Mystery Bags Lesson Plan
Teacher Candidate: Mary Takle
Lesson Date: 11/1/2010
Cooperating Teacher: Dawn Withee
Grade: 9-11 (mostly grade 9 students)
School District: Edmonds School District
School: Lynnwood High School
University Supervisor: Andrea Escame-Hedger
Subject/Grade Level: Algebra 1
Unit: Solving Equations
Grouping for Instruction: Students will sit in heterogeneous groups of 4 and work cooperatively using the ComplexInstruction model.
Objective(s)/Learning Target(s): Students will use words, pictures, or diagrams to solve for the unknown quantity in
each problem. Students will describe in writing the process they used to find the unknown quantity.
Standard(s): Algebra 1 A1.1 Core Content: Solving problems
Homework: Mystery Bags worksheet; Homework Answer Key
Materials/Preparation Needed: Survey, Daily Plan Sheet, Mystery Bags Task Card, Homework Sheet, paper or math
notebooks, pencil
Assessment of learning: Formative: Teacher checkpoint after each activity on task card. Individual: Completion of
homework.
Instructional Plan and Strategies
Opening: Survey of students
Homework Questions: Work any
problems that students request.
Explore:
Students:
Students complete short survey about their interests
Communications Manager: Record daily task and homework on Group
Score Sheet on group folder
There is no homework due today
Read through Daily Plan Sheet and have students write down objective
Have Task Managers read Mystery Bags Task and initiate group work.
Small group questions: Checkpoint 1 (after question 3): Task Answer Key
 How did you find the answer to question 1, 2, or 3?
 Explain your reasoning or procedure for finding how much each
mystery bag contains.
 Questioning to make sure the students have done the same thing
to both sides. How did you know to subtract/divide?
 Problem 1 (P1) – looking for multiplication/division
 P2 & P3 – subtraction first, then division
Checkpoint 2 (after question 8):
 P4 – need to subtract mystery bags (x) from one side.
 P5 – subtract both bags and coins from each side
 P6 – unequal balance, no solution
 P7 – both sides are equal, so the exact number cannot be
dtermined – infinite solutions
 P8 – Students document procedure for solving equations – if time
allows ask one student in the group to solve a new problem using
the procedure. Give the student a small whiteboard and marker.
Checkpoint 3 (after question 3 in Part 2) – (Probably won’t get to this):
 P1 – M = 9
 P2 – M = 1
 P3 – M = 47/7…discuss fractions can be answers!
Solving Equations
Page 1 of 10
Chapter 3L00.doc
Mystery Bags Lesson Plan
Wrap-Up
Have 2-3 groups put their work on the doc cam for problems:
P5, 6, & 7– procedure for solving. P8 - discuss the unequal solution is no
solution. P9 – discuss infinite solutions
Modifications (Gear Up/Gear Down):
Task has gear-up built into it.
Down – students may need credit for completing fewer problems in Checkpoint 2.
Reflection:
P2&P3 – Great task – kids really focused – great math discussions. Two groups were struggling with the
idea of working backwards and verbalizing what was happening. Some groups wanted to skip straight to
equation w/o thinking about the concepts…so good questioning makes them reveal what they are
thinking/doing. Senario #2 has an interesting gotcha. The left side is 8 bags and 10 weights and the right
side is 90 weights. The gotcha was that a couple of groups wanted to distribute the 10 weights into the 8
bags…it was very odd, but clearly the 10 extra weights and the mystery bags weighing 10 oz caused some
confusion. I had trouble understanding what the kids were thinking and they were clearly confused when
explaining their reasoning, but were very clear in showing that their answer worked.
P6 – Went straight to formulas – did not try to get the balance idea. This group need more work on the
concrete idea.
Solving Equations
Page 2 of 10
Chapter 3L00.doc
Mystery Bags Task
Objective: To describe the general process for solving for unknown quantities in a problem.
The Mystery Bags Game
Once upon a time, there lived a rich king who owned a lot of
gold. However, it can get very boring watching gold all day,
so he had the court jester make up games for him to pass
the time.
The game the king loves best is the mystery bags game.
