Tools 4 NC Teachers | Math Science Partnership Grant Website



Broken Calculator In this lesson, students will use multiplication strategies to find solutions to division expressions.NC Mathematics Standard(s):Operations and Algebraic ThinkingNC.3.OA.6- Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem.Standards for Mathematical Practice:1. Make sense and persevere in solving problems. 7. Looks for and makes sense of structure. Student Outcomes: I can find the missing factor in a multiplication equation.I can find the answer to a division problem by thinking of the missing factor in a multiplication problem.I can describe relationships between multiplication and division.Math Language:What words or phrases do I expect students to talk about during this lesson? AddMultiplyGroups DivideSubtractTotalMaterials: Manipulatives Counters Square tilesSnap cubesAdvance Preparation: Gather manipulativesMath journals or independent work spaceLaunch:Warm Up (10 minutes)Start with a warm-up problem to get the students thinking. Verbally share the following problem. Give students about 3 minutes to think about the problem.“Today you are going to be thinking about division expressions. Before we begin you are going to imagine using a calculator with broken keys to solve addition and subtraction problems. The broken keys on your calculator are the 0 and 1 keys. Think about how you would use your calculator to help you solve the following problems without using the broken keys. Write the keys you would press to help you solve the problems.”Begin by showing students each problem, allowing them a minute to work and think with a partner and 1 minute to share solutions with the group before moving to the next expression.15 - 9108 - 72415 - 11Allow students to turn and talk about how they solved it and solicit a couple of students to share their thinking.Ask these questions to promote reasoning and productive talk:How did you make the calculator show 15 when the 1 is broken? Where did you start?If you cannot use the 0 or 1 what number might help you get to 108?Can someone explain what _____ just said?If you understand what _____ just explained and can say it in your own words please raise your hand.Explore:Working With Partners (15-20 minutes)Share the following with students. Say: in a moment you are going to work with your partner on a broken calculator problem. In this problem the division key is not working. Using this rule, work with your partner to solve each problem on your student sheet. Be sure to record the keys you used as you solved each problem. As students are working observe students for the following:How are students solving division expressions without the division key?What struggles do students face first?What strategy do they use?How many students are using multiplication to solve?How many are using subtraction to solve?After about 10 minutes of work time bring students back together by asking students to share their strategies for solving problems. Be prepared to intentionally discuss students who use multiplication as a strategy. Explain to students that they are going to go back to their groups to think about the following questions and that they will take 5 minutes to write, draw or build something that explains their thinking to the group: Why can we use multiplication to solve division? Will this work every time?Discuss:Discussion (10-15 minutes)When preparing for discussion, pay attention to the strategies students used. Discuss strategies from basic understanding to complex understanding. Students who used drawings or blocks as their strategy should be presented first. As students are discussing, record their work on an anchor chart so that students can visually connect ideas. Discussion Questions:Is it true that we can use multiplication to solve division?Can we always so this?Can you think of a time this would not work?How does the drawing, explanation or block representation prove that this is true?End the discussion with students by writing some form of the following statements. If no student has arrived at this conclusion do not share this statement. Instead, record one of the statements students are suggesting and explain that we are going to continue to think about this. Evaluation of Student UnderstandingInformal Evaluation: Based on the students’ work, their connection between multiplication and division can be evaluated along with their connection of repeated addition/subtraction. Where they are in the understanding of multiplication and division can be assessed and built upon during the discussion. Meeting the Needs of the Range of LearnersIntervention:Require students to use tools as one form of explanationProvide students with a frame to start their justification: “You can just multiply when you need to divide because______________”“Multiplication and division are similar because ___________”“This will always work because___________”Extension: Ask students to think about addition. What if the subtraction key was broken. Would addition work? What could you build, write or draw to justify this.Special Notes: This lesson may not be a full 45 minutes to 1hr. It is designed to provide children with space and context to notice a relationship between multiplication and division. You may need to repeat this as a routine or warm up for 10 minutes at different points in time throughout this cluster.Possible Solutions: Solutions will varyActivity Sheet Solve each equation:Record the keys you would use here:56 ÷ 842 ÷ 716 ÷ 484 ÷ 836 ÷ 9What do you and your partners notice about multiplication and division? Use, writing, drawing or tools to show your thinking. ................
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