Grade 4 Mathematics Lesson Plan - ?· Grade 4 Mathematics Lesson Plan ... • Students will understand that one math sentence may be ... like to plan a lesson that will take advantage of

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<ul><li><p>This lesson plan is originally written in Japanese and translated into English by the Global Education Resources for the Lesson Study Immersion Program in Japan, June 21- July 5, 2007. 2007 Global Education Resources L.L.C. All rights reserved. </p><p>Grade 4 Mathematics Lesson Plan </p><p>Date: June 27 (Wed.), 2007, Period 5 Teachers A: Masako Adachi (Classroom 1) </p><p>B: Akihiko Suzuki (Classroom 2) C: Masako Koizumi (Math Open) </p><p>Research Theme: Nurturing students to become people who can be trusted in an international society: Developing instruction that will </p><p>foster students ability to communicate 1. Name of the unit: Lets think about how to divide </p><p>2. About the unit </p><p> Flow of the contents </p><p>Grade 3 Grade 4 Grade 5 </p><p>(3) Division Meanings of </p><p>division and the division sign </p><p> Division that can be solved by using the basic multiplication facts (no remainder) </p><p>This unit: The division algorithm (1) The division algorithm for a 2- or </p><p>3-digit number divided by a 1-digit number </p><p> Methods of calculating math sentences with o both multiplication and </p><p>division operations o consecutive division </p><p>Extending the meanings of division and times as much (1st and 3rd uses of times as much) </p><p>(2) Multiplication and division of decimals (I) Division of whole numbers with decimal quotients and dividing decimals by whole numbers </p><p>(4) Multiplication and division of decimals (II) Meaning of dividing by a </p><p>decimal and how to calculate </p><p> The division algorithm for dividing whole numbers and s by decimals </p><p>(6) Fractions and Decimals Quotients of whole </p><p>numbers can always be written as fractions </p><p>Division algorithm (2) Dividing by multiples of 10 Division algorithm for 2- or 3-digit </p><p>numbers 1-digit numbers How to check answers for division Meaning of a tentative quotient and </p><p>how to adjust it Properties of division </p><p>(7) Division with remainders Division that can be </p><p>solved by using the basic multiplication facts (with remainders) </p><p> How to check answers </p><p> Meaning of remainders </p></li><li><p>This lesson plan is originally written in Japanese and translated into English by the Global Education Resources for the Lesson Study Immersion Program in Japan, June 21- July 5, 2007. 2007 Global Education Resources L.L.C. All rights reserved. </p><p>Goals of the unit Current state of the students Students will understand the division algorithm for dividing 2- and 3-digit numbers by 1-digit numbers and be able to use it appropriately. [Interest, Desire, Attitude] Students will try to use their previous study of division to </p><p>think about how to divide 2- and 3-digit numbers by 1-digit number. </p><p>[Mathematical Thinking] Students will be able to clearly explain that the division </p><p>algorithm proceeds from the tens digit and then the ones when you are divide 2-digit numbers by 1-digit numbers. </p><p> Students will be able to clearly explain that the division algorithm for dividing 3-digit numbers by 1-digit numbers works in the same way as was learned previously (2-digit 1-digit). </p><p>[Representations, Procedures] Students will be able to accurately calculate 2- and </p><p>3-digit numbers 1-digit numbers. Students will be able to mentally calculate 2- and 3-digit </p><p>numbers 1-digit numbers with 2-digit quotients. [Knowledge, Understanding] Students will understand how to divide 2- and 3-digit </p><p>numbers by 1-digit numbers using the division algorithm. Students will understand that they can use division to </p><p>determine times as much. Students will understand that one math sentence may be </p><p>used even when situations involve both multiplication and division or two consecutive divisions. </p><p>According to the results of the readiness test, virtually all students can accurately calculate division problems that use the basic multiplication facts once, which was studied in Grade 3. Although a few students missed remainders on some problems, all problems were correctly answered by at least 97% of the students. </p><p>There were 2 problems that involve the ideas to be studied in Grade 4: (1) 40 2, and (2) 600 3. Although it seems like students should be able to anticipate the answers, the success rates were (1) 85% and (2) 70%. Moreover, for both problems, 9% of the students left them blank. </p><p>Given the success rates on the items involving previously learned topics, we would like to plan a lesson that will take advantage of their ability to read and interpret math sentences and further extend this ability. However, in the prior unit on circles and spheres, some students had difficulty using compasses appropriately, indicating that some children still lack fine motor skills. </p><p>Moreover, some students understanding may still be rather superficial, and their computational skills are more advanced than their ability to think and reason. Therefore, we want to provide opportunities for students to enjoy solving problems by thinking carefully and manipulating objects. </p></li><li><p>This lesson plan is originally written in Japanese and translated into English by the Global Education Resources for the Lesson Study Immersion Program in Japan, June 21- July 5, 2007. 