in Math! · Contents Meeting 1 Winter 2018 Cooperating in Math! January 10th INSTRUCTORS MANUAL 1) STEM Mystery 2) Our Values 3) Strange Coins Teaching Tips

Contents

Meeting 1 Winter 2018

Cooperating in Math!

January 10th

INSTRUCTORS MANUAL

1) STEM Mystery

2) Our Values

3) Strange Coins

Teaching Tips www.math.uci.edu/mathceo

2018 UCI MATH CEO COMMUNITY EDUCATIONAL OUTREACH. UNIVERSITY OF CALIFORNIA AT IRVINE

Math CEO You Tube Channelhttps://www.youtube.com/channel/UCvMQNFt-hPf-xKsNixhzYXw

Math CEO Facebook Page https://www.facebook.com/UCIMathCEO

About MATH CEO

2018 UCI MATH CEO COMMUNITY EDUCATIONAL OUTREACH. UNIVERSITY OF CALIFORNIA AT IRVINE

Our Goals

Inspire and support the interest in mathematics of middle

school students from nearby communities who might not

otherwise have access to math enrichment activities.

Impart the mathematical foundations and critical thinking

skills required for students to successfully pursue a college

education and a career in STEM areas.

Instill the desire in these young achievers and their families

for a college education and share college access information

and financial aid opportunities.

UC Irvine Math CEO program is committed

to offering free enrichment activities in

mathematics for middle school students in

underserved communities, and creating

free educational material to be used in

classrooms around the world. An essential

goal of our program is to encourage

students in low income, minority

communities in Southern California to

pursue a college degree in Mathematics,

Science or related fields through a solid

foundation and adequate planning.

https://www.youtube.com/channel/UCvMQNFt-hPf-xKsNixhzYXw

https://www.youtube.com/channel/UCvMQNFt-hPf-xKsNixhzYXw

https://www.facebook.com/UCIMathCEO

https://www.facebook.com/UCIMathCEO

CH

ECKL

IST

◻ Identify the Leader mentor◻ Write names of any new mentors and students (find form inside folder, write new names if needed)◻ Place check marks in the Meeting 1 column (same form inside folder)◻ Tell math goals to students in each activity◻ Call students by their name, it helps bonding◻ Keep students silence while doing the Quiz◻ Keep your table neat and clean at all times◻ Get help if there are behavior problems before they escalate

◻ Quiz PROBLEM 1 (pink) (end of Activity 2)◻ Student Survey (pink) (start survey no later than 3:40 PM)◻ Fill Meeting Report (blue) (if you are the Leader)◻ Put back into folder: Student Surveys (pink), Meeting Report (blue)

Cooperating in Math! (Meeting 1, Jan 10)

NS2 1201 (Lathrop), PSCB 140 (Villa)

Dear Mentor

In this meeting we will begin Winter Quarter, and do three activities to serve as icebreakers and also to reinforce our program expectations. Activity 1 is about STEM Careers, Activity 2 will help you know your students and set the learning and behavior expectations during the quarter. Activity 3 has mathematical problems. Please do not rush or panic if you don’t get to the finish line. The goal is not to finish the booklet, but rather that students understand.

To see explanatory videos, please visit this link.

UCI Math CEO • Meeting 1INTRODUCTION

Math Goals

Kids can define in their own words what a horizontal or vertical stretching is, giving examples.

Kids understand the difference between “AND” and “OR” when connecting 2 conditions or restrictions.

Kids understand visually how stretching of a figure (horizontal, vertical, or both) affects its original area.

Kids apply the concept of “directly proportional” in real life situations to find new values from given values and proportionality relations.

Kids can locate different type of data given by basis charts.

ANDOR

https://www.youtube.com/playlist?list=PLdc-KjVOkiPfT104HuYw5-bMUIGYiolsm

MATERIALS & AGENDA

MATERIALS TRANSPARENCIESOne per person

INSTRUCTOR MANUALGreen color(No student Booklet)

STUDENT SURVEYS(INCLUDES QUIZZES)Pink ColorOne per student

WHITEBOARDSOne per student

DRY ERASE MARKERSA pouch with several

IMPORTANT!

Please count the number of markers in the pouch. Ask the students to return them to the pouches when they're finished. Make sure that at the end, no kid takes any markers home.

MEETING REPORTBlue colorOne per table

Online meeting report

End of the meetingCollect all student surveys with all mentor’s meeting reports on top, and return to the organizers in the folder. Make sure kids clean table and floor, and take all their belongings with them.

UCI Math CEO • Meeting 1

Im

Mr

Ss

Fp

AGENDA

2:10 pm Introduction

2:15 pm 1) STEM Mystery A game of asking questions and discovering careers

2:45 pm 2) Our Values Exploring the values at Math CEO and writing examples of how to promote them

3:00 pm Quiz: Problem 1

3:05 pm 3) Strange Coins A game of proportionality and areas

3:40 pm Student Survey

3:45 pm End of the meeting

+

INTRODUCTION

INDIVIDUAL ASSESSMENT

● Right after Part 2 (Our Values), there is time for an individual Quiz (PROBLEM 1 IN THE SURVEY). Give students 5 minutes to do both parts A and B and have them answer individually (in their surveys). After collecting answers, grade them and quickly correct them with the kids.

TIPS● Build the habit of having students complete the quiz in

complete silence and without any help of peers of mentors. This may take a few meetings, but make perfectly clear that we will work with these expectations. Do not ignore this.

BEHAVIOR EXPECTATIONSIf a kid is behaving improperly or disrupting students, or does not follow directions at all, talk to them. If problem persists or is really serious, please let Brandi, Alessandra, Li-Sheng or an Assistant know immediately.

UCI Math CEO • Meeting 1

This icon refers to specific tips which you will find embedded in the booklet activities: procedures, questions to ask to the students, recommended methodologies, and so on.

Can you explain the concept in your own words?

Example: After you introduce a new concept, it is a good idea to ask students to rephrase the concept, explain it in their own words. You can choose particular students, for example those who are disengaged.

Can someone read the instructions out loud?

Example: It is convenient to ask one student to read out instructions for a problem or definitions of a concept. This keeps your group focused on the task and improves their reading skills if you give feedback on reading.

UCI MATH CEO MEETINGS: BASIC GUIDELINES FOR VOLUNTEERS

CHECK WORKVerify that the

students write the answers to the

problems and that they are correct and complete.

KNOW YOUR STUDENTSCall students by their

names most of the time: make sure they know your

name, talk briefly about their day before you start

the math activities.

