Understanding By Design Unit Template
Math 7 Unit 2: Integers
|Title of Unit | Integers |Grade Level | 7 |
|Curriculum Area | Number Strands |Time Frame | 3-4 weeks |
|Developed By | |
|School | |
|Identify Desired Results (Stage 1) |
|Content Standards –Curricular Outcomes |
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|N7.6 |
|Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially, and symbolically. [C, CN, PS, R, V] |
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|Essential Questions |Enduring Understandings |
|Open-ended questions that stimulate thought and inquiry linked to |What do you want students to understand & be able to use several years from now? |
|the content of the enduring understanding. | |
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| |Integers involve two concepts of size and sign. |
|What are negative and positive numbers? |A negative number and a positive number that have the same size are opposites. |
| |The sum of two opposite numbers is zero. |
|What are opposite integers? |The result of subtracting an integer is the same as adding the opposite integer. |
| |Integers are used to describe relative changes and values. |
|How can positive and negative integers be used in the real world? |Use integers in real life situations, such as temperature, time zones, and money concepts. |
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|How can one add and subtract integers? | |
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| |Misconceptions |
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| |Students are confused by the many ways to model an integer. |
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| |Students do not group all possible pairs of tiles that form zero pairs. |
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| |Students incorrectly illustrate addition on a number line. |
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| |Students are unable to determine the number of tiles necessary to solve a subtraction problem. |
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| |Students do not understand that the difference of two integers can be written two ways and that the|
| |differences are opposite integers. |
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|Knowledge |Skills |
|Students will know… |Students will be able to… |
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|How to represent opposite integers concretely, pictorially, and |Represent opposite integers concretely, pictorially, and symbolically and explain why they are |
|symbolically and explain why they are opposite integers. |opposite integers. |
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|How to explain integers using integer tiles, number lines and |Explain integers using integer and diagrams. |
|diagrams. | |
| |Illustrate a number line, the results of adding or subtracting negative and positive integers. |
|How to use a number line to understand how to add or subtract | |
|integers. |Add two integers using colored integer tiles record symbolically. |
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|How to use patterns to add and subtract integers. |Subtract two integers using colored integer tiles and record the process symbolically. |
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|How to solve word problems involving adding and subtracting of |Investigate patterns in adding and subtracting integers using number tiles. |
|integers. | |
| |Solve problems involving the addition and subtraction of integers using number lines or colored |
| |integers tiles. |
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|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 |Helpful tips for writing a performance task. |
|situation that requires students to apply knowledge and skills to demonstrate their understanding in a real life | |
|situation. Describe your performance task scenario below: | |
| |Goal: |
| |What should students accomplish by completing |
|Unit Problem: “What Time is It?” |this task? |
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|Students can apply and explain the conflict of different time zones around the world and how it affects people from | |
|country to country. The problem also gives students the chance to create their own problem about time zones and solve | |
|it. Students will accomplish a deeper understanding of integers, as well as develop a real life understanding of how | |
|integers are present in everyday life. | |
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| |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: |Digital Taxonomy for Bloom: |
|REMEMBERING: Can the students recall or remember |KNOWLEDGE: Highlighting, bookmarking, social networking, searching, googling |
|the information? |COMPREHENSION: Advanced searches, blog journaling, twittering, commenting |
|UNDERSTANDING: Can the students explain ideas or |APPLICATION: Running, loading, playing, operating, hacking, uploading, sharing, editing |
|concepts? |ANALYSIS: Mashing, linking, tagging, validating, cracking, reverse-engineering |
|APPLYING: Can the students use the information in|SYNTHESIS: Programming, filming, animating, blogging, wiki-ing, publishing, podcasting, video casting |
|a new way? |EVALUATION: Blog commenting, reviewing, posting, moderating, collaborating, networking, posting moderating |
|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? | |
|Standards Rubric |
|The standards rubric should identify how student understanding will be measured. |
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|Unit 2 Problem Rubric: What Time Is It? (BC 2006) |
|This chart can be used to make decisions about students’ achievement on the Unit Problem. |
|Aspect |
|Not Yet Within Expectations |
|Meets Expectations (Minimal – Moderate) |
|Fully Meets Expectations |
|Exceeds Expectations |
