Roswell Independent School District Math Curriculum … Maps/2012-2013... · 2012-08-16 · 1 Roswell Independent School District Math Curriculum Map 2012 Subject: Math Grade Level:

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Roswell Independent School District Math Curriculum Map 2012

Subject: Math Grade Level: 7th Essential Question: What is a decimal? How would life be different without knowledge of fractions? How do negative numbers affect our lives? How can multiplication and division of integers be explained by addition and subtraction? Strand/Benchmark: Numbers and Operations (15 points possible NMSBA)

Quarter 1 Performance Strand Core Standards Activity/Assessment/Resources Math Practices/ Key Vocabulary

Target 1: Choose the appropriate operation and apply it to solve problems with: fractions, decimals, and integers (+,-, x, and ÷).

*Add, subtract, multiply, and divide fractions and mixed numbers

*Add, subtract, multiply, and divide integers

*Add, subtract, multiply, and divide decimals

*Model on a number line Vocabulary: Rational, Irrational, Place value, unit price, mixed numbers, improper fractions, reciprocal, factor, precision, integers, absolute value, opposites, additive inverses, product, equivalent, quotient, estimate

7.N.2.1 – (+ - x /) rational numbers (e.g. integers, fractions, terminating decimals) and take positive rational numbers to whole number powers. CC: (7.NS.1a,d, 7.NS.2a,c 7.NS.3) 7N.2.4 – Add and subtract fractions with unlike denominators. CC: (7.NS.2d, 7.NS.3)

7N.2.9 - Solve addition, subtraction, multiplication, and division problems that use positive and negative integers and combinations of these operations CC: (7.NS1b,c; 7.NS.2a,b,c; 7.NS.3, 7.EE.3)

7.NS.1a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom had 0 charge because its two constituents are oppositely charged. 7.NS.1b 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. 7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p-q = p+(-q). Show that the distance between the two rational numbers on the number line is the absolute value of their differences, and apply this principal in real-world contexts. 7.NS.1d Apply properties of operations as strategies To add and subtract rational numbers. 7.NS.2a 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) and rules for multiplying signed numbers. Interpret products of rational number by describing real-world contexts. 7.NS.2b 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 –(pl/q) = p/(-q). Interpret quotients of rational numbers by describing real-world contexts. 7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s eventually repeats. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and

Activities Operations with Decimals

Add and subtract decimals using personal checkbook register

Write and solve application problems involving money, unit price, and gas mileage

Operations with Fractions Use colored number cubes to represent

numerators and denominators to perform operations with fractions

Operations with Integers Use colored number cubes to represent

positive and negative integers to perform basic operations

Assessments Prentice Hall Course 2

Activity lab 4-16 Pg. 173 Using Spreadsheets

Resources: http://www.ezschool.com/Grade6-12MSheets.html http://www.math-play.com/7th-grade-math-games.html http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8 http://www.ezschool.com/Grade6-12MSheets.html Materials Checkbook register Number cubes or wooden blocks Expression keeper template

Check Register Activity: MP #2- Contextualize/Decontextualize MP #4- Real World MP #5- Appropriate tools MP #6- Precision Colored Number Cubes Activity: MP #2- Contextualize/Decontextualize MP #4- Modeling MP #6- Precision MP #8- look for repeated reasoning

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decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary on hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 ¾ in. long in the center of a door that is 21 ½ in. wide, you will need to place the bar about 9 in. from each edge; this estimate can be used as a check.

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Subject: Math Grade Level: 7th Essential Question: How does following order of operations affect an outcome? Why is it necessary to follow order of operations? Strand/Benchmark: Numbers and Operations (15 points possible NMSBA)

Quarter 1 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 2a: Evaluate and create problems using the Order of Operations (special attention to exponents and absolute value)

*Apply the order of operations to solve problems containing exponents and absolute values.

Target 2b: Solve problems with square roots (perfect squares and approximates)

*Solve problems with perfect square roots

*Solve square root problems using approximates Vocabulary: Equations, expression, exponent, square roots, evaluate

7N.1.1 – Determine the absolute value a rational number. CC: (7.NS.1a,b,c) 7N.1.5 – Simplify numerical expressions using Order of Operations. CC: (7.NS.1d, 7.NS.2c)

7N.2.6a – Interpret the absolute value as the distance of the number from zero on a number line. CC: (7.NS.1b,c)

7N.2.6b – Determine the absolute value of real numbers. CC: (7.NS.1b,c) 7N.2.7 – Find square roots of perfect whole-number squares.

7.NS.1a 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. 7.NS.1b 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. 7.NS.1c 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 principal in real-world contexts. 7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.