First, the jester takes one or more empty bags and fills
each bag with the same amount of gold. These bags of equal
weight are called the “mystery bags.” Next, the jester digs into his collection of lead weights.
He takes out his pan balance and places some combination of mystery bags and lead weights on
the two pans so that the two sides balance.
The game is to figure out the weight of each mystery bag.
Your Task: Part 1 – You’re the King
The game may sound rather easy, but it can get very difficult for the king. See if you can win
the mystery bags game in the various situations described here by figuring out how much gold
there is in each mystery bag.
On a separate sheet of paper, you are responsible for explaining how to play the game for each
of the 7 scenarios below. Explain how you know you are correct. Your explanation should
consist of a combination of words, pictures, or diagrams that show what’s going on. For full
credit, you must write in complete sentences.
1. There are 3 mystery bags on one side of the balance and 51 ounces of lead weights on the
other side.
2. There is 1 mystery bag and 42 ounces of weights on one side and 100 ounces of weights
on the other side.
3. There are 8 mystery bags and 10 ounces of weights on one side and 90 ounces of weights
on the other side.
***Teacher Check Point****
Mystery Bags Task
Objective: To describe the general process for solving for unknown quantities in a problem.
4. There are 3 mystery bags and 29 ounces of weights on one side and 4 mystery bags on
the other side.
5. There are 11 mystery bags and 65 ounces of weights on one side and 4 mystery bags and
100 ounces of weights on the other side.
6. The king wants to be able to win easily all of the time, without calling you in. Therefore,
your task is to describe in words a procedure by which the king can find out how much is
in a mystery bag in any situation.
Try out your procedure on the following problem. Does it work? If not, revise it.
7. There are 12 mystery bags and 4 ounces of weights on one side and 5 mystery bags and
18 ounces of weights on the other side.
***Teacher Check Point****
The jester was tired when he set up the scales for the following problems. Can you
describe what is wrong with the following situations?
8. There are 6 mystery bags and 13 ounces of weights on one side, and 6 mystery bags and
14 ounces of weights on the other side. (The jester could get in a lot of trouble for this
one!)
9. There are 15 mystery bags and 7 ounces of weights on both sides. (At first, the king
thought this one was easy, but then he found it to be incredibly hard.)
Part 2 – You’re the Jester
Now, you’re the jester. For each equation below, do two
things.
 Describe how the jester must place the mystery bags
and lead weights so that the equation will be a
representation of the situation.
 Find the weight of one mystery bag and explain how you
got the answer.
1. 5M  24  51  2M
2. 43M  37  56M  24
3. 12M 15  5M  62
***Teacher Check Point****
Mystery Bags Task (Answer Key)
Objective: To describe the general process for solving for unknown quantities in a problem.
Look for pictures or symbols to describe the process. Look for a complete sentence
with the answer.
1. There are 3 mystery bags on one side of the balance and 51 ounces of lead weights on the
other side. Students should show that 51/3 = 17.
2. There are 1 mystery bag and 42 ounces of weights on one side, and 100 ounces of weights
on the other side. Students should show 42 subtracted from 100 = 58.
3. There are 8 mystery bags and 10 ounces of weights on one side, and 90 ounces of weights
on the other side. Students should show 10 subtracted from 90 and then 80/8 = 10.
4. There are 3 mystery bags and 29 ounces of weights on one side, and 4 mystery bags on
the other side. Students should show 3 bags subtracted from 4 bags and then 1 bag
= 29
5. There are 11 mystery bags and 65 ounces of weights on one side, and 4 mystery bags and
100 ounces of weights on the other side. Students should show 65 subtracted from 100
= 35 and 4 bags subtracted from 11 bags. The result should be 7 bags = 35, bag =
5.
6. The king wants to be able to win easily all of the time, without calling you in. Therefore,
your final task in this assignment is to describe in words a procedure by which the king
can find out how much is in a mystery bag in any situation. Students should have a
series of statements that mention addition/subtraction first, then multiplication and
division as the second step for solving.
7. There are 12 mystery bags and 4 ounces of weights on one side, and 5 mystery bags and
18 ounces of weights on the other side. Students should show 4 subtracted from 18 =
14 and 5 bags subtracted from 12 bags. The result should be 7 bags = 14, bag =
2.
