.
Exploring Problem Solving
Solving Mathematical Problems and Reinforcing Basic Math Facts
Inside this Unit
Page
Lesson 1:
Solving Problems as a Group
5-6
Lesson 2:
Writing Your Own Problems
7-8
Lesson 3:
Organizing and Checking
9-10
11-12
Lesson 4:
Find & Solve Hidden Problem
Lesson 5:
Using a Picture or Diagram
13–14
Lesson 6:
Simplify
15– 16
Lesson 7:
Find and Use Patterns
17-18
Lesson 8:
Work Backwards
19–20
Lesson 9:
Problems Solving Quickly
Lesson 10:
Review and websites
Evaluations:
At the first and last class,
please have the class fill out
the Student Evaluation sheet.
Doing so will enable the club
teacher and Zeno to track student progress.
Also, teachers please fill out
the Curriculum Evaluation
Form so that Zeno learns how
to better serve you and the
students in the future.
THANK YOU!
Unit Standards for Grades
Analyze a situation to define a problem




Use strategies to determine if there is a problem to solve.
Generate questions that would need to be answered in order to solve the problem
Identify known and unknown information
Identify needed and not needed information
Apply strategies to construct solutions



Gather and organize data
Determine what tools should be used to construct a solution
Recognize when an approach is unproductive and try a new approach
Communicate their mathematical thinking clearly and coherently to peers, teachers and others.
Use the language of mathematics to express mathematical ideas precisely.
Compute fluently and make reasonable estimates