Activities Students will explore the need for order of operations, and learn how to use it through small group discussion and presentation by solving the same multi-step problem without any teacher direction as to process and NO discussion between groups until each group has achieved their own solution. Students should then present their process for solving and their finite solution. (Increase level of difficulty over the cycle by adding exponents and square roots) Assessment Small group presentation of accurate demonstration of order of operations Resources http://www.ezschool.com/Grade6-12MSheets.html http://www.gips.org/Technology/T.I.E./Alberts/Order%20of%20Operations%20Web%20Page/Order_of_Operations_Lesson.html Rubric http://www.gips.org/Technology/T.I.E./Alberts/Order%20of%20Operations%20Web%20Page/Game_Rubric.html http://www.math-play.com/7th-grade-math-games.html http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8

MP #1- Make sense and persevere MP #3- Construct viable arguments MP #5- Appropriate tools MP #6- Attend to precision

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Subject: Math Grade Level: 7th Essential Question: What problem situation would benefit from using number properties? Strand/Benchmark: Algebra (26 points possible NMSBA)

Quarter 1 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 3: Name, identify, and apply Number Properties (associative, commutative, distributive, etc…)

*Solve problems by applying the following properties: Associative, Commutative, Distributive, and Identity, inverse too. Vocabulary: Number Properties, associative, commutative, distributive, identity.

7N.1. 2 – Illustrate the relationships among natural (i.e., counting) numbers, whole numbers, integers, rational and irrational numbers. CC: (7.NS.2a,b, 7.NS.3, 7.NS.1d)

7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.2a 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) and rules for multiplying signed numbers. Interpret products of rational number by describing real-world contexts. 7.NS.2b 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 –(pl/q) = p/(-q). Interpret quotients of rational numbers by describing real-world contexts. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.

Activity 1 “Spoons” or “Books” style card game involving matching cards for each property (1 property name card and 1 property example card) Assessment Students create Foldable and/or a group poster to summarize the N umber Properties, including algebraic and numeric examples, pictures to aid memory, and/or pneumonic devices Prentice Hall Mathematics Course 2 textbook and materials http://www.math-play.com/7th-grade-math-games.html Materials Plastic spoons (or something to represent spoons) Paper to create cards One deck of cards per group (student created) http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8

Activity1 MP #1- Make sense and persevere MP #3- Construct viable arguments Assessment MP #2- Abstract to concrete MP #5- Use appropriate tools

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Subject: Math Grade Level: 7th Essential Question: How would your grades be different if we gave them in fractions instead of percents? Why do we have sales tax? If you owned a business, how would percent change affect quarterly profit? Strand/Benchmark: Numbers and Operations (15 points possible NMSB A)

Quarter 1 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 4: Create equivalencies and calculate decimal, fractional, and percentage parts of given quantities

* Recognize the relationship between equivalent fractions, decimals, and percents (1/4, .25, and 25%)

*Convert between fractions, decimals, and percents Vocabulary: Conversion, prime numbers, composite numbers, numerator, denominator, simplest form, formula, function, principal, commission, percent of change, proportion, unit rate, unit cost, mark up, discount, simple interest, gratuity (tip), tax.

7N.2.3 – Calculate given percentages of quantities and use them to solve problems (e.g., discounts of sales, interest earned, tips, markups, commission, profit, simple interest). CC: (7.NS.3, 7.RP.3)

7N.3.2 – Convert fractions to decimals and percents; and use these representations in estimations, computations, and applications. CC: (7.NS.2d, 7.NS.3, 7.RP.3)

7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s eventually repeats. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, mark ups & mark downs, gratuities & commissions, fees, percent increase and decrease, and percent error.

Activity 1 Using current newspaper ads and/or the internet, students calculate discounts/sales tax/etc and compile a table to compare better prices per unit between similar items, as well as, the total cost of their shopping list and/or expense. Assessment Completed comparison chart presented in a table. Activity 2 Use 10 x 10 grids or geo-board to explore the relationship of fractions with percents. Then calculate decimal equivalency. Assessment Teacher observation Additional Supportive Activity/Extension Prentice Hall Course 2 2-6a Activity Lab Pg. 95 Comparing Fractions & Decimals Suggestion: Teachers might want to have students add an additional column for %. Resources Prentice Hall Mathematics Course 2 textbook and materials http://www.math-play.com/7th-grade-math-games.html http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8 http://www.ezschool.com/Grade6-12MSheets.html

Activity 1 MP #1- Analyze and ask “Does this make sense?” MP #2- Contextualize/Decontextualize MP #4- Model with real world MP #5- Logical reasoning Activity 2 MP #2- Contextualize/Decontextualize MP #4- Model with manipulatives MP #5- Appropriate tools

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Subject: Math Grade Level: 7th Essential Question: How would your grades be different if we gave them in fractions instead of percents? Why do we have sales tax? If you owned a business, how would percent change affect quarterly profit? Strand/Benchmark: Numbers and Operations (15 points possible NMSB A)

Quarter 2 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 4: Create equivalencies and calculate decimal, fractional, and percentage parts of given quantities

*Calculate percent of whole numbers, percent increase, and percent decrease.

7N.2.3 – Calculate given percentages of quantities and use them to solve problems (e.g., discounts of sales, interest earned, tips, markups, commission, profit, simple interest). CC: (7.NS.3, 7.RP.3)

7N.3.2 – Convert fractions to decimals and percents; and use these representations in estimations, computations, and applications. CC: (7.EE.2, 7.NS.3, 7.RP.3)

7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 7.RP.3 Use proportional relationships to solve multistep ration and percent problems. Examples: simple interest, tax, mark ups & mark downs, gratuities & commissions, fees, percent increase and decrease, and percent error. 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Example: a+0.05a = 1.05a means that “increase by 5%” is the same as “multiplied by 1.05”.