ASK FOR EXPLANATIONSAsk students how they got their answers. Say things like “How do you know?”, “Why?”, “Draw a picture”, “Convince me!”, “Can you

explain to Juan?”, etc.

AT THE ENDAsk students to fill

out the survey individually (no

help), and to help pick up trash from the table and floor.

MOVE & MONITORMove around your table; monitor all students; use an adequate tone of

voice; encourage kids to work in teams.

TEACHING TIPS

1This icon means that the students should work individually in the corresponding problem, before discussing. Be flexible and adapt to your situation.

1 2 3 4 5

2Activity to be done in pairs

Note: if not specified, the booklet problem can be done as a group activity involving a discussion.

(a) Match

5 4.5

STEM MYSTERY

What does STEM mean?

What are some examples of STEM careers and professions?(See list in next page)

Suppose that Ana has a STEM career, but she will not tell you which one. Which questions about the career can you ask Ana to figure out this career?

Discuss in your group. Everyone talks.

Our Goals: To bond everyone in your table (both students and mentors)

125-30 min

AerodynamicistAllergistAndrologistAnesthesiologistArchaeologistAstrobiologistAstronautAstronomerAstrophysicistAudiologist

BiochemistBioengineerBiologistBotanist

CardiologistChemistChiropractorClimatologist

DermatologistDoctor

EcologistEconomistEndocrinologistEngineerEntomologistEpidemiologist

GastroenterologistGastrologistGeneticistGeographerGeologistGeophysicistGeriatricianGynecologist

HematologistHepatologist

ImmunologistInventor

Limnologist

MathematicianMeteorologistMicrobiologist

NeonatologistNephrologistNeurobiologistNeurologistNeurophysiologistNeurosurgeonNurseNutritionist

ObstetricianOceanographerOncologistOphthalmologistOpticianOptometristOrthotist

PaleoclimatologistPaleontologistPaleopathologist

ParasitologistPathologistPediatricianPerinatologistPharmacistPharmacologistPhysiatristPhysicianPhysicistPhysiologistPodiatristPsychiatristPsychologistPulmonologist

RadiologistRheumatologistScientistStatisticianSurgeonUrologistVeterinarianVolcanologistZoologist

The Full list of STEM Careers

https://www.studentpuzzles.com/uploads/WordSearch_STEM_Careers2.pdf

STEM PROFESSIONS

Materials

● 1 STEM Careers table per student

● Post it notes (or small chunks of paper)

● 1 Timer for 5 minutes (can use a smartphone)

UCI Math CEO • Meeting 11) STEM MYSTERY

STEM MYSTERY

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In STEM Mystery, students play a game similar to the board game SpyFall, in which they need to find who is the “spy” (called the APPLICANT), and the spy needs to identify the STEM career of the corresponding round (which all players know, except him). The game flows through a series of questions amongst players: whoever answers a question gets to ask another person (different that the one who just asked him).

This game promotes the thinking skill of asking useful questions (which is key in mathematics), using logic and deduction. It also helps students familiarize with STEM Careers.

Before you start the game, have students familiarize with the 9 STEM Careers of the table, and have a quick discussion of what each consists of.

You can play several rounds, depending on the time. In what follows we describe a round. A typical round lasts around 8 minutes.


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SetupHand the STEM Careers table to each player, so that they are familiar with those 9 careers listed.

The mentor secretly selects a STEM Career (numbered 1-9) from the STEM Careers table and prepares a bunch of notes (for example, post-its or small chunks of paper), one for each player. These notes will be used to assign roles to the players, and must be kept secret throughout the game. The mentor writes A (for Applicant) on one note; on all the other ones, he/she writes the number of the selected career. Then the mentor shuffles the pile of notes and secretly deals 1 note to each player. The player with the A card will be the Applicant, all the others will have the common profession indicated by the number, which they can identify by looking at the STEM Career table.

ECONOMISTPlayer 1

ECONOMISTPlayer 4

ECONOMISTPlayer 2

ECONOMISTPlayer 5

ECONOMISTPlayer 6

APPLICANTPlayer 3

Example: Suppose that there are 6 players. The mentor secretly chooses

“Economist” (Career #4) for this round. Then he/she forms a pile with a total of

six notes: five will be marked with a 4, and one will be marked with an A. After, the mentor shuffles and deals these notes to the players, to assign them roles. In this round, five players will be economists and one player will be the APPLICANT (who does NOT know the common career of the rest of players).

Player 1

Player 4

Player 2

Player 5 Player 6

Player 3

#4 #4

#4 #4#4

A

As on Bi c is

Nut on

En i rEco s

Ne r o s

Mat ti

Dat e t

Sur

1 2 3

4 5 6

7 8 9

UCI Math CEO • Meeting 11) STEM MYSTERY 12

Goal of the game

● The APPLICANT must discover the common career of the rest of the players (one of the 9 in the table), and not be caught during the game.

● The rest of players must discover who the APPLICANT is before the game ends, by nominating it and having everyone to vote unanimously that he is.

The applicant wins the game if the rest of players vote for another player to be the applicant (“wrong conviction”), or if 5 minutes go by and he was not voted to be the applicant.

PlayThe mentor sets up a timer of 5 minutes. During this time, a designated starting player asks a question to another player about the career. That player responds (however he/she likes), and then asks another question to a different player (not to the player that just asked). This sequence of questions and answers continues.


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Example: Ana starts. She asks Ben: “how much traveling you need in this career?”. Ben answers: “Well, not much really, I need to work on desks for a long time”. Then Ben asks Carl: “What type of Lab do you need in this career?”. Carl responds: “You don’t need any labs in this career, it's more like analyzing things”. Now Carl asks...

Nominating a suspectAt any time during play (right after a question has been answered), a player can make an accusation that another specific player is the APPLICANT (based on the incorrect responses or lack of details, etc). After that, all players except the one being accused, vote at the same time: At the count of three, every player reveals a Thumbs-UP or Thumbs-DOWN.

● Thumbs-UP indicates GUILTY.

● Thumbs-DOWN indicates INNOCENT.

If all players voted Thumbs-UP and the nominated player was indeed the APPLICANT, then he loses the game, and the rest of players win.

APPLICANT Vs. Rest of players


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If all players voted Thumbs-UP and the nominated player was NOT the APPLICANT, then whoever was the applicant wins the game, and the rest of players lose.If at least one player votes Thumbs-DOWN, nothing happens and play continues.

Note: even the Applicant can nominate someone.

