# Enhanced Instructional Transition Guide

Size: px
Start display at page:

## Transcription

2 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days 8.3A Compare and contrast proportional and non-proportional linear relationships. Supporting Standard 8.4 Patterns, relationships, and algebraic thinking.. The student makes connections among various representations of a numerical relationship. The student is epected to: 8.4 Generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description). Readiness Standard 8.5 Patterns, relationships, and algebraic thinking.. The student uses graphs, tables, and algebraic representations to make predictions and solve problems. The student is epected to: 8.5A Predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations. Readiness Standard 8.7 Geometry and spatial reasoning.. The student uses geometry to model and describe the physical world. The student is epected to: 8.7D Locate and name points on a coordinate plane using ordered pairs of rational numbers. Supporting Standard Underlying Processes and Mathematical Tools TEKS: 8.14 Underlying processes and mathematical tools.. The student applies mathematics to solve problems connected to everyday eperiences, investigations in other disciplines, and activities in and outside of school. The student is epected to: 8.14A Identify and apply mathematics to everyday eperiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. 8.14B Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. 8.14C Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. 8.14D Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, page 2 of 144

3 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days and number sense to solve problems Underlying processes and mathematical tools.. The student communicates about mathematics through informal and mathematical language, representations, and models. The student is epected to: 8.15A Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. 8.15B Evaluate the effectiveness of different representations to communicate ideas Underlying processes and mathematical tools.. The student uses logical reasoning to make conjectures and verify conclusions. The student is epected to: 8.16A Make conjectures from patterns or sets of eamples and noneamples. 8.16B Validate his/her conclusions using mathematical properties and relationships. Performance Indicator(s): page 3 of 144

4 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Grade8 Unit05 PI01 Create a graphic organizer (e.g., four-corner model, concept map, etc.) that includes a table, graph, equation, and given verbal description of a real-life linear problem situation. Use a calculator to find the solution to the problem situation, and write an inequality statement using numbers and symbols when given a specific parameter within the problem. Justify the solution to the problem with each representation by locating and naming the solution on the graph, finding the solution in the table, and using appropriate operations to find the solution algebraically. Validate the solution process in a written justification, and describe the connections between the representations, detailing if the linear relationship is proportional or non-proportional. Sample Performance Indicator: The speed of a vehicle and a driver s reaction time determine the amount of time it will take a vehicle to stop. If driving on a dry street surface, a person takes 2.5 seconds to react to an emergency, and with reasonably good tires, the vehicle decelerates at a rate of 15 feet per second, then the formula: can calculate t, the time it takes a vehicle to stop in seconds, when traveling r, miles per hour. Create a four-corner model that includes the equation, verbal description, table, and graph for the problem situation. If a vehicle is traveling 65 miles per hour, use a calculator to calculate the time it will take for the vehicle to come to a complete stop. Write an inequality statement, using numbers and symbols, to identify the speeds in which a vehicle can stop in less than 10 seconds. Solve the problem by locating and naming each solution on the graph, finding each solution in the table, and using appropriate operations to find each solution algebraically. Validate each solution process in a written justification, and describe the connections between the representations, detailing if the linear relationship is proportional or non-proportional. Standard(s): 8.2A, 8.2B, 8.3A, 8.4, 8.5A, 8.7D, 8.14A, 8.14B, 8.14C, 8.14D, 8.15A, 8.15B, 8.16A, 8.16B ELPS ELPS.c.1C, ELPS.c.4B, ELPS.c.5G Key Understanding(s): Conjectures from everyday problem situations are helpful in validating patterns in tables, involving proportional and non-proportional linear relationships, and symbolically representing epressions or equations. Relationships among quantities may be epressed in a variety of forms. Different representations of data may be generated given one form of representation. The process of solving an equation involves using a plan or strategy to keep the values on both sides of the equation equally balanced and validating the solution for reasonableness. page 4 of 144

5 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days An ordered pair can be useful in everyday situations to communicate specific points on the coordinate plane. Underdeveloped Concept(s): Students may think equal means find the answer, rather than has the same value as. Some students may think variables are letters representing an object as opposed to representing a number or quantity of objects. Vocabulary of Instruction: equation equivalent equations equivalent epressions epression isolating the variable representations solution solving an equation variable Materials List: algebra tiles (12 1 tiles, 12 1 tiles, 5 tiles, 5 tiles) (1 set per student, 1 set per teacher) Bag of Algebra Tiles (12 1 tiles, 12 1 tiles, 5 tiles, 5 tiles) (1 set per student, 1 set per teacher) (previously created) calculator (1 per student) cardstock (2 sheets per 6 students, 3 sheets per 4 students) cardstock (24 sheets per teacher) cardstock (optional) (2 sheets of red, 2 sheets of green) (1 set per 4 students, 1 set per teacher) map pencil (1 red, 1 green) (1 set per student) math journal (1 per student) plastic zip bag (sandwich sized) (1 per 2 students, 1 per teacher) plastic zip bag (sandwich sized) (1 per 6 students, 1 per 4 students) plastic zip bag (sandwich sized) (1 per student, 1 per teacher) scissors (1 per teacher) square tiles (15 per 2 students, 15 per teacher) page 5 of 144

6 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days STAAR Reference Materials (1 per student) sticky notes (3 3 ) (30 per teacher) tape (masking) (1 roll per teacher) two-color counters (15 per 2 students, 15 per teacher) Attachments: All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website. Horses and Birds KEY Horses and Birds Variables and Epressions Notes KEY Variables and Epressions Notes I Have, Who Has Epress and Evaluate Student Recording Sheet KEY Epress and Evaluate Student Recording Sheet Epress and Evaluate Phrase Cards Epress and Evaluate Epression Cards Epress and Evaluate Solution Cards Variables and Epressions KEY page 6 of 144

7 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Variables and Epressions Variables and Epressions Practice KEY Variables and Epressions Practice Algebra Tiles Simplifying Algebraic Epressions KEY Simplifying Algebraic Epressions Which One Does Not Belong KEY Which One Does Not Belong Balance Scale Balance Scale Problems KEY Balance Scale Problems Parallel Representations on the Balance Scale KEY Parallel Representations on the Balance Scale Multiplication/Division Equations Addition/Subtraction Properties of Equality Algebra Tiles and One-Step Equations KEY Algebra Tiles and One-Step Equations Solving Equations Student Notes KEY page 7 of 144

8 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Solving Equations Student Notes Two-Step Equations and More KEY Two-Step Equations and More Mi-It Madness KEY Mi-It Madness Solve Equations Algebraically KEY Solve Equations Algebraically Formulating Equations KEY Formulating Equations Different Representations Practice KEY Different Representations Practice Different Representations KEY Different Representations Graphs and Data Representation KEY Graphs and Data Representation Graphs and Data Representations Etensions Equations and Data Representations KEY Equations and Data Representations page 8 of 144

9 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Quad Card Recording Sheet KEY Quad Card Recording Sheet Quad Card Activity GETTING READY FOR INSTRUCTION Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using the Content Creator in the Tools Tab. All originally authored lessons can be saved in the My CSCOPE Tab within the My Content area. Suggested Day Suggested Instructional Procedures Notes for Teacher 1 Topics: Introduction to variables and epressions Engage 1 Students use eperience and reasoning skills to review evaluating and simplifying epressions. Instructional Procedures: 1. Display teacher resource: Horses and Birds. 2. Place students in groups of 3 and instruct students to create a non-linguistic model to solve the problem in their math journal. Allow 5 minutes for student groups to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion about the different strategies students used to solve the problem. Ask: Spiraling Review ATTACHMENTS Teacher Resource: Horses and Birds KEY (1 per teacher) Teacher Resource: Horses and Birds (1 per teacher) Teacher Resource: Variables and Epressions Notes KEY (1 page 9 of 144