Activity 3 Students create scenarios in which they calculate sales tax and discounts by examining shopping ads to compile a list (4 items) and find a grand total. Assessments: Completed sales receipt Resources Prentice Hall Mathematics Course 2 textbook and materials http://www.math-play.com/7th-grade-math-games.html http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8

Activity 3 MP #2- Contextualize/Decontextualize MP #4- Modeling MP #5- Appropriate tools MP #6- Attend to precision

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Subject: Math Grade Level: 7th Essential Question: What are equations and inequalities? What are the similarities and differences between equations and inequalities? What do equations and inequalities represent? Strand/Benchmark: Algebra (26 points possible NMSBA)

Quarter 2 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 5: Simplify and solve expressions, single and multi-step equations, and inequalities

*Write and simplify expressions

*Write and solve single and multi-step equations

*Distinguish between expressions and equations

* Simplify single and multi-step inequalities Vocabulary: Variable, expression, equation, inequalities, solution, compound inequality, addition, subtraction property of inequality, multiplication, & division property of equality.

7A.1.3 – Simplify numerical expressions by applying properties of rational numbers, and justify the process used. CC: (7.EE.1, 7.EE.3)

7A.2.1 – Evaluate algebraic expressions. Write verbal expressions and sentences as algebraic expressions and equations: CC: (7.EE.2, 7.EE.4a)

7A.2.2 – Use variables and appropriate operations to write an expression, an equation, or an inequality that represents a verbal description. CC: (7.EE.2,4a)

7A.2.4 – Simplify numerical expressions by applying properties of rational numbers, and justify the process used. CC: (7.EE.3)

7A.4.1 – Use variables and appropriate operations to write an expression, an equation, and/or an inequality that represents a verbal description involving change. CC: (7.EE.4a,b)

7A.4.4 – Solve two-step equations and inequalities with one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. CC: (7.EE.3, 7.EE.4a,b; 7.RP.3, 7.NS.3)

7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.2 Understand that rewriting and expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Example: a+0.05a = 1.05a means that “increase by 5%” is the same as “multiplied by 1.05”. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary on hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 ¾ in. long in the center of a door that is 21 ½ in. wide, you will need to place the bar about 9 in. from each edge; this estimate can be used as a check. 7.EE.4a Solve word problems leading two equations of the form px+q=r and p(x+q)=r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example: the perimeter of a rectangle is 54 cm, it’s length is 6 cm. What is its width? 7.EE.4b Solve word problems leading to inequalities of the form px+q>r or px+q < r where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For

Brain Teasers Activity Have the students read "Sideways Arithmetic from Wayside School." (The book is full of middle school brain teasers and word problems.) For example, students must solve cryptograms where numbers are replaced by letters in arithmetic equations and they must determine the numbers the letters represent. Either assign the students to go through the book and read the stories and complete the math teasers and assign the students to devise their very own seemingly impossible math teasers.

Assessment: completed activity Resources

http://www.ixl.com/math/grade-7 http://www.ezschool.com/Grade6-12MSheets.html

http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8

Hands on balance scale with two-step equations Word problems using equations Singapore Math+ Algebra Day 1 Presentation Problems Day 1 Answer Key Day 2 Presentation Problems

Activity MP #1- Analyze & persevere MP #2- Contextualize/Decontextualize MP #3- Break down complexity MP #4- Modeling MP #5- Appropriate tools MP #6- Precision (labeling model) MP #7- Make use of structure

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example: as a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, mark ups & mark downs, gratuities & commissions, fees, percent increase and decrease, and percent error.

Day 2 Answer Key Day 3 Presentation Problems Day 3 Answer Key Day 4 Presentation Problems Day 4 Answer Key Day 5 Presentation Problems Day 5 Answer Key Quiz Quiz Answer Key Prentice Hall Mathematics Course 2 textbook and materials http://www.math-play.com/7th-grade-math-games.html

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Subject: Math Grade Level: 7th Essential Question: How does the concept of slope depend on the properties of the coordinate plane? Strand/Benchmark: Geometry (20 points possible NMSBA)

Quarter 2 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 6: Graph and interpret linear equations (introduce slope-intercept form)

* Solve linear equations to calculate ordered pairs

*Recognize and apply the components of a linear equation (slope intercept)

*Graph a linear equation (3 or more points) Vocabulary: Patterns (arithmetic, geometric), x-coordinate, y-coordinate, coordinate plane, ordered pair, run, rise, slope, linear

7A.2.1b – Solve simple linear equations CC: (7.EE.4a, 7.RP.2c)

7A.2.1c – Write verbal expressions in order to graph and interpret results. CC: (7.EE.4a, 7.RP.2d)

7.A.2.5 Graph linear functions and identify slope as positive or negative. CC: (7.EE.1, 7.RP.2d)

7A.2.6 – Use letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. CC: (7.EE.2, 7.RP.2a,b)

7A.4.3D.3 – Graph and interpret linear functions as they are used to solve problems. CC: (7.EE.1)

7D.1.6 – Identify ordered pairs of data from a graph and interpret the data in terms of the situation depicted by the graph. CC: (7.RP.2a,b)

7.EE.1 Apply properties of operations as strategies to add, subtract, factor and expand linear expressions with rational coefficients. 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05” 7.EE.4b Solve word problems leading to inequalities of the form px+q>r or px+q < r where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: as a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. 7.RP.2a Decide whether two quantities are in a proportional relationship, e.g. testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7.RP.2c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t= pn. 7.RP.2d Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate.

