Understanding By Design Unit Template
Understanding By Design Unit Template
|Title of Mini-Unit |Multiplying and Dividing Integers |Grade Level |7th |
|Curriculum Area |The Number System |Time Frame |2 Weeks |
|Developed By |Stephanie Butman |
|Identify Desired Results (Stage 1) |
|Content Standards |
|Use patterns and properties to explore the multiplication of integers. (7th Grade Common Core suggested learning targets 7. NS. 2) |
|Use patterns and properties to develop procedures for multiplying integers. (7th Grade Common Core suggested learning targets 7. NS. 2) |
|Use real-world situations represented by the multiplication of integers. (7th Grade Common Core suggested learning targets 7. NS. 2) |
|Recognize and solve problems involving multiplication and division of integers. (Accentuate the Negative Connected Mathematics Textbook) |
|Use the relationship between multiplication and division to develop procedures for dividing integers. (7th Grade Common Core suggested learning targets 7. NS. 2) |
|Recognize and use the relationship of multiplication and division as inverse operations. (Accentuate the Negative Connected Mathematics Textbook) |
|Interpret products of rational numbers by describing real-world contexts. (7th Grade Common Core Standard 2.a in 7. NS. 2) |
|Describe real-world situations represented by the division of integers. (7th Grade Common Core suggested learning targets 7. NS. 2) |
|Understandings |Essential Questions |
|Overarching Understanding |Overarching |Topical |
|U1: Students will understand that procedures can be generalized from patterns in computations. |OQ1: What kind of problem is this and how do |TQ1: How do I determine that given any |
| |I know? |problem, I will be required to multiply or |
|U3: Students will understand the inverse relationship between multiplication and division. | |divide? |
| |OQ2: What should I do when I get stuck? What | |
|U4: The inverse relationship between multiplication and division will help students understand the procedures |questions should I ask myself to help guide |TQ2: Why is it helpful to see |
|involved in division. |me through the problems? |multiplication and division as inverse or |
| | |opposite operations? |
|U5: Use understanding of multiplication, and multiplication patterns, to better understand and explore division. |OQ3: What is the pattern I should be noticing| |
| |across all these problems? |TQ3: When multiplying or dividing integers,|
|U6: Recognizing patterns will help students to explore more deeply multiplication and division. | |how can I tell if the answer will be |
| | |positive or negative? |
|U7: Using real world situations and contexts to make sense of the mathematical concepts. | | |
| | | |
| | | |
| | | |
|Related Misconceptions | | |
|RM1: Not understanding when to multiply and when to divide. | | |
| | | |
|RM2: Not seeing the connection between multiplication and division, or not understanding how they are inversely | | |
|related. | | |
| | | |
|RM3: Executing multiplication and division procedures incorrectly. | | |
| | | |
|RM4: Not being able to relate multiplication and division to real world examples or scenarios. | | |
| | | |
|RM5: Not understanding the rules for getting a positive or negative answer given two positive/negative integers. | | |
|Objectives |
|Knowledge |Skills |
|Students will know… |Students will be able to… |
|K1: Students will know how to correctly multiply and divide integers. |S1: Students will use the proper procedures to multiply and divide integers. |
|K2: Students will understand integers as numbers using a number line. |S2: Students will use real world examples to find products and quotients of integers. |
|K3: Students will understand how to apply or represent multiplication and division problems using |S3: Students properly execute and use rules for receiving positive and negative answers. |
|real world examples. |S4: Students will be able to write multiplication/sentences given a certain context. |
|K4: Students will understand the idea of multiplication as repeated addition. |S5: Students will be able to come up with division that “undoes” a given multiplication sentence. |
|K5: Students will know that multiplication and division are inversely related. | |
|Assessment Evidence (Stage 2) |
|Performance Task Description |
|Goal |This assessment will evaluate how well students understand the procedures of multiplication and division of integers. It will also assess their |
| |ability to apply multiplication and division to real world scenarios or examples. |
|Role |It is a quiz involving both multiple choice and short answer problems. |
|Audience |My mentor teacher and I will be viewing and evaluating the assessment. |
|Situation |The assessment will be completed in class on Friday, November 9, 2012. |
|Product/Performance |Student work and answers will be the products our students provide to show us their understanding of the desired concepts and outcomes. We hope |
| |students will correctly multiply and divide for all procedural problems. We also hope that students will understand the real world connections and |
| |examples for multiplication and division. |
|Standards |Describe real-world situations represented by the division of integers. (7th Grade Common Core suggested learning targets 7. NS. 2) |
| |Recognize and solve problems involving multiplication and division of integers. (Accentuate the Negative Connected Mathematics Textbook) |
| |Use real-world situations represented by the multiplication of integers. (7th Grade Common Core suggested learning targets 7. NS. 2) |
|Other Evidence |
|Journals (given at the beginning of class), Quick Checks (given during class the day after an assigned homework video), Exit Slips (given and collected at the end of class before students leave). |