10 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher What strategy did you use to determine the number of horses and the number of birds if there is a total of 284 legs? Answers may vary. I drew a circle with 4 legs and another circle with 2 legs. I kept track of how many of each in a table until I reached 284; etc. How many legs would be on 5 horses? 5 birds? (number of horse legs: ; number of bird legs: ) How many total legs are there on 5 horses and 5 birds? (30) What numeric epression could you write to represent the total number of legs on 5 horses? 5 birds? (5 4 number of horse legs and 5 2 number of bird legs) What numeric epression would you write to represent the total number of legs on 5 horses and 5 birds? ( ) What would be the correct order of operations to evaluate this epression? (multiply 5 4, then multiply 5 2, and then add the two products 20 10) How would you represent the number of legs on any number of horses? Birds? (4 h, where h represents the number of horses; 2 b, where b represents the number of birds) How would you represent the total number of legs on any number of horses and birds? (4 h 2 b, where h represents the number of horses and b represents the number of birds) What equation would you write to show you want this epression to have a value of 284? (4h 2b 284) Was your answer reasonable? Answers may vary. Yes, because ; etc. How many horses and how many birds would there be if there was a total of 70 legs? Answers may vary. 11 horses and 13 birds; 10 horses and 15 birds; etc. What equation would you write to show there is a total of 70 legs? (4h 2b 70) How could you use the description, Each horse has 4 legs and each bird has 2 legs to generate a table that would show the total number of legs for a given number of horses and birds? Answers may vary. per teacher) Handout: Variables and Epressions Notes (1 per student) MATERIALS math journal (1 per student) page 10 of 144

11 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher 3. Distribute handout: Variables and Epressions Notes to each student. Facilitate a class discussion about variables and epressions. Instruct students to complete the handout throughout the class discussion. Topics: ATTACHMENTS Multiple representations Eplore/Eplain 1 Students connect a verbal description to an algebraic epression. Instructional Procedures: Card Set: I Have, Who Has (1 set per 6 students) Teacher Resource: Epress and Evaluate Student Recording Sheet KEY (1 per teacher) page 11 of 144

12 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher 1. Prior to instruction, create a card set: I Have, Who Has for every 6 students by copying on cardstock, cutting apart, and placing in a plastic zip bag. Additionally, create card sets: Epress and Evaluate Phrase Cards; Epress and Evaluate Epression Cards; Epress and Evaluate Solution Cards for every 4 students by copying on cardstock, cutting apart, and placing in a plastic zip bag. 2. Place students in groups of 6 and distribute a card set: I Have, Who Has to each group. Instruct each student to select 4 cards from the set. Eplain to students that the student with the card with an * and the student statement, Who has four more than three times a number? will begin the game. The student reads their card aloud and the student with the matching card responds to by stating, I have 3 4, who has two less than one fifth of a number. This process continues until the students end on the card with an *. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief student solutions, as needed. 3. Place students in groups of 4. Distribute handout: Epress and Evaluate Student Recording Sheet to each student and card sets: Epress and Evaluate Phrase Cards; Epress and Evaluate Epression Cards; Epress and Evaluate Solution Cards to each group. 4. Instruct students to match each phrase card with an epression card and a solution card, and then record the matches on their handout: Epress and Evaluate Student Recording Sheet. Allow time for students to complete the matches. Monitor and assess students to check for understanding. Facilitate individual group discussions to clarify the understanding of how to evaluate an epression, as needed. Ask: Handout: Epress and Evaluate Student Recording Sheet (1 per student) Card Set: Epress and Evaluate Phrase Cards (1 set per 4 students) Card Set: Epress and Evaluate Epression Cards (1 set per 4 students) Card Set: Epress and Evaluate Solution Cards (1 set per 4 students) Teacher Resource: Variables and Epressions KEY (1 per teacher) Handout: Variables and Epressions (1 per student) Teacher Resource (optional): Variables and page 12 of 144

13 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher How do you write the epression, a number u times 5? (5u) What do you do with the u 8? (Substitute -8 for u in the epression 5u.) How do you solve the epression? (multiply 5 times -8) What is the solution for this epression? (-40) Why is the answer negative? (When you multiply a positive and a negative, the answer is negative.) Epressions Practice KEY (1 per teacher) Handout (optional): Variables and Epressions Practice (1 per student) 5. Distribute handout: Variables and Epressions to each student as independent practice and/or homework. MATERIALS cardstock (2 sheets per 6 students, 3 sheets per 4 students) scissors (1 per teacher) plastic zip bag (sandwich sized) (1 per 6 students, 1 per 4 students) ADDITIONAL PRACTICE The handout (optional): Variables and Epressions Practice may be used as additional practice if needed. page 13 of 144

14 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher 2 Topics: Simplifying algebraic epressions Eplore/Eplain 2 Students simplify algebraic epressions and translate written phrases to algebraic symbols. Instructional Procedures: 1. Prior to instruction, create a Bag of Algebra Tiles for each student and a Bag of Algebra Tiles for each teacher by placing 12 1 tiles, 12 1 tiles, 5 tiles, and 5 - tiles in a plastic zip bag. If algebra tiles are not available, use class resource: Algebra Tiles to create a Bag of Algebra Tiles for each student and a Bag of Algebra Tiles for each teacher by copying pages 1 and 3 on green cardstock and pages 2 and 4 on red cardstock, laminating, cutting apart, and placing 12 1 tiles, 12 1 tiles, 5 tiles, and 5 - tiles in a plastic zip bag. 2. Distribute a Bag of Algebra Tiles for each student and display a model of each shape of the algebra tiles. Facilitate a class discussion eplaining that algebra tiles are a concrete area model used to represent values and model algebraic symbols such as and 1. Spiraling Review ATTACHMENTS Class Resource (optional): Algebra Tiles (1 per 4 students, 1 per teacher) Teacher Resource: Simplifying Algebraic Epressions KEY (1 per teacher) Handout: Simplifying Algebraic Epressions (1 per student) MATERIALS 3. Display the small square algebra tile from a Bag of Algebra Tiles. Facilitate a class discussion to name the algebra tile. Ask: algebra tiles (12 1 tiles, 12 1 tiles, 5 tiles, 5 - tiles) (1 set per student, 1 set per teacher) plastic zip bag (sandwich sized) (1 per student, 1 per teacher) page 14 of 144

15 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures What is the name of this shape? (square) How do you find the area of a square? (s² or side times side) What is the width of this square algebra tile? (1) What is the length of the square algebra tile? (1) What is the area of this square tile? (1 times 1 1 unit 2 ) Notes for Teacher cardstock (optional) (2 sheets of red, 2 sheets of green) (1 set per 4 students, 1 set per teacher) scissors (optional) (1 per teacher) map pencil (1 red, 1 green) (1 set per student) Eplain to students that since the area of this tile is 1, these tiles are called unit tiles, and they represent Display the tile for net to the unit tile to show that the tile is 1 unit in width. Ask: What is the width of the larger tile? (It is unknown.) What variable can you use to represent an unknown? () What is the area of this tile if it is 1 unit in width and units in length? ( times 1 ) Eplain to students that since the area of this tile is, these tiles are called the tiles and will be used to represent most variables. 5. Display the following algebra tiles for the class to see. TEACHER NOTE Algebra tiles help students make sense of the language of algebra. They are concrete models of abstract thought. Middle school students (and most high school students) need a firm foundation in the use of algebra before moving to purely abstract algebraic manipulations. TEACHER NOTE The ² algebra tile will not be used page 15 of 144