Example: After 4 minutes of play, Ben accuses Carla to be the APPLICANT. Carla is NOT the APPLICANT. The vote takes place and all players (except Carla, who does not vote), vote Thumbs-UP. Players have mistaken Carla for The APPLICANT. The real APPLICANT, whoever he or she is, wins the game.

Example: After 2 minutes of play, Mary says: “I will nominate David to be the APPLICANT because...”. It turns out that David is indeed the APPLICANT. Players vote (except for David) and all players show Thumbs-Up. David reveals his APPLICANT note. This means that he loses and all other players win.

Example: After 3 minutes of play, Carl nominates Ana to be the APPLICANT. All players except Ana vote as follows:● Carl: Thumbs UP● Mary: Thumbs DOWN● Peter: Thumbs UP● Zhao: Thumbs DOWN● Bob: Thumbs UP

Since at least one player showed a Thumbs DOWN, nothing happens and players continue asking questions.

Recall that if 5 minutes pass and the APPLICANT is not caught, then he wins the game.

Discovering the careerAt any time during the game (right after a question has been answered), the APPLICANT can reveal himself, and then guess the career for that round. If he is right, he wins the game, otherwise, he loses the game. In any case, the game ends.

Example: After 3 minutes, Ana reveals herself as the APPLICANT, showing her note. She then guesses the the rest of the players are mathematicians. Since the players were economists, she guessed wrong and she loses the game.

Asking Questions

The questions can be yes/no questions or open questions, but they need to refer to careers. Here are some examples of questions that you can use (it is helpful that students know some examples):● How much math do you need for this career?● What kind of jobs can you get if you study this

career?● Do you need to spend much time in a desk in this

career?

Remind students that if they are not the APPLICANT, it is in their best interest to answer with the truth, as otherwise they will be wrongly accused of not knowing. But, if they answer with too much information, then whoever is the APPLICANT will know the career easily.

Of course, since the APPLICANT does not know the career, he must do his best to provide reasonable answers, based on what he has heard so far from others.


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Rules summary:

Setup: secretly choose a career, form a pile with APPLICANT note + notes of the same career (chosen by the mentor). Deal one note to each player (secretly and randomly). Whoever got the APPLICANT note (A) is called the Applicant. Notes are secret. All other players get the same number 1-9 corresponding to a specific career

Play: 5 minutes, questions. Whoever answered gets to ask, but cannot bounce back. If 5 minutes pass, the Applicant wins.

Nomination: Player A nominates player B to be the applicant. Even the applicant can nominate.

● Voting: all players except B vote at the same time, Thumbs UP for guilty, Thumbs DOWN for non guilty.

○ If all players voted Thumbs UP and player B is the Applicant, then he loses.

○ If all players voted Thumbs UP and player B is not the Applicant, then the Applicant wins.

○ If at least one player voted Thumbs DOWN, play continues.

Guessing the career: The applicant reveals himself and guesses the career from the ones in the table.

● If he is right, he wins the game● If he is wrong, he loses the game

Setup: Suppose that there are 6 players. The mentor secretly chooses “Economist” (Career #4) for this round. Then he/she forms a pile with a total of six notes: five will be marked with a 4, and one will be marked with an A. After, the mentor shuffles and deals these notes to the players, to assign them roles. Roles are secret, so players should not share the information on their notes!

In this round, five players will be economists and one player will be the APPLICANT (who does NOT know the common career of the rest of players). The APPLICANT’s goal is to figure out the common STEM career; the goal of the Economists is to figure out who the APPLICANT is before the APPLICANT guesses the career and before time runs out.


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Example of one game

ECONOMISTPlayer 1: Ally

ECONOMISTPlayer 4: Delia

ECONOMISTPlayer 2: Ben

ECONOMISTPlayer 5: Eduardo

ECONOMISTPlayer 6: Fiona

APPLICANTPlayer 3: Chris

Game Play: The group decides that Ally will go first.

Ally can choose any player and ask that player a question about the secret STEM career. Ally asks Delia: “Can you give some examples of math you do in this career?” Delia answers, “Yes! You have to add, subtract, multiply, and divide a iot.”

Now it is Delia’s turn to choose any player and ask a question. Delia asks Eduardo: “Do you think jobs in this field make people wear special uniforms?” Eduardo answers, “No.”

It is Eduardo’s turn to choose any player and ask a question. Eduardo asks Chris: “How many people study this career?” Chris answers, “Lots of people.”

Chris in turn asks Ally: “Is this the type of career that you would see in a cool TV show?” Ally answers, “Probably not… or, at least, I’ve never heard of a show like that.”

Ally asks Fiona: “Do you interact with other people a lot?” Fiona replies, “Not really. It is more of a solitary job.”

Etc.

Ending the game: The game can end in four different cases: (1) the APPLICANT reveals himself or herself, (2) the APPLICANT is correctly discovered by the group, (3) a NON-APPLICANT is accused by the group, (4) time runs out.

Case 1. The APPLICANT is revealed. Before time runs out, Chris can announce, “I am the Applicant!” At this point there are two possible results: Chris wins if he guesses correctly the correct group STEM career. If he does not announce the correct career, he loses and the Economists win!


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Example of one game (continued)

ECONOMISTPlayer 1: Ally

ECONOMISTPlayer 4: Delia

ECONOMISTPlayer 2: Ben

ECONOMISTPlayer 5: Eduardo

ECONOMISTPlayer 6: Fiona

APPLICANTPlayer 3: Chris

Before time runs out, any player can accuse someone of being the APPLICANT. For example, Ben can stop the game and say, “I think the Applicant is _____!”. The accused must wait while the other players vote. If all other players agree that the accused is the APPLICANT, there are two possible results:

Case 2. The APPLICANT is discovered. If Ben said “I think the Applicant is Chris,” and the other players unanimously agree, then Chris admits to being the Applicant. Chris loses and the Economists win.

Case 3. A NON-APPLICANT is accused by the group. If Ben said “I think the Applicant is Fiona,” and the other players unanimously agree, then Chris admits to being the Applicant. Chris wins and the Economists lose.

If someone is accused but the other players do not unanimously agree, then Chris should not reveal that he is the APPLICANT. The game continues where it left off.

Case 4. Time runs out. If time runs out without a winner being determined with Cases 1,2,3, then the APPLICANT automatically wins and the Economists lose.

(a) Match

5 4.5

OUR VALUES

Why is it important to have values and agreements when working together?

What are some positive values that you can think of when learning math?

What are some effective ways to make sure that the values agreed on are in fact followed and respected?


