Multiplication Unit Plan. Katie Kramer Spring 2013

Transcription

1 1 Multiplication Unit Plan Katie Kramer Spring 2013

2 2 Class: Fifth Grade math with integration of Language Arts. Background: This unit covers the topic of multiplication in math. This unit asks students to apply previous knowledge of multiplication to solve multi-digit, multi-step, and decimal multiplication problems. This is an important math topic because it lays the foundation for future math topics, and multiplication is a skill in which students will use throughout life. Rationale: My rationale for this unit is to educate students on solving multi-digit, decimal multiplication problems. This is an important topic, because multiplication is something that students will encounter in future grades. Even more so, multiplication of decimals (money) will be something that students will encounter on nearly an everyday basis as they grow up. In this unit, students will be asked to, Perform operations with multi-digit whole numbers and with decimals to hundredths (CCSS). Students should be exposed to this topic in order to lay the foundation for future life and math skills. In one lesson, I integrate the language arts curriculum-- in which students are asked to integrate their writing skills into math. Unit Objective: Students identify and apply knowledge of the important multiplication steps in order to solve multi-digit, decimals problems that are applicable to the real world. Unit Goals: Identify that pattern when multiplying numbers by 10, 100, Identify the area model of multiplication Solve multi-digit multiplication problems using the traditional method Explain the steps of solving multiplication with decimals. Apply knowledge of multiplication of decimals to solve real world problems regarding to money. Overview: Fifth grade Common Core State Standards: CCSS.Math.Content.5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

3 3 CCSS.Math.Content.5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. CCSS.Math.Content.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. CCSS.Math.Content.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Content Outline: Day One: The student will understand the shift in places and zero pattern that results when you multiply the a number by 10, 100, or 1,000 CCSS.Math.Content.5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. CCSS.Math.Content.5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Day Two: The student will use the area model of multiplication to solve double digit multiplication patterns. There is no standard for this lesson, however I felt that it was important because it exposes students to a more visual method for solving multiplication problems. In addition, it reviews some of the place value properties from earlier in the year. Day Three: The student will solve two digit multiplication problems fluently using various methods. CCSS.Math.Content.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Day Four: The student will solve 2x3 and 3x3 digit multiplication problems. CCSS.Math.Content.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Day Five: The student will apply knowledge of multiplication in order to multiply a whole number by a decimal.

4 4 CCSS.Math.Content.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Day Six The student will understand and explain the process of multiplying two decimals together. CCSS.Math.Content.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Day Seven: The student will apply knowledge of multiplication in order to solve multiplication problems when the other factor is either a whole number or a decimal. CCSS.Math.Content.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Day Eight: The student will apply knowledge of multiplication in order to solve multistep word problems and explain the process in which they solved it. CCSS.Math.Content.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. CCSS.Math.Content.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Day Nine: Review day Day Ten: Brief review of material, and then students will take a summative assessment on the entire unit. Meeting Diverse Needs: Learning Styles: Visual: Throughout the unit, I will incorporate a large amount of visual aids. These will range from you tube clips, to writing information on the board.

5 5 In addition, students will be shown a model for multiplying that is very visual based. Auditory: Throughout the unit I incorporate whole group discussion, as well as opportunities for students to work in groups and discuss their thought process. Students will also be asked to repeat the directions back to the teacher after they are given. Read / Write: Throughout the unit, a variety of different worksheets are available to students. In addition, students will often times be asked to explain their thinking in words, in order to better describe their thought process. Kinesthetic: Throughout the unit, students will be moving around the room for different activities. Students will also be encouraged to come up to the board to solve problems, in addition to an activity in which students move a decimal through standing up. Gifted: Students who have proved that they have mastered a skill, will be given the chance to go on Khan Academy or Ten Marks Math -- an online resource which explains sixth grade math concepts. Learning Disabled: In order to accommodate these students, we will focus more attention on certain topics. In addition, an RTI time at the end of each math session will be given, if time. This time will enable the teacher to provide additional support to these students and walk them through more problems. In addition, students will be asked to repeat the directions back to the teacher so that all the students will hear the directions twice. ADHD: Throughout the unit, students will never be sitting in the same desk for the entire period. Students will be asked to move around the classroom -- by means of group work, partner work, or in-class activities. In addition at the beginning of the lesson, the general outline of the lesson will be given by the teacher to all students, in order to inform them of what is occurring. Behavior Management: These students have been following the same behavior management system since the beginning of the school year. At the beginning of each lesson, students will be called to attention by the teacher giving the time out symbol. Also students are broken into teams that compete for the blue chairs If teams are prepared and ready, they may earn a point. If an individual