16 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher until Algebra 1 for factoring and solving quadratic equations. TEACHER NOTE It is important to help students Ask: What do you think the red side represents? (negatives) Eplain to students that the color of positive values may be blue, green, yellow, or some other color but not red. 6. Facilitate a class discussion to clarify zero pairs. Ask: What does a red 1 unit and a green 1 unit equal? (zero, according to integer rules, negative 1 plus positive 1 equals zero.) What does a green unit and a red unit equal? (zero according to integer rules, negative plus positive equals zero.) What name represents this relationship? (zero pair) 7. Facilitate class discussion to practice using algebra tiles. Ask: How do you represent 3 using algebra tiles? (3 green 1 tiles) develop an understanding of the various ways variables are used. 1. Specific unknown Eample: Variable- a pattern generalizer Eample: A L W 3. Variable- as quantities that vary in joint variation Eample: C 2 r Usiskin (1988) TEACHER NOTE Students have been eposed to variables throughout elementary school; however, studies indicate that most children have a vague understanding of the concept of a variable. Many students believe page 16 of 144

17 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures How do you represent (-5) using algebra tiles? (5 red 1 tiles) Notes for Teacher that is different from 4y How do you represent 2 1 using algebra tiles? (2 green tiles and 1 green 1 tile) How do you represent 3 4 using algebra tiles? (3 green tiles and 4 red 1 tiles) Remind students that a number and an unknown or variable written side-by-side, such as 3y, indicates multiplication of 3 and the unknown/variable: 3 y, or has the same value as y y y. TEACHER NOTE As a strategy for ELL students, line 8. Display the epression for the class to see. Instruct students to use their Bag of Algebra Tiles to create a model of the epression. Allow time for students to complete the model. Monitor and assess students to check for understanding. Facilitate a class discussion about combining like terms and zero pairs. up the tiles and have students name the tiles as you write the epression under each name. Eample Ask: What can you do first to simplify this epression? (Look for zero pairs.) What zero pairs are displayed? (There are two sets of zero pairs for the tiles and two sets of zero pairs for the ones tiles.) What does the model look like once the zero pairs are removed? TEACHER NOTE As a strategy for ELL students, when removing zero pairs, model the removal of the tiles as follows. page 17 of 144

18 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher Use one hand. Place inde finger on the negative tile and the middle What algebraic epression can you use to represent this simplified model? (2 1) 9. Place students in pairs and distribute handout: Simplifying Algebraic Epression to each student. Instruct students to use their Bag of Algebra Tiles to model each epression and record the model, simplified model, and simplified epression. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief student solutions, as needed. finger on the positive tile and slide the two opposing colors off the screen at the same time. TEACHER NOTE The answer key will show the algebra tile models using the following symbolism. TEACHER NOTE Students may have some difficulty relating the epressions 2 10 and 1 9 as being equivalent. The students may have some difficulty relating the epressions (2 10) 2 and 5 as being equivalent. The students may have some difficulty relating the epressions page 18 of 144

19 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher 5 5 and as being equivalent. 3 Topics: Introduction to solving equations with a balance scale Engage 2 Students use eperience and reasoning skills to lay the foundation for connecting the parallel representation of models to the algebraic symbolism used to solve equations. Instructional Procedures: 1. Display set 1 from teacher resource: Which One Does Not Belong. Instruct students to analyze each diagram, determine and record the ratio of squares to circles for each diagram in their math journal, and for each set, determine which diagram does not have the same number of circles per square as the other diagrams in the set. Allow students 1 2 minutes to complete the activity. Monitor and assess students to check understanding. Facilitate a class discussion for students to justify how they determined which diagram was not correct. Ask: Spiraling Review ATTACHMENTS Teacher Resource: Which One Does Not Belong KEY (1 per teacher) Teacher Resource: Which One Does Not Belong (1 per teacher) MATERIALS math journal (1 per student) What does the balance scale imply? (The values on both sides of the balance scale are equal.) Which diagram does not belong? Eplain. (Diagram C: a square 1.5 circles. In the other diagrams, a square 2 circles.) How did you determine which diagram did not belong? Answers may vary. Diagram A: divided the objects on each side of the balance scale into 3 groups; Diagram B: divided the objects on each side of the balance scale into 3 groups; Diagram C: divided the objects on each side of the balance scale into 2 groups; Diagram D: 2 circles balance 1 square; Diagram E: removed 2 circles from each side of the balance scale and then divided TEACHER NOTE Solving application problems involves identifying the unknown and the given, translating the English phrase to algebraic symbols and checking answers page 19 of 144

20 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher the objects on each side of the balance scale into 3 groups; etc. How does Diagram E differ from the other diagrams? (It has circles on both sides of the balance scale.) What can you do so there are only squares on one side of the balance scale and the scale remains balanced? (Remove 2 circles from each side of the balance scale.) What operation does this action represent? (subtraction) with the conditions of the problem through the use of diagrams, tables, formulas, and graphs. 2. Display set 2 from the teacher resource: Which One Does Not Belong. Instruct students to analyze each diagram, determine and record the ratio for each diagram in their math journal, and determine which diagram does not have the same number of circles per square. Allow students 1 2 minutes to complete the activity. Monitor and assess students to check understanding. Facilitate a class discussion for students to justify how they determined which diagram was not correct. Ask: Which diagram does not belong? Eplain. (Diagram E: a square 2 circles. In the other diagrams, a square 1 circle.) How did you determine which diagram did not belong? Answers may vary. Diagram A: divided the objects on each side of the balance scale into 3 groups; Diagram B: removed 2 circles from each side of the balance scale and then divided the objects on each side of the balance scale into 3 groups; Diagram C: 1 circle balances 1 square; Diagram D: remove 1 circle from each side of the balance scale and then divide the objects on each side of the scale into 3 groups; Diagram E: divide the objects on each side of the balance scale into 2 groups; etc. Topics: ATTACHMENTS Solving one-step equations with a balance scale Teacher Resource: Balance page 20 of 144

21 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher Eplore/Eplain 3 Students apply previous knowledge to solve equations with pictorial representations. Instructional Procedures: 1. Prior to instruction create a Bag of Circles and Squares for every 2 students and a Bag of Circles and Squares for each teacher by placing 15 square tiles and 15 two-color counters in a plastic zip bag. 2. Place students in pairs. Distribute handouts: Balance Scale Problems and Balance Scale to each student and a Bag of Circles and Squares to each pair. 3. Display teacher resource: Balance Scale. Using a Bag of Circles and Squares model problem 1 from teacher resource: Balance Scale Problems. Instruct students to use their Bag of Circles and Squares and handout: Balance Scale to replicate the model and record the solution in their math journal. 4. Instruct student pairs to use their Bag of Circles and Squares and handout: Balance Scale to complete the remainder of the problems from handout: Balance Scale Problems and record their solutions in their math journal. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate small group discussions as needed. Ask: How could you use words to describe this diagram? Answers may vary. Three squares and 2 circles equal 8 circles; etc. What is the same on both sides of the balance scale? Answers may vary. Circles; etc. How do you decide what to remove (or add) from both sides of the scale? Answers may vary. Since there are circles on both sides, you need to get the squares by themselves, so you will remove 2 circles from both sides; etc. Scale (1 per teacher) Handout: Balance Scale (1 per student) Teacher Resource: Balance Scale Problems KEY (1 per teacher) Teacher Resource: Balance Scale Problems (1 per teacher) Handout: Balance Scale Problems (1 per student) Teacher Resource: Parallel Representations on the Balance Scale KEY (1 per teacher) Handout: Parallel Representations on the Balance Scale (1 per student) MATERIALS square tiles (15 per 2 students, 15 per teacher) two-color counters (15 per 2 page 21 of 144

22 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher Why must you perform the same action to each side of the balance scale? (So the scale will be in balance. If you change one side of the scale without doing the same thing to the other, the scale will not be balanced anymore.) 5. Distribute handout: Parallel Representations on the Balance Scale to each student as independent practice or homework. students, 15 per teacher) plastic zip bag (sandwich sized) (1 per 2 students, 1 per teacher) math journal (1 per student) TEACHER NOTE The purpose of the balance scale activity is to help students review their work with models for solving equations from Grade 7. 4 Topics: Solve one-step equations Eplore/Eplain 4 Students review mathematical properties and procedures to solve one-step equations algebraically and with concrete models. Instructional Procedures: 1. Prior to instruction cover each model on teacher resources: Addition/Subtraction Property of Equality and Multiplication/Division Equations with a sticky note. 2. Distribute a Bag of Algebra Tiles to each student. Spiraling Review ATTACHMENTS Teacher Resource: Addition/Subtraction Properties of Equality (1 per teacher) Teacher Resource: Multiplication/Division Equations (1 per teacher) Card Set: Algebra Tiles (1 page 22 of 144