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|Snapshot |
|unable to complete most parts of the problem without ongoing help |
|satisfies most basic requirements of the problem, but work is flawed or incomplete |
|satisfies basic requirements; complete, accurate (may have minor errors) |
|thoroughly satisfies all requirements; work is complete, accurate, efficient, and often insightful; innovative |
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|Concepts and Applications |
|Demonstrates and applies understanding of integers by explaining and/or demonstrating how integers were used to solve each problem |
|may be unable to demonstrate or apply understanding of integers |
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|demonstrates and applies partial understanding of integers |
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|demonstrates and applies understanding of integers appropriately |
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|demonstrates and applies understanding of integers thoroughly and precisely |
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|Strategies and Approaches |
|Uses appropriate strategies to solve problems based on interpreting a time zone map |
|Verifies/checks reasonableness of solutions |
|does not use appropriate strategies to solve problems |
|does not provide a reasonable solutions |
|tries to use appropriate and systematic strategies to solve problems; partial success; does not adjust or check procedures |
|needs help to verify or explain the reasonableness of the solutions |
|uses appropriate and systematic strategies to solve problems; may be inefficient |
|appropriately verifies and explains the reasonableness of the solutions |
|uses effective and often innovative strategies to solve problems |
|effectively and efficiently verifies and explains the reasonableness of the solutions |
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|Accuracy |
|Adds and subtracts integers accurately as required |
|major errors or omissions in adding and subtracting integers |
|partially accurate; some errors or omissions in adding and subtracting integers |
|generally accurate; few minor errors in adding and subtracting integers |
|accurate and precise; very few if any minor errors in adding and subtracting integers |
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|Representation and Communication |
|Presents work clearly |
|Explains procedures and results using appropriate terms (e.g., negative integer; positive integer; opposite integers) |
|work may be unclear and confusing |
|provides incomplete or illogical explanations as required; few or no appropriate terms |
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|work is partially clear; confusing in places |
|provides partial explanations as required using some appropriate terms; parts may be vague, incomplete, or illogical |
|work is generally clear; easy to follow |
|provides complete, logical explanations as required using some appropriate terms |
|work is clear, precise, and well-organized |
|provides clear, often insightful explanations as required, using appropriate and precise terms |
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|Based on the BC Performance Standards for Numeracy (Grade 7). |
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|Math Unit Quiz: Math Common Assessment |
|Math Common Assessment Rubric N7.6 |
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|Part A: Number Strand |
|N7.6 Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially, and symbolically. |
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|Beginning (1) |
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|Approaching (2) |
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|Proficiency (3) |
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|Mastery (4) |
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|Student needs assistance in adding and subtracting integers. |
|Student is able to add or subtract integers. (concretely, pictorially, symbolically) |
|Student is able to add and subtract integers. (concretely, pictorially, symbolically) |
|Student is able to apply their understanding of adding and subtracting integers to a situational problem. |
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|Other Assessment Evidence: (Formative and summative assessments used throughout the unit to arrive at the outcomes.) |
|Conversation |Observation |Product |
|Launch |Master 2.2 “Ongoing Observation: Integers” |Math Common Assessments Pre and Post tests |
|Explore |Homework Checks |Performance Task (summative) |
|Reflect |Discussion |Mid Unit Review (formative) |
| | |Unit Review (formative) |
| | |Unit Quiz (summative) |
| | |Lesson Self-Assessments (pg. 54 Program Guide) |
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|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? |
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|Students will be headed towards the comprehension of adding and subtracting integers using number lines and number tiles. They will also be able to apply integers to |
|real life situations such as temperatures, and time zones. Students will activate prior knowledge regarding the use of number lines and < > signs. The outcomes will be |
|present in the room to ensure students are aware of what they are learning for the unit. |
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|How will you hook students at the beginning of the unit? (motivational set) |
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|I will hook the students through the Launch activity. Time Zones and Canada. They will discuss the questions that are provided on the page. Students will understand the|
|importance of time zones in real life. This will be a transition to integers. |
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|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? |