6 student s behavior is causing problems, they will be asked to sign the PRIDE book. At the end of the month, if they have signed four times, they are unable to attend the PRIDE Party on Friday afternoon. 6

7 Lesson Plans 7

8 8 Day One: What is a shift pattern in multiplication? How will they help make multiplication easier? Objective: The student will understand the shift in places and the zeros pattern that results when you multiply a number by 10, 100, or 1,00. Standard: CCSS.Math.Content.5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Anticipatory Set: Have students solve a set of problems, with each one multiplied by 10, 100, or Write student responses on the board. Ask students to turn and talk to their neighbor to discuss any patterns that they might be seeing. Activity: Explain process of simply adding the zeroes to the right of the number when you multiply by these numbers. Have students break into partners...assigned for differentiation. Group One: Have students get in pairs: Hand out base ten blocks. Have a sheet to guide student learning, in which they have to discover the pattern if you take 6 x 3 then 6 x 30, then 6 x 300. Have students experiment with 4, 5, and 6 Group Two: In pairs: Extend the list of multiplication for 1,800. Try to find all of the factors that create a product of 1,800. Create a list of all multiplication of 32,000. Compare list with another partner group, and check that all possible multiplications have been found Discuss different methods for finding all the possible multiplications. Closure: Discuss with students what they found. have students explain in partners what the pattern is that they will use. Have them share their responses with class. Technology: Pre-Test might be done with clickers and on the smartboardd Document camera.

9 9 Materials: Pre-Test for students Worksheets for each group Students need to be divided into groups. Assessment: Pre-Test Day Two: What is the area model for multiplication? How do I use it to solve multi-digit multiplication problem? Objective: The student will use the area model of multiplication to solve double digit multiplication problem. Standard: CCSS.Math.Content.5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Anticipatory Set: Review homework from day earlier. Put the following multiplication problem on the board: 54 x 39. Ask students to turn and talk to a neighbor and explain how they might solve this problem. Explain that I want them to think about how they might solve the problem in multiple ways. That you might think of one way to solve it, but is there another way to also solve it. Brainstorm as an entire class the ways to solve this problem...write on board. Activity: Explain to students that these are all great ways to solve the problem, but today we are going to focus on the area model of multiplication. Ask students based off the name of this, what do they think they are going to be asked to do. Have students share their responses. Explain area model of multiplication. Work through a couple as a class, offering students to come up to the board and solve the problems step by step. After practicing some problems as class, give students two choices: To work in partners / individually to begin the next days homework...if they completely understand the concept.

10 10 Also explain that I will be available to continue working through some problems if they are still confused. --Work through some problems and also some homework problems. Closure: Explain the homework for the next day, and give students time to work on homework --Explain that for today, students need to use this area model, but in the future they will be able to choose the method that works best for them. Materials: Student worksheets / workbook pages 163: 1, 4, 8, 5, 7 164: evens Technology Document Camera Assessment: Formative: Student responses, and student choices for what they choose to do. This will enable me to take note of which students might need extra help. Day Three: What are the strategies I can use to multiply 2 by 2 digit numbers? Objective: The student will solve two digit multiplication problems fluently using various methods. Standard: CCSS.Math.Content.5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. CCSS.Math.Content.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Anticipatory Set: Review previous day s homework with students. After reviewing homework with students...ask: What are the ways that we can solve 2 x 2 multiplication problems? Turn and talk to your neighbor and explain it to them. Ask students to share what they talked about with entire class. Write student responses on the board Take vote on which strategies students found that they like best. Activity: Hold class discussion about the various methods. Have students turn to page 269 in their student book.

