Which Number Does Not Belong?

Developed by Karen DeFilippis and adapted from Tyler Reed in Edu@scholastic.

Content Standards:

4.OA.B.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Math Practices:

MP1 Make sense of problems and persevere in solving them.

MP2 Reason abstractly and quantitatively.

MP3 Construct viable arguments and critique the reasoning of others.

MP7. Look for and make use of structure.

Introduction

Teachers can use this problem to listen to the deeper mathematical thinking and reasoning of their students.  Students will be asked to apply their understanding of mathematics by justifying their conclusions and communicating those understandings to others.

Description/Teacher Instructions

Allow students time to make a case for each number not belonging to the group based on four different sets of criterion.  Then have students share their case with one another either in a Pair/Share setting or small group.  As students share their cases, the teacher should circulate the classroom while jotting down students’ names and ideas that will be later shared with the whole group. When discussions are complete, begin calling on students based on what you overheard while using some of the comments below when appropriate.

• Thank you for sharing.
• Please let me know if I’m not rephrasing you correctly. (I'm only rephrasing when I have trouble hearing the student.)
• I want to make sure we’re writing down your thinking correctly, please slow down and tell us more about this step.
• I’m not worried about the correct answer right now.  I’m just interested in how you thought about the problem.
• Your sharing of how you arrived at the incorrect answer is really important — I think we learn a lot from our mistakes, and as you can see, you weren't the only one who thought about it that way.
• Did you change your mind or question your strategy after you talk with your neighbor?
• Who did the problem differently than the 3 people whom I called on to share?
• I really appreciate how you questioned [and responded to] _____’s sharing.
• I know it’s kind of tough to articulate your thinking. That’s okay. Take your time.
• Math teachers sometimes get it wrong too.

Anticipated Answers

• 43 - The other numbers can be reached by multiplying a number by itself. 3x3, 4x4, 5x5
• I could say 9 is the number which doesn't belong. A simple reason would be "Because it only has one digit".
  • I think, in fact, 9 is the number doesn't belong, but for another reason: All the digits of 16, 25 and 43 sums to 7. 1+6 = 2+5 = 4+3 = 7.

• 9 doesn't belong, because if you add up the digits in all of the other numbers, they give you 7. 9 is the only number that doesn't give you 7.
  1+6=7
  2+5=7
  4+3=7
• I say 16 is the number that doesn't belong because 9, 25, and 43 are all odd numbers and 16 is even.
• The number I first looked at was the number 16, because it is an even number and the other numbers are odd. But then I really digged deeper into these numbers and came up with the number 43 because the other numbers are square numbers and this made more sense. So depending on where the student is in Math would be how they look at these numbers.
• I think number 25 doesn't belong. In each number, except 25, we can divide last number on 3. 9/3=3. 16 - 6/3=2. 43 - 3/3=1. And you also can see, that there is decreasing arithmetic progression
  • 25 doesn't belong because the product of the digits of all the numbers is a multiple of three; except 25.
  • 9 = 9
    1*6 = 6
    2*5 = 10
    4*3 = 12

Download this month's rich math task as a Word Document here.