| |Time Frame |
|Lesson 1: Representing Integers: N7.6 Math Common Assessment pre-test. After pre-test, students will use tiles to represent positive and | |
|negative integers. The red tiles represent negative numbers and the yellow tiles represent positive numbers. | |
|Assignment: pg. 54-55 #1-7 | |
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|Lesson 2: Adding Integers with Tile: Students will use colored tiles to add integers. Students will learn to pair or group yellow tiles and red | |
|tiles together, as well as write addition equations. | |
|Assignment: Pg. 56-59 #1-8 | |
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|Lesson 3: Adding Integers on a Number Line: Students will be given and asked to draw number lines to add integers. Students will learn two | |
|different methods when using a number line. One, start at zero and the other start at the first number that was indicated on the number line. | |
|Assignment: pg. 60-63 #1-5 | |
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|Mid Unit Review pg.65 #1-9 | |
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|Lesson 4: Subtracting Integers with Tiles: Students will use colored tiles to subtract integers. Students will learn to remove tiles from a | |
|group by matching up zero pairs. | |
|Assignment: Pg. 66-70 #1-5 and 7 | |
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|Lesson 5: Subtracting Integers on a Number Line: Students will be given and asked to draw number lines to subtract integers. | |
|Assignment: pg 71-75 #1-6 | |
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|Unit Review pg. 79-80 #1-10 and 12, 13 | |
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|Unit Quiz: Taken from Math Common Assessment N7.6 | |
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|Unit Problem pg. 83 | |
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|Reflecting on Learning: Integers: Master 2.5 Math Makes Sense | |
|Students will use this assignment to reflect and evaluate their learning and understanding within this unit. | |
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|Reflecting on Learning: Unit 2 | |
|1. Read each of the Learning Goals for integers. Think about your learning. | |
|Rate your learning for each goal using these symbols: | |
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|+ = I can understand and do this very well. | |
|( = I can understand and do this all right. | |
|– = I am still having some trouble with this. | |
|( = This is a big problem for me. | |
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|Learning goal | |
|My rating | |
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|Model integers with coloured tiles. | |
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|Add integers using coloured tiles and number lines. | |
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|Subtract integers using coloured tiles and | |
|number lines. | |
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|Solve problems that involve adding and subtracting integers. | |
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|2. Think about all the explorations, explanations, and practice in this unit. Write about one activity that really helped you understand or | |
|learn something important about integers. Tell how it helped. | |
|_______________________________________________________________________________ | |
|_______________________________________________________________________________ | |
|_______________________________________________________________________________ | |
|_______________________________________________________________________________ | |
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|3. List one strategy or support you could use to help your learning in the next unit. | |
|_______________________________________________________________________________ | |
|_______________________________________________________________________________ | |
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|4. Overall, is learning mathematics getting easier or harder for you? Explain why. | |
|_______________________________________________________________________________ | |
|_______________________________________________________________________________ | |
|_______________________________________________________________________________ | |
|_______________________________________________________________________________ | |
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|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 will answer the Reflect at the end of every practice to rehearse, revise and refine their understanding. |
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|How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit? |
|Students will complete a self-assessment at the end of the unit. This will be handed in as a formative assessment and returned to the students after I have reviewed |
|them. Pg. 54 in Program guide |
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|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? |
|“Reaching All Learners”- Math Makes Sense 7. Each lesson provides an adaption or extension to accommodate to all learners. |
|“What to do if you don’t see it” – Math Makes Sense 7. Each lesson provides an assessment for learning activity that includes questions and different instruction to |
|reach all learners. |
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|What resources will you use in the learning experiences to meet the outcomes? |
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|Saskatchewan Math Curriculum |
|Math Makes Sense 7 |
|Math Common Assessment |
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|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.
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Master 2.5
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