Riddle Card #14 1. We are five numbers. 2. Our mean is 5 ...€¦ · 20 reusable “What numbers are we?” cards that can be easily laminated, cut up, and distributed to students

20 reusable cards that provide a fun method for your students to remember the meaning and usage of the terms “median”, “mode”, “mean”, and “range”. Complete with definitions, examples, and instructions that are sure to make this game a success!

http://www.teacherspayteachers.com/Store/Barry-Schneiderman © Barry Schneiderman, 2013

Riddle Card #14 1. We are five numbers. 2. Our mean is 5. 3. Our mode is 7. 4. Our median is 6. 5. Our range is 6. What numbers are we?

Instructions for the teacher

This product is a must for the beginning of the year (to be reused at any point during the year!) for any

late elementary or middle school classroom. It is the remedy for the “Wait a minute; which one was

the middle number again, mean or median?” scenario later in the school year. The product consists of

20 reusable “What numbers are we?” cards that can be easily laminated, cut up, and distributed to

students to play a who-can-get-the-most-correct-answers game. Also provided are instructions to the

students, the definition of the key words used on the cards, an answer sheet to record answers and any

necessary work, and an answer key for teacher use.

To best utilize the Median, Mode, Mean, Range Riddle Card Challenge, follow the

steps below:

1. Let the students know they will be reviewing some math vocabulary today, and that they will be

doing so by playing a game involving riddles.

2. Review the instructions on page 3 with the students. Go through the different definitions with

them. The amount of time and level of detail you go into with your students regarding these

definitions will depend upon their grade level and their level of knowledge regarding the

terminology.

3. Review the “Practice Riddle Card” (page 4) with the students. Many may be confused as to what

steps to take when they see a riddle card containing several clues, and I have found the review of

the practice card to be very helpful. To do the review, have the students attempt to work out

solutions by projecting the riddle card without the solution (page 4). After letting them work on it

for a few minutes, either walk through the solution on page 5, or talk them through your own steps

to find the solution.

4. Distribute packets of the 20 riddle cards and the answer sheet to the students. I find it best if they

work in pairs on this competition. Let them know the cards get harder and harder as the riddle

numbers increase (some are quite challenging!). Also, to avoid too many quick “guesses”, let

them know that a point will be subtracted for each incorrect answer. Feel free to build enthusiasm

by offering prizes to the winners if you so choose. Finally, let them know we are only dealing with

positive numbers, so all answers are whole numbers greater than zero.

5. Give the students 30 – 45 minutes to work on the solutions to the cards. The most basic version of

the game allows the students to come up with as many answers as possible (with no feedback,

though you may provide hints to all if you so choose) in the allotted time. A variation of the game

involves having the students approach you in teams after they have completed the first five or ten

cards, giving them feedback as to which answers are incorrect, and sending them back to the

drawing board for these. This variation is harder on you, the teacher, but allows the students to

learn from their mistakes.

6. Grade the answer sheets and review key problems with the students as appropriate.

7. Reuse the cards as many times as necessary any time you feel the students may be beginning to

lose their grip on these all-important and often-used math vocabulary words.

Good luck with your use of the Median, Mode, Mean, Range Riddle Card Challenge!

2 http://www.teacherspayteachers.com/Store/Barry-Schneiderman © Barry Schneiderman, 2013

Name:________________ Date: ____________ Class: ___________

Median-Mode-Mean-Range Riddle Card Challenge!!

You will soon receive 20 different “What numbers are we?” riddle cards. Each card will give you several

clues. You will need to use the clues to get the correct answers. Solve as many riddles as you can in the time

given to you. Show any necessary work, then write the correct answers on the answer sheet. The definitions

of the words you will need to know to solve the riddles are given below. One point will be awarded for each

correct answer. One point will be subtracted for each incorrect answer, so make sure you are sure about your

answers before writing them down on the answer sheet. The student or group with the most points wins!

