NCDPI – AIG Instructional Resource: Background Information
Resource Title: Fair Prizes
Subject Area/Grade Level (s): Math/4
Time Frame: One-two days
Common Core Standards Addressed:
Operations and Algebraic Thinking
Gain familiarity with factors and multiples.
4.OA.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 given one-digit number. Determine whether a given whole number in the
range 1–100 is prime or composite.
Mathematical Practice
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively.
7. Look for and make use of structure.
Additional Standards Addressed: NA
Brief Description of Lesson/Task/Activity: In this activity, students will receive a flyer listing the prizes available to the first 100 people in line at
the state fair. Using the information on the flyer, students will determine which people in line will win a prize. Since the flyer contains
statements such as “every 5th person will receive a stuffed animal” and “every 6th person will receive a concert ticket,” students will need to
apply knowledge of factors and multiples while problem solving.
Type of Differentiation for AIGs (include all that apply):
Enrichment
Adaptations for AIGs:
x Product
x Content
x Process
x Extension
Acceleration
Explanation of How Resource is Appropriate for AIGs: The first part of this task addresses the fourth grade mathematics concept of finding
multiples and factors of quantities through 100. However, this concept is at a much higher level since it is embedded in a complex problem
situation. Part 2 of this problem extends past fourth grade standards as students work with larger quantities and begin to generate rules for
taking shortcuts while problem solving.
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project
Needed Resources/Materials
 State Fair Flyer
 Calculators
Sources: NA
TEACHER NOTES: Since it may not be immediately obvious that factors and multiples are needed to solve this problem, students may first rely
on looking for patterns or trial and error strategies. Once students grapple with the problem and notice some patterns, they should start to
realize that their knowledge of factors and multiples will be essential in obtaining accurate solutions.
NCDPI AIG Curriculum Resource Outline
STAGE ONE: ENGAGE
The state fair is finally here! In order to entice people to arrive early, the fair has sent out promotional flyers (show attached flyer). The flyer
explains that the fair will be offering a series of prizes to the first 100 people.
Have students look at the prize list. Discuss which prize(s) they would prefer. Ask students if it is possible to win more than one prize? (Yes, it
would be possible. For example all of the people who are in a position that is a multiple of two, will win free games for the day. All of the people
in positions that are multiples of three will win free pizza. Therefore, the sixth person will actually win free games and a pizza.)
STAGE TWO: ELABORATE
Part 1: Ask students to look at the prize list and determine which place in line they hope to stand. Students should use mathematics to explain
and justify their thinking.
Once students have solutions, ask them to call out the place where they would most prefer to stand. Record places on the board. Then,
conduct a discussion about the strategies used to solve this problem. Ask,
 How did you determine which place you would prefer to stand in line? (By grappling with this problem, students should start to see that
the places in line that will receive the most prizes have the factors of 2, 3, 4, 5, and 6. Therefore, the 60th place in line would receive the
most prizes because it is a multiple of all of these numbers.)
 Are there any places in line where you would not like to stand? (Record on the board; places where students would not want to stand
will not have the factors of 2, 3, 4, 5, and 6. They may include 1, 7, 11, 13, 17, 19, 23…)
Redirect students to the numbers on the board that represent the most preferred and least preferred places in line. Ask students to make
observations about the two groups of numbers. (e.g., All of the most preferred places are even numbers. All of the least preferred places are
prime numbers.) Based on observations, ask follow up questions (e.g., Will all places with even numbers be a preferred place to stand in line?
Will any person standing in a place with a prime number win a prize?). Encourage students to justify their thinking.
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project
Part 2: Explain to students that the state fair decided not to limit prizes to the first 100 people. Instead, they chose to extend the opportunity to
win prizes to every person in line on opening night. The fair even changed the last line of the flyer to say, “Every 100th person will receive a prize
winning pig.” In what place would you need to stand in order to win every prize on the list? How can you prove that you have correct answer?
If students need an additional challenge, ask, “What shortcuts can you find to determine all of the places in line that would win every prize?”
STAGE THREE: EVALUATE
Students will be evaluated on their ability to notice that this problem relates to factors and multiples. Students will be assessed on accuracy and
justification of strategies. Students should articulate that the prize-winning positions in line will be one that is a multiple of 2, 3, 4, 5, 6, (and 100
in Part 2). Students should also be able to articulate that they can determine if a position will receive a prize by examining its factors.
TEACHER NOTES: Students may not realize that a person in line can win more than one prize; this may need to be stated. If students struggle
with this idea, the teacher may ask guiding questions: Can you make a list of the places in line where you would win free games for a day? Can
you make a list of the places in line where you would win a free pizza? Can you use a chart/table to organize your work? What math do you
need to find all of the places in line that will receive a ticket to go bungee jumping? How can you use your knowledge of multiples and factors to
solve this problem?
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project