Quadrant Construction

Activity Constructing the four quadrants on a desk presents a visual enhancement of coordinates and negative numbers. The center of the desk can be designated as point (0,0) and given objects can be described as being in various quadrants in relation to the point of origin. Plot points in coordinate space, graph the ordered pairs, and calculate and interpret the slope.

Assessment: completed activity Resources http://www.ixl.com/math/grade-7 http://www.ezschool.com/Grade6-12MSheets.html

http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8

Prentice Hall Mathematics Course 2 textbook and materials http://www.math-play.com/7th-grade-math-games.html http://www.ezschool.com/Grade6-12MSheets.html

Activity MP #2- Contextualize/Decontextualize MP #4- Modeling MP #5- Appropriate tools MP #6 Attend to precision (labeling)

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Subject: Math Grade Level: 7th Essential Question: How are transformations present in architecture, art, and fashion? Strand/Benchmark: Geometry (20 points possible NMSBA)

Quarter 2 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 7: Construct transformations (reflections, rotations, translations)

*Distinguish between reflections, rotations, and translations

*Solve problems by constructing reflections, rotations, and translations

*Recognize linear and rotational symmetry

Vocabulary: Line symmetry, reflection, rotation, equilateral, vertex, transformation, translation, image

7.G.2.1 Construct and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine the image under translations and reflections.

Not addressed in 7th grade CCSS- Concept picked up in 8th grade 8.G.1a & 8.G.2,3,4 & 8.EE.1,2.

Activity (Intro to Translations & Reflections) Prentice Hall Course 2 Pg. 518 Extension- Tessellations & Reflections

Assessment : completed activity Resources: http://www.ixl.com/math/grade-7 http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8

Prentice Hall Mathematics Course 2 textbook and materials http://www.math-play.com/7th-grade-math-games.html

Activity MP #2- Abstract idea of transformations to a concrete model.

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Subject: Math Grade Level: 7th Essential Question: How can objects be described and compared using geometric attributes? Strand/Benchmark: Geometry (20 points possible NMSBA)

Quarter 3 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 8: Identify properties of plane figures, and classify angles, triangles, and quadrilaterals by their angle measures and side lengths.

* Right, acute, obtuse

* Equilateral, scalene, and Isosceles

* Square, rectangle, rhombus, and parallelogram

Vocabulary: Point, acute angle, obtuse angle, rhombus, skew lines, isosceles triangle, segment, plane

7.G.4.2 Identify and describe the properties of two-dimensional figures: a. identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms b. use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle c. draw quadrilaterals and triangles from given information

CC: (7.G.2, 7.G.3, 7.G.5 )

7.G.2 Draw (free hand, with ruler and protractor, and technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.G.3 Describe the two-dimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. 7.G.5 Use facts about supplementary, complimentary, vertical, and adjacent angles in a multi-step problem to solve and write equations for an unknown angle in a figure.

Activity Students will create individual graphic organizer/ foldable for identifying properties of plane figures, classifying angles, triangles, and quadrilaterals by their angle measures and side lengths showing similarities and differences. Assessment Complete an accurate graphic organizer Resources Promethean Flipcharts

Area.flp angle_facts.flp Prentice Hall Mathematics Course 2 textbook and materials Promethean board www.dr-mikes-math-games-for-kids.com http://www.math-play.com/7th-grade-math-games.html http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8

Activity MP #2- Reason abstractly MP #4- Modeling MP #5- Appropriate tools MP #6- Attend to precision (labeling) MP #7- Structure

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Subject: Math Grade Level: 7th Essential Question: Why is it important to understand the difference between similar and congruent figures? Why would it be important to understand the concept of indirect measurement? Strand/Benchmark: Geometry (20 points possible NMSBA)

Quarter 3 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 9: Distinguish between congruence and similarity properties, write proportions for corresponding sides of a figure, and solve to discover missing side measure.

* Identify and determine congruent and/or similar figures

* Create proportions for corresponding sides of given figures

* Use proportions (indirect measurement) to solve for missing side measures

Vocabulary: ratio, proportions, congruence, similarity, corresponding angles, corresponding sides

7.G.1.1 Classify geometric figures as similar or congruent. CC: (7.RP.1)

7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, area and other quantities measured in like or different units. For example: if a person walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½ / ¼ mph, equivalently 2 mph.

