Practice Task Partners Multiplication MGSE3.OA.1 In this task students determine the factors of 100 by creating addition and/or multiplication models by using Base Ten Blocks. Scaffolding Task Partners/Small Group Multiples of Ten MGSE3.NBT.3 This task allows students to apply their understanding of place value to multiplication of tens. Constructing Task Small Group Multiplying 1 digit numbers by multiples of 10 MGSE3.NBT.3 This task further relates multiples of ten to place value by giving students the opportunity to build onto the concept that 10 tens equal one hundred, and 10 hundreds equal one thousand. Constructing Task Individual/Partners Division MGSE3.OA.4 In this task, students will use estimation skills to multiply by groups of ten. Constructing Task Individual/Partners Division MGSE3.OA.2 MGSE3.OA.3 In this task, students will decide how to share pumpkin seeds fairly with a group of children. 3-Act Task Whole Group Multiplication and Arrays MGSE3.OA.1 In this task, students will view a picture and tell what they noticed. Next, they will be asked to discuss what they wonder about or are curious about. Students will then use mathematics to answer their own questions. Practice Task Individual/Partners Multiplication and Division MGSE3.OA.5 MGSE3.OA.6 In this task, students will make models on grid paper of arrays that show both multiplication and division number sentences. Constructing/Practice Task Small Group/Partners Multiplication and Division MGSE3.OA.5 MGSE3.OA.6 MGSE3.OA.7 This is a several part task in which students find factors through work with multiplication and division. Practice Task Individual/Partners Multiplication MGSE3.OA.1 MGSE3.OA.2 In this task, students will roll two cubes to get factors and use factors to find the product. Practice Task Individual/Partner Unknown Factors MGSE3.OA.6 In this task, students use multiplication facts and strategies to identify the unknown factor in a division problem.
Watermelon Farm (Part 1) Wanda has a watermelon farm. In each row she has 12 watermelon plants and there are 4 rows. How many watermelon plants does she have in all? Prediction Solution Watermelon Farm (Part 2) Wanda wants to double the size of her watermelon farm each year. How many plants will she have in all after… 1 year 2 years 3 years Record your strategies on an array Airplane Rides Over the Farm (Part 1) Henry is giving airplane rides over his farm. His plane has 6 seats in each row. The seat row numbers go up to 21. How many passengers can Henry’s plane hold? Prediction Solution Airplane Rides Over the Farm (Part 2) Henry’s plane makes 2 trips over the farm each day. If the plane was full each time, how many passengers would get to see Henry’s farm from the airplane? Prediction Solution
Once students have their question, ask the students to estimate answers to their questions (think-pair-share). Students will write their best estimate, then write two more estimates – one that is too low and one that is too high so that they establish a range in which the solution should occur. Students should plot their three estimates on an empty number line. Note: As the facilitator, you may choose to allow the students to answer their own posed questions, one question that a fellow student posed, or a related question listed above. For students to be completely engaged in the inquiry-based problem solving process, it is important for them to experience ownership of the questions posed. Important note: Although students will only investigate the main question(s) for this task, it is important for the teacher to not ignore student generated questions. Additional questions may be answered after they’ve found a solution to the main question, or as homework or extra projects. Act 2 – Student Exploration - Provide additional information as students work toward solutions to their questions. (Dan Meyer ) “The protagonist/student overcomes obstacles, looks for resources, and develops new tools.” During Act 2, students decide on the facts, tools, and other information needed to answer the question(s) (from Act 1). When students decide what they need to solve the problem, they should ask for those things. It is pivotal to the problem solving process that students decide what is needed without being given the information up front. Required Information: 30 panels in each row 10 rows in each section Some groups might need scaffolds to guide them. The teacher should question groups who seem to be moving in the wrong direction or might not know where to begin. Questioning is an effective strategy that can be used, with questions such as: What is the problem you are trying to solve? What do you think affects the situation? Can you explain what you’ve done so far? What strategies are you using? What assumptions are you making? What tools or models may help you? Why is that true? Does that make sense? Act 3 – Whole Group – Share solutions and strategies. Students to present their solutions and strategies and compare them. Reveal the solution:
CONTENT STANDARDS MGSE3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. 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. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Background Knowledge This task is designed to develop the concept of what happens to a number when multiplied by a multiple of ten. To help build context, the teacher may read 100 Hungry Ants by J. Pinzces. Students need to know that 10 tens make 100 and 10 hundreds make one thousand. COMMON MISCONCEPTION It is important to address any misconceptions that students may have with “just adding zeros”. Students need to be able to think in terms of ___ groups of ____ tens. Additionally, student misconceptions with this task may be with their understanding of place value. When working with longs, students may see the group as a group of 1 instead of a group of 10. For example, when counting 5 longs the student may count them as “1, 2, 3, 4, 5” with a total of 5 objects instead of counting them as “10, 20, 30, 40, 50” or “5 groups of 10” with a total of 50. It is important for students to have this understanding of the long consisting of 10 units. Essential Questions How can I model multiplication by ten? How is multiplying by ten related to place value? Materials Money Manipulatives “How many 10s” recording sheet
