Understanding by Design Unit Template
Title of Unit / Multiplying/Dividing Whole Numbers / Grade Level / 5Curriculum Area / Number / Time Frame / 6 Weeks
Developed By / Trever Kutnikoff
School / W.J.Berezowsky
Identify Desired Results (Stage 1)
Content Standards –Curricular Outcomes
N5.2 Analyze models of, develop strategies for, and carry out multiplication of whole numbers.
N5.3 Demonstrate, with and without concrete materials, an understanding of division (3-digit by 1-digit) and interpret remainders to solve problems.
N5.4
Develop and apply personal strategies for estimation and computation including:
o front-end rounding
o compensation
o compatible numbers
Essential Questions / Enduring Understandings
Open-ended questions that stimulate thought and inquiry linked to the content of the enduring understanding. / What do you want students to understand & be able to use several years from now?
1. How are mathematical operations related?
3. How can multiplication and division help us in our life? / Using mental math strategies will make learning multiplication and division concepts easier for students to understand.
Multiplication and division facts are connected to each other.
We need to learn these concepts because multiplying and dividing is connected to daily living such as shopping and paying bills.
Misconceptions
(Optional)
Knowledge
Students will know… / Skills
Students will be able to…
Students will know that…
Skip counting, doubling, halving, repeated halving are some mental math strategies they can use to understand multiplying and dividing.
Multiplying any number by zero will result in a product of zero.
Using place value as a strategy to multiply products.
Choosing a strategy will help multiply numbers of 2 digit numbers.
There are different models to use to identify equal sharing and equal grouping.
Dividing can be solved using different strategies
Any number divided by zero is not possible because the quotient is always zero. / Students will be able to…
Describe mental mathematics strategies used to determine multiplication facts to 81 (e.g., skip counting from a known fact, doubling, halving, 9s patterns, repeated doubling, or repeated halving).
Explain concretely, pictorially, or orally why multiplying by zero produces a product of zero.
Generalize and apply strategies for multiplying two whole numbers when one factor is a multiple of 10, 100, or 1000.
Pose a problem which requires the multiplication of 2-digit numbers and explain the strategies used to multiply the numbers.
Model the division process as equal sharing or equal grouping using various models and record the resulting process symbolically.
Generalize, relate, and apply concrete, pictorial, and symbolic strategies for dividing 3-digit whole numbers by 1-digit whole numbers.
Explain concretely, pictorially, or orally why division by zero is not possible or undefined (e.g., 8 ÷ 0 is undefined or not possible to determine).
Assessment Evidence (Stage 2)
Performance Task Description
The performance task describes the learning activity in “story” form. Typically, the P.T. describes a scenario or situation that requires students to apply knowledge and skills to demonstrate their understanding in a real life situation. Describe your performance task scenario below: / Helpful tips for writing a performance task.
Goal: You goal is to solve the math problem about the amount of hay and milk is needed to feed your cows.
Role: You are a cattle rancher in Saskatchewan.
Audience: The students in your class will be your audience.
Situation: You work on a dairy farm doing various jobs to help the cattle grow to provide money for your business. Your dairy cows need to be fed using 70kg of hay that feeds two cows for 1 week. How much hay does 1 cow eat each week and day? You have a total of 90 cows on your farm. Each day you collect twenty-seven litres of milk from 1 cow. Estimate the amount of milk produced by 9 cows. Your task is to find out the amount of hay and milk needed to keep your cows healthy for all people who are interested in agriculture.
Product/Performance:
You may share your findings in written form, in oral form or in a form that you are comfortable with. / Goal:
What should students accomplish by completing this task?
Role:
What role (perspective) will your students be taking?
Audience:
Who is the relevant audience?
Situation:
The context or challenge provided to the student.
Product/Performance:
What product/performance will the student create?
Standards
(Create the rubric for the Performance Task)
BLOOMS TAXONOMY:
REMEMBERING: Can the students recall or remember the information?