Activity Students compile a list of objects/structures on school grounds that cannot be directly measured due to height or inaccessibility. Outdoors, students measure their height and their shadow. Immediately following students measure the shadows of the other objects and use similar triangles and proportions to calculate their approximate height. Assessment Teacher observation of project completion and accuracy of calculations Teacher created rubric Resources Zike, Dinah (Big Book of Math: For Middle School & High School) ISBN: 1-882796-19-5 http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8 Singapore Math + Ratios Day 1 Presentation Problems Day 1 Answer Key Day 2 Presentation Problems Day 2 Answer Key Day 3 Presentation Problems Day 3 Answer Key Day 4 Presentation Problems Day 4 Answer Key Quiz Quiz Answer Key Promethean board Student White boards

Activity MP #1- Make sense & persevere MP #2- Reason abstract to concrete MP #4- Real-world modeling MP #5- Use appropriate tools

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Prentice Hall Mathematics Course 2 textbook and materials Materials needed: Singapore math chart Tape measure per group http://www.math-play.com/7th-grade-math-games.html

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Subject: Math Grade Level: 7th Essential Question: How does knowing special angle relationships help us in geometry? Strand/Benchmark: Geometry (20 points possible NMSBA)

Quarter 3 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 10: Identify and determine angles and their relationships and solve for missing angle measures

* Identify angles based on angle measure (acute, right, and obtuse)

*Identify angle relationships (vertical, adjacent, complementary, and supplementary)

*Calculate missing angle measurements based on relationships for triangle sum theorem

Vocabulary: complementary, supplementary, vertical, adjacent, parallel, perpendicular

7M.2.1 – Apply strategies and formulas to find missing angle measurements in triangles and quadrilaterals. CC: (7.G.1,2,5)

7G.4.2a – Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms CC: (7.G.5)

7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 7.G.2 Draw (free hand, with ruler and protractor, and technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.G.5 Use facts about supplementary, complimentary, vertical, and adjacent angles in a multi-step problem to solve and write equations for an unknown angle in a figure.

Activities: Geometry Map Project Assign students the task of designing a map that includes several different kinds of lines, angles and triangles. The map can be of a town, their neighborhood or school, or even a made-up place. Instructors can feel free to be as specific or vague as to what the map includes, but is should contain parallel and perpendicular streets; one obtuse angle and one acute angle formed as the result of two streets intersecting; and buildings in the shape of equilateral triangle, a scalene triangle, and an isosceles triangle. Finally, the map must also include a compass rose. Then, students should include at least five directions from one to place to another on the map using the words parallel, perpendicular and intersect.

Assessment Completed map according to rubric Resources http://www.ixl.com/math/grade-7

http://www.abcteach.com/free/g/geometry_maps.pdf Prentice Hall Mathematics Course 2 textbook and materials http://www.math-play.com/7th-grade-math-games.html http://www.khanacademy.org/#arithmetic

Geometry Map Project MP #1- Make sense and persevere MP #4- Model MP #5- Appropriate modeling MP #6- Precision MP #7- Structure/Pattern

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Subject: Math Grade Level: 7th Essential Question: What is the relationship between linear measurements and area in regular and irregular figures? How is the circumference of a circle related to the diameter? Strand/Benchmark: Geometry (20 points possible NMSBA)

Quarter 3 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 11: Identify, apply, and calculate perimeter, area, and circumference of polygons and irregular figures

*Identify figures and choose corresponding formulas in order to calculate: perimeter, area, and circumference

* Transform and manipulate formulas for desired variables

Vocabulary: Linear measurement (perimeter, base, height), precision, circumference, polygon, quadrilateral, Pi, radius, diameter, area, perimeter, chord, central angle, arc, semicircle,

7G.1.2 – Understand the concept of a constant (e.g., pi) and use the formulas for the circumference and area of a circle. CC: (7.G.4)

7G.3.1 – Determine the radius, diameter, and circumference of a circle and explain their relationship. CC: (7.G.1,4)

7G.4.1 – Compute the perimeter and area of common geometric shapes and use the results to find measures of less common objects. CC: (7.G.4,6)

7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.6 Solve real-world and mathematical problems involving area, volume, and surface area of two and three dimensional objects composed of triangle, quadrilaterals, polygons, cubes and right prisms.

Activity

Create and solve for areas of regular and irregular polygons using geoboards to explore plane figure properties and dimensions. Additional Supportive Activity/Extension Prentice Hall Course 2 Geometry in the Coordinate Plane 10-16 Activity Lab Suggestion for extension- Find the slope of the diagonal(s).

Assessment

Teacher observations Resources

Sir Cumference series by Cindy Neuschwander Prentice Hall Mathematics Course 2 textbook and materials http://www.math-play.com/7th-grade-math-games.html http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8

http://www.ezschool.com/Grade6-12MSheets.html

Activity MP #4- Modeling MP #5- Appropriate tools MP #6- Structure

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Subject: Math Grade Level: 7th Essential Question: When is the Pythagorean Theorem applicable in a job situation? Strand/Benchmark: Geometry (20 points possible NMSBA)

Quarter 3 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 12: Apply the Pythagorean Theorem for given variables (review square roots and triangle characteristics)

* Illustrate proper use of perfect squares and square roots

*Recognize characteristics of triangles (ex. Acute-isosceles)

*Apply Pythagorean Theorem to solve for unknowns

Target: Solve problems with square roots (perfect squares and approximates)

*Solve problems with perfect square roots

*Solve square root problems using approximates

Vocabulary: hypotenuse, legs, right triangle, pythagorean

7N.1.3 – Explain and use the Pythagorean theorem CC: (7.NS.3)

7N.2.7 – Find square roots of perfect whole-number squares. CC: (7.EE.3)

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Important Notes: 1.) Pythagorean theorem is not addressed in 7th grade common core standards, it is specifically introduced and applied in 8th grade common core standards (8.G.6, 8.G.7, 8.G.8).