23 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher 3. Display problem 1 from teacher resource: Addition/Subtraction Property of Equality. Model how to solve 2 5 using addition. Begin on the left side of the teacher resource uncovering each model representing the Addition Property of Equality while facilitating a class discussion about solving equations using addition. Ask: What does the left side represent? (2) What does the right side represent? (5) What does the line represent? () What part of the balance scale resembles the equal sign? (The fulcrum in the middle.) What was the rule for solving on the balance scale? (Whatever operation you perform to one side of the scale, you must perform the same operation to the other side of the scale.) Why? (To keep the scale balanced.) When working with the squares and circles, what was the goal? (To isolate circles on one side and squares on the other side.) What do you think will be the goal for this equation? (To isolate on one side and units on the other side.) This is called isolating the variable. We are going to eamine two ways of looking at solving equations containing a plus sign. What is happening in the second row of the model? (negative 2 is added to both sides) Why did I add negative 2 to both sides? (to get zero pairs on the left side) Why do I need zero pairs on the left side of the equal mark? (to get the by itself) What is the solution to the equation? ( 3) 4. Recover the left side of teacher resource: Addition/Subtraction Property of Equality. Model how to solve 2 5 using subtraction. Referencing the right side of teacher resource, uncover each model representing the per 4 students) Teacher Resource: Algebra Tiles and One-Step Equations KEY (1 per teacher) Handout: Algebra Tiles and One-Step Equations (1 per student) MATERIALS sticky notes (3 3 ) (30 per teacher) Bag of Algebra Tiles (12 1 tiles, 12 1 tiles, 5 tiles, 5 - tiles) (1 set per student, 1 set per teacher) (previously created) map pencil (1 red, 1 green) (1 set per student) TEACHER NOTE Equations are used to epress relationships between two page 23 of 144

24 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher Subtraction Property of Equality while facilitating a class discussion about solving equations using subtraction. Ask: What does the line represent? () What was the rule for solving on the balance scale? (Whatever operation you perform to one side of the scale, you must perform the same operation to the other side of the scale.) Why? (To keep the scale balanced.) What is the goal for this equation? (To isolate on one side and units on the other side.) What is happening in the second row? (2 is being removed from both sides) Why was 2 removed from both sides? (to get the by itself) What is the solution to the equation? ( 3) Why did both methods lead to the same answer for the value of "? (In both cases, balance is maintained. The variable is alone on one side of the equal sign, and I know what the variable represented in the problem.) How are the methods alike and how are they different? (In one problem I added zero pairs to isolate the variable. In the other, I subtracted.) How do you know the solution is correct? (When I substitute 3 for in the original equation and simplify both sides of the equation, I have a true statement: 2 5, ) 5. Display Problem 2 from teacher resource: Addition/Subtraction Property of Equality and facilitate a class discussion about each property while uncovering each row of the model. 6. Display Problem 1 from teacher resource: Multiplication/Division Equations to facilitate a class discussion, uncovering each row of the model. Ask: quantities. This functional relationship is important for algebra readiness. TEACHER NOTE It is very important to establish the understanding that is equivalent to. TEACHER NOTE It is important students view the as a symbol of the equality relationship between the left and right sides of an equation. TEACHER NOTE It is important for students to view solving an equation as performing the same operation on both sides of an equation to keep the equation balanced. TEACHER NOTE page 24 of 144

25 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher What does the line represent? () What part of the balance scale resembles the equal sign? (The fulcrum in the middle.) What was the rule for solving on the balance scale? (Whatever operation you perform on one side of the scale, you must perform on the other side.) Why? (To keep the scale balanced.) What operation is in the equation? (multiplication) What is the inverse operation of multiplication? (division) How can you isolate the variable? (Divide both sides of the equation by 4.) Why does this isolate the variable? (Because division undoes multiplication. The operation of division is the inverse of multiplication.) What does division mean? (Separating into equal groups.) How does that help you solve this equation? (I will separate the 8 units into 4 equal groups. This will give me two in each group.) What is the solution to the equation? ( 2) How do you know the solution is correct? (When I substitute 2 for in the original equation and simplify both sides of the equation, I have a true statement: 4 8, 4(2) 8.) Since there are some limitations to using algebra tiles to solve equations, students need to develop an understanding of the process with equations that are easily modeled using algebra tiles. For equations that are difficult to model using algebra tiles, it is important students are able to connect the process used with algebra tiles to the algebraic method for solving equations. The equation in Eample 1 is easily modeled using algebra tiles. page 25 of 144

26 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher 7. Display Problem 2 from teacher resource: Multiplication/Division Equations and facilitate a class discussion about each property while uncovering each row of the model. Eample 1 8. Display Problem 3 from teacher resource: Multiplication/Division Equations and facilitate a class discussion about each property while uncovering each row of the model. Ask: Why was this model difficult to create? (It is difficult to model dividing an algebra tile in half.) What could you do to solve this problem? Why? (I could double each side of the equal sign. Now, we could think of the tile representing only of 3. If we double both sides of the equation, we now have plus which is 1. The representation is now: 6. This keeps the balance and solves the problem with the fraction.) What operation is another way to double? (Multiply by 2.) What does multiplication mean? (Combining equal size groups.) How does that help you solve this equation? (I will combine 2 equal groups. This will give me 1 whole.) What is the solution to the equation? ( 6) How do you know the solution is correct? (When I substitute 6 for in the original equation and simplify both sides of the equation, I have a true statement:.) 9. Display Problem 4 from teacher resource: Multiplication/Division Equations and facilitate a class discussion using the questions above while uncovering each row of the model one at a time. The equation in Eample 2 may not be as easily modeled using algebra tiles, but students should connect the process used with algebra tiles to the algebraic method for solving equations. Eample Place students in pairs. Distribute a red and green map pencil to each pair and handout: Algebra Tiles and One- Step Equations to each student. Instruct student pairs to complete the handout using the map pencils to represent page 26 of 144

27 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher the colors of the algebra tiles. Allow time for students to complete the activity. Monitor and assess students to check for understanding. 5 Topics: Solve multi-step equations Eplore/Eplain 5 Students review procedures to solve multi-step equations algebraically and with concrete models. Instructional Procedures: 1. Distribute handout: Solving Equations Student Notes to each student. 2. Display teacher resource: Solving Equations Student Notes and facilitate a class discussion to summarize the basic process for solving equations. 3. Instruct students to complete each eample on their handout: Solving Equations Student Notes. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief student solutions. 4. Distribute handout: Two-Step Equations and More and a Bag of Algebra Tiles to each student. 5. Display problem 1 from teacher resource: Two-Step Equations and More. Using algebra tiles, facilitate a class discussion to model solving two-step equations. Ask: How is this equation different from the other equations you modeled earlier? (This equation has two operations involved.) Spiraling Review ATTACHMENTS Teacher Resource: Solving Equations Student Notes KEY (1 per teacher) Teacher Resource: Solving Equations Student Notes (1 per teacher) Handout: Solving Equations Student Notes (1 per student) Teacher Resource: Two- Step Equations and More (1 per teacher) Teacher Resource: Two- Step Equations and More KEY (1 per teacher) Handout: Two-Step Equations and More (1 per student) page 27 of 144