Here come the cards! Be careful! Ready, set, go!

Definitions: 1. Median – The middle number in any set of numbers (after the numbers have been put in increasing

order).

Example: What is the median of 1,5,4,3,2?

To find the median:

a. Write the numbers in order 1,2,3,4,5

b. Cross off one number from each side until reaching the middle number 1,2,3,4,5

The median is 3!

Note 1: If there are two numbers left in the middle, the median is found by adding these two

numbers and dividing by 2.

Note 2: The median can be a fraction or decimal, even if all the numbers in the data set are

whole numbers.

2. Mode – The most common number in any set of numbers.

Example: What is the mode of 4,1,4,3,6?

Answer: There are two 4’s, so the mode is 4!

Note 1: If no number in a set occurs more than once, there is no mode. For example, if the data set

consists of 1,2,3,4,5, there is NO mode.

Note 2: If there is more than one most common number and these numbers occur more than once (for

example: two 4’s and two 6’s), both of these numbers are modes.

3. Mean – The average of the numbers in a set of data. Found by adding all of the numbers and

dividing by the number of numbers.

Example: What is the mean of 1,3,7,9?

To find the mean:

a. Add the numbers: 1 + 3 + 7 + 9 = 20

b. Divide the sum of the numbers by the number of numbers (4) 20 ÷ 4 = 5

The mean is 5!

Note: The mean can be a fraction or a decimal, even if all numbers in the data set are whole numbers.

4. Range – The “span” of the numbers. Found by subtracting the smallest from the largest number.

Example: The range of the data set 4,6,7,9 is 5 because 9 – 4 = 5.

5. Minimum – The smallest number in a data set.

6. Maximum – The largest number in a data set.


Riddle Card 1. We are five numbers. 2.Our mean is 4. 3.Our median is 3. 4.Our mode is 2. 5.Our range is 6. What numbers are we?

“What numbers are we?” Practice Riddle Card


a. Look at the first clue first (“We are five numbers.”) We use this clue by drawing five blanks to represent the five numbers.

b. Looking at the second clue (“Our mean is 4.”), we see that we don’t have enough information to use this clue, so we ignore it for now.

c. Examining the third clue (“Our median is 3.”), we realize that the middle number must be 3, and enter it on the middle blank.

d. Attacking the fourth clue (“Our mode is 2.”), we realize that the first two numbers must be 2 (to make 2 the most common number).

e. Now we use the last clue (“Our range is 6.”). We realize the fifth number must be 8 so that the biggest, 8, minus the smallest, 2, will be 6.

f. Finally, we go back to the second clue (“Our mean is 4.”). We know that if we add all the numbers and divide by five, we must get four.

Therefore, the sum of the five numbers must be 20.

Since 2 + 2 + 3 + 8 = 15, the missing number must be 5! So the answer to the riddle is:

Ignore this clue for now.

_?_ _?_ _?_ _?_ _?_

“What numbers are we?” Practice Riddle Card SOLUTION


Riddle Card Practice Example 1. We are five numbers. 2. Our mean is 4. 3. Our median is 3. 4. Our mode is 2. 5. Our range is 6. What numbers are we?

_?_ _?_ _3_ _?_ _?_

_2_ _2_ _3_ _?_ _?_

_2_ _2_ _3_ _?_ _8_

(2 + 2 + 3 + ? + 8) ÷ 5 = 4

2 + 2 + 3 + ? + 8 = 20

_2_ _2_ _3_ _5_ _8_

Finding The Solution: Question: How do you solve a riddle with so many clues? Answer: ONE CLUE AT A TIME! To solve this riddle:

“What numbers are we?” Riddle Cards 1 – 12

Name:_______________ Date: ____________ Class: ___________


Riddle Number 1 1. We are two numbers. 2. Our range is 6. 3. Our minimum is 2. What numbers are we?

Riddle Number 2 1. We are two numbers. 2. Our mean is 4. 3. Our maximum is 6. What numbers are we?