Our Goals: To bond everyone in your table (both students and mentors)

210 - 15

min

UCI Math CEO • Meeting 12) OUR VALUES

OUR VALUES ActivityTime

periodCalories burned

Cal / min

Playing Video Games 30 min 42

Walking 30 min 80

Running 10 min 115

Dancing 30 min 200

Jumping Rope 1 min 10

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Materials: ● “Values at MATH CEO” card (1 per student, see next page).● Small Flashcards or Blank Paper (1 for each student and 1 for each mentor,

plus some extra)

Instructions:

Tell the students that we will review 10 important values of Math CEO, where each has a typical phrase that people say all the time during the teaching sessions. Their job is to read each phase and highlight the part (word or words) that they like the most from it. This should be done as a group discussion

After that, explain students that we will all have 5 minutes to select 1 value and write a new phrase that they would like to hear a lot during the meeting in their table. This needs to be done individually. Remember that all mentors will also be doing this part of the activity.

When time is up, give extra 30 seconds to finish. Then, collect the answers and share them with students. You may ask students to explain why the phrase reflects the chosen value or even to modify the phrase to improve it or extend its scope.

1 OPPORTUNITIES

2 VISUALIZE

3 PERSEVERE

4 REASON

5 COMMUNICATE

6 EFFORT

7 CHALLENGES

8 RISK-TAKING

9 COOPERATE

10 REFLECT

Monitoring student’s work:

Observe student’s work. Specifically:

● Make sure that they highlight the words they find interesting (you may ask them why to engage in reflection).

● Make sure that students know the meanings of the ten words. If not, give examples of them in various contexts (both inside and outside of a classroom).

For the discussion:

● Make students accountable for what they wrote, asking to explain or build on. Accountability is an important element when you teach.

UCI Math CEO • Meeting 12) OUR VALUES

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1 OPPORTUNITIES

Do you want to try? I’m sure you can make this work!

2 VISUALIZE

Can you draw a

picture to explain

this to me?

3 PERSEVERE

I am sure that if I keep trying I will

find a way

4 REASON

Help me understand why this is true, convince me!

5 COMMUNICATE

I would like to share my thoughts with you

6 EFFORT

I’m going to do the best I can, focus and listen to my mentor

and peers at all times

7 CHALLENGES

It does not matter if it’s

hard, what matters is

that this will make me

learn

8 RISK-TAKING

I am not afraid of making mistakes.

Mistakes make me learn!

9 COOPERATE

I want to work with others. I learn from

other people

10 REFLECT

I will always check if

my answer makes

sense. How can I

check? What did I do

in this problem?

Values at MATH CEO

UCI MATH CEO - WINTER 2018 SURVEYMEETING 1 JANUARY 20, 2018

PLEASE WRITE YOUR NAME IN THE BACK PROBLEM 2(Take right Before activity 4)

PROBLEM 1(Take at the end of Activity 2)

(A) Every time I eat 6 grapes, I eat 4 pears:

If I ate 10 pears, draw how many grapes I ate.

Please answer all questions individually

(B) I have 200 bats in total. Some are wooden, some metallic. If the ratio WOODEN : METALLIC is of 3 : 2, how many bats are Wooden?

Answer:

Answer

Ss

(A) Suppose that we have a rectangle of area of 6. If we stretch it horizontally by a factor of x2 and then we stretch it vertically by a factor of

x2, what is the area of the new rectangle?

Justify your choices. Write your work:

MEETING 5 MAY 10, 2017 (Percentages 2)

Answer

(A) When we stretch Figure 1 horizontally by a factor of x3, we obtain Figure 2:

We stretch Figure 3 horizontally by a factor of x3 to obtain figure 4. Draw this figure.

Figure 1 Figure 2

Figure 3 Figure 4

Dear mentors:Dedicate 5 minutes for Individual Quiz, both parts A and B

(Pink papers in your Mentor’s folder).

STRANGE COINS

What is a horizontal / vertical stretching of a shape? What is a stretching factor?

What does it mean in words that the stretching factor is equal to 1?

Draw a shape. Then draw a new shape that results of stretching it vertically by a factor of 2 and horizontally by a factor of ½.


Our Goals: Convert between different values of objectsUse ratios and proportionality to figure out the cost or value of objectsInterpret information used in charts and tables

3

4444

30-35 min

Materials:● 5 different coin cards of different shapes● 11 buy cards numbered 2-12 (each having items to buy)● 1 Restrictions card● 1 coin with labels “AND”, “OR” on each face.● 2 dice● Chart template

In this activity the students will manipulate three different types of coins by performing horizontal and vertical stretches on them, in order to buy items. The main rule is that the value of a given type of coin is proportional to its area.

Start by introducing students the first type of coin: the “Brick coin”. Explain that a standard brick coin is worth $6. Now explain that we will be able to stretch the coin, whether horizontally (its length) or vertically (its height), or both, to change its value, so that its value is proportional to the area. For example, if we do a

horizontal stretch of ×4, the value of the new coin will be $24, because the area of the stretched brick coin is 4 times the value of the standard brick coin.

UCI Math CEO • Meeting 13) STRANGE COINS

STRANGE COINS

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Can someone explain again how can we find the price of a

stretched coin?

Before we start, I’m going to show you some examples and

the steps that you need to follow

Example: A standard Brick coin is worth $6.

We stretch it horizontally by a factor of 4, so that its new shape is the following:

As we see, the new area is 4 times the area of the standard coin. Therefore, the new value of the coin is 4 times the value of the original coin. Thus, the new coin is worth $24.


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Hinge Questions

Before you continue, ask questions to students to test their understanding of stretching. Explore these with a guided discussion, in which shapes are drawn. Here are some examples:

● If I stretch a brick coin vertically and horizontally both by a

factor of ×3, what is the value of the coin?

● If I bought an item worth $35 and I paid using standard brick coins, how many coins did I give? Why?

● If I bought an item and I paid for it using 3 brick coins, all with a horizontal stretch of 5, how much was the item? (I got no change.)

● If I bought an item worth $36 and I paid for it using a single brick coin with a horizontal and a vertical stretch, what are possible values of the stretch factors?

● If I bought an item worth $60 and I paid for it using a 4 equal brick coins having the same vertical stretch, what was the stretch factor?