28 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher What should you do first? (subtract 3) What should you do second? (divide by 2) How could you record your actions using algebraic symbols? (Two long bars with a positive sign can represent 2 and a square with a positive sign can represent the 3 and 7.) How can you verify your answer is reasonable? (Substitute the value for in the original equation and simplify both sides of the equation using the correct order of operations.) 6. Place students in pairs. Instruct student pairs to use their algebra tiles to complete problems 2 4 on their handout: Two-Step Equations and More. Allow time for students to complete the activity. Monitor and assess students to check for understanding. 7. Display problem 5 from teacher resource: Two-Step Equations and More. Using algebra tiles, facilitate a class discussion to model solving two-step equations. Ask: How is this equation different from the other equations you modeled earlier? (This equation has variables on both sides of the.) What should you do first? (Make a zero pair with the.) What should you do second? (Add 3 to isolate the variable.) How could you record your actions using algebra tiles? (The positive 2 will be represented by 2 long bars with positive signs, the negative 3 will be represented by 3 squares with negative signs, the will be represented with one long bar with a positive sign, and the negative 1 will be represented by one square with a negative sign.) How can you verify your answer is reasonable? (Substitute the value for in the original equation and simplify each side of the equation using the correct order of operations.) Teacher Resource: Mi-It Madness KEY (1 per teacher) Handout: Mi-It Madness (1 per student) Teacher Resource: Solve Equations Algebraically KEY (1 per teacher) Handout: Solve Equations Algebraically (1 per student) MATERIALS Bag of Algebra Tiles (12 1 tiles, 12 1 tiles, 5 tiles, 5 - tiles) (1 set per student, 1 set per teacher) (previously created) TEACHER NOTE While the focus of this portion of the lesson is to move students page 28 of 144

29 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher 8. Instruct student pairs to complete problems 6 9 from handout: Two-Step Equations and More. Allow time for students to complete the activity. Monitor and assess students to check for understanding. 9. Distribute handout: Mi-It Madness to each student. Instruct student pairs to solve each equation by selecting a response from Table B and recording it in the appropriate location in Table A. Remind students that not all the responses in Table B will be used. Allow time for student pairs to complete the activity. Monitor and assess students to check for understanding. 10. Distribute handout: Solve Equations Algebraically to each student as independent practice or homework. towards solving equations abstractly, students should be allowed to use the algebra tiles if they choose. Algebra tiles are shown on the high school assessments and it is appropriate to allow the use of tiles on assessments as well. TEACHER NOTE Students may have a conceptual understanding of solving equations and may need to show only equivalent equations after a step has been completed. They may not need to show the operation they are doing to both sides of the equation. This is not skipping a step." 6 Topics: Multiple representations Eplore/Eplain 6 Spiraling Review ATTACHMENTS page 29 of 144

30 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher Students generate a table, epression, or equation when given another algebraic representation. Instructional Procedures: 1. Display teacher resource: Formulating Equations. 2. Place students in pairs and distribute handout: Formulating Equations to each student. Instruct students to match the equations to the problem situations. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief student solutions. Ask: How did you determine the situation that matched the equation? Answers may vary. I used process of elimination by determining which eample best fit the scenario; etc. What is the constant rate of change in each table? Eplain. Answers may vary. 60; etc. How did you determine the constant rate of change? ( ) Where is the constant rate of change in the equation? (The number being multiplied by the value.) Where is the constant rate of change in the table? (Look at the consecutive differences in the right hand column over the corresponding consecutive differences in the left hand column.) 3. Distribute handout: Different Representations Practice and a calculator to each student. Instruct student pairs to generate the missing representations for each problem situation, using the calculator to assist in the finding of solutions and verification of responses. Allow time for student to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief student solutions. Teacher Resource: Formulating Equations KEY (1 per teacher) Handout: Formulating Equations (1 per student) Teacher Resource: Formulating Equations (1 per teacher) Teacher Resource: Different Representations Practice KEY (1 per teacher) Handout: Different Representations Practice (1 per student) Teacher Resource (optional): Different Representations KEY (1 per teacher) Handout (optional): Different Representations (1 per student) MATERIALS page 30 of 144

31 Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Suggested Day Suggested Instructional Procedures Notes for Teacher calculator (1 per student) ADDITIONAL PRACTICE The handout (optional): Different Representations may be used as additional practice if needed. 7 Topics: Multiple representations Eplore/Eplain 7 Students generate a table, graph, epression, or equation when given another algebraic representation. Instructional Procedures: 1. Place students in pairs and distribute handout: Graphs and Data Representation and a STAAR Reference Materials to each student. Instruct students to generate tables and equations to match the given graphs and record a written description for each problem. Allow time for students to complete the activity. Monitor and assess student pairs to check for understanding. Facilitate individual group discussions about the activity, as needed. Ask: What are the two quantities represented in the graph? Answers may vary. Number of cups and number of pints; etc. Spiraling Review ATTACHMENTS Teacher Resource: Graphs and Data Representation KEY (1 per teacher) Handout: Graphs and Data Representation (1 per student) Teacher Resource: Graphs and Data Representation (1 per teacher) Teacher Resource: Graphs and Data Representations Etensions KEY (1 per page 31 of 144

### Enhanced Instructional Transition Guide

Enhanced Instructional Transition Guide / Unit 02: Suggested Duration: 6 days Unit 02: Numerical Operations: Integers and Positive Rational Numbers (16 days) Possible Lesson 01 (6 days) Possible Lesson

### Enhanced Instructional Transition Guide

Enhanced Instructional Transition Guide High School Courses/Algebra I Unit 03: Suggested Duration: 12 days Unit 03: Linear Equations, Inequalities, and Applications (12 days) Possible Lesson 01 (12 days)

### Enhanced Instructional Transition Guide

Enhanced Instructional Transition Guide / Unit 07: Suggested Duration: 3 days Unit 07: Measurement (15 days) Possible Lesson 01 (9 days) Possible Lesson 02 (3 days) Possible Lesson 03 (3 days) Possible

### Enhanced Instructional Transition Guide

1-1 Enhanced Instructional Transition Guide High School Courses Unit Number: 7 /Mathematics Suggested Duration: 9 days Unit 7: Polynomial Functions and Applications (15 days) Possible Lesson 1 (6 days)

### Enhanced Instructional Transition Guide

Enhanced Instructional Transition Guide High School Courses/Algebra II Unit 04: Suggested Duration: 1 days Unit 04: Systems of Linear Equations (1 days) Possible Lesson 01 (1 days) POSSIBLE LESSON 01 (1

### Enhanced Instructional Transition Guide

Enhanced Instructional Transition Guide / Unit 08: Suggested Duration: 10 days Unit 08: Measurement: Capacity, Weight, Time, Temperature, and Volume (10 days) Possible Lesson 01 (10 days) POSSIBLE LESSON

### Science Grade 01 Unit 07 Exemplar Lesson 02: Investigating the Moon, the Stars, and the Sky

Grade 1 Unit: 07 Lesson: 02 Suggested Duration: 5 days Grade 01 Unit 07 Exemplar Lesson 02: Investigating the Moon, the Stars, and the Sky This lesson is one approach to teaching the State Standards associated

### Enhanced Instructional Transition Guide

Enhanced Instructional Transition Guide High School Courses/ Unit 01: Suggested Duration: 6 days Unit 01: Foundations of (10 days) Possible Lesson 01 (4 days) Possible Lesson 02 (6 days) POSSIBLE LESSON

### Science Grade 01 Unit 01 Exemplar Lesson 02: Observing and Recording Weather

Unit: 01 Lesson: 02 Suggested Duration: 5 days Grade 01 Unit 01 Exemplar Lesson 02: Observing and Recording Weather This lesson is one approach to teaching the State Standards associated with this unit.