2007 Global Education Resources L.L.C. All rights reserved. </p><p>3. Abilities we would like to foster in this unit and special instructional strategies </p><p>Target abilities for this unit Instructional strategies </p><p>Note: Arrows indicate how particular strategies may foster specific target abilitie</p><p>1. To make well-grounded explanations [Using prior understanding as the foundation for reasoning] Ability to use properties of </p><p>division in explanations instead of just learning the algorithm procedurally. </p><p> Ability to explain the reasons for the steps of the division algorithm instead of simply reciting, estimate, multiply, subtract, and bring-down. </p><p>2. To communicate effectively [Creating concise representations, diagrams and writing] Ability to describe situations </p><p>involving times as much and division appropriately, utilizing diagrams and math sentences effectively. </p><p>3. To perceive and reason from multiple perspectives [Selecting more appropriate reasoning] Ability to interpret math </p><p>sentences to know how others thought about problems involving both multiplication and division. </p><p> Ability to select more appropriate reasoning using the criteria: efficient, simple, and accurate (ESA). </p><p>1. Level-raising strategies The first 3 lessons of the unit will be used to discover the properties of division. To improve students ability to interpret math sentences, we will frequently have them sort shared solutions and strategies. Repeatedly ask students to use diagrams and math sentences as they explain. To make number lines a more familiar tool, we will frequently ask students to label the number lines. Use missing number problems to promote algebraic reasoning while exploring the algorithm and the properties of division. Employ small group instruction. </p><p>2. Effective learning tasks Use carefully selected numbers in the task to make it </p><p>more realistic (problem involving both x and ). Use a familiar setting to make the task more </p><p>interesting (times as much). Use a new type of problem to think deeply about the </p><p>division algorithm and the properties of division (missing number). </p><p>3. Question posing In all lessons, include as many questions as possible </p><p>to encourage students to look for more appropriate reasoning, foe example, Which operation is more ESA to calculate times as much/ or Which strategy is more ESA? </p><p> Carefully sequence students strategies to be shared publicly, and ask students to share their observations so that they may recognize similarities in reasoning. </p><p>4. Interpreting students reasoning. Throughout every lesson, ask students to record their </p><p>thinking in their notes to capture the change in their thinking. </p><p> Have students write in a learning journal. </p></li><li><p>This lesson plan is originally written in Japanese and translated into English by the Global Education Resources for the Lesson Study Immersion Program in Japan, June 21- July 5, 2007. 2007 Global Education Resources L.L.C. All rights reserved. </p><p>3. Group research examining the research theme </p><p>(1) On times as much </p><p>(2) On the use of number line model </p><p>(3) Proposals on times as much and number line model </p></li><li><p>This lesson plan is originally written in Japanese and translated into English by the Global Education Resources for the Lesson Study Immersion Program in Japan, June 21- July 5, 2007. 2007 Global Education Resources L.L.C. All rights reserved. </p><p>4. Plan of instruction </p><p> Plan for Class 1 (Ms. Adachi) </p><p># Goals Learning Task Evaluation Class 2 (Suzuki) </p><p>Open (Koizumi) </p><p>(1) Properties of division (1) (1) 1 Readiness test </p><p>To discover patterns in division when the dividend stays constant. </p><p>Administer the test. To discover patterns </p><p>from the math sentence, 24=. </p><p>Preassessment Are Ss trying to discover </p><p>patterns in division? (Interest) </p><p> (1) 1 (1) 1 </p><p>2 To discover patterns in division when the divisor stays constant. </p><p> To discover patterns from the math sentence, 3 = . </p><p> Can Ss discover that when the dividend becomes times as much, the quotient also becomes times as much (constant divisor)? (Mathematical Thinking) </p><p> (1) 2 (1) 2 </p><p>3 To discover patterns in division when the quotient stays constant. </p><p> To discover patterns from the math sentence, = 3. </p><p> Can Ss discover patterns and represent them clearly (constant quotient)? (Representation) </p><p> (1) 3 (1) 3 </p><p>(2) Dividing multiples of 10 and 100 (2) (2) 4/5 </p><p> To understand how the division algorithm works when dividing multiples of 10 and 100 by 1-digit numbers. </p><p> To think about how to calculate 80 4. </p><p> To practice similar problems. </p><p> To think about how to calculate 240 6. </p><p> To practice similar problems. </p><p> Can Ss consider the dividends using 10 as a unit and apply the basic multiplication facts to find the quotient? (Math Thinking) </p><p> Can Ss divide multiples of 10 and 100 by a 1-digit number by using the relative sizes of the dividends? (Representations) </p><p> (2) 4/5 </p><p>(2) </p><p>(3) Division