21–22 
23
A Ten Lesson Unit
Develop fluency with basic number combinations for multiplication and division
Develop fluency in adding, subtracting, multiplying and dividing whole numbers
Teaching Tips
In order to best help students develop strong problem solving skills, children should be placed
in random groups of four, and kept in these groups for at least two to three weeks. This practice will help them learn how to work within a group.
If you cannot make even groups of four, then one student may join a group of four. In this
instance however, students need to sit in a circle rather than a rectangle in order to have
even lines of communication. If there are two extra students, have them join a group of four
but consider the group as two subsets: a group of four and a group of two.
Rules for groups:
1.
You are responsible for your own behavior
2.
You must be willing to help anyone in your group who asks.
3.
You may not ask the teacher for help unless all students in group have the same question.
Rules for teacher: listen, interact, pay attention and do not interfere. Listen to the groups,
become a member of the group if they are having difficulties getting started, help them figure
out the answers without telling them, BUT refrain from being the boss.
Exploring Problem Solving
Supply List for 24 Students
Activity Sheets:
Supplies and Books:
Student Contract
1
Teaching Manual
Parent Letter
1
Grapes of Math by Greg Tang
Color Square
1
Logic Safari Book 2 by Bonnie
Risby
1
Logic Safari Book 3 by Bonnie
Risby
1
Sudoku Puzzles for Kids by
Michael Rios
Input/Output
1
whiteboard markers
Towers of Hanoi
6
boxes of crayons
Magic Squares
12
decks of cards
Boxes Inside of Boxes Problem
24
journals
Kidville Problem
24
pencils
Math Headlines
Math Millionaire Version I
Letter Cards A B C D
Funny Money
River Crossing Scenarios
Travel Problem
Logic Problem
Apple Problem
Math Millionaire Version II
Games:
1
1
1
1
2
Club Evaluations:
Return envelope for evaluations
Student Club Evaluation form
Teacher Club Evaluation form
24 Game by Suntex
Apples to Apples by Out of
the Box
Muggins! by Old Fashioned
Products, Inc.
Snap by Gamewright
Mastermind by Pressman
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 5
Lesson 1 Focus: Solving Problems as a Group
Using deductive reasoning to solve problems as a group.
Lesson Prep: Make copies of the Color Squares sheet, Student Contract and
Parent Letter.
Introductions, Student Contract, What is Problem Solving?
Material:
*Parent Letter
*Pre-Math Club
Student Evaluation
*Student Contract
Welcome students, go over the Student Contract, and ask students what they
know about problem solving. Why is it important? What are the different
ways that math problems can be solved? Guess and check, working backwards,
drawing a picture or diagram, simplify, look for patterns, make an organized list,
table or chart, logical reasoning.
Hand out the Pre-Math Club Student Evaluation sheet (copies are in the manila
envelope in the back of the Teaching Manual), and ask students to answer the
questions as best they can. Remind students that this is not a test, but rather a way
for you to understand their thinking. When students have finished, collect the sheets
and hold onto them until the last day of club.
Remember to send home the Parent Letter at the end of class.
Activity 1: Digit-Place Game
The goal of the game is to guess a secret three or four digit number. The
leader writes down a three digit number and does not disclose the number.
Students take turns guessing three digit numbers. Each time someone
guesses, the leader gives one of the following clues:
Place: correct digit in the correct place.
Digit: correct digit but not in the correct place.
The game ends when someone deduces the correct number. For the next
round, increase the number to a four digit number. Give the students hints
and clues to help them become more proficient with their guesses.
Example: Guesses one and two have a
“7” in them and one digit is correct in
each. Guess three has a “7” and none
of the digits are correct, so “7” cannot
be the number. Neither can “3” be a
number because guess one has a “3”
and one digit is correct but guess
three has a “3” and no digits are correct.
EXAMPLE
Secret number
849 Digit Place
1st guess:
793
1
0
2nd guess
472
1
0
3rd guess
317
0
0
4th guess
942
1
1
5th guess
549
0
2
6th guess
849
0
3
VOCABULARY
ROW—horizontal
COLUMN — vertical
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 6
Activity 2: Color Square Game
Students are given the Color Square sheet; they are to figure out the color
scheme of the grid, which was designed by another person. The first game
can be played on a 3 x 3 square grid. Each of the nine squares is colored;
there are three squares of three different colors. All the squares of one
color are linked together along edges. See the example on the right.
First round: play it all together as a class, using a 3 x 3 grid. The teacher
designs a color square pattern or uses the example provided to the right,
below.
Material:
*Color Squares sheet
*Crayons
Permitted
Students ask the teacher for information (for example, “What’s in row
two?”) the teacher (in this example) responds, “one green, two blue” and
writes the information next to row two.
Game example:
hidden pattern
1 green, 2 blue
After each request for information, the teacher asks students if they can
correctly determine the color of any square. (For example, the middle
square of row two has to be blue.) Ask students to explain/justify their
thinking.
As students correctly discern the pattern, the teacher can color in boxes for
the class grid. The game is scored on the number of requests made of the
designer before the players can accurately recreate the original pattern.
Y
Y
Students may color what they know to be true in the
B
correct boxes.
After the 3 x 3 grid play the game again with a 4 x 4,
(four colors in four squares.)
Y
B
Y
B
B
B
Y
Y
B
G
Y
R
R
G
R
R
G
G
Place students into groups of four; give each group a box of crayons. One
student in the group will design the pattern and keep it hidden. The other
players, using a blank 3 x 3 or a 4 x 4 grid, try to recreate the pattern.
Rotate the designer position among group members as time allows.
Not permitted
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 7
Lesson 2 Focus: Writing Your Own Problems
Writing and solving your own math problems.
Lesson Prep: Make copies of the Blank Calendar sheet.
Material:
*Apples to Apples
*Decks of cards
Activity 1: Salute
Place students in groups of three. Pass out a deck of cards to each group and have
the students remove the tens, Jacks, Queens, and Kings. The teacher or the
players can decide if they are going to use addition or multiplication.
One player is the judge. The judge gives the other two players a card, face down.
When the judge says “salute,” each player, without looking at their card, puts it
up on their forehead so the judge and the other player can see the number on the
card.
The judge then announces the sum or product of the two numbers. The first
player to correctly announce their own number wins the two cards. (Each player
needs to say what number is on their card even if they do not say it first.)
Example: Judge says “salute,” Player A and Player B put their cards on their
foreheads and then the judge says that the product of the two cards is 21. Player
A sees that Player B’s card has a 7 on it so Player A deduces hers must be a 3.
Player B then says the card on his head. The judge should then state the number
sentence: 3 x 7 = 21. Player A gets to keep the cards 7 and 3.
Rotate the judge position after each round. The game winner is the player with
the most cards.
Game: Apples to Apples® by Out of the Box
Though this is a word comparison game, it requires students
explain their reasoning — a skill much needed for
mathematical purposes.
In groups as large as ten students, select one student to be
the judge (rotate this position every four or five rounds so
everyone has a chance to be the judge). The judge will deal
five red cards to each player, will select one green card, and
will place that card face up on the table.
The players look at their cards and pick one card that best represents the word or
concept on the green card. The players then get an opportunity to justify their
choice and the judge chooses a winner s/he feels best matches the green card. The
winner then keeps the green card.
VOCABULARY
CONSECUTIVE– going in
order
DIAGRAM—a drawing that
represents a mathematical
situation
EQUATION– a number
sentence which shows equality between two sets of values.
EXPRESSION-a symbol
representing a value or relation
GRAPH– a “picture” showing how certain facts are
related to each other or how
they compare to one another.
Math
Millionaire Game
If playing the Math Millionaire I Game, directions can be found on
page 22.
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 8
Activity 2: Writing Your Own Problems
Students may work alone or in pairs for this activity. Give
each student or pair of students a Calendar sheet and have
them write the dates (1-31) small in the upper left hand
corner. For each date of the month, students are to write a
problem whose answer is that date.
Example: On the 8th, a student might write 48 ÷ 6, or 2 x
2 x 2.
Tell students they must vary the types of problems used. For example, 0 + 1
= 1, 0 + 2 = 2, 0 + 3 = 3 will not count; they have to use a variety of math
skills, problems and operations.
Tell them to be creative:
 write problems that require more than one step, such as (4x3) - (3+2) = 7
 use fractions
 area or perimeter problems
 polygon problems
In order to allow sufficient time to complete the calendar, you might want to
divide the students into four groups and assign each group a different week to
complete. Another possibility is for the girls to do the odd dates, and boys the
evens.
When they finish, call on students to share their problems; their classmates
will solve the problem to determine the calendar date.
NOTES:
Material:
*Calendar sheet
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 9
Lesson 3 Focus: Organizing and Checking
Students will learn to look at the information given, organize it in a coherent
way and check the answer to see if it fits the pattern.
Material:
* Input-Output
examples
Lesson Prep: Make copies of the Towers of Hanoi game sheet.
Activity 1: Buzz
The object of this game is to avoid saying any number that is a multiple of 7,
or one that has a 7 in it. Thus, instead of saying aloud the numbers 7, 14, 17,
21, 27, 28, etc., a student will say “buzz.”
All students stand. The first person starts counting with “1,” the next person
“2”and so on, in consecutive numerical order.
If a student loses track of the counting, buzzes at the wrong time or says a
number that should be a buzz, he or she must sit down. The last student
standing wins the game.
HELPFUL HINT: To reduce anxiety, allow students to choose if they want
to play or sit out on the first couple of rounds.
Activity 2: Input/Output
The teacher is to think of a rule/function for converting one number (input) into another number (output).
The students are going to guess the rule.
The teacher needs to first think of a function rule. (Examples of function
rules are to the right. Gauge the function rules to the abilities of the Rule
students in the class.) Ask the students for ten input numbers. (The N x 12 =
students can state any number, but you may want to limit the range the Example:
first time by keeping numbers between 1 and 20.) An example is on right. Give only the
The teacher puts in the first three output numbers.
