UCI MATH CEO Meeting 2, Oct 11 Multipl(a)y Last updated: OCT. 9 2017
Im Instructor Manual (GREEN PAPER) Print 65 copies (2 per folder, save 5 extra)
INSTRUCTORS MANUAL Im Meeting 2 Fall 2017 3 6 Mulipl(a)y 9 October 11th 12 Contents? 15 1) What do you think about math? 2) Number Tempo 3) Magic Chickens www.math.uci.edu/mathceo 2017 UCI MATH CEO COMMUNITY EDUCATIONAL OUTREACH. UNIVERSITY OF CALIFORNIA AT IRVINE
Mulipl(a)y (Meeting 2, Oct 11) CHECKLIST Identify the Leader mentor Write names of all mentors and students (find form inside folder) 3 6 Tell math goals to students in each activity Call students by name Keep students silence while doing surveys Keep your table neat and clean at all times Get help if there are behavior problems Quiz PROBLEM 1 (pink) (end of Activity 2) Student Survey (pink) (start survey at 3:35 PM) Fill Meeting Report (blue) (if you are the Leader) Give students Family Project (Yellow) to collect next week. Put back into folder: NAMC Surveys, Student Surveys (pink), Meeting Report (blue)? 1 9 1
INTRODUCTION Meeting 2: Multipl(a)y Activity Breakdown Dear mentor, In this meeting we will develop additive and multiplicative number sense through sequences of multiples of a given number (e.g. 3, 6, 9, 12, ) and also by playing a multiplication table game where students can explore and justify numerical facts in a contextual situation, and solidify the conceptual properties of the operation of multiplication. Activity 1: What do you think about math? Individual Student survey (25 minutes) Activity 2: Number tempo Exploring multiples of numbers (20 minutes) Activity 3: Magic Chicken Board Game, Exploring the multiplication table (30 minutes) Math Goals 2,4,6 8 16 24 4 8 12 Students understand and represent a multiplication concretely and by pictures in terms of groups of equal size, and translate this representation to symbols (e.g.: 5 groups of 4 each is represented by 4 x 5 or 5 x 4). Students can generate the first 10 (or so) multiples of a given number and correctly use corresponding vocabulary (multiple of, factor of).. Students understand the numerical relations between various different sequences of multiples. For example: that the multiples of 8 are obtained by doubling the multiples of 4. 5x7 = 5x6+5 Students understand and justify the distributive property of multiplication over addition (e.g.: 5x(3+1) = 5x3 + 5) by using different contextual representations, and use this property to calculate products.
MATERIALS & AGENDA Im INSTRUCTOR GUIDE Green color Sw STUDENT WORKBOOK White color Mr MEETING REPORT Blue color One per table + Online meeting report Ss STUDENT SURVEYS (INCLUDES QUIZZES) Pink Color Fp FAMILY PROJECT Yellow Color WHITEBOARDS One per student DRY ERASE MARKERS A pouch with several AGENDA MATERIALS 2:10 pm General Introduction (10 min) 2:20 pm 1) What do you think about math? (25 min) 2:45 pm 2) Number Tempo (15 min) Quiz: Problem 1 (5 min) 3:05 pm 3) Magic Chicken (30 min) 3:35 Student Survey (5 min) 3:40 End of the meeting
INTRODUCTION INDIVIDUAL ASSESSMENT At the end of Part 2 (Number Tempo), 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. Correcting the Quiz after the students are done can help you check for understanding BEHAVIOR EXPECTATIONS If 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. Refer to the expectations matrix and point to it if students are not meeting expectations
UCI MATH CEO MEETINGS: BASIC GUIDELINES FOR VOLUNTEERS 1 2 KNOW YOUR STUDENTS Call 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 EXPLANATIONS Ask 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. 3 4 MOVE & MONITOR CHECK WORK Move around your Verify that the table; monitor all students write the students; use an answers to the adequate tone of problems and that voice; encourage kids they are correct to work in teams. and complete. 5 AT THE END Ask students to fill out the survey individually (no help), and to help pick up trash from the table and floor. TEACHING TIPS 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? Can someone read the instructions out loud? 1 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. 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. This icon means that the students should work individually in the corresponding problem, before discussing. Be flexible and adapt to your situation. 2 Activity to be done in pairs Note: if not specified, the booklet problem can be done as a group activity involving a discussion.