11 11 Ask students how the methods at the top are different or similar to each other. Hold classroom discussion Review the different ways to solve the multiplication Remind students that it is ultimately their decision on what method they use...and what methods work best for them. Closure: Assign student homework: Workbook page 165: 1-8 and page , 5, 7,9 Give students time to work on their homework. Exit Slip Materials: Student Workbooks. Technology: Document Camera Assessment: Formative: Students will be given an exit slip at the conclusion of this lesson. This will enable me to take note of which students are struggling with this concept in order to give them further support. Day Four: How do I multiply 2 x 3 digit numbers and 3 x 3 digit numbers? Objective: The student will solve 2 x 3 and 3 x 3 digit multiplication problems. Standards: CCSS.Math.Content.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Anticipatory Set: Review homework from day before. Put the following problem on the board: 200 x 100. Ask students to turn and talk to their neighbor and explain how they might solve that problem. After students have had time, ask them to share their responses with the entire class. After student responses write this problem on the board: 243 x 25...have students turn and talk and explain how they might solve this problem. Allow students to share their responses. Remind students that there answers were great! But lets think about the past couple of days...what strategies did we talk about to solve 2 x 2 digit multiplication.

12 Activity: Ask students if they think that they can use those multiplication strategies to solve 2 x 3 digit multiplication. What about 3 x 3 digit multiplication. Solve following problems 243 x x x x 123 Invite students to share what methods they might use..making sure to include all of the strategies that we have been talking about Independent Practice: Give students the opportunity to run through some of the problems on their own. Students will get into groups of three or four..with each student coming prepared with a problem that they solved on their own. Have students pass their sheet to the left, where the person will complete and solve the problem. Then have them fold the sheet down to cover their answer, and then pass the sheet. Continue the process until each person has the problem that they wrote. Have students share their answers and discuss answers...why they got it etc. Share what method works best for them and why. Closure: Have students return to their seat. Have some students share their question with the class. Have class solve it. Assign Homework: Workbook page Evens and 168 9, 11, If time, allow students to work on their homework. Materials: Printer paper for student to write their problems on Student workbook Technology: Document Camera Assessment: Formative: Student responses / how well they do on the individual practice activity. 12

13 13 Day Five: How do I multiply whole numbers by decimals? Objective: The student will apply knowledge of multiplication in order to multiply a whole number by a decimal. Standard: CCSS.Math.Content.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Anticipatory Set: Go over homework from Thursday night? Write the following problem on the board: Patty wants to buy 25 jump ropes. In a magazine she found them for.75 cents each. How much money will patty spend on her jump ropes? Have students turn and talk to a neighbor on how the might solve the problem. Go over how to solve it with students. Activity / Content: Have students solve the following problem: Maggie buys marbles. The marbles cost.412 Cents, if Maggie wants to buy 10 marbles. How much money will she spend? What about if she wants to buy 100 marbles? What if she wants to buy 1000 marbles? Have students talk about any patters that they might see. Explain content / do examples: Multiply the numbers normally, then move the decimal over however many numbers are after the decimal. Introduce money activity. finding how much money Tapanga made at her garage sale. Run through some examples with students. Then allow the students to work in pairs to complete the rest of the sheet. Give students about minutes to work through some of the problems. Closure: Come back as an entire class. Have students share their responses with the rest of the class / how they found out the answer. Go over rest of sheet Assign homework: Page 173- Evens Page number 13 Strategies:

14 14 Whole Class discussion Teacher modeling Partner Practice Assessment: Student responses / worksheet will be collected. Day Six How do I multiply two decimals together Objective: The student will apply knowledge of multiplication in order to solve multiplication problems when the other factor is either a whole number or decimal. Standard: CCSS.Math.Content.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Anticipatory Set: Go over homework from day before. Have students take out the sheet from the day before. Ask students what the pattern was. Write 1.25 x.25 on the board. Have them turn and talk about what they might do to solve that problem. Ask students if they think they need to line up the decimals? Activity: Explain to students how they will solve this problem. First, ignore the decimals and just solve the problem. Then count up how many numbers are after the decimal, finally moving it over to the left that many times. Visual example. Have students work through the following problems. Each student will have a sheet of construction paper, have the students with those numbers, come forward. One student will be a decimal. Ask students how many times the decimal should move. Have the decimal move that many times. That is your answer. Review the steps again. Run through more examples the same way. Closure: Have students review the steps of solving a decimal multiplication problem. Assign homework to students: Page 175: 1-10 and 15-17