If a student thinks they know the rule they can come up and write in an
output number. If the number is correct it is left; if the number is
incorrect the teacher erases the number. Do not let a student state the rule
out loud yet — wait for other students to come up and add numbers. Once
all the output numbers are filled in, have one student explain the rule and
how they were able to figure it out. Example: “I multiplied 4 x 12 and got
48, multiplied 2 x 12 = 24, and continue to apply the rule of multiplying by 12
to the other numbers.”
first three
input numbers. Italicized
numbers are
answers for
teacher.
Other Possible
Rules:
Input
Output
4
48
2
24
7
84
10
120
15
180
6
72
0
0
11
132
1
12
5
60
NxN+1=
NxN+N=
3N—2 =
If students are having difficulty figuring out the output numbers, ask for suggestions on making it easier.
One solution is to list the input numbers in numerical order.
HELPFUL HINT: Playing this game in silence allows students that may not figure out the rule right
away to still have time to figure it out without the help of others. Once someone gives the rule, thinking
will stop for all others.
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 10
Activity 3: Towers of Hanoi
Remove the 1—5 cards out of a deck of cards and give them to each student
along with a Towers of Hanoi game board.
The object of the game is to move the entire stack of cards to another place
on the board without putting a higher-numbered card on top of a lowernumbered card.
Students start with all the cards in one stack in the center square of the game
board. The cards will be in numerical order, with the 5 card on the bottom of
the stack.
To play, a student can only move a card to one spot on the right or left of the
stack or back on the middle stack. Students may only move one card at a
time, remembering to never place a higher-numbered card on top of a lowernumbered card.
If students are able to get all the cards to another square on the board in
ascending order, have them do this a second time, while charting their
moves.
The students should examine the moves chart to discern a pattern.
If students are having difficulty solving the puzzle using five cards, reduce
the number to three or four cards.
Tower of Hanoi example: http://www.superkids.com/aweb/tools/logic/towers/
NOTES:
Materials:
*Decks of cards
*Towers of Hanoi
game board
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 11
Lesson 4 Focus: Guess and Check
Looking at problems and making reasonable guesses to possible answers.
Material:
*24 Game
*Sudoku puzzles
Lesson Prep: Make copies of the Magic Squares sheet.
Activity 1: 24 Game by Suntex International Inc.
The object of this game is to make 24 by adding,
subtracting, multiplying, and/or dividing the four
numbers given on the card. Students must use all
four numbers once (and only once).
Levels of challenge are indicated by a dot on the
corner of the game card. One dot represents the
easiest level; three dots are the most difficult to solve.
When playing for the first time, show the class a onedot card and write the numbers up on the board. As a class, see if the
students can figure out how the numbers can equal 24. (One dot cards
usually have two or more solutions.) Once they have an understanding of
how the game is played, hand out one card to each group to solve.
Have a representative from each group come to the board and show the
class their solution.
Activity 2: Sudoku
Sudoku is a game that has nine small squares in a larger group of nine
squares. The object of the game is to have the numbers 1—9 used only once
in each square of nine and then the numbers 1—9 can only appear once in
each row and column. An example of a Sudoku game board is to the right.
Students continually need to make reasonable guesses as to where each
number is placed and then check to make sure the number is in the correct
place when further numbers are added.
The book included in this club has varying degrees of difficulty. Students
can work their way through the different levels throughout the length of
this club unit.
VOCABULARY
JUSTIFY-to prove or show to be
true or valid using logic and/or evidence.
OPERATION-a mathematical process that combines numbers; basic
operations of arithmetic include
addition, subtraction, multiplication, and division.
PRODUCT –the result of a multiplication expression
QUOTIENT-the result of dividing
one number by another number
STANDARD FORM– a number
written with one digit for each place
value
SUM-the result of addition
WHOLE NUMBER-any counting
number or zero: 0, 1, 2, 3, ….
1
2
3
4
5
7
8
4
5
6
7
8
9
6
1
2
3
9
4
5
6
8
9
1
1
3
6
2
4
5
7
8
5
7
4
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 12
Activity 3: Magic Squares
Magic Squares was a game greatly enjoyed by Benjamin
Franklin; he would create elaborate 16 x 16 squares “to
avoid wear-iness.”
The magic square consists of numbers arranged in a square so
that all rows, columns, and usually the two diagonals will
add up to the same sum. If the square is 3 x 3 then one can
only use the numbers 1 –9 once in each square to total the same sum.
If students succeed at 3 x 3, try a 4 x 4 with the numbers 1—16. Answers to
two of the grids on the Magic Square sheet are below.
HELPFUL HINT: With an odd number of squares, the center number is
always the average of all the two other numbers in the column, row or
diagonal.
8
1
6
3
5
7
4
9
2
=15
16
3
2 13
5
10 11 8
9
6
4
15 14 1
7 12
=34
Notice how many ways there are to total 34. Ask students to find them;
write the possibilities on the board.
NOTES:
Material:
*Magic Squares
sheets
Solving Mathematical Problems and Reinforcing Basic Math Facts
Lesson 5 Focus: Using a Picture or Diagram to Solve
Problems
Students will solve word problems with the use of pictures or diagrams.
Lesson Prep: Make copies of the River Crossing Scenarios sheets.
Activity 1: Take It All
This game is played in pairs. Students with equal math abilities should be
paired up.
Each pair is given a deck of cards. Students should remove all face cards and
then divide the deck evenly between the two players.
On the count of three, each player lays one card out, face up. The first person
to say the sum or product of both cards gets to keep them. Once all the cards
are played, the player with the most cards wins. If there is a tie, then the
students can both lay down another card and whoever gets the correct answer
the quickest wins all the cards.
Play the first couple of rounds using addition and the next couple as
multiplication.
Activity 2: Draw a Picture
Drawing a picture is one way in which students can solve a problem. In the
problem below students can draw out the total number of boxes. Display the
Boxes Inside of Boxes sheet to students. Let students think about it, record
their response in their journals and then draw and solve the problem
together.
Jane has three large boxes. Inside each large box
are two medium boxes. Inside each medium box
are four small boxes. How many boxes does Jane
have in all?
Solution:
Page 13
Material:
*Decks of cards
*Boxes Inside of
Boxes sheet
*Journal
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 14
Activity 3: River Crossing
Students can act out or draw different river crossing scenarios. Place students into
groups of four or five (having them grouped by age or ability is probably best so that
the more capable groups can take on more challenging problems).
Give each group a River Crossing Scenario sheet (there are a total of four scenarios).
Let each group have 10 to 15 minutes solve it, and then have each group act out
their scenario.
Material:
*River Crossing
Scenario sheets
*Cards
Solution #1: Both children row across, Child #1 comes back, Father goes across, Child #2 goes
back to pick up Child #2.
Solution #2: Farmer rows across with Goose. Farmer rows back, picks up Fox, rows across to
drop off Fox and pick up Goose, rows back with Corn only, returns for Goose.
Solution # 3: Farmer takes the Fox, returns to pick up Corn, takes Corn across, returns and
picks up Dog, leaves Dog but takes Fox, picks up Goose, leaves Fox, drops off Fox and returns for
Fox.
Solution #4: Circus owner takes Cat across, returns and picks up Elephant, drops off and
returns with Mouse, returns with Cat, picks up Dog, goes back and gets Cat.
Game: Eleusis Express by John Golden
Eleusis is a reasoning game first developed in 1956 by Robert Abbott. In 2006, Eleusis was adapted and simplified for use in elementary school populations by John Golden. For more information and links, please see www.logicmaze.com (Abbott) and http://
faculty.gvsu.edu/goldenj/ (Golden). The following adaptation of version CC3.0 is with the developer’s permission.
Place students in groups of 3-5 and give each group two decks of cards. The object of the game is to be the first to
deduce the dealer’s secret rule. Shuffle the cards and have the dealer generate a rule. (This rule may be written secretly on a piece of scratch paper.) Seven cards are dealt to each player, and the top card of the remaining stack is
turned over for all to see. The dealer declares whether this card fits the rule or not. If so, it begins a horizontal row
of rule-fitting cards beneath the stock pile of face-down cards. If not, it begins a row of non-rule-fitting cards above
the stock pile. The player to the left of the dealer goes first and play continues around the table to the left. A player selects a card from her hand and shows it to the group; the dealer declares whether or not the card follows the
rule and places in a line as noted above (rule-fitting cards in one area, non rule-fitting cards in another.) Players
who plays a card that does not fit the rule gets a replacement card from the stock pile. If the card fit the rule that
player does not take a replacement card.
A player has the option of declaring that she has no correct card to play. She shows her hand to everyone and the
dealer says whether the player is right or wrong. If wrong, the dealer chooses one correct card from her hand and
plays it in the “correct” row. The player keeps her hand and draws one card from the stock pile. If right, the dealer
counts her cards and puts them on the bottom of the stockpile and deals the player a new hand that is one card less
than what she had. If the player was down to the last card and was correct, the player wins. Otherwise, the next
player takes his turn.
Guessing the Rule: When a player makes a correct play or a correct declaration of “no-play,” she is given the right
to guess the rule. Everyone must hear her guess. If she is wrong, the game continues. If correct, she wins. When
someone wins, the player to the left of the dealer is the new dealer and rule maker.
Examples of rules: even card, odd card [Jack is 11, Queen is 12, King is 13, Ace is 1], or red cards only, or patterns
(3 red, 2 black) or no face cards. Students will become quite creative in rule-making.
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 15
Lesson 6 Focus: Simplify
Using easier numbers, estimation, and /or fewer steps to achieve an answer to a
story problem.
Material:
Starter: Mental Math
Give the class numbers and operations verbally; they are to listen carefully to
the verbal problems, and come to a final answer.
HELPFUL HINTS: This activity may need to be adjusted based on the
abilities of the students. The instructor should give students think time before
calling on students. When a student answers, the teacher should ask students
to raise hands if they agree with the answer in order for validation to come
from peers rather than the instructor.
Examples of some mental math problems.

