people is $445. The cost for six people is $510. How much money per person will Sam and each of his friends save if they can find one more friend to go on their fishing trip? Assume that they will split the total cost equally.

Ronaldo needs to apply fertilizer to his lawn on his farm. A 30-pound bag of fertilizer will cover an area of 2500 square feet.

(a) How many pounds of fertilizer are needed to cover an area of 24,000 square feet

(b) If Ronaldo has only 150 pounds of fertilizer, how many square feet can he fertilize?

Most insurance companies reduce premiums by 10% for people under the age of 25 who successfully pass a driver’s education course. A particular driver’s education course costs $60. Patrick, who just turned 18, has auto insurance that costs $1030 per year. By taking the driver’s education course, how much would he save in auto insurance, including the cost of the course, from the age of 18 until the age of 25?

If 1.5 milligrams of a medicine is to be given for 10 lb of body weight, how many milligrams should be given to a child who weighs 52 lb?

Serena’s bank will grant her a mortgage provided the monthly mortgage payments are not greater than 28% of her monthly take-home pay. What is the maximum monthly mortgage payment the bank will grant to Serena if her gross monthly salary is $5500 and her payroll deductions are 30% of her gross monthly salary?

New York City is on eastern standard time, St. Louis is on central standard time (1 hour earlier than  eastern standard time), and Las Vegas is on Pacific  standard time (3 hours earlier than eastern standard time). A flight leaves New York City at 9 a.m.eastern standard time, stops for 50 min in St. Louis, and arrives in Las Vegas at 1:35 p.m.Pacific time. How long is the plane  actually  flying?

The international date line is an imaginary line of longitude (from the North Pole to the South Pole) on Earth’s surface between Japan and Hawaii in the Pacific Ocean. Crossing the line east to west adds a day to the present date. Crossing the line west to east subtracts a day. At 3:00 p.m.on July 25 in Hawaii, what is the time and date in Tokyo, Japan, which is four time zones to the west?

Conversions If 1 mi =1.6 km,

(a) Convert 65 miles per hour to kilometers per hour. 

(b) Convert 90 kilometers per hour to miles per hour.

If the following pattern is continued, how many dots will be in the hundredth figure?

The following magic square uses each number from 6 to 21 exactly once. Complete the magic square by using the unused numbers from 6 through 21 exactly once.

Create a magic square by using the numbers 13, 15, 17, 19, 21, 23, 25, 27, and 29. The sum of the numbers in every row, column, and diagonal must be 63.

A colony of microbes doubles in number every second. A single microbe is placed in a jar, and in an hour the jar is full. When was the jar half full?

Jim has four more brothers than sisters. How many more brothers than sisters does his sister Mary have?

Three friends check into a single room in a motel and pay $10 apiece. The room costs $25 instead of $30, so a clerk is sent to the room to give $5 back. The friends each take back $1, and the clerk is given $2 for his trouble. Now each of the friends paid $9, a total of $27, and the clerk received $2. What happened to the missing dollar?

An average grade of 80 on all exams in a course is needed to earn a B in the course. On her first four exams, Jacqueline’s grades are 93, 88, 81, and 86. What is the minimum grade that Jacqueline can receive on the fifth exam to earn a B in the course?

Could a person have $1.15 worth of change in his pocket and still not be able to give someone change for a dollar bill? If so, what coins might he have?

Volume of a Cube Here is a flat pattern for a cube to be formed by folding. The sides of each square are 6 cm. Find the volume of the cube.

You have 13 coins, which all look alike. Twelve coins weigh exactly the same, but the other one is heavier. You have a pan balance. Tell how to find the heavier coin in just three weighings.

Find the sum of the first 500 counting numbers.

On a balance scale, three green balls balance six blue balls, two yellow balls balance five blue balls, and six blue balls balance four white balls. How many blue balls are needed to balance four green, two yellow, and two white balls?

How many three-digit numbers greater than 100 are palindromes?

Draw the next figure in the pattern

Patterns How many orange tiles will be required to build the sixth figure in this pattern?

Place the numbers 1 through 12 in the 12 circles so that the sum of the numbers in each of the six rows is 26. Use each number from 1 through 12 exactly once.

People stand in a line at movies, the grocery store, and many other places.

(a) In how many ways can two people stand in a line? 

(b) In how many ways can three people stand in a line? 

(c) In how many ways can four people stand in a line? 

(d) In how many ways can five people stand in a line?

(e) Using the results from parts (a) through (d), make a conjecture about the number of ways in which n people can stand in a line.

Use inductive reasoning to determine the next three numbers in the pattern.

2, 8, 14, 20, …

Use inductive reasoning to determine the next three numbers in the pattern.

1, 1/2, 1/3, 1/4, . . . 

Pick any number, multiply the number by 5, and add 10 to the number. Divide the sum by 5. Subtract 1 from the quotient.

(a) What is the relationship between the number you started with and the final answer?

(b) Arbitrarily select some different numbers and repeat the process. Record the original number and the results.

(c) Make a conjecture about the relationship between the original number and the final answer. 

(d) Prove, using deductive reasoning, the conjecture made in part (c).

Estimate the answers.

0.51 x 96,000

Estimate the answers

188,000/0.11

The federal government gives a procedure to determine if a child is overweight. To make this decision, first determine the child’s body mass index (BMI). Then compare the BMI with one of the two charts, one for boys and one for girls, provided by the government. Below, we give the chart for boys up to age 20. To determine a child’s BMI: 

1. Divide the child’s weight (in pounds) by the child’s height (in inches).

2. Divide the results from part 1 by the child’s height again.

3. Multiply the result from part 2 by 703.

Richard is a 14-year-old boy who weighs 130 lb and is 63 in. tall.

(a) Determine his BMI.

