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Technology-Embedded Lesson Plan
Roger Gray
Liberty University
EDUC 630-B01
Multiplying 2 digit factors using array models and partial products
|Topic/Grade Level: Grade 5 / Multiplying 2 digit factors using array models and Partial Products |
|Boulder Valley School District (BVSD) and Colorado Department of Education (CDE) Standards: |
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|BVSD & CDE Mathematics Curriculum Standard 1.2.b.ii - Illustrate and explain calculations by using equations, rectangular arrays, and/or area models.|
|(CCSS: 5.NBT.6) |
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|BVSD & CDE Mathematics Curriculum Standard 1.2.c.i - Use concrete models or drawings and strategies based on place value, properties of operations, |
|and/or the relationship between addition and subtraction. (CCSS: 5.NBT.7) |
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|BVSD & CDE Mathematics Curriculum Standard 1.1.a.i - Explain patterns in the number of zeros of the product when multiplying a number by powers of |
|10. (CCSS: 5.NBT.2) |
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|BVSD & CDE Mathematics Curriculum Standards Prepared Graduate Competencies in Matematics; Patterns, Functions, and Algebraic Structures Standard - |
|Use critical thinking to recognize problematic aspects of situations, create mathematical models, and present and defend solutions |
|Goals and Student Learning Outcomes (Objectives): |
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|Goal 1: Students will build area models to solve 2 digit muliplicaiton problems |
|Student Learning Outcome 1: Students will make an array, break it apart, and transfer |
|that knowledge to the window pane strategy to solve multi-digit multiplication problems. |
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|Goal 2: Students will calculate the product of multiplying each place value of multi-digit factors. |
|Student Learning Outcome 1: Students will discuss the calculation of multi-digit factors |
|as they evaluate the products of each place value |
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|Goal 3: Students will investigate the use of multi-digit multiplication by solving word problems. |
|Student Learning Outcome 1: Students will use word problems to construct multi-digit |
|calculations and construct area arrays to solve them. |
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|Goal 4: Students will demonstrate the use of area models / window pane arrays. |
|Student Learning Outcome 1: Students will calculate the product of muti-digit factors |
|utilizing area models / window pane arrays. |
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|Goal 5: Students will discuss and explain the use of area models / window pane arrays to solve muli-digit multiplication problems. |
|Student Learning Outcome 1: Students will present results and describe the procedure |
|they used in calculating the product of multi-digit factors using area models / window |
|pane arrays. |
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|Goal 6: Students will show understanding of area models / window pane arrays. |
|Student Learning Outcome 1: Students will reproduce area models / window pane arrays |
|individually by completing assessment calculations independently. |
|Learning Environment(s): |
|Flipped Classroom Model - Students will participate in online learning off-site in place of traditional homework and then attend the brick-and-mortar|
|school for face-to-face, teacher-guided practice and projects in a cooperative learning setting. |
|Resources: |
|Computer, Chromebook, or tablet |
|Internet Access |
|Textbook – Math Expressions |
|Two regular dice |
|Pre-Made multiplication problems to post around the classroom |
|Paper and Pencil |
|Document Camera |
|Vocabulary & explanation video - |
|Video 1; Khan Academy - |
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|area-models |
|Video 2; Ten Marks - |
|Screencast - |
|Screencastify App on Chromebooks |
|Three word problems for group work |
|Three word problems for individual assessment |
|Exit ticket 2 digit multiplication problem |
|Diversity / Differentiation: |
|Higher-level learners will be encouraged to take it a step further and see if they can use the same steps to multiply 2 digit by 3 digit problem |
|using the window pane strategy. The teacher can also show them the lattice way of multiplying 2 digit numbers for fun. |
|Visuals, extended thinking time, small group instruction, and extra modeling will be provided for students with special needs and ELLs. Tutorials |
|will be provided as well before school once a week for review of current and past concepts learners who are struggling. |
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|Technology Inclusion: |
|Online learning off-site will utilize comuter, chromebook, and/or tablet to access videos for review, instruction, and practice. |
|In class use of Screencastify App on Chromebooks for cooperative learning exercise. |
|Technology Projector/Document Camera for presenting group work. |
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|Prior Knowledge: |
|Prior to this lesson, students have: reviewed single-digit multiplication, use of dot arrays for multiplication, and multiplication vocabulary as |
|well as learned new vocablulary for utilizing area/window arrays. Students also have prior ecperience using Screencastify on Chromebooks. |
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|Lesson Placement in the Unit: This is lesson 1 of 6. |
|Procedures: |
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|Lesson Introduction / Anticipatory Set: |
|At home: |
|This lesson and links will be available to students through their Schoology account in the Math folder. Students will view a review vocabulary & |
|example video to activate prior knowledge. They will then watch video 1 from Khan Academy that will explain how to multiply 2 digits by 2 digit |
|factors using an area model array and has practice available. Then the students will watch video 2 from Ten Marks which will shows students step by |
|step procedures for breaking an array apart to make it easier to multiply big numbers. Finally the students will watch a short screencast of Mrs. Ali|
|explaining the window pane method of solving 2 digit factors connecting it to the array. After the students have viewed everything they will complete|
|five problems which will be assigned updated into the screencast on their own using the window pane strategy. These completed problems will be the |
|student’s entrance ticket the next day. |
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|At school: |
|Students will compare the work they did on the 5 problems with other students who are sitting in their table group. If they have different answers |
|then they will see if they can help each other find the correct solution. The teacher will give assistance if it is needed. All students should |