Start with 3, add 5, subtract 2, multiply 4, subtract 4. Who has an
answer? 20

Start with 5, double it, add 7, subtract 9, multiply by 3, divide by 6,
multiply by 4. Who has an answer? 16

Start with 9, add 6 - 4, double answer, multiply by 2 - 8. Who has
an answer? 36

Pick a number between 10 - 200, Add 3. Multiply by 2, subtract 4,
divide by 2. Subtract the number you started with. Who has an
answer? It will always be 1.
Challenge students to see if they can figure out why the answer will always be
1. Look to the right for an example of one way to solve it.
NOTES:
Pick a # X
+ 3
X***
x2
XX * * * * * *
- 4
XX * *
/2
X*
-#
*
*
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 16
Activity 1: Simplifying the Question
Material:
*Kidville Problem
sheet
*Travel Problem
sheet
When a problem is too complex to solve in one step, it often helps to divide
it into simpler problems and solve each one separately. Creating a simpler
problem from a more complex one may involve rewording the problem;
using smaller, simpler numbers, or using a more familiar scenario to
understand the problem and find the solution. The last question in the
previous Mental Math Activity uses simplification.
Display the Kidville Problem sheet to the class.
The new town of Kidville is laid out on a grid. There are 21 avenues
that run north and south. There are 9 streets that run east and west.
The avenues and streets all cross each other, and at each intersection
there is one stoplight. How many stoplights are there in Kidville?
Solution: This is a good problem for introducing the idea of simplifying in
order to solve. Instead of using the number of streets and avenues given in the
problem, have students reduce it to four avenues and three streets. They can
draw this grid in the work space and then mark the intersections with stoplights.
There will be a total of 12: 4 avenues times 3 streets = 12 intersections. To
prove it conclusively, have them pick two other numbers for streets and avenues,
do the multiplication and then draw the grid and count the lights. Now they will
be able to solve the problem.
Display the Travel Problem sheet and have groups of students work
together to solve this problem.
On your way to visit a friend, you leave your house at 2:45 P.M. and
travel 1 3/4 miles to the train, 12 1/2 miles on the train, and 3/4 mile
to your friend's house from the train station. If you get there at 4:15
P.M., how many miles per hour did you travel?
Once they have an answer, go around to each group and check their
answers. Groups that can explain their reasoning for their correct answer
can play other games.
Look to the right for steps to solving this problem.
Games
As groups finish their problems, they can play any of the following critical
thinking games: Snap, Mastermind, Apples to Apples, and Muggins.
Travel Problem
What problems do they need to
answer.

Time traveled

Distance traveled

Miles per hour
Use more familiar numbers

Time : 2 and 4; difference of
2 hours

Distance: 12 = 12 hours

Miles per hour: 2/12 = 6
miles per hour
Now that they know the steps,
put in actual numbers.

Time: 2:45 to 4:15 = 1 1/2
hours or 1.5 hours

Distance: 1 3/4 + 12 1/2 +
3/4 = 15 miles

Miles per hour: 1.5/15 = 10
miles per hour
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 17
Lesson 7 Focus: Charting and Graphing
Creating charts and graphs to solve a problem.
Material:
*White board
markers
Activity 1: Multiplication Chart Race
Create a large multiplication chart on the board, such as the example below.
It need not be the multiplication chart from 1 to 10; the teacher can choose
sections such as 5 to 9 or 3 to 7.
Do this activity as a timed race or as a team race and make two charts.
The students are to race to the board and fill in one square on the chart; the
next student enters another product or corrects a previous product. Students
continue to race until all numbers are filled in; the first team to correctly
complete the chart is declared the winner.
HELPFUL HINT: To avoid one team seeing the answer of another team,
use the same factors, but in a different order.
4
6
7
8
9
NOTES:
5
6
7
7
6
5
4
9
24
8
35
56
7
6
56
35
24
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 18
Activity 2: Logic and Reasoning Problems
Material:
*Logic Safari 2
*Logic Safari 3
*24 Game
*Apples to Apples
*Mastermind
*Muggins!
*Snap
Choose a logic problem from one of the Logic Safari books provided with the
club kit; solve the problem as a class. (Class abilities will determine from
which book the problem should be chosen.)
The logic problems help students organize information in a systematic way
and draw conclusions based on clues given.
Example:
On a recent trip to the zoo, we visited three of our favorite animals. They
were each in a different colored pen and each had a different trainer.
From clues given below, can you place each animal in their proper pen
with their proper trainer?

Brian is the trainer for the koalas.

The eagles are kept in the yellow pen.