15 15 Page 176: 1-2 and 5-7 If time, allow students to work on homework and explain to students if they need extra help they can come to the back table and work through a couple of problems. Possibly show video: Strategies: Whole Class discussion. Individual practice (homework) Assessment: Formative: Student responses and observation. Day Seven: How do I multiply two decimals together? Objective: The student will understand and explain the process of multiplying two decimals together. Standard: CCSS.Math.Content.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Anticipatory Set: Go over homework from the day before. Explain to students that today we will simply be practicing multiplying. Hand out white boards and supplies to students. Activity: Today will be a day in which students can simply practice multiplication since the final quiz will be given tomorrow. Write a variety of multiplication problems on the board, and have students solve them on the white board. Invite students up to the main board to explain the answer and how they solved for it. Closure: Explain to students that there will be a quiz tomorrow. If students have any questions, answer them. Strategies: Whole Class discussion Individual practice. Assessment:

16 16 Formative: Student responses on white boards. Day Eight: How do I use my knowledge of multiplication to solve word problems? Objectives: The student will apply knowledge of multiplication in order to solve multistepped word problems and explain the process in which they solved it. Standard: CCSS.Math.Content.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used CCSS.Math.Content.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Anticipatory Set: Go over homework from day before. Write the following problem on the board: Marcus sails his boat 94.5 miles every day. If he sails for 25 days, how far will he sail? Have students turn and talk and explain how they might solve the problem. Allow students to go ahead and respond what process they would do. Activity: Go through a couple more examples as an entire class. Explaining techniques and how they might solve the problem. Hand activity sheet out to students: Allowing them to work with pairs, have them complete the sheet, and explain how they solved the problems. about minutes Then come back together as a class, and walk through the worksheet together. Closure: Explain to students that they will have a quiz tomorrow on multiplication, but will have time to review later in the day. Ask students to review how they solve for word problems, and share the tool that works best for them. Strategies: Whole Class discussion Turn and Talk Partner work

17 17 Assessment: Formative: Student responses / possible collecting of the sheet they did in pairs. Day Nine: Review day Objective: n/a Standard: CCSS.Math.Content.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. CCSS.Math.Content.5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Anticipatory Set: Explain to students that today we will be reviewing for the multiplication test they are going to have the next day. Walk through a couple of problems as an entire class.. Talking about the steps that they need to take, and asking students questions to confirm understanding. Activity: Option One: Have students work in pairs to complete worksheets that will solve a puzzle. Students will have to combine as a class in order to solve the riddle. Option Two: Review game: baseball --- > students will be split into teams and then have to answer questions as a team in order to progress around the bases. Closure: Ask students if there are any questions that they have regarding the test tomorrow. Remind students that they have a quiz tomorrow and to study! Materials: Worksheets (Option One) Note cards (Option Two) Document Camera Technology: No technology will be used. Assessment: Formative: Student responses / questions.

18 18 Evidence of Student Learning

19 19 Student Name Pretest Score Post Test Score Noah 60% 100% Adam 30% 100% Emma 30% 85% Angel 40% 95% Anna 50% 100% Nats 60% 100% Kim 60% 90% Dakota 60% 100% Hannah 40% 80% Tatum 80% 100% Zach 80% 100% Jaden 50% 100% Ty 70% 80% Logan 50% 100% Kaylee 20% 70% Mara Absent 100% Jaczeney 40% 100% Cam 90% 100% Lilja 100% 100% Michael 40% 100% Gabe 60% 100% Dean 10% 50% Gabrielle 50% 100%

20 20 Student Name Pretest Score Post Test Score Nick 30% 80% Alex 30% 100% Nick Absent 50% Zoey 50% 70%