|have correct examples of the 5 homework problems on their desk. |
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|Direct Instruction: |
|The teacher will circulate through the room and use a formative assessment checklist to verify if students understand the steps thoroughly. The |
|teacher will pull small groups for those students struggling and observe them to see what exactly they need clarification in. Additional small groups|
|will be organized for direct instruction using simplified calculations with students who are struggling with basic math skills. |
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|Student Interaction with lesson content / Guided Practice: |
|Cooperative learning: Students pair up with two dice and come up with two, two digit problems. One problem for partner A and one for partner B. They |
|both solve their problems using the Screencastify App on their Chromebook and the window pane strategy. Their process will be recorded as a video. |
|Once both students have completed their problem, they trade Chromebooks and watch and review their partner’s work. If there are no questions then |
|they continue so they complete 5 problems each. Students are encouraged to try a 3 digit by 2 digit and 3 digit by 3 digit. |
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|Presentations: |
|Each pair of students will get to present the problem they are most proud of solving and it will be projected for the class to review. |
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|Independent Practice: |
|The students are given 3 word problems to solve in groups (triads recommended). Once the teacher has seen that they are completed correctly, each |
|child must work 3 more problems individually to turn in for a grade. |
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|Review / Closure: |
|Each student will be given an exit ticket question in which they will have to solve a 2 digit multiplication problem using the window pane strategy |
|and get it checked by their shoulder partner who will inform their partner to leave after the answer is correct. |
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| Evaluation/Assessment: |
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|Formative assessment checklist; |
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|Student name________________________ Date:______________ |
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|______ Entrance ticket completed |
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|______ On task and participating. |
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|______ Basic math skills exhibited |
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|______ Understands Concept being practiced (Area Model) |
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|______ Work is neat and complete |
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|______ Showing leadership in group |
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|Notes:_______________________________________________________ |
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|____________________________________________________________ |
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|____________________________________________________________ |
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|____________________________________________________________ |
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|____________________________________________________________ |
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|Summative Assessment; |
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|Item |
|1 |
|2 |
|3 |
|4 |
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|Prepared with entrance ticket |
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|No entrance ticket or no work completed. |
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|Incomplete entrance ticket or less than 3 correct. |
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|Complete with most answers correct. (3 or 4) |
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|Complete with all answers correct. (5 correct) |
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|Class activity participation |
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|Did not participate or cooperate with group. |
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|Participated with group and completed class work. |
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|Participated with group and completed class work. |
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|Participated with group and completed class work. |
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|Individual calculations |
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|Individual class work not completed. |
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|Most answers incorrect to individual work. (0 or 1 correct) |
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|Most answers correct to individual work. (2-3 correct) |
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|Most answers correct to individual work. (3 correct) |
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|Notes; |
|(not scored) |
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|Observations, Extension Activities, etc. |
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|Total score:____________ Activity score (Total score / 3):__________ |
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| Risk Analysis: |
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|The greatest areas of risk in this lesson are technology issues in accessing the preparation links the night before and students not having the basic|
|math skills to correctly calculate products. To address these, it should be made clear that the links can be accessed using mobile technology as |
|well as computers, tablets, and chromebooks. To aid in group work, pairs and groups should be mixed ability. Small groups will be formed for those |
|needed higher levels of direct instruction and accommodations, at which time other students are encouraged to pursue higher level extension with 3 |
|digit factors or larger. |
|References: |
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|Boulder Valley School District. (2012). 5th grade mathematic curriculum essentials document. |
|Retrieved from |
|5th%20Grade%20Mathematics.pdf |
|Chritensen Institute. (n.d.). Blended learning definitions. Retrieved from |
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|Colorado Department of Education. (2010). Colorado academic standards in mathematics and the |
|common core standards for mathematics. Retrieved from |
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|Flipping the Classroom. (n.d.). Flipped K-12 sample lessons. Retrieved from |
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|-setting.html |
|Fuson, K. (2013). Math expressions: Common core. Boston, MA: Houghton Mifflin Harcourt. |
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