1 WHAT DO YOU THINK ABOUT MATH? Our Goals: To know more about you Give to each student a copy of the NAMC survey (which you can find in your folder. Give exactly 25 minutes to complete (there will be a short puzzle for those students who complete the survey before that time). Collect the surveys and check that students have filled out their names. Put them back into the folder. M A T H
1) WHAT DO YOU THINK ABOUT MATH? Please give the survey in a quiet environment, where the kids are not distracted by talking or other activities going on. This makes a big difference in the quality of their responses. The Survey is 2-page long. It has 9 questions, some with several subitems. We will be conducting research on these survey, it is important that students complete it by themselves
2 NUMBER TEMPO Our Goals: To make kids familiar and fluent with multiplication tables and terminology To develop multiplicative number sense Discuss in your group. Everyone talks. What numerical patterns do you know? Can you give examples? Sing them maybe? What does it mean to be a multiple of a number? Can you give some specific examples? Consider the pattern of multiples of 2: 2, 4, 6, 8, 10, 12, What can we say about this pattern? Does it grow? How? Do we find even/odd numbers? Are there other patterns hidden there?
2) NUMBER TEMPO Materials 6-8 Number Strips (depending on the number of students) 3-strip, 4-strip, 5-strip, 6-strip, 8-strip, 12-strip (8-strip and 12-strip are repeated). At any point feel also free to introduce and use the strips having the positions tagged (1, 2, 3, 4, ). 3 6 12 21 Pages 4-5 in the Student Workbook 33 1 2 3 6... 3 4 5 12 6...... Instructions Distribute the strips to your students. Let them choose which one they want: If you have 6 students, let them choose them the 3-strip, 4-strip, 5-strip, 8-strip and 12-strip. If you have a 7th or an 8th student, add the other 8-strip and the other 12-strip. Tell them that we will all follow the instructions in the Workbook, page, and do them helping us all. For Question (b), guide the students: give them hints such as: What can you say about the numbers in your strip? Do they increase or decrease? How? What numbers are being skipped? What is the relation between the numbers that are neighbors? Figure out a rule to find a number in the strip using the previous one. Where do you see even or odd numbers? How can this strip help you find multiplications? Give an example. Etc... Tip familiarize with the student s workbook before the meeting to know what will be shown to your students.
2) NUMBER TEMPO 3 6 12 21 33... (a) Choose a strip to work through this problem and take it. (b) Fill out the missing values in your strip, individually. Then share the filled strip with your peers: Rotate to your left several times until you get your strip back. (c) What do you observe about your strip? Write as many observations as possible. (d) Which relations do you see between some of the different strips? How do the values in these strips relate to each other? Example for the 8-strip: Numbers are increasing. The pattern is plus 8 Each number is 8 more than the previous number All numbers are multiples of the first number (8) If I add two numbers in the strip, I get also a number in the strip (assuming this strip can continue forever) All numbers in this strip are even. The strip would never end in theory. It is infinite. The strip is similar to the 4-strip, but it skips numbers. Examples: The numbers in the 6-strip are twice the ones in the 3-strip If I duplicate the values in the 4-strip, I get exactly the 8-strip, because multiplying by 8 is multiplying by 4 and then by 2. If I add the numbers in the 3-strip and the ones in the 5-strip, I obtain those in the 8-strip. If I triplicate the 4-strip, I obtain the 12-strip The 12 strip appears in the 6-strip if we skip the odd positions. Some more detailed explanations in the next page... How would you use your 4-stripe to find 28 divided by 4? Why? Can you put the 2 stripes together one above the other to show what you say?
2) NUMBER TEMPO 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90... 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180... If I put the 6-strip and 12-strip aligned, I can see that the value in the 12-strip are twice the values in the 6-strip. For example: 66 and 132 align. This gives me a useful rule for multiplying a number by 12: first multiply by 6 and then duplicate. 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 If I start with the 3-strip and highlight values every 4 entries, what I obtain is the 12-strip. So every multiple of 12 is also a multiple of 3, because I can find all multiples of 12 in the list of multiples of 3, by looking at every 4 positions. 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45... 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75... 8 16 24 32 40 48 56 66 72 80 96 104 112 120... 88 If I align the 3-strip, 5-strip and 8-strio, I can see that adding the values of the 3-strip and 5-strip give me the values of the 8-strip as result. So, multiplying a number by 8 is the same as separately multiplying it by 3 and 5, then adding the values.