8. There are 6 mystery bags and 13 ounces of weights on one side, and 6 mystery bags and
14 ounces of weights on the other side. (The jester could get in a lot of trouble for this
one!) The result should be 13 ounces does not = 14 ounces.
9. There are 15 mystery bags and 7 ounces of weights on both sides. (At first, the king
thought this one was easy, but then he found it to be incredibly hard.) The result should
be 0 = 0 or 15 bags = 15 bags…or the answer cannot be determined.
Part 2 – You’re the Jester
1. 5M  24  51  2M M = 9
2. 43M  37  56M  24 M = 1
3. 12M 15  5M  62 M = 47/7
Daily Plan Sheet
Subject: Algebra 1
Date: 11/1/10
Lesson: Mystery Bags
Goal(s)/Standard(s):
 Solve for unknown quantities in a problem
 Write a procedure for solving for unknown quantities
Materials:
 paper
 pencil
 Task card
Look fors:
Descriptions in words or equations
Everyone able to explain the group’s reasoning
Today you will need someone who can…
 Generalize
 Draw diagrams
 Find patterns
 Make connections
 Write an equation
 Discover a procedure
 Substitute numbers into equations
 Explain
 Ask “Why?”
 Say “Wait, I don’t understand!”
Solving Equations
Page 6 of 10
Chapter 3L00.doc
Mystery Bags Homework
5. There are 3 mystery bags and 18 ounces of weights on
Find the weight of one mystery bag and explain how
you found your answer. The “M” stands for mystery
bag.
one side of the scale, and 4 mystery bags and 17
ounces of weights on the other side of the scale.
Weight:
1. 2M + 73 = 5M + 7
Weight:
Explanation:
Explanation:
Simplify
6. −32 + (−5)2
2. 5M + 1 = 3M + 11
Weight:
7. 50 ÷ 5 ∗ 2
Explanation:
8. Write the rule for the following table
3. 14M + 107 = 19M + 12
Weight:
Explanation:
4. M + 16 = 8M + 2
Weight:
Explanation:
x
y
-2
0
-1
3
0
6
1
9
2
12
3
15
4
18
5
21
3
4
Rule:__________________
10. Fill in the able for the rule y = -2x +5
x
y
-3
-2
-1
0
1
2
Mystery Bags Homework (Answer Key)
Find the weight of one mystery bag and explain how you found your answer. The “M”
stands for mystery bag.
1. 2M + 73 = 5M + 7
Weight: 22
2. 5M + 1 = 3M + 11
Weight:
5
3. 14M + 107 = 19M + 12
Weight: 19
4. M + 16 = 8M + 2
Weight: 2
5. There are 3 mystery bags and 18 ounces of weights on one side of the scale, and 4
mystery bags and 17 ounces of weights on the other side of the scale.
Weight:
1
6. −32 + (−5)2 = 16
7. 50 ÷ 5 ∗ 2 = 20
8. Write the rule for the following table
x
y
-2
0
-1
3
0
6
Rule:
y = 3x + 6
1
9
2
12
3
15
4
18
5
21
1. Fill in the able for the rule y = -2x +5
x
y
-3
11
-2
9
-1
7
0
5
1
3
2
1
3
-1
4
-3
List 5 activities you enjoy participating in
outside of school.
List your favorite music, movies, and/or
books
List 5 activities you enjoy participating in
outside of school.
List your favorite music, movies, and/or
books
List 5 activities you enjoy participating in
outside of school.
List 5 activities you enjoy participating in
outside of school.
List your favorite music, movies, and/or
books
List your favorite music, movies, and/or
books
Who is your favorite person, alive or dead,
and why do you admire him or her?
List your favorite subjects from elementary
school, middle school, and high school.
Who is your favorite person, alive or dead,
and why do you admire him or her?
List your favorite subjects from elementary
school, middle school, and high school.
Who is your favorite person, alive or dead,
and why do you admire him or her?
Who is your favorite person, alive or dead,
and why do you admire him or her?
List your favorite subjects from elementary
school, middle school, and high school.
List your favorite subjects from elementary
school, middle school, and high school.