Daily/Weekly Instructional Guides Content Area/Subject: 7 plus Grade: 7 SCoS Objective(s): 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.1 a Describe situations in which opposite quantities combine to make zero. For example, a hydrogen atom has zero charge because it’s two constituents are oppositely charged. 7.NS.1 d Apply properties of operations as strategies to add and subtract rational numbers. MP.4 Model with mathematics MP.8 Look for and express regularity in repeated reasoning. National Objective(s): Day(s) of Instruction: 4 Date: Allocated Time for Instruction: 45 to 90 minutes, depending upon the school Connections to EOG/EOC/Assessment: During a football game, the Tigers team gained 2 yards, lost 5 yards, lost 3 yards, and gained 4 yards in four consecutive plays. How many yards did the team gain or lose altogether? A gained 14 yards B lost 14 yards C lost 2 yards D gained 2 yards Learner Objective(s): As a result in learning, students should Adapted from former WCPSS be able to… modeling adding integers. common assessment 2 Language Objective(s): Answer: C Topic(s): Modeling adding integers Prerequisite skills/knowledge: How to model integers Additive inverse Zero Pairs Real World importance of objective(s) – Essential Questions Why do students need to know or be able to do this? Overall value (debt vs. income) Where do you see the need to add integers in the real world? Absolute Value Definitions of Critical Vocabulary and Underlying Concepts The distance a value is from zero C&I/MS Math/Fall 2011 Additive inverse Integer Zero pair Two numbers whose sum s 0 are additive inverses of one another. Example 3 and -3 are additive inverses of one another because 3 + (-3) = 0. A number expressible in the form a or –a for some whole number a. A positive algebra tile paired with a negative algebra resulting in a sum of zero. Introduction/Focus/Anticipatory Activities/Guiding questions/Connections to what students already know through learning, culture, or experience: Have the students model owing their friend two dollars and another friend giving them four dollars. Ask the students how much money they have total. Initial Instructional Strategies (research-based teaching strategies): A. Direct Instruction – What the Teacher does: Be careful, today is all about modeling and allowing students to create a conjecture about an algorithm for adding integers. Resource for showing five different ways to model adding integers. http://www.vdoe.whro.org/math-strategies2/DOE_MATH_5/DOE_MATH_5.swf You should use at least three of these ways with your students. It is best if you model them (rather than having students watch the video) One of them must be the number line since it is specifically referenced in Common Core (7.NS.1). You could use this activity to reinforce the idea of using the number line: Human Number Line Addition (Teacher Key) Facilitate Adding Integers Notes Students can use any of the five models from above to complete the notes sheet. (Do not give the students the algorithm. Your task today is to help students develop it.) Facilitate Guided Practice activity At the end of class, have a discussion about any patterns students noticed when adding integers. This discussion will lead into tomorrow’s lesson on adding integers without the models. B. Questions to Promote Higher Level and Critical Thinking (i.e., Socratic): You add two integers and the answer is negative. What could the two integers be? (from More Good Questions Marian Small and Amy Lin) Instructional Resources (specific to each objective): Primary o Adding Integers Notes o Integers: Adding and Subtracting Activity from www.doe.virginia.gov/testing/solsearch/sol/math/7/mess_7-3ab_2.doc (only use adding section!) o Provide the students with more single digit addition. (Prentice Hall textbook page 27 and Prentice Hall workbook 1-5 pages 9 &10) C&I/MS Math/Fall 2011 Supplemental o Human Number Line Addition (Teacher Key) o Adding Integers Exploration o TI-73 Number Line APP Guided Practice Strategies or Activities: Allow to students to work in pairs to complete the Integer Addition page from the “Integers: Adding and Subtracting Activity” found here: www.doe.virginia.gov/testing/solsearch/sol/math/7/mess_7-3ab_2.doc Formative Assessment (Include context and accuracy percentage) Informal - Skill/Knowledge Acquisition (Ex. Teacher monitor, analyze student questions) In two minutes, students recall and list in rank order the most important ideas from previous day's class (Modeling Integers); in two more minutes, they summarize those points in a single sentence, then write one major question they want answered. Formal - Skill/Knowledge Mastery (ex. Open-ended quiz, prompted written response) Describe/write to a friend how to model adding integers. Provide examples with same signs and different signs. Create a practical problem involving addition with integers. Differentiated Instructional Strategies/Modifications: Some students may need additional problems such as those used in Guided Practice in order to see the pattern. Relate the problems to practical situations such as money, temperatures, altitude, elevator and floors of a building, etc. Continue to work with single digit addition for struggling students For students that are mastering single digit ask them double digit. For students that have mastered double digit ask them how they could tell whether the solution would be positive or negative with any integer addition problem. Re-teaching Strategies or Activities: o Integer Addition Using Heaps and Holes (2003 7th grade Strategies DPI Pages 9-10) o Alternative Ways to Teach Integer Operations Enrichment: Place students in small groups, and have them use decks of cards and play War. Black cards are positive; red cards are negative. Each student flips two cards and finds the sum. The student with the higher sum wins the round. Use the newspaper or an Internet search to find examples of addition and subtraction of integers. C&I/MS Math/Fall 2011 Integer Addition Race (taken from 2003 7th grade DPI Strategies): Pawns for the players, 2 dice of different colors, playing mat. Before starting the game, decide which color die will represent positives and which will represent negatives. On a turn, each player rolls the two dice and determines the sum of the roll. The player with the largest distance from 0 (i.e. larger absolute value) moves forward one. If a winning player rolls a sum of 5 or –5, he/she will move ahead two instead of one. If the players tie, they each roll again. The first player to reach the finish is the winner. Independent Practice: (ex. WebQuest, textbook problem, interview, etc…) integer addition practice interactive (http://mathstar.lacoe.edu/newmedia/integers/add/activities/activities.html) Prentice Hall textbook practice problems pp.27-28 Prentice Hall workbook 1-5 pages 9 &10 Comments /Notes: Teacher resource for ways to model adding integers: http://www.vdoe.whro.org/mathstrategies2/DOE_MATH_6/DOE_MATH_6.swf Particularly if you are new to teaching adding integers, this is a must see! Not a riveting video but information is good : ) Optional technology activity from TI: Integer Addition Exploration (Number Smash) C&I/MS Math/Fall 2011