Let’s consider an example: if I stretch a Horseshoe vertically

×2, what happens?Other types of coinsNow introduce the other 4 types of coins, with their corresponding values (for a standard coin):

● Horseshoe: worth $2

● Sofa: worth $3

● Camel: worth $4

● Triangle: worth $5


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Some examples of stretching of coins

Example 1: Let us stretch a Sofa coin

Vertically by a factor of ×2:

Standard Sofa coin

After the transformation

Some Examples of stretching of coins

Example 2: Let us stretch a Horseshoe coin Horizontally by a factor of 3:

Students can convince themselves, by several ways, that the area of the transformed coin is twice as the original area. One way is counting: the original is composed of 8 mini-squares, and the transformed coin has 16 mini-squares.

Here is a visual way to argue:

One can see that the transformed shape is made out of two original shapes, so the area must be twice.

+

Original, sliced in 3

Original, sliced in 3

=

Another visual way to argue is given in the next example.


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Example 2: Let us stretch a Camel coin vertically by a factor of ×2, and then horizontally by a factor of ×3:

Standard Camel coin

After the vertical transformation



This shows a third visual way to argue:One can see that the a vertical stretch with factor ×2 causes each individual tile to double into a “size two block.” So a vertical stretch will cause overall area to double.

Similarly, a horizontal stretch with factor ×3 causes each individual tile to triple into a “size three block.” This means our size-two-blocks transform into size-six blocks (figure 2 to figure 3), and consequently each individual tile from the original figure transforms into a size-six block (figure 1 to figure 3).

Discuss with students: How does this compare to a horizontal shift with factor ×18 of a standard Camel coin? (talk about shape and area)

After the horizontal transformation


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Example 3: Let us stretch a Triangle coin horizontally by a factor of ×4:

Standard Triangle coin(Area: 4.5)



After the horizontal transformation (Area: 18 = 4.5 x 5)

Example 4: Let us stretch a Horseshoe coin vertically by a factor of × ½:

Standard Horseshoe coin(Area: 7)

After the vertical transformation(Area: 7 x ½= 3.5)

Missions

Now tell students that they will play several rounds of the collaborative game of Missions, in which they have to pay the exact amount for a certain item or collection of items, with some potential restrictions. Here is how a mission is set up:

i) Roll 2 dice and add the results. Pick the corresponding buy card, which includes an item or set of items to buy.

ii) Roll 1 die and chose the corresponding Restriction according to the restriction card.

iii) Figure out a way to use one or more coins, but at most 10 coins total, to buy the item or set of items, by paying the exact value and following the restriction.


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b

Play as many missions as you can within the time for this activity. Even one mission is enough. Do not rush in the missions, as there are several mathematical elements that you can use as learning opportunities. If your students are struggling, only roll 1 die in step i) (reroll if you get a 1), as missions 2-6 are easier than missions 7-12.

(i) Choose what to buy

Roll 2 dice and add the results. Choose the corresponding buy card 2-12. [To start, you may roll only 1 die.]

(ii) Determine the restrictions

Roll 1 die. Choose the corresponding restriction 1-6.

(iii) Choose the coins

Choose at most 10 coins (different stretchings are possible) that add to the value of the buy card

28

Variant for missions: using 2 restrictions

In this variant, in step (ii), roll 2 dice instead of 1,, to pick 2 restrictions (reroll if they are the same). Then toss the “AND / OR” coin to determine if you need to fulfill both restrictions, or you need to fulfill at least one of the restrictions.

This variant makes the game a bit more complex, but also more interesting. Use this variant if you consider that the level of development of your students is adequate, or after students have successfully completed several missions with the standard rules.

A MISSION

An Example of a Mission (Example 1)

(i) Buy: Tom rolls a 2 and a 3, thus obtaining 5. The team needs to buy the Pirate Ship (US$187), using 10 coins or less.

(ii) Restriction: Tom rolls a 3:● 3:You must use more than one type of

coin.

(iii) Solving the mission: The team decides to use Sofa, Camel and Horseshoe coins.

A single Camel coin is worth $4. The team discovers that if such coin is stretched both vertically and horizontally by 4, then the area gets multiplied by 16. Therefore one such coin will be worth 16 x 4 = $64.


a

b

29

If we use 2 of these coins, this will add up to $128.

A single Sofa coin is worth $3. By stretching it horizontally by a

factor of ×3, the team discovers that the area gets multiplied by 3, so its value will be $9. Using 5 of these coins, we get a value of $45.

So far we have $128 + $45 = $173, so we need $14 more.

A single Horseshoe coin is worth $2. By stretching it vertically by

a factor of ×7, the team discovers that its area gets multiplied by 7, so its value is now $14. This is what we needed!

In summary:

2( Camel, V=4, H=4) + 5 ( Sofa, H=3 ) + 1 ( Horseshoe, V=7 )= 2( 64 ) + 5 ( 9 ) + 1( 14 )= 187.

Also, we used 8 coins in total.

Coin type StretchL x W

New Value Quantity Total $

Camel $4

Sofa $3

Horseshoe $2

4 x 4

3

7

16 x 4 = $64

3 x 3 = $9

7 x 2 = $14

2

5

Subtotal

1

8

$128

$ 45

$173

$ 14

$187

Explaining the mission using the Chart (Example 1)

Mission: Pirate Ship $187, more than 1 coin1. Complete column 1 “Coin type”: Camel $4, Sofa $3, Horseshoe $22. Camel: stretch 4x4 (LxW). The new value of Camel is $64 (16x4). If we use 2 Camels the total is

$128 (64x2).3. Sofa: stretch length by 3. The new value of Sofa is $9 (3x3). If we use 5 Sofas the total is $45 (9x5).4. The subtotal is $173. Since the Pirate Ship is $187, we need an additional $14.5. Horseshoe: stretch length by 7. The new value of Horseshoe is $14 (7x2). We only need 1

Horseshoe.6. We used 8 coins to buy our $187 Pirate Ship. It’s time to sail away.

UCI Math CEO • Meeting 13) STRANGE COINS 30

A Second Example of a Mission (Example 2)

(i) Buy: Nikki rolls a 1 and a 6, thus obtaining 7 in total. The team needs to buy the Discounted Hobbit House ($120000 before a %20 discount), using 10 coins or less.

(ii) Restriction: Nikki Rolls a 1:● 1: You cannot use any Camel coin nor any

Horseshoe coin.

(iii) Solving the mission: The team calculates the discounted value of the house, which is $96000. They do so in this way: 100% is $120000, so 10% is $12000, so 20% is $24000. 120000-24000=96000. To buy the house, the team decides to use Brick and Triangle coins.

