Differentiated Unit – Lesson Plan



|Week/Lesson: |Unit Topic: Multi-Digit |Unit Theme: Multiply multi-digit numbers using arrays, charts, area |Essential Question for LESSON: How can we use multiples of 10 and 100 to|

|Week One/ Lesson 2 |Multiplication |models, and vertical records |help us solve multi-digit multiplication problems? |

|Texas Essential Knowledge and Skills: |

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|4.4 (B) represent multiplication and division situations in picture, word, and number form; |

|4.4 (D) use multiplication to solve problems (no more than two digits times two digits without technology); |

|4.6 (B) use patterns to multiply by 10 and 100. |

|STUDENT OUTCOMES |

|Students will know these key facts (discrete bits of information that are believed to be true): |

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|Definition of multiple: a number that is the product of another number, i.e. 70 is a multiple of ten |

|Students will understand these organizing concepts (categories of things with common elements that help students organize, retain and use information): |

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|Place value and its role in multiplication |

|Students will understand these guiding principles (rules that govern concepts): |

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|The place values of the factors of a multiplication problem affect the place value of the product. |

|Students will demonstrate (do) associated attitudes (degrees of commitment to ideas and spheres of learning): |

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|Facts that I already know can help me solve harder math problems |

|I will show my work and not just add zeros to the answers, showing that I understand the underlying concept. |

|Students will demonstrate (do) these essential skills (how students use their understanding): |

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|Using manipulatives, pictures, or word problems, solve problems containing multiples of ten and hundred |

|PROCEDURES |

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|Preassessment: |

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|The preassessment was designed to evaluate student’s preexisting understanding of multi-digit multiplication and how to use multiples of 10 and 100 to solve more complex multi-digit multiplication problems. The |

|students were given about ten minutes to complete a worksheet with four simple multiplication problems and one word problem with three questions. By creating a preassessment with both simple problems and word |

|problems, I collected good information about the students’ abstract math skills because many of the students had trouble translating the math that they showed mastery of in the simple problems to the word problem. |

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|BEFORE: Content decisions based on READINESS – |

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|BEFORE: |

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|The students will be grouped homogenously based on readiness demonstrated through the preassessment. Each group will receive guided practice with the teacher, while the other students are working on specific |

|independent work that will be discussed in the small groups. |

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|The following students are “below readiness” for this lesson, meaning that they have demonstrated the need for additional guided practice and more teacher support and modeling so that they can achieve a high degree of|

|mastery. During the rotations, they will start in Guided Math to extend the whole-group guided practice, with and without manipulatives. Then they will complete the worksheet with simple multi-digit multiplication |

|problems. |

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|The following students are “at readiness” for this lesson. During the rotations, they will start in independent work and will complete the worksheet with simple multi-digit multiplication problems. Then they will go |

|to Guided Math to discuss how they are solving those problems, receive some modeling for how to solve them from the teacher, as well as how to solve word problems. Then the students will return to independent work to |

|complete the worksheets with word problems, one where a visual aid is given and one where they draw their own visual aid. |

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|The following students are “above readiness” for this lesson. During the rotations, they will start in independent work and will complete the worksheets with word problems, one where a visual aid is given and one |

|where they draw their own visual aid. Then they will go to Guided Math to discuss how they are solving those problems, model their strategies for each other, as well as receive some modeling for how to solve word |

|problems without visual aids from the teacher. Then the students will return to independent work to complete the worksheets with word problems, without any kind of visual aid. |

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|DURING: Anticipatory Activities: |

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|“Today we are going to be doing some more complex multiplication problems and using what we know about multiples of ten and one hundred to solve them. Knowing how to use what you already know to solve harder problems |

|will help you to be more successful in solving even more complex problems than these!” Review meaning of the word multiples in the context of math: a number that is the product of another number, i.e. 70 is a multiple|

|of ten. Students will then be shown a list of numbers and asked to identify as a whole group which numbers are multiples of 10 and 100. While the students are reviewing the list, teacher will pass out base-ten blocks |

|and instruct students to create one of the multiples of ten listed using the base ten blocks. |

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|DURING: Primary Lesson Procedures: |