2) NUMBER TEMPO (e) Work together: use the strips to solve the following multiplication problems. Draw the solutions in the right (see example). (1) 3 x 6, using the 3-strip or using the 6-strip. (2) 12 (3) 6 x 5, using the 6-strip or the 5-strip x 3, using the Example for (1): Use the 3-strip: 6-strip 3 6 3x1 3x1 6 12 9 12 15 3x6 18 36 (4) 8x7, using the 4-strip (5) 8x9, using the 5-strip and the 3-strip (6) 8x9, using the 3-strip (and others if you want) (7) 12 x 7, using any strips you want. 12x3 5 10 18 15 20 25 30 6x5
2) NUMBER TEMPO (4) 8 x 7 using the 4-strip: (5): Use the 5-strip and the 3-strip: 3x9 Recognize that the multiples of 8 are in some of the positions of the 4-strip: 3 6 9 12 15 18 21 24 5x9 4 8 12 16 20 24 28 32 5 10 15 20 36 40 44 48 52 56 Now look for the 7-th such value, which will be 7x8. So we see that 7x8 = 56. 25 30 35 40 Add 45 8x9 72 (6) 8X9 using the 3-strip: Another way: We know that the 4-strip when duplicated becomes the 8-strip. Since 4 x 7 = 28 (by looking at the strip), then 8 x 7 = 2 x 28 = 56 (we did not have to look at the 8-strip for this). 27 You may find 8x3 using the 3-strip and then triplicate the result, because 8x9 is equal to (8 x 3) x 3. You can also use the 3-strip and the 6-strip (add) (7) 12 x 7 using any strips you want. Some options: For example, use the 12-strip directly You may also use the 4-strip and triplicate, the 6-strip and duplicate or the 3-strip and quadruplicate. You may use the 8-strip to find 12 x 8, and then subtract 12. You may use the 6-strip to find 12 x 6, and then add 12.
3 MAGIC CHICKENS Our Goals: Explore the properties of multiplication, being able to represent them in different ways and develop mental math skills to compute products using number sense. Practice reading comprehension skills Learn to work in teams. Discuss in your group. Everyone talks. How do you usually find the answer to a multiplication problem? Memory? Calculator? Mental tricks? Give some examples. If Dana has a total of 24 eggs in different baskets, and we know how many baskets she has, can we know how many eggs per basket she has? If Carl has some number of baskets and he has 6 eggs in every basket, how can we know how many eggs in total he has? Draw a picture.
3) MAGIC CHICKENS 3) MAGIC CHICKENS Materials A big 12 x 12 board (a multiplication table but not with all spaces filled out) 5 Mission Cards 4 Pawns (one for each team) Tokens ( eggs ) Coffee filters ( baskets ) 1 Deck of regular cards 15 Action Cards 1 Die Introduction In this board game, each team (of 2 students) represents a family that starts with a given number of eggs, distributed evenly among a certain number of baskets. During the game, a magic chicken will change the the number of baskets or the number of eggs per basket of the teams, but during all times, all the baskets of a team must have the same number of eggs. However, different teams may have different number of baskets and different number of eggs per basket. Total number of eggs = Number of baskets Number of eggs per basket Teams take turns using action cards or dice which allows them to move their pawns on a board that represents a 12 x 12 multiplication table, where the values correspond to the total number of eggs. Each team has a goal value to reach (which corresponds to several possible entries in the board). Whoever reaches the goal first wins the game.
3) MAGIC CHICKENS Setup: Make teams of 2 players (mentor does not play). Give a pawn to each team. Each team receives a random mission card with two values: starting value and goal value. Each team puts its pawn in an entry of the board corresponding to the starting value. They take the corresponding number of baskets and eggs per basket. They also take two cards from the regular deck to represent this information (see example below) Example: John and Jake starting value is 88 and their goal is 12. They can choose to put their pawn in position (8,11) or (11,8) of the board,, because 88 = 8x11 = 11x8. They choose 11x8: they take 11 baskets and put 8 eggs in each basket. They also take an J (11) of spades and an 8 of hearts to represent this (use black suits for baskets, red suits for eggs per basket). Their goal is getting to 12, so he wins by reaching any of these positions: (12,1), (1,12), (2,6), (6,2), (4,3) or (3,4). Shuffle the 13 action cards making a face down pile. Draw the top 5 cards and place them face up in the middle of the table. Leave the draw pile visible: more action cards will be used during the game. 8 x 11 x A=1 J = 11. Q = 12.
3) MAGIC CHICKENS Play: Teams take turns to play. In each turn the team selects one action card, moves its pawn according to the card, and finally rolls a die to see if there is some extra move. See more details below. A team s turn Select one action from 5 action cards in the table. The team members execute the action and explains how and why they moved their pawn on the board. Sometimes an action may not be executed, because it would result in less than one egg, or more than the maximum in the board. If so, the team simply skips the action. Put the action card in the discard pile face up. When you play an action, the team members need to explain: how many eggs you had before the action, how many you have after the action, and why you now have this many eggs. Remember that at all given times, all chests need to have the same number of eggs. After executing the action, the team rolls a dice: if the result is a 6, the team draws an action card from the draw pile and decide if they want to execute the action, or save it for later, keeping the action card. This ends the team s turn. Play continues counterclockwise. Example: The team s pawn was in the 4x5 position (20 eggs). The team selects the action card shown. The team takes 2 eggs per basket, Team places a post-it note with the value 28 in the 4x7 position, and moves its pawn to that position over the post it note.