A single Brick coin is worth $6. Using a H-stretch with factor x1000 means it is worth $6000. So if the team uses one stretched Brick to pay for the house, $90000 still needs to be paid with other coins.


a

b

31

The team realizes that 5 x 18000 = 90000, but they are not allowed to use 18000 Triangle coins to pay the remaining balance (that is too many coins!). So the team wants to try stretching one Triangle coin instead. There are many options:

● H-stretch with factor x18000● V-stretch with factor x18000● H-stretch with factor x90, V-stretch with factor x200● V-stretch with factor x600, H-stretch with factor x30● etc.

The team decides to stretch one Triangle coin horizontally with a factor of x90, then vertically with a factor of x200. They realize that this will multiply the original value of $5 by 900, then by 200. So the value of the stretched Triangle coin is $90000.

In summary: 1 Brick (H=1000, V=1) + 1 Triangle (H=9, V=2)

= $6 (x1000) + $5(x90, x200)=$6000 + $90000= $96000

Coin type StretchL x W


Brick $6

Triangle $5

1000 x 1

90 x 200

6 x 1000 = $6000

5 x 18000 = $90000

1

1

Subtotal

2

$6000

$ 90000

$96000

$96000

Explaining the mission using the Chart (Example 2)

Mission: Discounted Hobbit House $96000, without Camel or Horseshoe Coins1. Complete column 1 “Coin type”2. Brick: Do not stretch, OR use scale factors of 1. The value of the unstretched Brick coin is $6.3. Triangle : stretch length by 90. The new value of Triangle is $450 (5x90). Then stretch width by 200.

The new value of Triangle is $90000 (($5x90)x200). If we use 1 Triangle the total is $90000.4. The subtotal is $96000, which is the exact cost of the discounted house.5. We used 2 coins to buy our $96 Hobbit House!

UCI Math CEO • Meeting 13) STRANGE COINS 32

An Example of a Mission with the Variant (Ex 3)

(i) Jorge rolls a 2 and a 3, thus obtaining 5. The team needs to buy the Pirate Ship (US$187), using 10 coins or less.

(ii) Jorge Rolls a 2 and a 4:● You cannot use any Sofa nor any

Horseshoe Coin.● You must use exactly 2 coins in total.

Also, Jorge tosses the coin and obtains an “AND”. This means that both conditions must be met.

(iii) Since Sofa and Horseshoe coins are forbidden, the team considers only Camel and Triangle types:


a

b

33

Since we have to use exactly 2 coins, we could either use 2 camel coins, use 2 triangle coins or use 1 camel coin and 1 triangle coin. The team chooses to use 1 triangle coin and 1 camel coin.

The triangle coin, which starts as standard, is worth US$5. By stretching this coin x7 horizontally and x5 vertically, the team notices that the new area is 7x5=35 times the original area, because A = (1/2) base x height, and the base was stretched x7 and the height was stretched x5.

So the value of the stretched coin is: 35 x 5 = US$175.

This means that the camel coin must be worth $12. A standard camel coin is worth $4, so if we stretch it horizontally by a factor or 3, we get a $12 coin. We have solved the problem!

Note: notice that we can perform different stretchings on different coins if we like, unless restrictions tell otherwise.

Standard triangle coin Stretched triangle coin

Another Example of a Mission with the Variant (Example 4)

(i) Marie rolls a 1 and a 2, thus obtaining 3 in total. The team needs to buy the Carousel Toy ($85 before), using 10 coins or less.

(ii) Marie rolls a 5 and a 6, which gives the following restrictions:

● 5: All the coins that you use (no matter what type) must have the same horizontal stretching factor and also the same vertical stretching factor. This means the team must pick ONE V to use on all coins, and ONE H to use on all coins

● 6: In every coin you use, the horizontal and vertical stretching factors must be the same. This means that if the team usesa coin, V=H for that coin.

Also, Marie tosses the coin and obtains an “OR”. This means that the team can choose to meet both conditions, or they can choose to meet only one of the conditions.


a

b

34

(iii) The team decides to follow only one restriction and chooses Restriction 5. Thus, the goal is to purchase the Carousel Toy (US$85 before), using 10 coins or less, by using the same same horizontal stretching factor and also the same vertical stretching factor on all coins.

The team decides to start by setting the stretch factors H=3, V=5. These must be applied on all coins the team wants to use. The team calculates that with these factors, the stretched values of the coins are:

Brick: $6 → $90Horseshoe: $2 → $60Sofa: $3 → $45 These new values are too

Camel: $4 → $60 large to make $85!!!Triangle: $5 → $75

Then team tries the stretch factors H=1, V=5. The team calculates that with these factors, the stretched values of the coins are:

Brick: $6 → $30Horseshoe: $2 → $10Sofa: $3 → $15Camel: $4 → $20Triangle: $5 → $25

The team sees that with factors H=1 & V=5, the toy can be purchased with three stretched Triangle coins ($75 total) and one stretched Horseshoe coin ($10 total ).

1) Today activities were: 2) How good were you at solving today’s activities? 3) While I was solving the activities, I felt:4) How hard did you try in today’s activities? 5) How often do you feel you can really talk to your mentor?6) How often do you feel that you and your peers are

really a group?

Feedback for your mentor: ____________________________ 3 words to describe Math CEO: _______________________ ______________________________________________________ ________________________ _____________________________

UCI MATH CEO MEETING REPORTMEETING 1, JANUARY 10, 2018

First AND Last Name: _______________________________________________________ Table Number: ________ Lathrop ( ) Villa ( )

1= no fun at all1= no good at all 1= not anxious at all1= not hard at all 1= never 1= never

2 3= somewhat fun2 3= somewhat good 2 3=somewhat anxious . 2 3= somewhat hard 2 3= sometimes 2 3= sometimes

4 5 = lots of fun4 5 = very good4 5 = very anxious4 5 = very hard4 5 = always4 5 = always

Scale from 1 to 5 (Please circle your answers)

Thanks for your responses!

Clean your table when you finish, return the dry-erase markers, pick up your trash and take your belongings. Thank your mentor!

2 THINGS WHICH I LEARNED TODAY 2 THINGS THAT I FOUND INTERESTING 1 QUESTION THAT I STILL HAVE

Dear mentors:

Dedicate 5 minutes for the Student Survey

(Pink paper, at the back of the Quiz).

Teaching Tips

1) STEM MysteryTeaching Tips

● Before starting the game, you may play the following warm-up game. You pick up one of the STEM Careers (either secretly or revealing which), and ask students to bombard you with questions about this career. This will get them going.

● You may play during the first round (make sure you are not the Applicant), in order to model the types of questions that are useful in the game.