UNDERSTANDING: Can the students explain ideas or concepts?
APPLYING: Can the students use the information in a new way?
ANALYZING: Can the students distinguish between the different parts?
EVALUATING: Can the students justify a stand or decision?
CREATING: Can the students create new product or point of view? / Digital Taxonomy for Bloom:
KNOWLEDGE: Highlighting, bookmarking, social networking, searching, googling
COMPREHENSION: Advanced searches, blog journaling, twittering, commenting
APPLICATION: Running, loading, playing, operating, hacking, uploading, sharing, editing
ANALYSIS: Mashing, linking, tagging, validating, cracking, reverse-engineering
SYNTHESIS: Programming, filming, animating, blogging, wiki-ing, publishing, podcasting, video casting
EVALUATION: Blog commenting, reviewing, posting, moderating, collaborating, networking, posting moderating
Standards Rubric
The standards rubric should identify how student understanding will be measured.
Please attach rubric to unit plan.
Multiplication and Division Rubric
Criteria / 1-Excelling / 2-Achieving / 3-Beginning to Achieve / 4- Not Yet Achieving
N5.2 Analyze models of, develop strategies for, and carry out multiplication of whole numbers. / Multiply whole using a variety of strategies. / Multiply whole consistently using one strategy. / Multiply whole numbers with occasional errors. / Multiply whole numbers with support.
N5.3 Demonstrate, with and without concrete materials, an understanding of division (3-digit by 1-digit) and interpret remainders to solve problems. / Divides a 3 digit number by a 1 digit number in a problem solving context. / Divides a 3 digit number by a 1 digit number consistently with no errors. / Divides a 3 digit number by a 1 digit number inconsistently with some misconceptions. / Divides a 3 digit number by a 1 digit number with additional support.
Develop and apply personal strategies for estimation and computation including:
front-end rounding compensation compatible numbers. / Can estimate using a variety of strategies in a problem solving context involving multiplication and division. / Can estimate using a variety of strategies consistently involving multiplication and division. / Can estimate using a variety of strategies inconsistently involving multiplication and division / Can estimate 1 strategy with additional support.
Other Assessment Evidence: (Formative and summative assessments used throughout the unit to arrive at the outcomes.)
Conversation / Observation / Product
Journal entries
Reflection questions from each lesson (think-pair-share activity) / Observation Checklist (Master 3.2)Discussions
Discussion
Anecdotal records / Assessment assignments (Master Copy:Step-by-Step sheets)
Reflection Sheet Math Make Sense (Master 3.5)
Journal entries (Reflection questions from each lesson
Weekly multiplication facts quiz (Math Factory Sheets)
Quiz on unit concepts
Performance Task
Learning Plan (Stage 3)
Where are your students headed? Where have they been? How will you make sure the students know where they are going?
Throughout the unit, students will learn various strategies to help multiply and divide. Students will explore these concepts through inquiry. Students will draw on prior knowledge, ask questions, share their own understanding of concepts, and reflect on the importance on each lesson.
The essential questions of the unit and performance task will also be introduced at the start of the unit so the students know what they need to understand right from the start. Throughout the unit, the essential questions and performance task will be revisited to organize the direction of learning for the both the students and the teacher.
How will you hook students at the beginning of the unit? (motivational set)
To hook the students at the beginning of this unit I will use flyers and catalogs to have students make the connection that multiplication and division is a daily skill that is used to buy times. Using real money to multiply and divide will engage the students.
What events will help students experience and explore the enduring understandings and essential questions in the unit? How will you equip them with needed skills and knowledge? How will you organize and sequence the learning activities to optimize the engagement and achievement of all students?
Lesson 1: Patterns in Multiplication and Division. Use step-by-step 1 (3.12) to assess student learning. Students will write an entry into their book about the reflection question. N5.2
Lesson 2: Other strategies for Multiplying and Dividing. Use step-by-step 2 to assess student learning.(3.13) Students will write an entry into their book about the reflection question.