2.) Exponents and square roots are introduced in the 5th and 6th grade common core standards, however the concepts are not explicitly listed in 7th grade standards but need to be reinforced in order for students to be prepared for 8th grade learning targets.

Activity: Students construct a basic proof of the Pythagorean Theorem by building a right triangle with angles and constructing perfect squares on each side with square units Assessment Teacher observation of completed and accurate constructions using angles and/or Promethean Board. Resources What’s Your Angle, Pythagoras by Julie Ellis angles (plastic manipulative) Promethean Board Prentice Hall Mathematics Course 2 textbook and materials http://www.math-play.com/7th-grade-math-games.html http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8

Activity MP #1- Persevere MP #2- Abstract to Concrete MP #3- Viable Arguments MP #4- Modeling MP #7- Structure

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Subject: Math Grade Level: 7th Essential Question: How is the probability of an event determined and described? Strand/Benchmark: Data Analysis and Probability (22 points possible NMSBA)

Quarter 3 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 13: Use ratios and proportions to solve probability problems

*Create ratios to solve simple probability problems (experimental and theoretical)

*Use ratios to create proportions to solve for unknowns Vocabulary: probability, odds, experimental, theoretical, replacement

7D.4.5 – Use probability to generate convincing arguments, draw conclusions, and make decisions in a variety of situations. CC: (7.RP.2a,b,c,d; 7.SP.4,5,6,7a,7b,7c; 7.SP.8a,b,c)

7.RP.2a Decide whether two quantities are in proportional relationship, eg. By testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin (0,0). 7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7.RP.2c Represent proportional relationships by equations for example: if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total and the number of items can be expressed as t=pn. 7.RP.2d Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate. 7.SP.4 Use measures of center and measures of variability for a numerical date from random samples to draw informal comparative inferences about two populations, for example: decided whether the words in a chapter of a 7th grade science book are generally longer than the words in a chapter of a 4th grade science book. 7.SP.5 Understand that probability of a chance event is a number between 0 and 1 that expressed the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicated an unlikely event, the probability around ½ indicates an event that is neither likely nor unlikely, and the probability near 1 indicated a likely event. 7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing it’s long run relative frequency, and predict the approximate relative frequency given the probability. For example: when rolling a number cube 600 times predict that a 3 or 6 would be rolled likely 200 times, but probably not exactly 200 times. 7.SP.7a Develop a uniform probability model by assigning rqual probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

Real-World Probability Activity Give the students the following probability problem to solve and illustrate. In the real-world scenario, there are 350 parking spaces in the parking lot of the school. On a normal Tuesday, 150 people drive and park in random parking spots. The students must determine the number of different ways the cars can be parked in the lot. Determine the probability of two or more specific cars parking side by side on any day, for two and three consecutive days, and for no consecutive days. Illustrate the four probability days.

Assessment: completed activity Resources RISD Media Library- Baseball math statistics & data analysis (PF-5795) & Activity card 2009. Prentice Hall Course 2 12-2a activity lab pg. 585 Exploring Probability 12-4a activity lab pg. 597 Multiple Events Vocabulary Builder pg. 603 http://www.ixl.com/math/grade-7

http://www.math-play.com/7th-grade-math-games.html http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8

Activity MP #1- Make sense and persevere MP #2- Abstract to concrete MP #3- Complex into plausible arguments MP #5- Appropriate tools MP #7- Structure/Patterning

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7.SP.7b Develop a probability model (which may not be uniform by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? 7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. 7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. 7.SP.8c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

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Subject: Grade Level: 7th Essential Question: How does the type of data influence the choice of graph? Strand/Benchmark: Data Analysis and Probability (22 points possible NMSBA)

Quarter 3 Performance Strand Core Standard Activity/Assessment/Resources Math Practices Target 14: Evaluate problems with central tendencies (mean, median, mode, range, and outliers… etc)

*Analyze data and calculate central tendencies

*Recognize, explain, and model the effects of outliers

*Analyze data and create: stem and leaf, box and whisker, etc.

*Analyze charts and graphs for inconsistencies or inaccuracies

Vocabulary: trend, mean, median, mode, range, outliers

7D.1.3 – Use measures of central tendency and spread to describe a set of data. CC: (7.SP.1,2)

7D.1.4 – Choose between median and mode to describe a set of data and justify the choice for a particular situation.

7D.2.1 – Choose and justify appropriate measures of central tendencies (e.g., mean, median, mode, range) to describe given or derived data. CC: (7.SP.3,4)

7.D.2.2 – Know various ways to display data sets (e.g., stem and leaf plot, box and whisker plot, scatter plots) and use these forms to display a single set of data or to compare two sets of data. CC: (7.SP.8a,b,c)

7D.2.3 – Use the analysis of data to make convincing arguments. CC: (7.SP.3,6)

7D.3.2 – Analyze data to make accurate inferences, predictions, and to develop convincing arguments from data displayed in a variety of forms.