(b) Does he appear to be at risk for being overweight, or is he overweight? Explain

The following graph shows the annual sales revenue, in billions of dollars, for Facebook for 2012 and 2013.

(a) Estimate the sales revenue for Facebook for 2013.

(b) Estimate the difference in the sales revenue for Face-book from 2012 to 2013.

A truck costs $35 a day plus 20 cents a mile to rent. If the total cost for a one-day rental is $50.40, how many miles were driven?

At a local store a six-pack of soda costs $2.59 and individual cans cost $0.80. What is the maximum number of cans of soda that can be purchased for $15?

How much time does it take Carla, a carpenter, to cut a 10-ft length of wood into four equal pieces, if each cut takes 2 1/2 min?

In this photo of Sunflowers, an 1889 painting by Vincent van Gogh, 1 in. equals 15.8 in. on the actual painting. Find the dimensions of the actual painting.

Kono gets $12.75 per hour with time and a half for any time over 40 hours per week. If she works a 50-hr week and gets paid $652.25, by how much was she underpaid?

Create a magic square by using the numbers 5, 10, 15, 20, 25, 30, 35, 40, and 45. The sum of the numbers in every row, column, and diagonal must be 75

Mary drove from her home to the beach that is 30 mi from her house. The first 15 mi she drove at 60 mph, and the next 15 mi she drove at 30 mph. Would the trip take more, less, or the same time if she traveled the entire 30 mi at a steady 45 mph?

Three teaspoons equal one tablespoon. A recipe for chili calls for teaspoon of salt for 2 pounds of ground beef. How many tablespoons of salt are needed for 6 pounds of ground beef?

A 10 meter by 12 meter rectangular lawn has a concrete walkway 1 meter wide around the outside of the lawn. What is the area of the walkway?

One guess is off by 9, another guess is off by 17, and yet another guess is off by 31. How many jelly beans are in the jar below?

David wants to purchase nine herb plants. Countryside Nursery has herbs that are on sale at three for $3.99. David has a coupon for 25% off an unlimited number of herb plants at the original price of $1.75 per plant. 

(a) Determine the cost of purchasing nine plants at the sale price.

(b) Determine the cost of purchasing nine plants if the coupon is used. 

(c) Which is the least expensive way to purchase the nine plants, and by how much?

In how many different ways can four letters, A, B, C, D, be arranged?

Estimate the answer. There is no one correct estimate.

86 + 47.2 + 289.8 + 532.4 + 12.8

Estimate the answer. There is no one correct estimate.

197,500/4.063

Estimate the answer. There is no one correct estimate.

1776 x 0.0098

Estimate the answer. There is no one correct estimate.

405/0.049

Estimate the answer. There is no one correct estimate.

0.63 x 1523

Estimate the answer. There is no one correct estimate.

51,608 x 6981


Estimate the answer. There is no one correct estimate.

11% of 8221

Estimate the answer. There is no one correct estimate.

22% of 9116

Estimate the answer. There is no one correct estimate.

296.3/0.0096

Estimate the answer.

The cost of one tire if a set of 4 tires costs $410

Estimate the answer.

The cost of dinner per person if dinner for 8 people costs $210 and they split the bill evenly.

Estimate the answer.

The amount of money Issac spends on fast food in a year if the average amount he spends per month is $47.

Estimate the answer.

The cost of 12 gallons of gas if one gallon costs $3.75.

Estimate the answer.

The cost of 5 items at a grocery store if the items cost $7.99, $4.23, $16.82, $3.51, and $20.12

Estimate the answer.

The cost of 5 items purchased at a hardware store if the items cost $1.29, $6.86, $12.43, $25.62, and $8.99.


Estimate the answer.

The total weight of three people on an elevator if their weights are 95 lb, 127 lb, and 210 lb.

Estimate the answer.

The weight of one pork chop in a package of six pork chops if the weight of the package is 3.25 lb.

Estimate the answer.

A 15% tip on a meal that costs $26.32.

Estimate the answer.

The number of months needed to save $400 if you save $23 each month.

Li’s total monthly expenses consist of room and board: $595; car payment: $289; gas: $120; insurance: $110; and miscellaneous expenses: $230. Estimate Li’s total monthly expenses.

A bag of Turf Builder Sun and Shade Mix grass seed covers an area of 4000 ft2. How many bags are needed to cover an area of 35,000 ft2?

According to the College Board, the average tuition at a public four-year college increased by 2.9% from 2013 to 2014. The average tuition at a public four-year college in 2013 was $8642. Determine the average tuition at a public four-year college in 2014. Round your answer to the nearest dollar.

Another name for the counting numbers is the numbers.


Fill in the blank with an appropriate word, phrase, or symbol(s).

The process of arriving at an approximate answer to a question is called _________.


Fill in the blank with an appropriate word, phrase, or symbol(s).

The symbol ≈ means is approximately ______________________ to.


Fill in the blank with an appropriate word, phrase, or symbol(s).

The scale on a map is 1 inch = 12 miles. How long a distance is a route on the map if it measures 4.25 in.?

Tony, an architect, is designing a new enclosure for the giraffes at a zoo. The scale of his plan is 1 in. = 2.5yd. He draws a 22.4-in. line on the blueprint to represent the northern boundary of the enclosure. What actual distance does this boundary line represent?

At a given time of day, the ratio of the height of an object to the length of its shadow is the same for all objects. If a 3-ft stick in the ground casts a shadow of 1.2 ft, find the height of a tree that casts a shadow that is 15.36 ft.

According to International Data Corporation, the average price of a smartphone decreased by 12.9% from 2012 to 2013. The average price of a smartphone in 2012 was $387. Determine the average price of a smartphone in 2013. Round your answer to the nearest dollar.

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