3) MAGIC CHICKENS The action cards: The heart of the game are the action cards. Some cards are phrased in eggs/basket language, whereas others are in terms of moving directions in the board. Kids should figure out how to translate between these two languages when executing their actions. There are 15 action cards. In what follows we explain some of them. Note: you can only execute an action card if after its effect you end up with between 1 and 144 egs, between 1 and 12 baskets and between 1 and 12 eggs per basket. Otherwise, you can take the card but do NOT apply its effect. ACTION CARD #1 ACTION CARD #2 You find 12 eggs buried in the sand. Take as many as you like, but you need to end up with the same number of eggs in each basket. The Magic chicken casts a spell that duplicates the total number of eggs that you have. Choose how many baskets you want to have now (all with the same number of eggs). Notice that a team may choose to take 0 eggs! This action card does not change the number of baskets Students should realize that they can for example duplicate their number of chests, or duplicate the number of eggs per chest. They could however increase both their number of basket and eggs per basket. Example: move from position 5x7 to 10 x 7 (duplicate number of baskets). ACTION CARD #3 ACTION CARD #4 The magic chicken casts a spell that duplicates the number of eggs that you have in each of your baskets. A gentle giant will gift you one egg per each basket that you have. This will move the pawn to the right several spaces. This will move the pawn one space to the right. Example: move from position 3x5 to 3 x 10 (duplicate eggs per basket). Example: move from position 8x2 to 8x3 (+1 egg in each basket). You cannot use this card if you have 7 or more eggs per basket. However, you may take the card and just lose your turn. You cannot use this card if you have 12 eggs in each basket. However, you may take the card and just lose your turn.
3) MAGIC CHICKENS ACTION CARD #8 ACTION CARD #6 ACTION CARD #5 You went to the market for eggs. Move your pawn 2 spaces to the right. This means that you got 2 eggs per basket. You don t change the number of baskets Example: move from position 5x7 to 5x9 (+2 eggs in each basket). You cannot use this card if you have more than 10 eggs in each basket. However, you may take the card and just lose your turn. You find a basket on the road surprise! It has as many eggs as you have in each of your chests! Take this basket. This means that you move your pawn 1 space down. Example: move from position 4x7 to 5x7 (+1 basket). You cannot use this card if you have 12 baskets. However, you may take the card and just lose your turn. ACTION CARD #7 A noble king has given you a gift!: move your pawn 2 spaces down. This means that the king gave you 2 new baskets, each with the same number of eggs as in your old baskets. Example: move from position 10x3 to 12x3 (+2 baskets). You cannot use this card if you have more than 10 baskets. However, you may take the card and just lose your turn. A thief came at night and stole one of your baskets. (If you have less than 3 baskets, nothing happens) The pawn will be moved 1 space up. Example: move from position 7x8 to 6x8 (-1 basket). You cannot use this card if you have 1 or 2 baskets. However, you may take the card and just lose your turn.
3) MAGIC CHICKENS ACTION CARD #9 ACTION CARD #13 ACTION CARD #10 There was an earthquake and all eggs in two of your baskets broke. Throw them away along with those baskets. (If you only had 1 or 2 baskets, no egg breaks). A hungry cat took two eggs from each of your baskets. (If you only had 1 or 2 eggs in each basket, nothing happens) This means that you move your pawn 2 spaces up. The pawn will be moved 2 spaces to the left. Example: move from position 4x7 to 2x7 (-2 baskets). Example: move from position 4x7 to 4x5 (-2 eggs per basket). You cannot use this card if you have less than 3 baskets. However, you may take the card and just lose your turn. You cannot use this card if you have less than 3 eggs per basket. However, you may take the card and just lose your turn. ACTION CARD #11 Your baskets are old. Recycle them and create new baskets. You may choose how many, as long as you can place all your eggs evenly in them. The magic Chicken casts a spell: gain or lose baskets until you have as many baskets as you have eggs in each basket. Each basket you gain will come with as many eggs as the rest of your baskets. This means that the pawn gets moved to a new position with the same value. The pawn will be moved vertically to end up in the main diagonal of the board. Example: move from position 6x4 to 8x3 (went from 6 baskets to 8 baskets). The total number of eggs did not change. Example: move from position 9x5 to 5x5 (-4 baskets). You may choose to build the same number of baskets as before, in which case you don t move your pawn. Another example: move from position 2x11 to 11x11 (+9 baskets).
3) MAGIC CHICKENS You will play the Magic Chickens board game. Make a team with a peer. As the game progresses you can use the board in this page to start filling the values of the different entries of the table. Your Turn: 1. 2. 3. 4. Choose an action card Execute the action, moving your pawn on the board. Explain your move. Roll the die: If you roll a 6, draw an action card from the draw pile. Decide to keep it or execute it. Execute any action cards in your hand if you want. The team to be first to complete its mission wins the game.