7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variability measuring the difference between the centers by expressing it as a multiple measure of variability. For example: the mean height of players on a basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot (line) plot, the separation between the two distribution of heights is noticeable. 7.SP.4 Use measures of center and measures of variability for a numerical date from random samples to draw informal comparative inferences about two populations, for example: decided whether the words in a chapter of a 7th grade science book are generally longer than the words in a chapter of a 4th grade science book. 7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing it’s long run relative frequency, and predict the approximate relative frequency given the probability. For example: when rolling a number cube 600 times predict that a 3 or 6 would be rolled likely 200 times, but probably not exactly 200 times. 7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample

Cafeteria Survey

Ask students to come up with five different questions to ask 50 people in the school about what foods they'd like to see in the cafeteria. The questions should ideally suggest five different food suggestions, but the creative angle is up to the students. The students then will decide the best way to graph and chart the results of their survey.

Assessment: completed activity Resources http://www.ixl.com/math/grade-7

Prentice Hall Mathematics Course 2 textbook and materials http://www.math-play.com/7th-grade-math-games.html http://www.khanacademy.org/#arithmetic http://www.illustrativemathematics.org/standards/k8

Cafeteria Survey MP #4- Modeling MP #5- Appropriate tools MP #6- Precision (labeling)

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space for which the compound event occurs. 7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. 7.SP.8c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

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Subject: Math Grade Level: 7th in preparation for the 1st quarter of 8th grade Cluster Task: Justify the approximation of an irrational number by estimating the value on a number line between two rational numbers.

Know Number Properties (Commutative, Associative, Distributive, Identity, Rational, Irrational, Prime, Composite, Perfect Square) Compare and order irrational and rational numbers

Strand/Benchmark: Numbers and Operations Quarter 4 Performance Strand Core Standard Activity/Assessment/ Resources Math Practices

Target: 1 Select the appropriate number property and apply the property to simplify operations. Academic Vocabulary Fraction Integer Evaluate Simplify Inverse Operations Opposites Additive Inverses Reciprocal Denominator Numerator Least Common Denominator (LCD) Factor Least Common Multiple Greatest Common Factor Composite Number Prime Numbers Prime Factorization Rational Number Rational Numbers Irrational Numbers Distributive Properties Associative Properties Commutative Properties Identity Properties

8. N.1.1 Sort numbers by their properties (e.g., prime, composite, square, square root). 8. N.2.1 Use real number properties (e.g., commutative, associative, distributive) to perform various computational procedures. 8.N.2.2 Perform arithmetic operations and their inverses (e.g., addition/subtraction, multiplication/division, square roots of perfect squares, cube roots of perfect cubes) on real numbers. 8. N.3.4 Use real number properties to perform various computational procedures and explain how they were used.

8.N.S 1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Activity: 1. Students will use index cards to define and give examples of the number properties. 2. After the number property index cards have been created, the students will be given an expression. The students will show each step taken to solve the expression on a separate index card. 3. After the expression has been completely simplified, the students will justify each step taken by matching it with a number property card.

The students will do this until all steps have been justified. Assessment: Students are given a different expression. Steps taken to simplify the expression must be matched with a number property card. The results will be used as a class poster. Resources: Prentice Hall Mathematics Course 3 textbook and materials www.YourTeacher.com www.khanacademy.org www.kutasoftware.com/ www.aaastudy.com www.illuminations.nctm.org www.thinkfinity.org www.nlvm.usu.edu/ http://www.discoveryeducation.com/teachers/free-lesson-plans/discovering-math-computations.cfm (more on next page)

MP. 1 Make Conjectures MP. 3 Justify Conclusions MP. 5 Pencil and Paper MP. 6 Precision MP. 7 Make use of Structure

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Interactive Integers http://nlvm.usu.edu/en/nav/frames_asid_162_g_3_t_1.html Factor Tree http://nlvm.usu.edu/en/nav/frames_asid_202_g_3_t_1.html Materials Class set of non-scientific calculators Class set of scientific calculators http://www.bbc.co.uk/education/mathsfile/shockwave/games/laddergame.html

Interactive Circle Game with Integer http://nlvm.usu.edu/en/nav/frames_asid_122_g_3_t_1.html?open=instructions&from=category_g_3_t_1.html

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Subject: Math Grade Level: 7th in preparation for the 1st quarter of 8th grade Cluster Task: Create two equivalent expressions containing integer (positive or negative) exponents and roots. Identify the simplified solution as rational or irrational.

Know how to write numeric expressions Compare rational and irrational numbers Apply scientific notation to real-world situations

Strand/Benchmark: Numbers and Operations Quarter 4 Performance Strand Core Standard Activity/Assessment/Resources Math Practices

Target: 2 Evaluate square roots, cube roots, and exponents and apply their properties to generate equivalent numerical expressions. Academic Vocabulary Exponents Power Base Square Root Perfect Square Scientific Notation Standard Notation

8.N.2.2 Perform arithmetic operations and their inverses (e.g., addition/subtraction, multiplication/division, square roots of perfect squares, cube roots of perfect cubes) on real numbers. 8. N.2.3 Find roots of real numbers using calculators.