Riddle Number 3 1. We are two numbers. 2. Our only mode is 4 What numbers are we?

Riddle Number 4 1. We are two numbers. 2. Our median is 3. 3. Our minimum is 2. What numbers are we?

Riddle Number 5 1. We are three numbers. 2. Our mode is 4. 3. Our range is 7. What numbers are we?

Riddle Number 6 1. We are three numbers. 2. Our mean is 3. 3. Our mode is 4 What numbers are we?

Riddle Number 7 1. We are three numbers. 2. Our range is 2. 3. Our median is 5. 4. We have no mode. What numbers are we?

Riddle Number 8 1. We are three numbers. 2. Our median is 3. 3. Our range is 5. 4. Our mean is 4. What numbers are we?

Riddle Number 9 1. We are four numbers. 2. We have two modes; 4 and 9 What numbers are we?

Riddle Number 10 1. We are four numbers. 2. Our mode is 5. 3. Our range is 0. What numbers are we?

Riddle Number 11 1. We are four numbers. 2. Our median is 5. 3. Our mode is 4. 4. Our range is 9. What numbers are we?

Riddle Number 12 1. We are four numbers. 2. Our mean is 3. 3. Our only mode is 4. What numbers are we?

“What numbers are we?” Riddle Cards 13 – 20

Name:_______________ Date: ____________ Class: ___________


Riddle Number 13 1. We are five numbers. 2. Our median is 4. 3. Our mode is 2. 4. Our range is 5. 5. Our mean is 4. What numbers are we?

Riddle Number 14 1. We are five numbers. 2. Our mean is 5. 3. Our mode is 7. 4. Our median is 6. 5. Our range is 6 What numbers are we?

Riddle Number 15 1. We are five numbers. 2. Our range is 9. 3. Our mean is 6. 4. Our median is 4. 5. Our mode is 3. What number are we?

Riddle Number 16 1. We are five numbers. 2. We have two modes; 12 and

16. 3. Our median is 13. What numbers are we?

Riddle Number 17 1. We are six numbers. 2. Our minimum is 2. 3. We have two modes; 4 and 6. 4. Our range is 13. What numbers are we?

Riddle Number 18 1. We are six numbers. 2. We have three modes: 4, 8,

and 10. What numbers are we?

Riddle Number 19 1. We are six numbers. 2. Our maximum is 6. 3. Our range is 3. 4. Our median is 4. 5. Our mean is 4. 6. Our mode is 4. What numbers are we?

Riddle Number 20 1. We are six numbers. 2. Our mode is 2. 3. Our range is 6. 4. Our minimum is 2. 5. Our mean is 3. 6. This is a hard one! What numbers are we?

“What numbers are we?” Riddle Cards 1 – 12 ANSWER SHEET

Name:_______________ Date: ____________ Class: ___________


Riddle Number 1 Work: What numbers are we? ____________

Riddle Number 2 Work: What numbers are we? ___________











“What numbers are we?” Riddle Cards 13 – 20 ANSWER SHEET

Name:_______________ Date: ____________ Class: ___________










“What numbers are we?” Riddle Cards ANSWER KEY

Name:_______________ Date: ____________ Class: ___________


Riddle Number 1 What numbers are we? ____________




















2, 8 2, 6

4, 4 2, 4

4, 4, 11 1, 4, 4

4, 5, 6 2, 3, 7

4,4,9,9 5,5,5,5

4,4,6,13 1,3,4,4

2,2,4,5,7 1,4,6,7,7

3,3,4,8,12 12,12,13,16,16

2,4,4,6,6,15 4,4,8,8,10,10

3,3,4,4,4,6 2,2,2,2,2,8

Documents

Riddle Card #14 1. We are five numbers. 2. Our mean is 5 ...€¦ · 20 reusable “What numbers are we?” cards that can be easily laminated, cut up, and distributed to students