HCPSS Worthwhile Math Task
It All Adds Up!
Common Core Standard
6.NS.B.4. Find the greatest common factor of two whole numbers less than or equal to 100 and
the least common multiple of two whole numbers less than or equal to 12. Use the distributive
property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a
sum of two whole numbers with no common factor.
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.
The Task
A popular game show is creating a spin-off of its show where each game is won by using various
math skills. The producers of the show want your class to test out a potential game. In this
game there are four prizes you can win, each prize is labeled with its price and an addition
problem. In order to win the game, you have to first solve each addition problem and then, using
only the numbers in the price of the prize, create another math problem whose answer is the
same as that of the addition problem. Each correct match wins you that prize! Correctly
matching all four wins you all the prizes and a bonus cash prize!
Here are the four prizes you could win. Good Luck!
Cruise to the Bahamas
A New iPad
__________
__________
Mountain Bike
Jet Ski
$942
36 + 8
$583
15 + 24
$768
48 + 42
$7,312
36 + 21
__________
__________
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Facilitator Notes
1. Place larger images of each prize on the front board; this is where students will post
answers once the task has been completed.
2. Have students work individually or in pairs to complete the task; give each student or pair
of students a copy of the sheet with the prizes on it and have them record their answers in
the respective boxes for each prize. Also give them 4 sticky notes and have them record
one answer on each to post on the board when directed. Allow students access to
multiplication charts. (Look for evidence of MP1 and MP2.)
3. Once students have completed the task, have each student or pair come up to the board
and place their sticky notes under each prize. Group common answers together and then
have students share their solutions and what strategies they used to solve the problems.
(You could also post each student’s or pair’s resource sheets around the room and allow
students to do a brief gallery walk to view each other’s answers as well.) (Look for
evidence of MP3.)
4. Lead class discussion about strategies, which worked best and why. (Look for evidence
of MP3.)
o Finding factors of each addend (quickest)
o Guess and check
5. Continue the discussion by finding one prize that had different answers. Compare the
answers and discuss whether or not they could be represented in the same way:
o Example: Cruise Ship: 9+2= 11, 11 4 = 44 can be written 11(9+2) so they are
actually the same answer. (Look for evidence of MP3.)
6. Complete the discussion by discussing the distributive property and how it could be/was
used to find each solution. (Look for evidence of MP3.)
7. Extension Question: Connect the task to the English Common Core objective of
argumentative writing by having students respond to the prompt below in a paragraph.
o Write a statement to the game show producers telling them why you would or
would not recommend they include this game on their show. Be sure to back up
your response with examples from your experience playing the game and include
any changes you think should be made and why they should be made. (Look for
evidence of MP2, MP3.)
8. Extension Activity: Have students play it as a timed game in the classroom with
different prizes and/or different amounts.
Follow-Up Questions
1.
2.
3.
4.
5.
What strategies did you use to find you answer?
Was there more than one way to solve each problem?
Was there more than one solution to each problem?
How are the strategies the groups used to solve similar?
How are the strategies the groups used to solve unique?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Solutions
Here are some potential solutions for the task:
Cruise to the Bahamas
A New iPad
$942
36 + 8 = 44
$583
15 + 24 = 39
4(9 + 2)
3(5 + 8)
4  9 = 36, 4  2 = 8
36 + 8 = 44
3  5 = 15, 3  8 = 24
15 + 24 = 39
2 + 9 = 11, 11  4 = 44
8 + 5 = 13, 13  3 = 39
Mountain Bike
Jet Ski
$768
48 + 42 = 90
$7,312
36 + 21 = 57
6(8 + 7)
3(12 + 7)
6  8 = 48, 6  7 = 42
48 + 42 = 90
3  12 = 36, 3  7 = 21
36 + 21 = 57
8 + 7 = 15, 15  6 = 90
12 + 7 = 19, 19  3 = 57
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.