### Pre-Algebra (6/7) Pacing Guide

Pre-Algebra (6/7) Pacing Guide Vision Statement Imagine a classroom, a school, or a school district where all students have access to high-quality, engaging mathematics instruction. There are ambitious

### Mathematics. Algebra I (PreAP, Pt. 1, Pt. 2) Curriculum Guide. Revised 2016

Mathematics Algebra I (PreAP, Pt. 1, Pt. ) Curriculum Guide Revised 016 Intentionally Left Blank Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction and

### Mathematics Grade 7 Transition Alignment Guide (TAG) Tool

Transition Alignment Guide (TAG) Tool As districts build their mathematics curriculum for 2013-14, it is important to remember the implementation schedule for new mathematics TEKS. In 2012, the Teas State

### INSTRUCTIONAL FOCUS DOCUMENT HS/Algebra 1

Possible Lesson 01 (12 days) State Resources: Algebra 1 End of Course Success: Representations and Support: Objective 1 Lesson 1 Problem Solving Boards, Equation Representation, On Your Own: Writing an

### Science Grade 08 Unit 10 Exemplar Lesson 01: Light Years and Origins of the Universe

Unit: 10 Lesson: 01 Suggested Duration: 5 days Grade 08 Unit 10 Exemplar Lesson 01: Light Years and Origins of the Universe This lesson is one approach to teaching the State Standards associated with this

### Common Core State Standards for Activity 14. Lesson Postal Service Lesson 14-1 Polynomials PLAN TEACH

Postal Service Lesson 1-1 Polynomials Learning Targets: Write a third-degree equation that represents a real-world situation. Graph a portion of this equation and evaluate the meaning of a relative maimum.

### INSTRUCTIONAL FOCUS DOCUMENT HS/Algebra 1

Possible Lesson 01 (7 days) State Resources: Algebra 1 End of Course Success CCRS: Objective 4 Lesson 2 Line Dancing, Systems of Equations Card Match, On Your Own: Systems of Equations, Using Technology:

### In this lesson, students model filling a rectangular

NATIONAL MATH + SCIENCE INITIATIVE Mathematics Fill It Up, Please Part III Level Algebra or Math at the end of a unit on linear functions Geometry or Math as part of a unit on volume to spiral concepts

### Standards of Learning Content Review Notes. Grade 7 Mathematics 3 rd Nine Weeks,

Standards of Learning Content Review Notes Grade 7 Mathematics 3 rd Nine Weeks, 2016-2017 1 2 Content Review: Standards of Learning in Detail Grade 7 Mathematics: Third Nine Weeks 2016-2017 This resource

### Adding and Subtracting Rational Expressions

COMMON CORE Locker LESSON 9.1 Adding and Subtracting Rational Epressions Name Class Date 9.1 Adding and Subtracting Rational Epressions Essential Question: How can you add and subtract rational epressions?

### MATHEMATICS. Perform a series of transformations and/or dilations to a figure. A FAMILY GUIDE FOR STUDENT SUCCESS 17

MATHEMATICS In grade 8, your child will focus on three critical areas. The first is formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a

### Nine Week SOL Time Allotment. A.4a, b and A.5a - Properties. A.1b and A.3c - Order of Operations. A.1b - Evaluating Expression

6/5/2018 Nine Week SOL Time Allotment A.4a, b and A.5a - Properties A.1b and A.3c - Order of Operations A.1b - Evaluating Expression 3 Days 1 Day 4 Days 1 8.17 and 8.18 - Simplifying Expressions 4 Days

### Solutions of Linear Equations

Lesson 14 Part 1: Introduction Solutions of Linear Equations Develop Skills and Strategies CCSS 8.EE.C.7a You ve learned how to solve linear equations and how to check your solution. In this lesson, you

### Nine Week SOL Time Allotment

6/5/2018 Nine Week SOL Time Allotment 1 Prerequisite Skills and Beginning of year activities A.1 Translating and Evaluating Expressions and Equations A.4 ace Solve Multi-step equations including variables

### Name Period Date MATHLINKS GRADE 8 STUDENT PACKET 5 EXPRESSIONS AND EQUATIONS 2

Name Period Date 8-5 STUDENT PACKET MATHLINKS GRADE 8 STUDENT PACKET 5 EXPRESSIONS AND EQUATIONS 2 5.1 Cups and Counters Expressions Use variables in expressions. Use the distributive property. Use the

### Objective: Construct a paper clock by partitioning a circle into halves and quarters, and tell time to the half hour or quarter hour.

Lesson 13 Objective: Suggested Lesson Structure Fluency Practice Concept Development Student Debrief Total Time (10 minutes) (40 minutes) (10 minutes) (60 minutes) Fluency Practice (10 minutes) Rename

### Unit 5 Algebraic Investigations: Quadratics and More, Part 1

Accelerated Mathematics I Frameworks Student Edition Unit 5 Algebraic Investigations: Quadratics and More, Part 1 2 nd Edition March, 2011 Table of Contents INTRODUCTION:... 3 Notes on Tiling Pools Learning

### Mathematics Review Notes for Parents and Students

Mathematics Review Notes for Parents and Students Grade 7 Mathematics 3 rd Nine Weeks, 2013-2014 1 2 Content Review: Standards of Learning in Detail Grade 7 Mathematics: Third Nine Weeks 2013-2014 June

### SUPPORTING INFORMATION ALGEBRA II. Texas Education Agency

SUPPORTING INFORMATION ALGEBRA II Texas Education Agency The materials are copyrighted (c) and trademarked (tm) as the property of the Texas Education Agency (TEA) and may not be reproduced without the

### Lesson 4: Strategies for Solving Simultaneous Equations (Substitution)

Lesson 4: Strategies for Solving Simultaneous Equations (Substitution) Brief Overview of Lesson: In this lesson students explore an alternate strategy for solving simultaneous linear equations known as

### Topic: Solving systems of equations with linear and quadratic inequalities

Subject & Grade: Mathematics, 9 th Grade Topic: Solving systems of equations with linear and quadratic inequalities Aim: How would you find the solution set of a linear and quadratic inequality? Materials:.

### 7.2 Multiplying Polynomials

Locker LESSON 7. Multiplying Polynomials Teas Math Standards The student is epected to: A.7.B Add, subtract, and multiply polynomials. Mathematical Processes A.1.E Create and use representations to organize,

### Integer Division. Student Probe

Student Probe What is 24 3? Answer: 8 Integer Division Lesson Description This lesson is intended to help students develop an understanding of division of integers. The lesson focuses on using the array

### Pre-Algebra Notes Unit Three: Multi-Step Equations and Inequalities (optional)

Pre-Algebra Notes Unit Three: Multi-Step Equations and Inequalities (optional) CCSD Teachers note: CCSD syllabus objectives (2.8)The student will solve multi-step inequalities and (2.9)The student will

### SOLVING EQUATIONS AND DEVELOPING THE FOUNDATION FOR PROOFS

12 SOLVING EQUATIONS AND DEVELOPING THE FOUNDATION FOR PROOFS INSTRUCTIONAL ACTIVITY Lesson 2 LEARNING GOAL Students will solve linear equations using concrete and semi-concrete models, algebraic procedures,

### Math 7 Notes Unit Two: Integers

Math 7 Notes Unit Two: Integers Syllabus Objective: 2.1 The student will solve problems using operations on positive and negative numbers, including rationals. Integers the set of whole numbers and their

### 6.2 Multiplying Polynomials

Locker LESSON 6. Multiplying Polynomials PAGE 7 BEGINS HERE Name Class Date 6. Multiplying Polynomials Essential Question: How do you multiply polynomials, and what type of epression is the result? Common

UNIT 6 Getting Ready Use some or all of these exercises for formative evaluation of students readiness for Unit 6 topics. Prerequisite Skills Finding the length of the sides of special right triangles

### SOLVING EQUATIONS AND DEVELOPING THE FOUNDATION FOR PROOFS

SOLVING EQUATIONS AND DEVELOPING THE FOUNDATION FOR PROOFS 6.EE.6 and 6.EE.7 CONTENTS The types of documents contained in the unit are listed below. Throughout the unit, the documents are arranged by lesson.