Daniel is in charge of the green pen.
Questions
trainers
Brian
animals
1. Michael is caretaker for which animal?
2. Which animal is in the blue pen?
3. Who trains the bears?
As time and interest permits, encourage students to select
and solve problems from the Logic Safari books.
color
Koalas
Daniel
Michael
Green
Yellow
X
X
X
X
Eagles
X
Bears
X
X
Green
X
X
Yellow
X
Blue
Games: Mastermind, Apples to Apples, 24 Game, Snap, Muggins
Repetition of these games helps students to start applying strategies and
utilizing what they have learned about problem solving to become a better
game player. So as students finish their logic problems, they can play any of
these critical thinking games.
colors
X
X
X
X
X
Blue
X
X
X
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 19
Lesson 8 Focus: Work Backwards
Learning that certain problems with several steps resulting in a known value
can most easily be solved by working backwards one step at a time.
Starter: 25
This game is for two to four players. Give each group a deck of cards; remove
face cards. Deal out all the cards, face down, to players.
The first person turns over a card and places it face up in the center of group.
The next person turns over a card, adds it to the card already played, says the
sum out loud, and places the card on top of the previously played card. The
next person turns over a card and adds the card to the sum of the first two
cards.
Play continues in this way until someone has a card that, when added, will
result in a sum of 25 or greater. If the sum is greater than 25, the player must
subtract rather than add. Play continues until someone gets a sum of exactly
25. The player who gets a sum of exactly 25 wins that round and goes first in
the next round.
Activity 1: Working Backwards
Display the Apple Problem sheet to the class. Read the story problem out
loud and have different students take each question and answer it.
In my kitchen is a bowl with apples in it. I ate half of
them. My brother ate half of what I left. My sister ate
half of what my brother left. There is now one apple in
the bowl. How many were there to begin with?
1. What is the question you are being asked to answer? How many apples were
in the bowl to start?
2. What is your best strategy for solving this problem? Work backwards or
guess and check
3. Show your strategy.
1—what was left in the bowl. Double that.
2—apples left by brother. Double that.
4—apples left after I ate. Double that.
8– apples to start in the bowl.
Material:
*Apple Problem sheet
*Decks of cards
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 20
Game: NIM
This activity is based on the 1,000 year old game of NIM.
Group students in pairs; give each group 21 cards*. Cards are placed
facedown (so that numbers on cards will not be distracting to students) in a
heap between the two players.
The goal of the game is not to get left with the
last card.
To play, on their turn each player can take 1, 2,
or 3 cards. The players continue in this fashion
until one player is left with the last card.
*Note that this game can also be played using
counters, paperclips, toothpicks, etc., in lieu of
cards.
EXTENSION: Challenge students to figure out a strategy or pattern so as to
never lose the game (you can hint to them to work backwards, starting with
one card).
The solution is for a player to create a sum of four cards taken in the round.
For example, if Player A takes three cards, then Player B should take one. If
the Player A takes two cards, Player B should take two.
Note that students can play with as many counters/cards as they choose, as
long as the total is one larger than a multiple of four.
NOTES:
Material:
*Decks of cards
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 21
Lesson 9 Focus: Problem Solving Quickly and Accurately
Students will be presented with a multiple choice question and they will have
to determine the correct answer quickly
Lesson Prep: Make copies of the A B C D cards; cut apart. Optional — make
copies of the Funny Money sheet; cut apart.
Activity 1: Salute Alternative
This game is played exactly like the original Salute, but instead of two players and a judge, there are three to four players and a judge. Each group will
need a deck of cards, with face cards removed.
Have the players face each other and the judge deals out one card face down
to each player. When the judge says “salute” all the players put their cards
on their foreheads, and the judge will either say the sum or the product of all
the cards.
The first player to figure out their card wins that round.
Make sure that all players state their own card value — not just the player
who won the round.
HELPFUL HINT: Multiplication among three or four players might prove
challenging for some groups. If so, limit the cards in the deck to numbers 1
through 5.
NOTES:
Material:
*Decks of cards
Solving Mathematical Problems and Reinforcing Basic Math Facts
Page 22
Activity 2: Who Wants to Be a Math Millionaire?
Place students into groups of four; all groups play at the same time. Give
each group a set of the A B C D letters. Math Millionaire Questions are valued
at different dollar amounts — as the dollar amount gets higher, the questions
become more difficult.
To play, the teacher reveals a question on the sheet and reads it and the four
possible answers aloud. The groups then privately confer as to which is the
correct answer. Allow one to two minutes for the groups to come up with a
solution. (A group can show that it is ready to answer by putting their hands
up. ) Once all the hands are up, the Math Millionaire Host counts to three;
the players reveal the letter that their group believes represents the correct
answer. Groups with the correct answer add the question value to their current total.
Material:
*A B C D cards
*Funny Money
* Math Millionaire
Questions sheet
*Math Millionaire
Answer Sheet sheet
Example: Teacher reads the $100 question. The groups with the correct answer can either collect that money from the teacher (if using Funny Money)
or the students can keep a tally on a piece of scratch paper.
Teacher reads the $200 question. Only three groups get the correct answer —
those three groups then add $200 to their previous total of $100. They now
have $300.
If a group needs help prior to answering the questions, they have three
options, but they can use each option only once during the entire game.
1. Ask the teacher (teacher can help that group solve the problem)
2. 50/50 (teacher reduces that group’s answers from four possible answers to
two possible answers)
3. Survey the class (all students show with hands if they think the answer is
A, B, C or D)
Play continues until the million dollar question has been answered. The group
with the highest dollar amount wins.
HELPFUL HINTS:
 Each group should have one person keeping track of their dollar amounts.
 The student keeping score can also keep track of what help options the group may have used.
 All students in the group have to agree upon the answer.
 The teacher should reveal only one question at a time and cover up the other questions so there is no confusion

