A Broken Gumball Machine - ridgewood.k12.nj.us · A Broken Gumball Machine Suggested Grade Span 3–5 Grade(s) in Which Task Was Piloted 3 and 4 Task Something was wrong with the

A Broken Gumball Machine

Something was wrong with the gumball machine at theshopping mall. If you put in 1 penny and then turned the knob,you got 3 gumballs. If you put 2 pennies and then turned theknob, you got 5 gumballs. If you put 3 pennies and then turnedthe knob, you got 7 gumballs. If you put in 4 pennies and thenturned the knob, you got 9 gumballs.

If John put 5 pennies in the machine and then turned the knob,how many gumballs would he get if this pattern continued? If Joyce puts in 10 pennies and then turns the knob, how manygumballs will she get?

BonusIf you put in a dollar in pennies and then turned the knob, howmany gumballs would you get?

1 of 9A Broken Gumball Machine

Copyright 2008, Exemplars, Inc. All rights reserved.

A Broken Gumball Machine

Suggested Grade Span

3–5

Grade(s) in Which Task Was Piloted

3 and 4

Task

Something was wrong with the gumball machine at the shopping mall. If you put in 1 penny andthen turned the knob, you got 3 gumballs. If you put 2 pennies and then turned the knob, yougot 5 gumballs. If you put 3 pennies and then turned the knob, you got 7 gumballs. If you put in4 pennies and then turned the knob, you got 9 gumballs.

If John put 5 pennies in the machine and then turned the knob, how many gumballs would heget if this pattern continued? If Joyce puts in 10 pennies and then turns the knob, how manygumballs will she get?

BonusIf you put in a dollar in pennies and then turned the knob, how many gumballs would you get?

Alternative Versions of Task

More Accessible Version:

Something was wrong with the gumball machine at the shopping mall. If you put in 1 penny andthen turned the knob, you got 2 gumballs. If you put 2 pennies and then turned the knob, yougot 3 gumballs. If you put 3 pennies and then turned the knob, you got 4 gumballs.



More Challenging Version:

Something was wrong with the gumball machine at the shopping mall. If you put in 1 penny andthen turned the knob, you got 2 gumballs. If you put 2 pennies and then turned the knob, you



got 5 gumballs. If you put 3 pennies and then turned the knob, you got 8 gumballs. If you put in4 pennies and then turned the knob, you got 11 gumballs.



NCTM Content Standards and Evidence

Algebra Standard for Grades 3–5: Instructional programs from pre-kindergarten through grade12 should enable students to ...

Understand patterns, relations and functions.

• NCTM Evidence: Describe, extend and make generalizations about geometric andnumeric patterns.

• Exemplars Task-Specific Evidence: This task requires students to continue a pattern tofind the number of gumballs that a student will get when she puts in 10 pennies.

Time/Context/Qualifiers/Tip(s) From Piloting Teacher

This task was piloted in grades three and four. It took one 45-minute class period.

This task allows the teacher to assess students’ abilities to identify and extend patterns in aproblem-solving situation. To make this task more or less complicated, you can change thepattern. After students solve the task, you can show them how they can create a rule for solvingthe problem for any number of pennies. Students can also analyze how to get the most gum fortheir money from this broken machine.

Links

Many teachers do a menu of activities with bubble gum. Project AIMS has many bubble gumactivities, such as determining the number of grams of sugar in each piece of gum by weighingthe gum before and after chewing. Another Exemplars task that involves the theme of gum is"Gum-dilly-icious."

Common Strategies Used to Solve This Task

Students will create a table to find the pattern and number of gumballs. Some students mayrequire manipulatives to represent pennies and/or gumballs.



Possible Solutions

Pennies Gumballs

1 3

2 5

3 7

4 9

5 11

10 21

100 201

x 2x + 1

More Accessible Version Solution:

Five pennies would be six gumballs. Ten pennies would be 11 gumballs. One dollar would be101 gumballs.

Pattern is p + 1 = g where p is number of pennies and g is number of gumballs.

More Challenging Version Solution:

Five pennies would be 14 gumballs. 10 pennies would be 29 gumballs. One dollar would be299 gumballs.

p x 3 – 1 = g where p is the number of pennies and g is the number of gumballs.

Task-Specific Assessment Notes

NoviceThe Novice will not be able to proceed toward a solution. Representations may be attempted,but little or no math language will be used.

ApprenticeThe Apprentice will achieve a partial solution, but all parts of the task will not be attempted orwill be attempted unsuccessfully. Representations will be used to organize the solution, but littlemath language will be used.

PractitionerThe Practitioner will have an approach that works and achieves a correct solution for both partsof the task. Math language will be used to communicate, and representations will be used toorganize the solution.



ExpertThe Expert will have an approach that works and achieves a correct solution for both parts ofthe task and for the bonus. Sophisticated math language will be used to communicate, andrepresentations will be used to organize the solution. The Expert will find a rule for solving theproblem for any number of pennies.



Novice



Apprentice



Practitioner



Expert



Documents

A Broken Gumball Machine - ridgewood.k12.nj.us · A Broken Gumball Machine Suggested Grade Span 3–5 Grade(s) in Which Task Was Piloted 3 and 4 Task Something was wrong with the