algorithm (I) [2-digit 1-digit] (3) (3) 6/7 </p><p> To understand how the division algorithm works when dividing 2-digit numbers by 1-digit numbers (no remainder) </p><p> To understand the the problem situation and write a math sentence. </p><p> To think about how to calculate 52 4. </p><p> To summarize how the algorithm works with 52 4. </p><p> To check the answer for 52 4. </p><p> To practice the algorithm. </p><p> Are Ss trying to use their prior learning to think about how to calculate 2-digit 1-digit? (Interest) </p><p> Can Ss explain clearly that the division algorithm should proceed from the tens digit and then the ones when you are dividing 2-digit numbers by 1-digit numbers? (Mathematical Thinking) </p><p> (3) 6/7 </p><p>(3) 6/7 </p><p>8 To understand how the division algorithm works when dividing 2-digit numbers by 1-digit numbers (with remainder, neither place is divisible). </p><p> To understand the problem situation and write a math sentence. </p><p> To think about how to use the division algorithm for 76 3. </p><p> To know what the quotient is. </p><p> To check the answer </p><p> Can Ss. calculate 2-digit 1-digit using the division algorithm (with remainder and neither place is divisible)? (Representations) </p><p> Do students know how to divide 2-digit numbers by 1-digit numbers (with </p><p> (3) 8 (3) 8 </p></li><li><p>This lesson plan is originally written in Japanese and translated into English by the Global Education Resources for the Lesson Study Immersion Program in Japan, June 21- July 5, 2007. 2007 Global Education Resources L.L.C. All rights reserved. </p><p>for 76 3. To practice similar </p><p>problems. To read the Math </p><p>Corner in the text and learn about the terms, sum, difference, and product. </p><p>remainder and neither place is divisible)? (Knowledge) </p><p>9 To understand how the division algorithm works when dividing 2-digit numbers by 1-digit numbers (with remainder but the tens place is divisible). </p><p> To be able to divide 2-digit numbers by 1-digit numbers by using the algorithm (with remainder and solvable by using the basic multiplication facts once). </p><p> To think about how to calculate 86 4 and 62 3. </p><p> To practice similar problems. </p><p> To practice dividing 2-digit numbers by 1-digit numbers (with remainder and solvable by using the basic multiplication facts once). </p><p> Can Ss divide 2-digit numbers by 1-digit numbers (with remainder and solvable by using the basic multiplication facts once)? (Representations) </p><p> Do Ss understand how the division algorithm works when dividing 2-digit numbers by 1-digit numbers (with remainder but the tens place is divisible)? (Knowledge) </p><p> (3) 9 (3) 9 </p><p>(4) Patterns in the division algorithm and math sentences involving division (5) 14 (4) 12 10 / </p><p>11 To understand that </p><p>there are patterns in the division algorithm through examination of missing-digit problems. (Lesson B in Class 2) </p><p> By using the relationships, divisor &gt; remainder and quotient x divisor &lt; dividend, find the numerals that go in the . </p><p> By thinking about the digit in the ones place of the dividend, explore the relationship between the quotient and the dividend. </p><p> Are Ss thinking logically as they look for the digit in each ? (Mathematical Thinking) </p><p> Can Ss use the remainder to figure out the quotient? (Representations) </p><p> Can Ss discover the relationship between the dividend and the divisor by looking at the three problems? </p><p>(5) - 15 (4) - 13 </p><p>12 To understand that situations that involve both multiplication and division or two consecutive divisions may be written as single math sentences. (Lesson A in Class 1) </p><p> Determine the number of pencils each person will receive when 4 dozen pencils are shared among 6 people. </p><p> To understand that two-step problems involving both multiplication and division or two divisions can be written as single math sentences. </p><p> Can Ss explain why situations that involve both multiplication and division or two consecutive divisions can be written as single math sentences? (Mathematical Thinking) </p><p> Do Ss understand how to calculate math sentences that contain both multiplication and division or two consecutive divisions? </p><p> (4) 10 [lesson A] </p><p>(5) 14 [lesson C] </p></li><li><p>This lesson plan is originally written in Japanese and translated into English by the Global Education Resources for the Lesson Study Immersion Program in Japan, June 21- July 5, 2007. 2007 Global Education Resources L.L.C. All rights reserved. </p><p> To practice problems involving both multiplication and division and two consecutive divisions. </p><p>(Knowledge) </p><p>13 To master what they have been studying so far. </p><p> To complete Lets master in the textbook. </p><p> Are Ss appropriately using what they have learned so far to solve problems correctly? (Representations) </p><p> (4) 11 (5) 15 </p><p>(5) Calculation involving times as much 14 To understand that </p><p>division is used to determine how many times as much a given quantity is as the base quantity. (Lesson C in Open) </p><p> To think about what operation should be used to determine how many times as long 15 m is as 3m by using diagrams. </p><p> To learn that division can be used to determine how many times...</p></li></ul>