*3-Act Task A Three-Act Task is a whole-group mathematics task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three. More information along with guidelines for 3-Act Tasks may be found in the Guide to Three-Act Tasks on georgiastandards.org and the K-5 CCGPS Mathematics Wiki. Task Name Task Type Grouping Strategy Skills Standard(s) Scaffolding Task Individual/Partners Multiplication and Arrays MCC.3.OA.1 Scaffolding Task Small Group/Partners Multiplication and Arrays MCC.3.OA.5 Scaffolding Task Individual/Partners Multiplication MCC.3.OA.1 Scaffolding Task Individual/Partners Division MCC.3.OA.2 Constructing Task Individual/Partners Multiplication and Division MCC.3.OA.5 MCC.3.0A.6 Constructing Task Individual/Partners Division MCC.3.OA.3 Constructing Task Individual/Partners Multiplication and Arrays MCC.3.OA.5 Scaffolding Task Individual/Partners Division MCC.3.OA2 * 3-Act Task Whole Group Multiples of Ten, Multiplying 1 digit numbers by multiples of 10 MCC.3.NBT.3
Practice Task Partners Multiplication MCC.3.OA.1 Scaffolding Task Partners/Small Group Multiples of Ten MCC.3.NBT.3 Constructing Task Small Group Multiplying 1 numbers by multiples of 10 MCC.3.NBT.3 Constructing Task Individual/Partners Division MCC.3.OA.4 Constructing Task Individual/Partners Division MCC.3.OA.2 MCC.3.OA.3 * 3-Act Task Group Multiplication and Arrays MCC.3.OA.1 Practice Task Individual/Partners Multiplication and Division MCC.3.OA.5 MCC.3.OA.6 Constructing/Practice Task Group/Partners Multiplication and Division MCC.3.OA.5 MCC.3.OA.6 MCC.3.OA.7 Practice Task Individual/Partners Multiplication MCC.3.OA.1 MCC.3.OA.2 Practice Task Individual/Partner Task Unknown Factors MCC.3.OA.6 Practice Task Individual/Small Group Multiplication MCC.OA.5 MCC.OA.6 MCC.OA.7 Constructing Task Small Group/Partners Distributive Property of Multiplication MCC.3.OA.5 MCC.3.OA.7 Practice Task Individual/Partners Unknown Factors MCC.3.OA.5 MCC.3.OA.6 MCC.3.OA.7 Constructing Task Individual/Partners Multiplication Stories MCC.3.OA.5 MCC.3.OA.6 Constructing Task Partners Multiplication MCC.3.OA.3 MCC.3.OA.4 Constructing Task Individual/Partners Line Plot Graph MCC.3.MD.4 Constructing Task Individual/Partners Pictograph and Bar Graph MCC.3.MD.3 Culminating Task Individual Multiplication, Division, and Data MCC.3.OA.5 MCC.3.OA.6 MCC.3.OA.7
Which table would you need the least? Show how you know. Choose two types of tables and draw your method for seating all 36 relatives for the family reunion. Write a number sentence to describe what you’ve drawn. Suppose the only tables you had were pentagonal. Explain how you would seat all of your relatives. FORMATIVE ASSESSMENT QUESTIONS What combinations of tables have you tried so far? How will you know when you find the right combination? Do you think there is more than one right solution for this task? Why do you think so? Do you have a way of finding out? How many _____ (square, circular, hexagonal, rectangular, or pentagonal) tables do you need? How do you know? DIFFERENTIATION Extension Use square tables that seat one person to a side, but this time push the tables together end to end and find out how many relatives can be seated. Continue adding tables this same way until you have enough tables to seat everyone. Enter the information in a table and describe any patterns you see. How many square tables pushed end to end would it take? # Tables # People Seated Sketch Number Pattern 1 4 (1 x 4) - 0 = 4 (1 x 2) + 2 = 4 2 6 (2 x 4) – 2 = 6 (2 x 2) + 2 = 6 3 8 (3 x 4) – 4 = 8 (3 x 2) + 2 = 8 4 10 (4 x 4) – 6 = 10 (4 x 2) + 2 = 10 5 12 (4 x 5) – 8 = 12 (5 x 2) + 2 = 12 . . . 17 36 (17 x 2) + 2 = 36
STANDARDS OF MATHEMATICAL PRACTICE (SMP) 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. ***Mathematical Practices 1 and 6 should be evident in EVERY lesson. *** Background Knowledge (Information quoted from Van de Walle and Lovin, Teaching Student-Centered Mathematics: Grades 3-5, page 62) “In the beginning, students will be able to use the same models – sets and number lines – for all four operations. A model not generally used for addition but extremely important and widely used for multiplication and division is the array. An array is any arrangement of things in rows and columns, such as a rectangle of square tiles or blocks. To make the connection to addition, early multiplication activities should also include writing and addition sentence for the same model.” COMMON MISCONCEPTIONS Traditionally multiplication tables are emphasized when students begin learning about multiplication. Students are sent