|Learning Plan (Stage 3) |
|Day in Unit |Lesson Topic |Lesson Learning Objective |Description of how lesson contributes to unit-level |Assessment activities |
| | | |objectives | |
|*Day 1: 10/29 |Exploring Multiplication |Students will observe, recognize, and use |This lesson will deepen students’ understanding of integer|Students will answer questions that will |
|Problem 4.3 |Patterns |patterns to multiply integers. Students will |multiplication through pattern usage and recognition. This|guide them in noticing and understanding |
| |Problem 4.3 |participate in the integer product game that |lesson will also help students develop skills of finding |multiplication patterns. |
| | |gives students an opportunity to continue |products of integers. | |
| | |exploring multiplication patterns and factors| | |
| | |of integers. | | |
|Day 2: 10/30 |Multiplication Practice, |Students will practice multiplication |This lesson will allow students time to practice their |Quick Check (form homework video the night |
|Applications Connections |Applications, and |problems and will apply multiplication to |multiplication procedures they have learned thus far, |before)– assess understanding and |
|Extensions problems (p. |Connections |real world contexts. |while connecting multiplication to real world examples |misconceptions as a class. |
|60-61) | | |that will help deepen their understandings. | |
| | | | |Exit Slip - assess how students understand |
| | | | |multiplication. |
|Day 3: 10/31 |Halloween – Mrs. Vance has a|Halloween |Halloween |Halloween |
|Halloween |Halloween Activity she uses | | | |
| |each year | | | |
|Day 4: 11/1 |Study Island 3.b |Students will practice division and |This lesson will allow students to practice what they have|Student work shown while completing |
|Study Island | |multiplication problems in Study Island. |learned about multiplication and look ahead to what they |questions in Study Island. |
| | | |will learn about division. This also gives students a | |
| | | |chance to use prior knowledge to work on concepts that | |
| | | |will be addressed on their future standardized tests. | |
|Day 5: 11/2 |Whiteboard multiplication |Students will practice different |This lesson will help students develop procedural skills |Quick Check (from homework video the night |
|ACE problems (Applications |practice |multiplication problems on whiteboards. They |for multiplying integers. |before) |
|Connections Extensions) | |will work individually and then show their | | |
| | |answers to me. We’ll then go over the | | |
| | |problems together and address any | | |
| | |misconceptions students still have about | | |
| | |multiplying integers. | | |
|Day 6: 11/5 |Division of Integers and |Students will learn how to divide integers |This lesson will help students begin to develop procedural| |
|Problem 4.4 |Seeing Division and |properly. Students will explore the idea that|skills for dividing integers. This lesson will also help | |
| |Multiplication as an Inverse|multiplication and division are inversely |students to relate multiplication and division as | |
| |Relationship |related. |inverses. | |
|Day 7: 11/6 |Exploring Division in Real |Students will practice division problems and |This lesson will gives students a chance to practice |Quick Check (from homework video the night |
|Division practice - |World Contexts and Division |explore real world scenarios that demonstrate|division problems and explore real world contexts that |before) – assess understanding and |
|Applications Connections |Practice |division. |demonstrate division. |misconceptions as a class. |
|Extensions | | | |Exit Slip to assess how students understand |
| | | | |division thus far. |
| | | | | |
| |Multiplication and Division | | |Quick Check (from homework video the night |
|Day 8: 11/7 |Practice/Review |Students will practice multiplication and |This lesson will give students a chance to practice |before) – assess understanding and |
|Division and multiplication | |division problems using whiteboards. Review |multiplying and dividing integers, including real world |misconceptions as a class. |
|practice/review | |any real world examples discussed in this |contexts discussed in the unit. | |
|(reflections on page 66) | |unit. | | |
| | | | | |
| | | | | |
|Day 9: 11/8 |Assessment | | |Students will correctly multiply and divide |
|Assessment | |This assessment will evaluate how well |This assessment will allow students to demonstrate, in |for all procedural problems. Students will |
| | |students understand the procedures of |many different ways, how well they understand the concepts|understand the real world connections and |
| | |multiplication and division of integers. It |of multiplication and division. |examples for multiplication and division. |
| | |will also assess their ability to apply | |There will be a clicker portion of the final|
| | |multiplication and division to real world | |assessment, but there will also be a written|
| | |scenarios or examples. | |portion that focuses mainly on real world |
| | | | |examples. |
*NOTE: On 10/25, we will start the unit by teaching multiplication patterns and completing problem 4.1 (and some of problem 4.2), 10/26 – problem 4.2
Multiplication and Division of Integers – Unit level objectives
Students will be able to recognize and use patterns to explore or develop procedures for multiplication and division of integers.
Students will learn to relate and think of multiplication and division as inverse operations.
Students will explore real world applications of multiplication and division of integers.
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