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|“Now that we have reviewed what the multiples of 10 and 100 are, let’s practice multiplying by multiples of ten! First let’s look at these problems: 6x3, 6x30, 3-60. You may know the answers to some of these |

|problems, but let’s work them out with base-ten blocks. Looking at the first one, I’m going to solve this by making six groups of three (teacher will emphasize “groups of” by demonstrating the formation of |

|multiplication symbol, a prompt that the class uses). Now that I have my six groups of three, I just have to count them to realize that 6x3 is 18. Does that make sense to everyone? Now, let’s look at the next problem:|

|6x30. For this I’m going to make six groups of what? Of 30. I’ll do this by using the rods rather than the units. Now that I have my six groups of 30, I just have to count my rods by tens, because each rod is worth |

|ten, to see that 6x30 is 180.” Repeat the same process for 3x60. “You can see that when the original problem asks you to make groups of ones, then the answer is in groups of ones. When the original problem asks you to|

|make groups of tens, then the answer is in groups of tens. What do you think would happen if I added the problem 6x300? The answer would be 1800, 18 groups of 100. This means that when the original problem is in |

|groups of one hundred, then the answer is in groups of one hundred. This strategy will be really helpful for you today as you work on your independent work assignments.” |

|Students will be split into math groups based on readiness, and those groups will switch between independent work and Guided Math with the teacher. While the teacher is working with the Guided Math groups, the rest of|

|the students are working independently and without talking on leveled worksheets |

|Beginning readiness group meets with teacher first to continue guided practice from whole-class but now in a small-group setting. Group will continue using manipulatives to illustrate multi-digit multiplication |

|problems. Part of the beginning readiness group will then be given the independent practice task of completing some multi-digit multiplication problems without manipulatives. The remaining members of the beginning |

|readiness group will be given additional practice on working on the multi-digit multiplication problems to ensure their understanding. |

|The teacher will then pull the at readiness group, which has already been working on some multi-digit multiplication problems without manipulatives. The teacher will ask the students to explain how they have been |

|solving the problems that they were given, then guide this group through some more complex problems, then introduce simple word problems with visual aides. This group will then return to independent work to continue |

|working on simple word problems with visual aides. |

|The teacher will pull the above readiness group, which has been working on word problems with visual aides, both given and that they draw themselves. The teacher will ask the students to explain how they have been |

|solving the problems that they were given, and will guide this group through some more complex problems of this variety, then guide them through working through word problems without visual aides. |

|Closing Procedures: (How will you bring the lesson to a close so that there isn’t an abrupt end?) |

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|The teacher will bring the class back together as a whole to practice some simple problems without the use of manipulatives (9x40, 6x300, 200x9, etc.) The teacher will ask for students to share not only their answers,|

|but also how they solved the problems. “Now we have solved many problems where one of the factors is a multiple of 10 or 100. We found out that if the problem is phrased as X groups of Y, we can figure it out based on|

|the place value of Y. If Y is in groups of tens, then the answer will be in groups of tens. This piece of knowledge will be very helpful for you for the rest of this chapter and higher-level math.” |

|MATERIALS |

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|Base-ten blocks, |

|worksheets for each student (attached) |

|Pencils for each student |

|Doc-cam/projector |

|ASSESSMENT EVIDENCE: |

|Embedded Performance Task: |

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|Within the guided math groups, the teacher will evaluate student work based on correct answers, as well as being able to explain how they solved a problem. These responses will be used to determine how much additional|

|support each group or individual needs as well as if they are ready to move on to a more complex task. |

|Post-Lesson Assessments: |

|Assess of student work sample for the following: |

|For the independent work, the teacher will evaluate student work based on correct answers, as well as showing their work in a way that demonstrates understanding of lesson objective. |

|A quality response includes not only the correct answer, but also their work. Ex. Ms. Strange really likes to write letters to her friends. Every day for 9 days, she wrote 20 letters. How many letters had she written |

|at the end of the 9 days? Student sets up the multiplication problem 9x20, then draws a “wrestling mat” or array, sets up a repeated addition problem, or drawings pictures of nine groups of twenty. Then the student |

|writes the answer 180. |

|It is also acceptable for students to show evidence of solving the basic multiplication problem, then adding the zeroes on at the end. They can do this by setting up the original multiplication problem, then boxing |

|the zero, then showing that they add it back at the end. |

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B. What do they need to learn next?

These students will receive guided practice in a small group with an emphasis on the students sharing the strategies that they would use to solve word problems, which have visual supports. Then the teacher will guide them through a word problem without visual aides.

These students will receive guided practice in a small group, first asking them to share their strategies for answering multi-digit multiplication problems, then the teacher guiding them through word problems with visual supports, both given and student created, such as diagrams and groups about multi-digit multiplication problems.

B

These students will receive guided practice in a small group setting with teacher modeling and use of manipulatives to help them solve basic multi-digit multiplication problems, such as 6x70

These students can solve basic multi-digit multiplication problems (i.e. 120x7), usually by breaking down the problem into a basic one (12x7) and adding a zero to the product. They can also at least partially solve word problems about multi-digit multiplication.

A

These students can solve basic multi-digit multiplication problems (i.e. 120x7), usually by breaking down the problem into a basic one (12x7) and adding a zero to the product

These students can solve basic multiplication problems (i.e. 4x10)

A. What do they know at the beginning of the lesson/unit of study?

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