8.EE 1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. 2. Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. 3. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger. 4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Activity: Using Math Tiles, plastic or made from paper, write math symbols +, -, x, ÷, x², √, ( ) on 15 tiles and place in bag to mix. In a separate bag, using math tiles, write whole numbers on at least 20 tiles. Students are to choose 5 whole numbers and 5 symbols from each bag. Students will use tiles to make an expression. After checking the expression for an answer, students create an equivalent expression and check its answer. Assessment: Clicker response quiz on matching multiple expressions to their equivalent. (Teacher made) Activity: Planetary size activity. Compare size and distance of planets using standard and scientific notation. Materials: Pencil, paper, table of planet dimensions, and calculator Resources: www.YourTeacher.com www.khanacademy.org www.kutasoftware.com/ www.aaastudy.com www.illuminations.nctm.org www.thinkfinity.org Equivalent Expressions

MP. 1 Make sense of problems MP. 2 Decontextualize and Contextualize MP. 3 Justify MP. 4 Hands on using tiles and able to manipulate expressions MP. 5 Detect Errors MP. 6 Use clear definitions in their own reasoning. MP. 7 Discern a structure MP. 8 Evaluate their reasonableness MP. 2 Contextualize MP. 4 Quantify approximations MP. 5 Appropriate tools (spreadsheets, calculator) MP. 6 Precision (units) MP. 7 Structure (standard vs. scientific notation)

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http://www.graniteschools.org/depart/teachinglearning/curriculuminstruction/math/elementarymathematics/K6%20Support%20Documents/6th%20Grade%20Support/Equivalent%20Expressions.pdf

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Subject: Math Grade Level: 7th in preparation for the 1st quarter of 8th grade Cluster Task: Formulate, simplify, and evaluate algebraic expressions to represent real world situations using appropriate terminology.

Know how to form algebraic expressions Substitute a numerical value for a variable to evaluate an expression

Strand/Benchmark: Numbers and Operations Quarter 4 Performance Strand Core Standard Activity/Assessment/Resources Math Practices

Target: 3 Formulate and simplify algebraic expressions.

Academic Vocabulary Like Terms Algebraic Expressions Variable Equation Inverse Operations Sum Difference Quotient Product Quantity Coefficient Constant

8. N.3.1 Formulate algebraic expressions that include real numbers to describe and solve real-world problems. 8. A.2.1 Demonstrate the difference between an equation and an expression.

* 6.EE. 2. Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. *7.EE. 2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

Activity: Students will provide a situation from their own life that can be represented by an algebraic expression. The students will exchange situations. They have to write an algebraic expression to represent the situation. Finally, using Algebra tiles (tiles that represent variables and constants), the students will have to provide a visual representation of the expression. Example: “A student buys multiple drinks a day at $2 a drink. An expression that would represent this would be 2d, where d is the number of drinks bought that day.” Assessment: Short (5 questions) cycle assessment to be taken at the end of the PDSA cycle. Resources: Prentice Hall Mathematics Course 3 textbook and materials www.YourTeacher.com www.khanacademy.org www.kutasoftware.com/ www.aaastudy.com www.illuminations.nctm.org www.thinkfinity.org Math Games for 7th & 8th Graders | eHow.com http://www.ehow.com/list_5955882_math-games-7th-8th-graders.html#ixzz1RWyeGXLx

MP. 1 Make sense of the problem MP. 2 Decontextualize and contextualize MP. 3 Critique the work of others MP. 4 Apply to real world situations MP. 6 Attend to Precision MP. 7 Make use of structure

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Roswell Independent School District Curriculum Map 2012

Grade Level: 7th in preparation for the 1st quarter of 8th grade Cluster Task: Create and solve linear equations in one variable with one solution, infinitely many solutions, and no solution. One equation must contain distributive property.

Solve multi-step equations and inequalities that include distributive property and/or variables on both sides

Strand/Benchmark: Algebra Quarter 1 Performance Strand Common Core Standard Activity/Assessment/Resources Math Practices

Target: 4 Solve multi-step linear equations and inequalities in one variable. Academic Vocabulary No solution One solution Infinitely Many Solutions

8. A.2.2 Solve two-step linear equations and inequalities in one variable with rational solutions. 8.A.2.7 Use symbols, variables, expressions, inequalities, equations, and simple systems of equations to represent problem situations that involve variables or unknown quantities.

8.E.E 7. Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Activity: Paper Toss Equations Students will pair up in teams (2 or 3). Each team will write an equation on separate scraps of paper. A trash can is placed in the center of the room. Students work the equation correctly. Then, wad up each equation with each member of the team attempting to make it in the basket. Students gather around at different distances and attempt to make it in the trash can. Other teams or teacher determine the difficulty of the question (distance from the basket). Easier equations farther away, more difficult ones closer. Team must attempt all three levels of difficulty before done. 1. Simple multi-step 2. Variables on both sides of equal sign 3. Inequalities Assessment: Use the equations the students created during the activity. Make certain to use the ones that were made in basket on the assessment. Have additional equations ready if nothing was made. Resources: Prentice Hall Mathematics Course 3 textbook and materials www.YourTeacher.com Interactive Equations http://nlvm.usu.edu/en/nav/frames_asid_201_g_3_t_2.html http://nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2.html Algebra Tiles http://nlvm.usu.edu/en/nav/frames_asid_189_g_3_t_2.html Game For Factors, Primes, Multiples, Powers http://www.bbc.co.uk/education/mathsfile/shockwave/games/gridgame.html

MP. 1 Make sense and persevere MP. 6 Calculate accurately and efficiently