● Make sure that you are quite familiar with each of the 9 STEM Careers. You can quickly do a web-search for each of them, in case you are unsure.

● A good way to prepare for teaching this game is to make a list of 15 good questions that you may ask in this game. You may bring the list to the meeting, it could be very handy if things get a bit slow.


a

b

37

● You may introduce a bit of storyline for the game. For example you can say that we are all in a convention of a certain career, but there is an Applicant who is confused about which career the convention is about, and everyone heard this, so they are trying to catch him, and the best way is to ask everyone questions about the career, to detect who is lying.

● At the end of the game, ask students which skills they learned in the game, and how they can use them in mathematics and learning in general. Hopefully they will say things like: ask questions, communicate, deduce things, rule out elements, etc.

2) Our ValuesTeaching Tips

● This activity is a Follow-up to an activity done during Fall 2017, so students should be somehow familiar with these values. You can ask them to relate them to their previous learning in MATH CEO and also in their schools.

● A good way to prepare for this activity is to identify how some of the values are present in Activities 1 and 3. That way, when you are doing Activity 2, you can talk about what happened in Activity 1 (making these values visible), and also in Activity 3 (during or at the end) you can explicitly mention which values were visible and even ask students about it. This can be a great closure for the meeting.

● You may ask students if they think that there should be other values for the table. As students share their answers, you can relate their answers to the values (or admit that the value is truly new) already in the table. This will be helpful for students to see how general values can be, and that even if they are reformulated or expressed in different words, they remain visible.

● You may share some good phrases with adjacent mentors in other tables, this can help you meet new mentors and also showcase your student’s work, which enhances motivation and a deep culture of learning.


a

b

38

3) Strange CoinsTeaching Tips

● The Quiz before this activity will help you check the background understanding of your students so that you can adapt to your teaching. For example, some students may not even understand the concept of a stretch. Go from there. You can ask some students to explain to others, thus stimulating collaboration.

● Remember that it is possible to use coins that suffer no stretch (which is equivalent to a stretch of a factor of x1). It is also possible to apply different stretchings to different coins, even if they are of the same type. For example, I could stretch a Sofa coin vertically by a factor of x3, and then stretch another Sofa coin vertically by a factor of x2.

● There are lots of “multiplicative discoveries” and “symmetrical discoveries” to be made by students when they explore the missions. Try to help students generalize these discoveries and have students apply the principles that they discover to other situations.


a

b

39

● We suggest that you model a mission before having students jump in. We suggest one of missions 2-4, and without the 2 restrictions variant.

● By the time you get to introduce the missions, you should have a general sense of the level of understanding on the group. To make the missions easier, remember that you may only roll 1 die in step 1, thus selecting only missions 2-6 (which are easier). To make the game more challenging, remember to roll 2 dice in step ii), thus introducing 2 restrictions at the same time. This also teaches logic to students.

● If students solved a mission in a very straightforward way, challenge them to do so in a different way. You can even create a restriction. For example: “how about you solve this mission but only using Sofa coins?” or “Can you solve this mission using all 4 types of coins?”

Additional Resources(we will have them at the meeting in your table)● Page 41: 160 copies, yellow paper (8 per table)● Page 42: 80 copies, cut in 2 (8 per table)● Page 43: 160 copies, cut (16 per table)● Page 44-48: 20 copies, one-sided, see page colors in each page. Form

20 kits (one per table) and clip them. (Each kit contains 6 figures of each shape: brick, horseshoe, sofa, camel & triangle)

● Page 49: 20 copies, 1 per table.● Pages 50-60: 20 copies, 1-sided, blue paper. Form 20 kits (one per table).

Each kit contains 11 different buy cards.

● Pages 62-63: SS 160 copies, PINK, 8 per table● Pages 57-58: MR 22 copies, BLUE, (1 per table + 2 extra)

MEETING 01 MANIPULATIVESACTIVITY 1) STEM MYSTERY

STEM CAREER TABLEYellow paper

As on Bi c is

Nut on

En i rEco s

Ne r o s

Mat ti

Dat e t

Sur

1 2 3

4 5 6

7 8 9

STEM

MYSTERY

a

b

1 OPPORTUNITIES


2 VISUALIZE

Can you draw a picture

to explain this to me?

3 PERSEVERE

I am sure that if I keep trying I will find a way

4 REASON


5 COMMUNICATE


6 EFFORT



7 CHALLENGES


hard, what matters is that

this will make me learn

8 RISK-TAKING

I am not afraid of making mistakes. Mistakes

make me learn!

9 COOPERATE


other people

10 REFLECT

I will always check if my

answer makes sense.

How can I check? What

did I do in this problem?

MEETING 01 MANIPULATIVESACTIVITY 2) OUR VALUES VALUES AND PHRASES

1 OPPORTUNITIES


2 VISUALIZE

Can you draw a picture

to explain this to me?

3 PERSEVERE

I am sure that if I keep trying I will find a way

4 REASON


5 COMMUNICATE


6 EFFORT



7 CHALLENGES


hard, what matters is that

this will make me learn

8 RISK-TAKING

I am not afraid of making mistakes. Mistakes

make me learn!

9 COOPERATE


other people

10 REFLECT

I will always check if my

answer makes sense.

How can I check? What

did I do in this problem?

MEETING 01 MANIPULATIVESACTIVITY 3) STRANGE COINS CHART TEMPLATE

Coin StretchL x W


Mission: __________________________________

_________________________________________

Solution: __________________________________

_________________________________________

_________________________________________

Coin StretchL x W


Mission: __________________________________

_________________________________________

Solution: __________________________________

_________________________________________

_________________________________________

MEETING 01 MANIPULATIVESACTIVITY 3) STRANGE COINS

COINSWHITE

Brick($6)

Brick($6)

Brick($6)

Brick($6)

Brick($6)

Brick($6)


COINSRED

Horseshoe($2)

Horseshoe($2)

Horseshoe($2)

Horseshoe($2)

Horseshoe($2)

Horseshoe($2)


COINSBROWN

SOFA($3)

SOFA($3)

SOFA($3)

SOFA($3)

SOFA($3)

SOFA($3)


COINSYELLOW

CAMEL($4)

CAMEL($4)

CAMEL($4)

CAMEL($4)

CAMEL($4)

CAMEL($4)


COINSBLUE

TRIANGLE($5)

TRIANGLE($5)

TRIANGLE($5)

TRIANGLE($5)

TRIANGLE($5)

TRIANGLE($5)

MEETING 01 MANIPULATIVESACTIVITY 3) STRANGE COINS RESTRICTION CARD

You cannot use any Camel nor any Horseshoe Coin

You must use more than one type of coin

You must use exactly 2 coins in total.

