Grade: 7 Lesson Title: Algebraic expressions, properties- commutative, associative, inverse, identity, distributive

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1 Targeted Content Standard(s): 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Targeted Mathematical Practice(s): 1 Make sense of problems and persevere in solving them 2 Reason abstractly and quantitatively 3 Construct viable arguments and critique the reasoning of others 4 Model with mathematics 5 Use appropriate tools strategically 6 Attend to precision 7 Look for and make use of structure 8 Look for an express regularity in repeated reasoning Supporting Content Standard(s): (optional) 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. a) Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. b) Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real world contexts. c) Understand subtraction of rational numbers as adding the additive inverse, p q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real world contexts. d) Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a) Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real world contexts. b) Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non zero divisor) is a rational number. If p and q are integers then (p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real world contexts. Student Friendly Learning Targets I can Use Commutative, Associative, Distributive, Identity, and Inverse Properties to add and subtract linear expressions with rational coefficients Use Commutative, Associate, Distributive, Identity, and Inverse Properties to factor and expand linear expressions with rational coefficients Rewrite an expression in a different form Choose the form of an expression that works best to solve a problem Explain your reasoning for the choice of expression used to solve a problem

2 c) Apply properties of operations as strategies to multiply and divide rational numbers. d) Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats Purpose of the Lesson: Students use their understanding of structure to rewrite general linear expressions in equivalent forms. Expressions include rational coefficients and multiple terms. Students will apply their understanding of properties when adding, subtracting, factoring, and expanding expressions with and without context. Explanation of Rigor: (Fill in those that are appropriate.) Conceptual: Students model expressions using manipulatives and create equivalent representations of expressions using the properties. Procedural: Students apply properties to add, subtract, factor and expand expressions. Application: Vocabulary: Distributive Property, Commutative Property, Associative Property, Multiplicative Property of Zero, Variable, Numerical expression, Algebraic expression, term, coefficient, constant, equation, inequality Evidence of Learning (): Pre-: Equivalent Expressions (Pre-assessment) Formative (s): Formative 7.EE.1, Rewriting Expressions Observational Checklist Summative : Summative 7.EE.1 Self-: Equivalent Expressions (Pre-assessment) skeleton

3 Lesson Procedures: Segment minutes Unit 4 Pre-assessment Equivalent Expressions (Pre-Assess) Equivalent Expressions (Pre-Assess) skeleton Students may need scaffolding or re-teaching. Practice (Homework): 1. Give each student the Unit 4 Pre- Equivalent Equations 2. Upon completion of assessment, have students complete the Equivalent Expressions Skeleton. 3. Scaffolding or re-teach as needed.

4 Segment minutes Rewriting expressions MP 1 Students create, solve, and rewrite expressions MP 3 Students will peer discuss MP 7 Students will rewrite expressions in as many ways as possible. MP 8 Look for patterns in expressions Rewriting Expressions Activity Rewriting Expressions Observational Checklist Students may need re-teaching: order of operations, subtracting integers Practice (Homework): Teacher created/current program practice page on combining like terms 1. (10-15 min) Review vocabulary variable, terms, like terms, coefficient, rewriting (replaces combine, simplify) 2. (30-40 min) Relate variables to some of the tools students have used in class (manipulatives or blanks in expressions). Show students manipulatives that are in different forms (i.e. 3 red counters, 4 blue counters, 2 red counters, 2 blue counters, 1 red counter.) Have them write an expression to represent the model: 3r + 4b + 2r + 2b + r Group the manipulatives and then rewrite the expression. Divide students into groups of 4 or 5 students. Give each group 3-4 spoons and a deck of cards. Students will play Spoons by getting a set of all 4 representations for the same expression. When a student gets a set of all 4, he or she grabs a spoon. Once a student grabs a spoon, all of the other students grab a spoon. The student who does not grab a spoon gets a strike. Once a student gets 3 strikes, he or she is out. The student who first grabbed the spoon must prove that their set is

5 complete by showing the simplest form of their expressions (done by combining like terms). If the student does not have equivalent forms, he or she gets the strike instead of the student who did not get a spoon. 3. (30-40 min) Have students complete Writing Expressions Activity. Provide examples as needed. Teacher should circulate throughout the classroom filling in the observational checklist. 4. (20-30 min) Reform groups for peer discussion. Students should focus on explaining and justifying why they choose to rewrite expressions in certain ways.

6 Segment minutes Commutative, Associative Property MP 3 students will peer discuss MP 7 students will look for similarities in expressions MP 8 student will look for patterns in expressions Commutative-Associative Properties Activity, Property Notes, Sample Practice Students may not easily find categories in the activity. The teacher may need to give leading questions for discovery. 1. (10-15 min) Give whole-class overview of the Commutative-Associative Properties activity. This activity is designed to let the students discover the properties as they go through each step. 2. Arrange students in pairs and have them sort the activity cards into as many different categories that they can. Each time they sort, they need to give the category a name (i.e.: all negatives, all addition...) Practice (Homework): Sample practice included in Lessons. 3. (10-15 min) Form larger groups and then discuss/critique the categories that were made. The groups should form one list, removing duplicates. 4. (10-15 min) Bring the entire class together to make one list. Make sure that these categories appear cards that have different orders, cards that are have different groups, and cards that are equal. Repeat the steps If these groups do not appear. Give leading questions as needed look for groups of 2, similarities, and\or differences.

7 5. (5-10 min) Refine definitions for Commutative and Associate Properties. Segment minutes Additive and Multiplicative Identity, Multiplicative property of zero Inverse Property MP 6 - Attend to precision MP 7 - Look for and make use of structure Property notes foldable Sample notes for foldable Properties cut n paste activity Practice (Homework): 1. Complete notes foldable for: additive identity, multiplicative identity, multiplicative property of zero, and inverse property. (sample notes provided) Provide additional instruction or examples as needed for each property to ensure understanding. 2. In groups of 2-4, have students complete the Properties cut n paste activity.

8 Segment minutes Distributive property MP 2 Students reason about the value of the expressions represented with algebra tiles. MP 3 Students explain or justify their choices in the activity. MP 4 Students use manipulatives to model the distributive property. MP 7 Students explore and use the distributive property and how it is used to create equivalent expressions. Distributive Property with Manipulatives Worksheet Equivalent or Not Equivalent Activity Practice (Homework): 1. Distribute Algebra Tiles and the Worksheet. Model how to represent the following expression with Algebra Tiles: 7(x-2) + 3 Have students create an equivalent expression and then record the expressions they have created. 2. Have students work through the problems on the worksheet. 3. Area and distributive property.

9 4. Equivalent or Not Equivalent Activity - Students will use their knowledge of properties to decide whether or not the two expressions are equivalent. Four problems are given as examples. 5. Students will create 6 of their own expressions. Teachers need to check to make sure that three of the expressions are equivalent and the other three are not equivalent. 6. The expressions need to be teacher/peer assessed and then cut apart and put into envelopes for the Equivalent or Not Equivalent Worksheet. Idea: Copy and laminate the worksheet use dry erase markers to complete the activity. Segment minutes Unit 4 Formative Unit 4 Pre-assessment Practice (Homework): Give students the formative assessment: Understanding Properties in Linear Expressions.

Algebra 1 Summer Packet

Algebra 1 Summer Packet Name: Solve each problem and place the answer on the line to the left of the problem. Adding Integers A. Steps if both numbers are positive. Example: 3 + 4 Step 1: Add the two numbers.