### Objective: Construct a paper clock by partitioning a circle and tell time to the hour. (10 minutes)

Lesson 10 1 Lesson 10 Objective: Construct a paper clock by partitioning a circle and tell time to the Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief

### Destination Math California Intervention

Destination Math California Intervention correlated to the California Intervention 4 7 s McDougal Littell Riverdeep STANDARDS MAPS for a Mathematics Intervention Program (Grades 4-7) The standards maps

### Polynomials. This booklet belongs to: Period

HW Mark: 10 9 8 7 6 RE-Submit Polynomials This booklet belongs to: Period LESSON # DATE QUESTIONS FROM NOTES Questions that I find difficult Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. REVIEW TEST Your teacher

### Agile Mind Mathematics 8 Scope and Sequence, Texas Essential Knowledge and Skills for Mathematics

Agile Mind Mathematics 8 Scope and Sequence, 2014-2015 Prior to Grade 8, students have written and interpreted expressions, solved equations and inequalities, explored quantitative relationships between

### Planned Course: Algebra IA Mifflin County School District Date of Board Approval: April 25, 2013

: Algebra IA Mifflin County School District Date of Board Approval: April 25, 2013 Glossary of Curriculum Summative Assessment: Seeks to make an overall judgment of progress made at the end of a defined

TEKSING TOWARD STAAR MATHEMATICS GRADE 6 Projections Masters Six Weeks 1 Lesson 1 STAAR Category 1 Grade 6 Mathematics TEKS 6.2A/6.2B Understanding Rational Numbers A group of items or numbers is called

### 2275 Speedway, Mail Code C9000 Austin, TX (512) Planet Fun

Lesson Plan for Grades: Middle School Length of Lesson: 70 min Authored by: UT Environmental Science Institute Date created: 12/03/2016 Subject area/course: Mathematics, Astronomy, and Space Materials:

### Elementary Algebra Study Guide Some Basic Facts This section will cover the following topics

Elementary Algebra Study Guide Some Basic Facts This section will cover the following topics Notation Order of Operations Notation Math is a language of its own. It has vocabulary and punctuation (notation)

### Eureka Lessons for 6th Grade Unit FIVE ~ Equations & Inequalities

Eureka Lessons for 6th Grade Unit FIVE ~ Equations & Inequalities These 2 lessons can easily be taught in 2 class periods. If you like these lessons, please consider using other Eureka lessons as well.

### Instructor Notes for Chapters 3 & 4

Algebra for Calculus Fall 0 Section 3. Complex Numbers Goal for students: Instructor Notes for Chapters 3 & 4 perform computations involving complex numbers You might want to review the quadratic formula

### First Semester. Second Semester

Algebra II Scope and Sequence 014-15 (edited May 014) HOLT Algebra Page -4 Unit Linear and Absolute Value Functions Abbreviated Name 5-8 Quadratics QUADS Algebra II - Unit Outline First Semester TEKS Readiness

### Standards of Learning Content Review Notes. Grade 7 Mathematics 2 nd Nine Weeks,

Standards of Learning Content Review Notes Grade 7 Mathematics 2 nd Nine Weeks, 2018-2019 Revised October 2018 1 2 Content Review: Standards of Learning in Detail Grade 7 Mathematics: Second Nine Weeks

### Understanding and Using Variables

Algebra is a powerful tool for understanding the world. You can represent ideas and relationships using symbols, tables and graphs. In this section you will learn about Understanding and Using Variables

### PAGE(S) WHERE TAUGHT (If submission is not a text, cite appropriate resource(s)) PROCESSES OF TEACHING AND LEARNING MATHEMATICS.

Utah Core Curriculum for Mathematics, Processes of Teaching and Learning Mathematics and Intermediate Algebra Standards (Grades 9-12) MATHEMATICS Problem Solving 1. Select and use appropriate methods for

### N-Q.2. Define appropriate quantities for the purpose of descriptive modeling.

Radnor High School Course Syllabus Revised 9/1/2011 Algebra 1 0416 Credits: 1.0 Grades: 9 Weighted: no Prerequisite: teacher recommendation Length: full year Format meets daily Overall Description of Course

### Mathematics Background

For a more robust teacher experience, please visit Teacher Place at mathdashboard.com/cmp3 Patterns of Change Through their work in Variables and Patterns, your students will learn that a variable is a

### In this lesson, students manipulate a paper cone

NATIONAL MATH + SCIENCE INITIATIVE Mathematics G F E D C Cone Exploration and Optimization I H J K L M LEVEL Algebra 2, Math 3, Pre-Calculus, or Math 4 in a unit on polynomials MODULE/CONNECTION TO AP*

### SCOPE & SEQUENCE. Algebra I

Year at a Glance August September October November December January February March April May 1. Functions, 4.Systems Expressions, 2. Polynomials and 6. Exponential STAAR SLA 3. Linear Functions of Break

### Prentice Hall Algebra 1, Oklahoma Edition 2011

Prentice Hall Algebra 1, Oklahoma Edition 2011 Algebra I C O R R E L A T E D T O, Algebra I (Updated August 2006) PROCESS STANDARDS High School The National Council of Teachers of Mathematics (NCTM) has

### Essential Question: What is a complex number, and how can you add, subtract, and multiply complex numbers? Explore Exploring Operations Involving

Locker LESSON 3. Complex Numbers Name Class Date 3. Complex Numbers Common Core Math Standards The student is expected to: N-CN. Use the relation i = 1 and the commutative, associative, and distributive

### Mifflin County School District Planned Instruction

Mifflin County School District Planned Instruction Title of Planned Instruction: Advanced Algebra II Subject Area: Mathematics Grade Level: Grades 9-12 Prerequisites: Algebra I with a grade of A or B Course

### and Transitional Comprehensive Curriculum. Algebra I Part 2 Unit 7: Polynomials and Factoring

Algebra I Part Unit 7: Polynomials and Factoring Time Frame: Approximately four weeks Unit Description This unit focuses on the arithmetic operations on polynomial expressions as well as on basic factoring

### BENCHMARKS GRADE LEVEL INDICATORS STRATEGIES/RESOURCES

GRADE OHIO ACADEMIC CONTENT STANDARDS MATHEMATICS CURRICULUM GUIDE Ninth Grade Number, Number Sense and Operations Standard Students demonstrate number sense, including an understanding of number systems

### Algebra II: Course Map--2013

Algebra II: Course Map--2013 Course Title: Algebra II Text: Algebra 2 (Holt, Rinehart and Winston) Duration: Two semesters Frequency: One class period daily Year: 2013/2014 Areas to be evaluated: Simplifying

### Algebra 1 Bassam Raychouni Grade 8 Math. Greenwood International School Course Description. Course Title: Head of Department:

Course Title: Head of Department: Bassam Raychouni (bassam@greenwood.sh.ae) Teacher(s) + e-mail: Femi Antony (femi.a@greenwood.sch.ae) Cycle/Division: High School Grade Level: 9 or 10 Credit Unit: 1 Duration:

Algebra 2, Quarter 2, Unit 2.1 Quadratics and Other Polynomials Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Know and apply the Fundamental Theorem of Algebra

### Unit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles

Unit 5 Linear equations and inequalities In this unit, you will build your understanding of the connection between linear functions and linear equations and inequalities that can be used to represent and

### Mathematics. Standards Plus. Grade COMMON CORE INTERVENTION SAMPLER

Mathematics Standards Plus COMMON CORE INTERVENTION Grade 7 SAMPLER Standards Plus COMMON CORE INTERVENTION Available for Grades 1-8 Language Arts and Math Standards Plus COMMON CORE INTERVENTION Mathematics

### FOR ALL STUDENTS TAKING ALGEBRA I SUMMER REVIEW PACKET

FOR ALL STUDENTS TAKING ALGEBRA I - SUMMER REVIEW PACKET Dear Student and Parent/Guardian, The math department at Central Dauphin School District wants ou to be successful in Algebra I. We also want ou

### Unit 4 Patterns and Algebra

Unit 4 Patterns and Algebra In this unit, students will solve equations with integer coefficients using a variety of methods, and apply their reasoning skills to find mistakes in solutions of these equations.