You cannot use any Sofa nor any Horseshoe Coin

All the coins that you use (no matter what type) must have the same horizontal stretching factor and also the same vertical stretching factor.

In every coin you use, the horizontal and vertical stretching factors must be the same.

Strange CoinsRestriction Card

MEETING 01 MANIPULATIVESACTIVITY 3) STRANGE COINS BUY CARDS

2

Buy: 1 Delicious Quinoa Plate$12


3

Buy: Carousel Toy$85


4

Buy: 1 Duck Suit$35


5

Buy: 1 Pirate Ship, Medium (M) Size

Size

Type S M L

Ghost $100 $200 $300

Navy $150 $200 $270

Pirate $146 $187 $200


6

Buy: All tickets for 12 kids, 3 babies and 2 adults

Saf Pa k Ad i s

Person $

Baby Free

Kid $5

Adult $7


7

Buy: 1 Discounted Hobbit House

Original Price: $120.000Buy it with a 20% discount


8

Buy: 164 lbs of bananas

Price of Bananas

Weight Price

20 lbs. $10

40 lbs. $20

60 lbs. $30

... ...


9

Buy: 250 Sugarless cookies

Sug sCo k e

$1 per cookie

Quantity to buy

Discount on the

total buy

1 to 10 cookies

0%

11 to 50 cookies

10%

51 to 500 cookies

40%

501 to 5000 cookies

60%http://www.raisingthecameronclan.com/ramblings/2012/07/25/sugarless-sugar-cookies/


10

Buy: A 441 mile taxi ride

Spa i dFirst 400 miles or less: $100.75

For every extra mile: $1.25


11

Buy: Cheapest route from Church to Zoo

$3

$3

$4

$1

$1

$4

$6

$2

$2

$4

$2


12

Buy: A bag of 10.5 kg of sand total, even mix of all 3 colors

The t e

Sand Color Price

White $3 per kg

Yellow $4 per kg

Pink $5 per kg

Student Survey(Pink paper)160 copies

2-sided

Ss

UCI MATH CEO - WINTER 2018 SURVEYMEETING 1 JANUARY 10, 2018

PLEASE WRITE YOUR NAME IN THE BACK PROBLEM 2(Take right Before activity 4)

PROBLEM 1(Take at the end of Activity 2)

(A) Every time I eat 6 grapes, I eat 4 pears:

If I ate 10 pears, draw how many grapes I ate.

Please answer all questions individually

(B) I have 200 bats in total. Some are wooden, some metallic. If the ratio WOODEN : METALLIC is of 3 : 2, how many bats are Wooden?

Answer:

Answer

Ss

(A) Suppose that we have a rectangle of area 6. If we stretch it horizontally by a factor of ×2 and

then we stretch it vertically by a factor of ×2, what is the area of the new rectangle?

Justify your choices. Write your work:

MEETING 5 MAY 10, 2017 (Percentages 2)

Answer

(A) When we stretch Figure 1 horizontally by a factor of ×3, we obtain Figure 2:

We stretch Figure 3 horizontally by a factor of ×3 to obtain figure 4. Draw this figure.

Figure 1 Figure 2

Figure 3 Figure 4

1) Today activities were: 2) How good were you at solving today’s activities? 3) While I was solving the activities, I felt:4) How hard did you try in today’s activities? 5) How often do you feel you can really talk to your mentor?6) How often do you feel that you and your peers are

really a group?

Feedback for your mentor: ____________________________ 3 words to describe Math CEO: _______________________ ______________________________________________________ ________________________ _____________________________

UCI MATH CEO STUDENT SURVEYMEETING 1 JANUARY 10, 2018

First AND Last Name: _______________________________________________________ Table Number: ________ Lathrop ( ) Villa ( )

1= no fun at all1= no good at all 1= not anxious at all1= not hard at all 1= never 1= never

2 3= somewhat fun2 3= somewhat good 2 3=somewhat anxious . 2 3= somewhat hard 2 3= sometimes 2 3= sometimes

4 5 = lots of fun4 5 = very good4 5 = very anxious4 5 = very hard4 5 = always4 5 = always

Scale from 1 to 5 (Please circle your answers)

Thanks for your responses!

Clean your table when you finish, return the dry-erase markers, pick up your trash and take your belongings. Thank your mentor!

2 THINGS WHICH I LEARNED TODAY 2 THINGS THAT I FOUND INTERESTING 1 QUESTION THAT I STILL HAVE

Ss

Meetings Report(Blue paper)

Mr

Date: ___________________ UCI MATH CEO MEETING REPORT

Mentor’s First and Last Name: ____________________________________________________________ Table: ________

Dear leader mentor, Please complete this survey about each of the students at your table. Circle the number that better reflects how you feel. We really value your input. THANK YOU for your thoughtful answers, and for your amazing contribution to Math CEO.

STUDENT’S FIRST NAME: ___________________ LAST NAME: ______________________Compared to his/her peers, how good was this student at solving today’s math activities? 1 (worse) .2 3 (average) 4 5 (a lot better)How much innate ability or talent in math did this student show today? 1 (not at all) 2 3 (a little) 4 5 (very much)How much effort did this student put in today’s math activities? 1 (not at all) 2 3 (a little) 4 5 (very much)How much did this student participate in today’s math activities? 1 (not at all) 2 3 (a little) 4 5 (very much)How interested was this student in today’s math activities? 1 (not at all) 2 3 (a little) 4 5 (very much)Note or comments about this student: _________________________________________________________________________________



Mr


STUDENT’S FIRST NAME: ___________________ LAST NAME: ______________________Compared to his/her peers, how good was this student at solving today’s math activities? 1 (worse) .2 3 (average) 4 5 (a lot better)How much innate ability or talent in math did this student show today? 1 (not at all) 2 3 (a little) 4 5 (very much)How much effort did this student put in today’s math activities? 1 (not at all) 2 3 (a little) 4 5 (very much)How much did this student participate in today’s math activities? 1 (not at all) 2 3 (a little) 4 5 (very much)How interested was this student in today’s math activities? 1 (not at all) 2 3 (a little) 4 5 (very much)

Note or comments about this student: _________________________________________________________________________________







in Math! · Contents Meeting 1 Winter 2018 Cooperating in Math! January 10th INSTRUCTORS MANUAL 1) STEM Mystery 2) Our Values 3) Strange Coins Teaching Tips

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