Lesson 3: Multiplying with Multiples of 10. Use step-by-step 3 to assess student learning. (3.14) Students will write an entry into their book about the reflection question.
Lesson 4: Estimating Products to Solve Problems. Use step-by-step 4 (3.15)to assess student learning. Students will write an entry into their book about the reflection question. N5.4
Lesson 5: Using Mental Math to Multiply. Use step-by-step 5 (3.16) to assess student learning. Students will write an entry into their book about the reflection question. N5.2
Lesson 6: Multiplying 2 Digit Numbers. Use step-by-step 6 (3.17) to assess student learning. Students will write an entry into their book about the reflection question. N5.2
Lesson 7: Estimating Quotients to Solve Problems. Use step-by-step 6 (3.18) to assess student learning. Students will write an entry into their book about the reflection question. N5.4
Lesson 8: Dividing a 3 Digit Number by a 1-Digit Number. Use step-by-step 6 (3.19) to assess student learning. Students will write an entry into their book about the reflection question. N5.3
Lesson 9: Other Strategies for Dividing Whole Numbers. Use step-by-step 6 (3.20) to assess student learning. Students will write an entry into their book about the reflection question. N5.4
Lesson 10. Solving Problems. Use step-by-step 6 (3.21) to assess student learning. Students will write an entry into their book about the reflection question. N5.4
Lesson 11: Show What You Know Review: Students will complete the questions to show their understanding. N5.2, N5.3, N5.4.
Lesson 12: Assign the performance task
Lesson 13: Student reflection on unit. / Time Frame
How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work based on your essential questions and enduring understandings?
Students reflect in journal book at the end of each lesson. Student responses will guide subsequent lessons
How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit?
Throughout the unit students’ will be asked to assess their ability to answer the essential questions of the unit with the goal that by the end of the unit they should be able to answer all the questions using exit cards. Students will also be required to self-assess their performance task solution. Teacher, peer and self assessment will guide students as they self evaluate.
How will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without compromising the goals of the unit?
Students will get the opportunity throughout the unit and in their performance task to apply their strategies to multiplication and division concepts
Instruction will vary depending on student needs: whole class, guided, independent, small group, partner, teacher modeling, explicit instruction, and individual instruction.
Students will be given a variety of options to show their understanding. (Ex: journal entries can be done orally or written, individual-partner reading, using visuals, math mastery booklets for students who can not copy notes into their rule book – highlight key information)
What resources will you use in the learning experiences to meet the outcomes?
Resources that will be used to support learning are:
Math Make Sense Textbook
Math Make Sense Teacher guide
Math Mastery Student Booklet
Smart Board Tools
Math Factory Sheets
Money
Flyers
Catalogs
Manipulatives
Calulators
Counters
Base Ten Blocks
Assess and Reflect (Stage 4)
Required Areas of Study:
Is there alignment between outcomes, performance assessment and learning experiences?
BAL’s:
Does my unit promote life long learning, encourage the development of self and community, and engage students?
CELS & CCC’s:
Do the learning experiences allow learners to use multiple literacies while constructing knowledge, demonstrating social responsibility, and acting autonomously in their world?
Adaptive Dimension:
Have I made purposeful adjustments to the curriculum content (not outcomes), instructional practices, and/or the learning environment to meet the learning needs of all my students?
Instructional Approaches:
Do I use a variety of teacher directed and student centered instructional approaches?
Student Evaluation:
Have I included formative and summative assessments reflective of student needs and interests based on curricular outcomes?
Resource Based Learning:
Do the students have access to various resources on an ongoing basis?
FNM/I Content and Perspectives/Gender Equity/Multicultural Education:
Have I nurtured and promoted diversity while honoring each child’s identity?
Blueprint for Life:
Have I planned learning experiences in the unit that prepare students for a balanced life and/or work career?
Adapted from: Wiggins, Grant and J. McTighe. (1998). Understanding by Design, Association for Supervision and Curriculum Development.