as to what question students are answering.
If a group can not come up with an answer within a pre-set time limit, they will need to guess.
Page 23
Solving Mathematical Problems and Reinforcing Basic Math Facts
Lesson 10 Focus: Review and Evaluations
Post-Math Club Evaluations:
Please ask the students to fill out a Post-Math Club Student Evaluation sheet. Remind students that this is not a test, but rather a way for you to understand their thinking.
Also, teachers please fill out the Curriculum Evaluation form so that Zeno learns how to better serve you and the students in
the future.
Please mail all the Student Evaluations (those from the first day of class, and those from the last) and your Curriculum Evaluation back to Zeno in the self-addressed envelope provided.
Thank You
Games/Activities for Review
Websites on Problem Solving
Games:
Digit-Place Game
Color Square Game
Salute
http://www.mathplayground.com
http://www.firstinmath.com
http://www.irt.org/games/js/mind/index.htm
http://www.coolmath-games.com
Apples to Apples
http://nlvm.usu.edu/en/nav/vlibrary.html
Buzz
http://www.matti.usu.edu
Mastermind
Eleusis
Muggins!
Bibliography
Snap
24 Game
Math War
Burns, Marilyn. About Teaching Mathematics 2nd Edition A K-8
Resource. Math Solutions Publications, 2000.
Multiplication Chart
Charlesworth, Eric 225 Fantastic Facts Math Word Problems,
Scholastics, 2001
Nim
Equals. Get it Together Math Problems for Groups Grades 4 –12.
Regents of the University of California, 1989
Sudoku
Meyer, Carol & Sallee, Tom, Make it Simpler A Practical Guide to
Problem Solving in Mathematics Dale Seymour Pulica
tions, 1983
Magic Squares
Towers of Hanoi
Logic Problems
Who Wants to be a Math
Millionaire?
Van de Walle, John, Elementary and Middle School Mathematics,
4th Edition, Longman Publishing, 2001
________, Navigating through Problem Solving and Reasoning in
Grades 3 – 5, NCTM, 2005
Dear Parents/Guardians and Students,
Welcome to a Zeno math club. In this ten lesson unit your child will be working on fun activities
that reinforce and expand on their regular classroom math curriculum. This club is an overview to
the mathematics of Problem Solving for elementary students in grades 3, 4 and 5. Students will
also be playing a number of games that will reinforce the basic math operations of addition,
subtraction, multiplication and division.
During class, students will work together on a variety of different problem solving techniques like
working backwards, finding hidden problems, and creating a picture or graph to help them find the
answer. Students will learn how to ask good questions in gathering information and how to work as
a group to help them solve the problems.
Students will play various games such as Color Square, Digit or Place, Mastermind, and Muggins to
help them analyze information and make mathematical deductions.
They will also have an
opportunity to play a game called Apples to Apples which helps students explain their reasoning for
giving a specific answer. All of these games are available at retail stores like Math ‘n Stuff, Blue
Highway Games, Target and Fred Meyer.
Students will also be learning a number of math reinforcement games that are both fun and easily
played with a deck of cards. Be sure to ask them how to play some of these games so that they can
continue to work towards reinforcing their math facts.
We hope your child enjoys participating in math club. If you would like to learn more about our
programs please check out our website at www.zenomath.org or call our office at 206-325-0774.
Sincerely,
Zeno
Student Contract
Welcome to a Zeno math club. In order for all students to have a positive experience in this
club, we have developed the following guidelines. The guidelines explain the positive behaviors we expect, as well as behaviors that are unacceptable.
Positive behavior will allow us to learn, play, grow and have fun together. Unacceptable behaviors will be handled by the club instructor, who may choose to contact the parents,
teacher, or principal of the misbehaving student. Consequences of unacceptable behavior
could include a warning or suspension from club activities.
Positive Behaviors
Listen and cooperate with students and teachers in the program.
Follow directions.
Wait quietly.
Be responsible and respectful with your words and actions.
Treat the materials carefully and use them in the way that you are instructed.
Help with clean up.
Unacceptable Behaviors
Not following school rules.
Put downs, teasing, and swearing.
Roughhousing, pushing, tripping, hitting, kicking or play fighting.
Damaging materials or taking them out of the room (without teacher permission).
I agree to follow these behavior guidelines and to do my best to help everyone have a positive experience.
___________________________________
__________
Signature
Date
Pre-Math Club Student Evaluation
Exploring Problem Solving
Club Teacher: Please read aloud the questions below to all students and allow a few seconds for response time.
Please mail to EIM pre and post student evaluations, along with the teacher evaluation at the completion of the
math club. Thank you.
Student Name: _______________________________________________ Date: __________________
School: ______________________________________________________ Grade: _________________
Is this your first time in an Zeno Club? ____ Yes ____ No
———————————————————————————————————————————————
I think math is fun.
No
Maybe
Yes
I am comfortable answering questions in math class.
Agree
Neutral
Disagree
Mathematics helps me develop my mind and teaches me to think.
Agree
Neutral
Disagree
I believe I am good at solving math problems.
Agree
Neutral
Disagree
Math is _____________________________________________________________
____________________________________________________________________
Pre-Math Club Student Evaluation
Exploring Problem Solving
1. Circle the vertical line.
2. Fill in the last box and write the rule for the following Input-Output table.
INPUT
OUTPUT
4
48
2
24
7
84
Rule:
10
3.
On your way to visit a friend, you leave your house at 2:45 P.M.
and travel 1 3/4 miles to the train, 12 1/2 miles on the train,
and 3/4 mile to your friend's house from the train station. If you
get there at 4:15 P.M., how many miles per hour did you travel?
What is the question that you are being asked to answer in the following problem?
A. How long did it take you to get to the train station?
B. How far is it from your house to the train station?
C. At what speed did you travel?
D. Was it farther from your house to the train station or farther from the train station to your friend’s
house?
4. Write the solution to these mental math problems:
Start with 5, double it, add 7, subtract 9, multiply by 3, divide by 6, multiply by 4.
Answer: ________________________
5.
Start with 7, double it, subtract 2, subtract 10, multiply by 3, subtract 6
Answer: ________________________
Color Square Game
Zeno: Exploring Problem Solving: Lesson 1 Activity 2
Math Millionaire Game I
$100
The value of a pile of nickels is 75¢. How many nickels are in the pile?
$200
Andy saved $18. He saved 3 times as much as Matt. How much did Matt save?
$500
$1000
$2000
$4,000
$8,000
17
A. $54
B. 14
B. $9
C. 16
C. $36
D. 15
D. $6
You can buy 3 books for $5. How much would 12 books cost?
A. $60
B. $36
C. $20
D. $15
C. 4/5
D. 5/12
Which is the greatest fraction?
A. 7/10