home with flash cards without a true understanding of what multiplication is. This way of learning multiplication can be difficult for students to understand. Naturally, students make groups and groups of groups. The creation of groups is a way to find the total of something in the most efficient way. The following activity allows students to build on their natural ability to form groups and learn multiplication without memorizing facts in isolation, but as number facts that can be related to each other in a multitude of ways (Frans van Galen and Catherine Twomey Fosnot, 2007, Context for Learning Mathematics). ESSENTIAL QUESTIONS How can we use arrays to help develop an understanding of the commutative property? How does drawing an array help us think about different ways to decompose a number? MATERIALS
Intervention: (SMP 5) student to use multiplication chart or reduce the amount of rounds. Find the Unknown Number (Partner Card A) Partner 2 18 ÷ 2 = _____ ____ ÷ 1 = 7 8 ÷ 4 = ______ 30 ÷ ______ = 6 20 ÷ ______ = 2
Partner 1 12 ÷ ______ = 2 16 ÷ 4 = ______ 5 ÷ 5 = _____ 18 ÷ ______ = 6 ______ ÷ 2 = 4 Find the Unknown Number (Partner Card B) Partner 2 20 ÷ 2 = _____ ____ ÷ 1 = 3 36 ÷ 4 = ______ 36 ÷ ______ = 6 16 ÷ ______ = 2
Partner 1 24 ÷ ______ = 6 12 ÷ 4 = ______ 6 ÷ 6 = _____ 60 ÷ ______ = 6 ______ ÷ 2 = 5 Find the Unknown Number (Partner Card C)
3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. BACKGROUND KNOWLEDGE Depending on the student’s reasoning and understanding of the problem, this could be solved using multiplication and division, but also acted out through manipulatives. Regardless of how the problem is solved, it is important that students use words, numbers, and pictures to communicate their reasoning. Common misconception Multiplication and division are usually taught separately. However, multiplication and division should be combined in order for students to see how they are related. “Experiences with making and counting groups, especially in contextual situations, are extremely useful. Products or quotients are not affected by the size of numbers as long as the numbers are within the grasp of the students” (Teaching Student-Centered Mathematics, 2006, John A. Van de Walle and LouAnn H. Lovin). This idea becomes evident in this task. essential questions How can multiplication and division be used to solve real world problems? How can we use patterns to solve problems? MATERIALS drawing paper, blocks, any other materials that will help students visualize the problem Day Blunder” student recording sheet GROUPING Partners NUMBER TALK By now number talks should be incorporated into the daily math routine. Continue utilizing the different strategies in number talks and revisiting them based on the needs of your students. In
Standard ↓ Exceeding Meeting Not Yet Meeting CCGPS.3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each Multiplication work use of diagrams, words, and/or other suitable representations for demonstrating mastery Evidence of estimation is shown with explanations Multiplication calculations are correct Evidence of estimation is shown Multiplication calculations are incorrect or omitted No evidence of estimation Interpret quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. Work shows all division sentences correctly Thorough explanation of remainders is given Explanation of all the possible solutions is given with reasons for which solution is the best Division number sentence corresponds to the question asked in word problem. Response indicates the presence or lack of a remainder and what this indicates Solution to division problem is correct Division number sentence does not correspond to question No mention is made of remainder Solution to division problem is incorrect CCGPS.3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. are thorough and detailed and include reasoning as well as multiple representations to support conclusions Explanations are logical and use specific math vocabulary to describe multiplication or division process Explanations are omitted or illogical Explanations do not describe the process used to derive an answer to the question asked CCGPS.3.MD.3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. All data relevant to the solutions of both multiplication and division problems are accurately recorded in an organized fashion Work is organized and logically presented Work shown supports conclusions about which ice cream to buy Work is not shown Work shown is disorganized, inaccurate, or fails to communicate mathematical ideas