### Essential Questions Warren County Public Schools First Grade Common Core Math Planning and Pacing Guide (1 st Quarter)

Essential Questions Warren County Public Schools First Grade Common Core Math Planning and Pacing Guide (1 st Quarter) Unit Time Frame Objective Number Common Core Standard Essential Questions Key Terms

### SFUSD Mathematics Core Curriculum Development Project

1 SFUSD Mathematics Core Curriculum Development Project 2014 2015 Creating meaningful transformation in mathematics education Developing learners who are independent, assertive constructors of their own

### Unit 6 Quadratic Relations of the Form y = ax 2 + bx + c

Unit 6 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics

### New Mexico Curriculum Framework Correlated to Merit Software Mathematics Programs

New Mexico Curriculum Framework Correlated to Merit Software Mathematics Programs Middle School 5-8 Benchmark: Use mathematical models to represent and understand quantitative relationships Grade Performance

### Mifflin County School District Planned Instruction

Mifflin County School District Planned Instruction Title of Planned Instruction: Algebra II Subject Area: Mathematics Grade Level: Grades 9-12 Prerequisites: Algebra I with a grade of A, B, or C Course

### Grades ALGEBRA TILES. Don Balka and Laurie Boswell. Rowley, MA didax.com

Grades 6 12 ALGEBRA TILES Don Balka and Laurie Boswell Rowley, MA 01969 didax.com CONTENTS Introduction Correlation to the h Standards Unit 1: Introduction to Algebra Tiles 1 Overview and Answers 2 Activity

### CREATIVE CONSTRUCTIONS: STUDENT-MADE CHALLENGE BOOKLETS FOR MATH IN THE PRIMARY GRADES FACT FAMILIES

UNIT THREE CREATIVE CONSTRUCTIONS: STUDENT-MADE CHALLENGE BOOKLETS FOR MATH IN THE PRIMARY GRADES FACT FAMILIES 5 + 2 = 7 2 + 5 = 7 7 5 = 2 7 2 = 5 47 CREATIVE CONSTRUCTIONS UNIT THREE: FACT FAMILIES TEACHER

### CCGPS Frameworks Student Edition. Mathematics. CCGPS Analytic Geometry Unit 6: Modeling Geometry

CCGPS Frameworks Student Edition Mathematics CCGPS Analytic Geometry Unit 6: Modeling Geometry These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

### Rising Algebra Students. Stone Middle School

Algebra Summer Packet 017 Dear Future Algebra student, Rising Algebra Students Stone Middle School We hope that you enjoy your summer vacation to the fullest. We look forward to working with you next year.

### Representing Balance with Scales, Bars and Equations

LESSON 1.2 Representing Balance with Scales, Bars and Equations Suggested Pacing: 2 Days In this lesson students will learn that a balance scale or a bar model can represent an algebraic equation. They

### Algebra II. In this technological age, mathematics is more important than ever. When students

In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,

### Granite School District Parent Guides Utah Core State Standards for Mathematics Grades K-6

Granite School District Parent Guides Grades K-6 GSD Parents Guide for Kindergarten The addresses Standards for Mathematical Practice and Standards for Mathematical Content. The standards stress not only

### Atoms. Grade Level: 4 6. Teacher Guidelines pages 1 2 Instructional Pages pages 3 5 Activity Pages pages 6 7 Homework Page page 8 Answer Key page 9

Atoms Grade Level: 4 6 Teacher Guidelines pages 1 2 Instructional Pages pages 3 5 Activity Pages pages 6 7 Homework Page page 8 Answer Key page 9 Classroom Procedure: 1. Display the different items collected

### Total=75 min. Materials BLM cut into cards BLM

Unit 2: Day 4: All together now! Math Learning Goals: Minds On: 15 Identify functions as polynomial functions. Consolidate understanding of properties of functions that include: linear, Action: 50 quadratic,

### Gary School Community Corporation Mathematics Department Unit Document. Unit Name: Polynomial Operations (Add & Sub)

Gary School Community Corporation Mathematics Department Unit Document Unit Number: 1 Grade: Algebra 1 Unit Name: Polynomial Operations (Add & Sub) Duration of Unit: A1.RNE.7 Standards for Mathematical

### Number of (Nested) Shopping Carts Three nested shopping carts are shown.

Randy must fit shopping carts into an area that has a length of 82 feet and a width of one shopping cart. He made some measurements necessary for his computations. The table shows the length of a set of

### Unit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles

Unit 5 Linear equations and inequalities In this unit, you will build your understanding of the connection between linear functions and linear equations and inequalities that can be used to represent and

### Sample: Do Not Reproduce EE6 STUDENT PACKET. EXPRESSIONS AND EQUATIONS Student Packet 6: Solving Equations 2. Name Period Date

Name Period Date EXPRESSIONS AND EQUATIONS Student Packet 6: EE6.1 Cups and Counters 3 Use a visual model to solve multi-step algebraic equations. Solve equations that require working with variables that

### Algebra 1 Prince William County Schools Pacing Guide (Crosswalk)

Algebra 1 Prince William County Schools Pacing Guide 2017-2018 (Crosswalk) Teacher focus groups have assigned a given number of days to each unit based on their experiences and knowledge of the curriculum.

### Exponents. Reteach. Write each expression in exponential form (0.4)

9-1 Exponents You can write a number in exponential form to show repeated multiplication. A number written in exponential form has a base and an exponent. The exponent tells you how many times a number,

### A Five Day Exploration of Polynomials Using Algebra Tiles and the TI-83 Plus Graphing Calculator

Page 1. A Five Day Exploration of Polynomials Using Algebra Tiles and the TI-83 Plus Graphing Calculator Pre- Algebra Grade Seven By: Cory Savard Page. Overall Unit Objectives Upon completion of this unit,

### This lesson examines the average and

NATIONAL MATH + SCIENCE INITIATIVE Mathematics 5 4 1 5 4 1 1 4 5 1 4 5 LEVEL Algebra or Math in a unit on quadratic functions MODULE/CONNECTION TO AP* Rate of Change: Average and Instantaneous *Advanced

### Unit Name: Unit 2: Quadratic Functions and Modeling. Lesson Plan Number & Title: Lesson 5: I See Where You Are Coming From

Unit Name: Unit 2: Quadratic Functions and Modeling Lesson Plan Number & Title: Lesson : I See Where You Are Coming From Grade Level: High School Math II Lesson Overview: Given a linear, quadratic, or

### All rights reserved. Reproduction of these materials for instructional purposes in public school classrooms in Virginia is permitted.

Algebra I Copyright 2009 by the Virginia Department of Education P.O. Box 2120 Richmond, Virginia 23218-2120 http://www.doe.virginia.gov All rights reserved. Reproduction of these materials for instructional

### SUMMER MATH PACKET. Geometry A COURSE 227

SUMMER MATH PACKET Geometry A COURSE 7 MATH SUMMER PACKET INSTRUCTIONS Attached you will find a packet of exciting math problems for your enjoyment over the summer. The purpose of the summer packet is

### Activity 1 Multiply Binomials. Activity 2 Multiply Binomials. You can use algebra tiles to find the product of two binomials.

Algebra Lab Multiplying Polynomials You can use algebra tiles to find the product of two binomials. Virginia SOL A..b The student will perform operations on polynomials, including adding, subtracting,

### Multi-Step Equations and Inequalities

Multi-Step Equations and Inequalities Syllabus Objective (1.13): The student will combine like terms in an epression when simplifying variable epressions. Term: the parts of an epression that are either

### Algebra I, Adopted 2012 (One Credit).

111.39. Algebra I, Adopted 2012 (One Credit). (a) General requirements. Students shall be awarded one credit for successful completion of this course. This course is recommended for students in Grade 8