B. 5/6
Jen spent 2.5 hours doing her homework. How many minutes was that?
A. 120 minutes
B. 150 minutes
C. 180 minutes
D. 90 minutes
The product of two numbers is 216. One of the numbers is 9. What is the other number?
A. 18
B. 14
C. 24
D. 21
Which of these is not a quadrilateral?
Zeno: Exploring Problem Solving: Lesson 2 Activity 1
Math Millionaire Game I
$16,000
$32,000
Put these in order starting with the smallest: 2.12, 2.3, 2.22, 3.21
A. 2.22, 2.3, 3.21, 2.12
B. 2.12, 2.22, 2.3, 3.21
C. 3.21, 2.3, 2.22, 2.12
D. 2.3, 2.12, 2.22, 3.21
A box of 6 candy bars weighs 18 ounces. The box alone weighs 3 ounces. What is the
weight of one candy bar?
A. 12 oz
$64,000
B. 2.5 oz
B. 64 cubes
C. 24 cubes
D. 12 cubes
B. 34
C. 3.4
D. 3400
10% of 340 =
A. .34
$250,000
D. 15oz
How many 1 cm³ cubes will fit inside a box measuring 4 cm on each side?
A. 16 cubes
$125,000
C. 2.25 oz
A football team won 55% of its games. What fraction of the games did the team lose?
A. 3/5
B. 9/20
C. 11/20
D. 2/5
$500,000
What is the value of a + b if a = -7 and b = 10?
$1,000,000
There are 120 coins on the table, 30 of them are quarters. What percent is that?
A. 17
A. 30%
B. 3
B. 15%
C. -3
C. 25%
D. -17
D. 20%
Zeno: Exploring Problem Solving: Lesson 2 Activity 1
Input/Output Examples
INPUT
OUTPUT
INPUT
OUTPUT
4
48
5
26
2
24
10
101
7
84
2
5
10
7
15
20
6
15
0
4
11
8
1
1
5
9
(N x 12)
(N x N + 1)
INPUT
OUTPUT
INPUT
OUTPUT
5
13
9
90
10
28
3
12
2
4
6
42
100
298
7
5
4
12
5
20
1
10
9
2
14
4
(3N– 2)
(N x N) + N
Zeno: Exploring Problem Solving: Lesson 3 Activity 2
MONDAY
MONTH:____________________
SUNDAY
TUESDAY
WEDNESDAY
THURSDAY
CALENDAR TEMPLATE
SATURDAY
Zeno: Exploring Problem Solving: Lesson 2 Activity 2
FRIDAY
Do you notice any patterns when solving the puzzle?
If you are unable to figure out 5 cards start with fewer cards, such as 1—3 or 4.
Zeno: Exploring Problem Solving: Lesson 3 Activity
Start with all the cards in one stack, in ascending order, in the center square of the game board. You can only
move one card at a time to a spot on the right or left of the stack or back on the middle stack.
The object of the game is to get all the cards from the center of the board to another place, by moving one card
at a time without putting a higher numbered card on top of a lower numbered card.
Remove the cards 1—5 from a deck of cards.
TOWERS OF HANOI
Magic Squares
8
2
7
= 15
= 15
9
2
4
2
11
16
= 34
12
10
13
11
= 34
9
1
Zeno: Exploring Problem Solving: Lesson 4 Activity 2
Boxes Inside of Boxes
Jane has three large boxes.
Inside each large box are two
medium boxes. Inside each
medium box are four small
boxes. How many boxes does
Jane have in all?
1. What is the question you are being asked to answer?
______________________________________________
______________________________________________
2. What is the best strategy for solving this problem?
______________________________________________
______________________________________________
______________________________________________
3. Use this space to show your strategy.
4. Now write the answer to the question in a complete
sentence. _____________________________________
Zeno: Exploring Problem Solving: Lesson 5 Activity 2
The Father and His Two Children
(Scenario #1)
A father is out walking with his
two children when they come to
a river. The father finds a small
boat to take them to the other
side of the river, but the boat will hold only 200 pounds.
(Any more than that and the boat will sink.)
The father weighs 200 pounds. Each of his children
weighs 100 pounds and they know how to row a boat.
How can all three get across the river in the boat?
Zeno: Exploring Problem Solving: Lesson 5 Activity 3
The Farmer, the Fox, the Goose, and the Corn
Scenario #2
A farmer is going to market; with him are a fox, a goose
and a bag of corn.
They come to a river, where the farmer has a small boat
in which to transport himself and his goods across the
river. The boat will hold only the farmer and either the
fox, the goose or the bag of corn. However, if the
farmer takes the corn, the fox will eat the goose. If the
farmer takes the fox, the goose will eat the corn. How
can he get himself, the fox, the goose and the corn
across the river in the boat?
Zeno: Exploring Problem Solving: Lesson 5 Activity 3
The Farmer, the Dog, the Fox, the Goose, and the
Corn
Scenario #3
A farmer is going to market; with him are a fox, a goose, a
bag of corn and a dog.
They come to a river where the farmer has a small boat
which can be rowed back and forth across the river. The
boat can carry the farmer and either the fox, the goose,
the corn or the dog.
The fox cannot be left with either the dog or the goose or
both. The goose can be left with the corn if the dog is
present to guard the corn. (The dog will not eat the
goose.)
How can the farmer get himself, the dog, the fox, the
Zeno: Exploring Problem Solving: Lesson 5 Activity 3
The Elephant, the Mouse, the Dog, and the Cat
(Scenario #4)
A circus owner must to take his elephant, his mouse, his
dog and his cat across a river. He can take one at a time
across the river in his boat. However, unless the farmer is
present, the cat will fight with the mouse, the dog will
fight with the cat and the elephant will fight with the
dog. As we all know, the elephant is frightened of the
mouse and if the mouse is present, the elephant will not
fight with the dog. By taking the animals back and forth,
how can the circus owner get all across without any
fighting?
Zeno: Exploring Problem Solving: Lesson 5 Activity 3
Kidville Problem
The new town of Kidville is laid out on a
grid. There are 21 avenues that run north
and south. There are 9 streets that run
east and west. The avenues and streets all cross
each other and at each intersection there is one
stoplight. How many stoplights are there in
Kidville?
1. What is the question you are being asked to answer?
______________________________________________
______________________________________________
2. What is the best strategy for solving this problem?
______________________________________________
______________________________________________
______________________________________________
3. Use this space to show your strategy.
4. Now write the answer to the question in a complete
sentence._____________________________________
Zeno: Exploring Problem Solving: Lesson 5 Activity 2
Travel Time
On your way to visit a friend, you leave
your house at 2:45 P.M. and travel 1 3/4
miles to the train, 12 1/2 miles on the train,
and 3/4 mile to your friend's house from the
train station. If you get there at 4:15 P.M.,
how many miles per hour did you travel?
1. What is the question you are being asked to answer?
______________________________________________
______________________________________________
2. What is the best strategy for solving this problem?
______________________________________________
______________________________________________
3. Use this space to show your strategy.
4. Now write the answer to the question in a complete
sentence. _____________________________________
Zeno: Exploring Problem Solving: Lesson 6 Activity 2
Logic Problem
On a recent trip to the zoo, we visited three of our favorite animals.
They were each in a different colored pen and each had a different
trainer. From clues given below, can you place each animal in their
proper pen with their proper trainer?