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. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. BACKGROUND KNOWLEDGE (Information quoted from Van de Walle and Lovin, Teaching Student-Centered Mathematics: Grades 3-5, page 113) For multiplication, the ability to break numbers apart in flexible ways is even more important than in addition or subtraction. The distributive property is another concept that is important in multiplication computation. For example, to multiply 43 x 5, one might think about breaking 43 into 40 and 3, multiplying each by 5, and then adding the results. Children require ample opportunities to develop these concepts by making sense of their own ideas and those of their classmates. Third grade students will not be required to use the distributive property for products greater than one hundred. COMMON MISCONCEPTIONS When using the distributive property to solve problems, students will partition numbers and arrays at different points. It is important for students to decide the appropriate way to partition a number, instead of the teacher, so that the problem makes sense to them. ESSENTIAL QUESTIONS How does understanding the distributive property help us multiply large numbers? What are strategies for leaning multiplication facts? MATERIALS Connecting cubes (bags of 100) Graph paper Making the Hard Facts Easy Recording Sheet Crayons or colored pencils Scissors Glue
Extension: Create a game board that has two missing components. Use number cards to 100, or use a spinner (top) on a 100s chart. (must place books on each side to keep spinner (top) on the 100s chart. Intervention: (SMP 5) Allow 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)
Partner 2 32 ÷ 8 = _____ ____ ÷ 1 = 7 16 ÷ 4 = ______ 63 ÷ ______ = 7 18 ÷ ______ = 2 Partner 1 80 ÷ ______ = 8 32 ÷ 4 = ______ 7 ÷ 7 = _____ 18 ÷ ______ = 6 ______ ÷ 2 = 3 CONSTRUCTING TASK: MAKING UP MULTIPLICATION In this task, students will learn three different ways a multiplication problem can be written. They will then practice writing their own problems.
The students can model these and similar types of problems with: Interlocking cubes Jumps on a number strip Drawing a picture Creating an array After the groups have solved their problems and explained their solutions, present the students with the task of making up their own story problems using the number sentence structure above with the different factors and products. The students can write their problems on index cards and swap with other groups. The students can solve the student created problem on a wipe off board or paper showing their strategies and multiplication sentences. Ask the students to label the two factors and one product in the problem. Ask for volunteers to share the problem and how they got the answers. Did all of the student-created problems work? If some did not work due to wording or values too high, collectively decide how to adjust the problem so it is able to be solved. Return the cards to the owners. Have the owners solve their problem on the back of the index card. The students should also label the factors and product. Collect and review for accuracy and content. Part II: Exploring different types of story problems (whole group/partners) First, begin with comparison problems (“times as many”), where possible, using a context familiar to students. Brainstorm with the class and decide on three separate topics to write their comparison problems. (Possible topic: lunch, pets, toys, types of cards, pencils) For example: Anna has 3 carrots in her lunchbox and Jessie has 3 times as many carrots as Anna. How many carrots does Jessie have in her lunchbox? Have students identify the factors and product in each multiplication problem you solve with the students. Pose a few questions to the whole group and have students solve collaboratively with their partner and then share their thinking. Ask them to pose their own problems using “times as many” in their problem. They can use index cards, wipe off boards or paper to present their own problems to partners to solve. Ask the students to label the two factors and one product in the problem. Share problems, solutions and strategies used. Next, work with several array problems (equivalent groups). Pose problems such as: The students are lined up in 3 teams. Each team has 6 members. How many students are there altogether? Identify and label the two factors and product. Students can use graph paper, peg boards, bead strings, or interlocking cubes to create arrays to solve the problems. Students can then create their own array problem for a partner to solve. Ask
3rd Grade Unit 2 Performance Assessment Rubric Standard ↓ Exceeding Meeting Not Yet Meeting MGSE3.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 shows 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 MGSE3.OA.2 Interpret whole number 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 (How many in each group?), or as a number of shares when 56 objects are partitioned into into equal shares of 8 objects each (How many groups can you make?). For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 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 MGSE3.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. See Glossary: Multiplication and Division Within 100. Explanations 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 MGSE3.MD.3. Draw a scaled All data relevant to the Work shown is organized Work is not shown