Brian is the trainer for the koalas.

The eagles are kept in the yellow pen.

Daniel is in charge of the green pen.
Questions
1. What animal does Michael take care of?
2. Which animal is in the blue pen?
3. Who trains the bears?
trainers
Brian
animals
Daniel
colors
Michael
Green Yellow
Blue
Koalas
Eagles
Bears
color
Green
Yellow
Blue
Zeno: Exploring Problem Solving: Lesson 7 Activity 2
Apple Problem
In my kitchen is a bowl with apples in it. I
ate half of them. My brother ate half of
what I left. My sister ate half of what my
brother left. There is now one apple in the
bowl. How many were there to begin with?
1. What is the question you are being asked to answer?
________________________________________________
________________________________________________
2. What is the best strategy for solving this problem?
________________________________________________
________________________________________________
________________________________________________
3. Use this space to show your strategy.
4. Now write the answer to the question in a complete
sentence._______________________________________
Zeno: Exploring Problem Solving: Lesson 8 Activity 2
AB
CD
Zeno: Exploring Problem Solving: Lesson 3 Activity 2
Math Millionaire Game II
$100
The value of a pile of nickels is 75¢. How many nickels are in the pile?
$300
Andy saved $18. He saved 3 times as much as Matt. How much did Matt save?
A. 17
A. $54
$600
C. $36
B. $36
D. $15
B. 5/6
C. 4/5
D. 5/12
Jen spent 2.5 hours doing her homework. How many minutes was that?
C. 180 minutes
D. 90 minutes
The product of two numbers is 216. One of the numbers is 9. What is the other number?
A. 18
$7,000
D. $6
C. $20
A. 120 minutes B. 150 minutes
$4,000
D. 15
Which is the greatest fraction?
A. 7/10
$2000
B. $9
C. 16
You can buy 3 books for $5. How much would 12 books cost?
A. $60
$1000
B. 14
B. 14
C. 24
D. 21
Which of these is not a quadrilateral?
A. Kite
B. Rhombus
C. Decagon
D. Rectangle
Zeno: Exploring Problem Solving: Lesson 9 Activity 2
Math Millionaire Game II
$15,000
$30,000
Put these in order starting with the smallest 2.12, 2.3, 2.22, 3.21
A. 2.22, 2.3, 3.21, 2.12
B. 2.12, 2.22, 2.3, 3.21
C. 3.21, 2.3, 2.22, 2.12
D. 2.3, 2.12, 2.22, 3.21
A box of 6 candy bars weighs 18 ounces. The box alone weighs 3 ounces. What is the
weight of one candy bar?
A. 12 oz
B. 2.5 oz
C. 2.25 oz
D. 15oz
$65,000
How many 1 cm³ cubes will fit inside a box measuring 4 cm on each side?
$125,000
10% of 340 =
$200,000
A. 16 cubes
A. .34
D. 12 cubes
B. 34
C. 3.4
D. 3400
B. 9/20
C. 11/20
D. 2/5
What is the value of a + b if a = -7 and b = 10?
A. 17
$300,000
C. 24 cubes
A football team won 55% of its games. What fraction of the games did the team lose?
A. 3/5
$250,000
B. 64 cubes
B. 3
C. -3
D. -17
There are 120 coins on the table, 30 of them are quarters. What percent is that?
A. 30%
B. 15%
C. 25%
D. 20%
Zeno: Exploring Problem Solving: Lesson 9 Activity 2
Math Millionaire Game
$100
D. 15
$300
D. $6
$600
C. $20
$1000
B. 5/6
$2000
B. 150 minutes
$4,000
$7,000
$15,000
$30,000
$65,000
$125,000
$200,000
$250,000
$300,000
C. 24
C. Decagon
B. 2.12, 2.22, 2.3, 3.21
B. 2.5 oz
B. 64 cubes
B. 34
B. 9/20
B. 3
C. 25%
Zeno: Exploring Problem Solving: Lesson 9 Activity 2
100
$
100
1000
$
1000
10000
$
10000
$
500
100
$
$
5000
1000
$
$
10000
500
500
5000
$
5000
50000
$
$
50000
Zeno: Exploring Problem Solving: Lesson 9 Activity 2
$
50000
Post-Math Club Student Evaluation
Exploring Problem Solving
Club Teacher: Please read aloud the questions below to all students and allow a few seconds for response time.
Please mail to EIM pre and post student evaluations, along with the teacher evaluation at the completion of the
math club. Thank you.
Student Name: _______________________________________________ Date: __________________
School: ______________________________________________________ Grade: _________________
Would you like to attend another Zeno Club? ____ Yes ____ No
———————————————————————————————————————————————
I think math is fun.
No
Maybe
Yes
I am comfortable answering questions in math class.
Agree
Neutral
Disagree
Mathematics helps me develop my mind and teaches me to think.
Agree
Neutral
Disagree
I believe I am good at solving math problems.
Agree
Neutral
Disagree
Math is _____________________________________________________________
____________________________________________________________________
Post-Math Club Student Evaluation
Exploring Problem Solving
1. Circle the vertical line.
2. Fill in the last box and write the rule for the following Input-Output table.
INPUT
OUTPUT
4
48
2
24
7
84
Rule:
10
3.
On your way to visit a friend, you leave your house at 2:45 P.M.
and travel 1 3/4 miles to the train, 12 1/2 miles on the train,
and 3/4 mile to your friend's house from the train station. If you
get there at 4:15 P.M., how many miles per hour did you travel?
What is the question that you are being asked to answer in the following problem?
A. How long did it take you to get to the train station?
B. How far is it from your house to the train station?
C. At what speed did you travel?
D. Was it farther from your house to the train station or farther from the train station to your friend’s
house?
4. Write the solution to these mental math problems:
Start with 5, double it, add 7, subtract 9, multiply by 3, divide by 6, multiply by 4.
Answer: ________________________
5.
Start with 7, double it, subtract 2, subtract 10, multiply by 3, subtract 6
Answer: ________________________
Curriculum Evaluation Form
Exploring Problem Solving
Dear Club Teacher,
Thank you so much for making math fun for students. In order to make these
clubs most effective for students and the club teachers we need to get some
information from you on the lessons and games. Any additional information that
you would like us to know please include on the back of this form.
Thank you.
Ages/Grades of Students:
How many weeks was the club?
How many lessons were completed:
How many students did you teach?
_________________________________________________________________________________________________________
From the beginning to the end of math club, overall, did you observe any shift in student confidence? Please explain.
Less confidence
No change
More confidence
_________________________________________________________________________________________________________
_________________________________________________________________________________________________________
What lessons and games did you find to be most helpful, and why?
__________________________________________________________________________________________________________
__________________________________________________________________________________________________________
What lessons and games did you find to be least effective, and why?
__________________________________________________________________________________________________________
__________________________________________________________________________________________________________
Is there anything that you feel needs to be changed or restructured?
__________________________________________________________________________________________________________
__________________________________________________________________________________________________________
Do the daily lessons provide enough activities to fill an hour?
__________________________________________________________________________________________________________
__________________________________________________________________________________________________________
Were there any supplies that should have been included in the tubs that were not available?
__________________________________________________________________________________________________________
__________________________________________________________________________________________________________
Please return evaluation forms to:
Zeno
1404 East Yesler Way; Suite 204
Seattle, WA 98122
If you have any other questions or concerns please feel free to
contact: Program Director, Jennifer Gaer at 206-325-0774 or
[email protected]