7th Grade Honors Unit 1 Foundations for Algebra

BY THE END OF THIS UNIT:

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

Enduring understanding (Big Idea): Students will understand that variables are used in place of numbers in equations, expressions or inequalities and that using variables in place of numbers allows the statement of relationships among the numbers that are unknown or unspecified. Students will make a transition from arithmetic to algebra as attention shifts from operations to the use of properties and that the facts of arithmetic and algebra follow from certain properties.

Essential Questions: How can you represent quantities, patterns, and relationships? How are properties related to algebra?

Students will know…Students will learn to write and evaluate expressions with unknown values and how properties are used to simplify expressions.

Vocabulary:Algebraic expression Equivalent expressionsBase IntegersCounterexample SetSimplify VariableDeductive reasoning EvaluateIrrational number Order of operationsReal numbers

Students will be able to… distinguish between variable and constant mathematical quantities that

occur in real world situations use real-world situation to introduce the concept of repeated multiplication

and provide motivation for learning exponential notation introduce the operation of square root as the inverse of the operation of

squaring use numerical expressions to illustrate properties of real numbers model a real-world situation by adding and subtracting negative real

numbers. derive the rules for multiplying real numbers by using inductive reasoning prepare students for using the area model to learn the distributive property utilize non-algebraic solution strategies for solving a linear equation recognize patters that exist in a table of values for a linear equation

Unit ResourcesLearning Task: Performance Tasks, Concept BytesPractice FormsPerformance Task: Lesson QuizzesUnit Project: Checks and BalancesUnit Review: Chapter Review for Part A, Chapter Test Part AChapter Review Part B, Chapter Test Part B

Mathematical Practices in Focus:1- Make sense of problems and persevere in solving them 2- Reason abstractly and quantitatively 3- Construct viable arguments and critique the reasoning of others4- Model with mathematics5- Use appropriate tools strategically 6- Attend to precision7- Look for and make use of structure8- Look for and express regularity in repeated reasoning

7th Grade Honors Unit 1 Foundations for Algebra

Unit Plans Chapter and Section Suggested Homework

Standard 7.EE.1;7.EE.2 1-1 Variables and Expressions

Problems 1-5 Exs. 9-37 odd, 38-42, 44-58

Standard 7.EE.4.a 1-2 Order of Operations and Evaluating Expressions

Part 1 Problems 1-2 Exs. 9-33Part 2 Problems 3-4 Exs. 6-24, 29-48

Standard 8.NS.1; 8.NS.2 1-3 Real Numbers and the Number Line

Problems 1-5 Exs. 9-17 odd, 18-34 even, 35-47 odd, 48,49-59 odd, 60-64 even, 66-79

Standard 7.NS.1.d 1-4 Properties of Real Numbers

Problems 1-4 Exs. 7-19 odd, 20-34 even, 35-45, 47-56

Standard 7.NS.1.a-c 1-5 Adding and Subtracting Real Numbers

Problems 1-4 Exs. 10-28 even, 29-39 odd, 41-53, 55-60, 61-76

Standard 7.NS.2 1-6 Multiplying and Dividing Real Numbers

Problems 1-4 Exs. 8-40 even, 41-50, 54-64, 66-74

Standard 7.EE.1; 7.EE.2 1-7 The Distributive Property

Part 1 Problems 1-3 Exs. 3-37, 39Part 2 Problems 4-5 Exs. 7-25 odd, 26-46 even, 47-57

Standard 7.NS.3; 8.NS.2 1-8 An Introduction to Equations

Problems 1-6 Exs. 8-32 even, 33-39 odd, 40-74

Standard 7.RP.2 1-9 Patterns, Equations, and Graphs

Problems 1-3 Exs. 8-20, 23-33, 36-55

CORE CONTENTSuccessive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for AlgebraCluster Title: Use properties of operations to generate equivalent expressions. Standard 7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Concepts and Skills to Master• Ability to understand linear expression terminology: sum, difference, term, product, factor, quotient, coefficient • Ability to factor by using division to express a linear expression by its factors; i.e., 2x – 6 = 2(x – 3) • Ability to expand by using multiplication to rewrite the factors in a linear expression as a product; i.e., 5(x+ 12) = 5x + 60 SUPPORTS FOR TEACHERSCritical Background Knowledge

Gathering data by conducting trials of an experiment or game: organizing data in tables and graphs I order to look for patterns and relationships

Identifying patterns in number and geometry Analyzing maximum and minimum values in measurement Organizing and displaying data in one and two dimensional graphs and tables Developing operation algorithms for fractions, decimals and percents

Academic VocabularyChange, Dependent and independent variables, variable, coordinate pair, distance/time/rate of speed, relationship, ruleSuggested Instructional Strategies

Introduce by discussing variables. Model how working with variables is the same as working with numbers.

Discuss distributive property and how to factor and expand with distributive property.

Resources Textbook Correlation

○ Algebra 1 Foundation Series – Ch1 Sections 1 & 7 MARS Tasks

o Short tasks Expressions and Equations o Answers to Short Tasks o A12 Fencing

MARs Assessment Lessons (MS) Solving Real-Life Problems: Baseball Jerseys (Problems-Solving Section) Steps to Solving Equations (Concept Development) Solving Linear Equations in One Variable (Concept Development) Texas Instrument Lesson Scavenger Hunt

Sample Formative Assessment TasksSuccessive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for AlgebraSkill-based task

Expand the expression 2(x-3). Then demonstrate your answer is correct by substituting a value in for the variable and showing the two expressions are equal in value.

Factor (3x-9). Then demonstrate your answer is correct by substituting a value in for the variable and showing the two expressions are equal in value.

Problem TaskI purchase six pieces of candy and I buy three of each type for a total of $3.75 and one of the candies is priced at $.50 how much is the other candy per piece?

Write an expression to demonstrate the problem.

CORE CONTENTStandard 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 Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebraby 1.05.”Concepts and Skills to Master

• Ability to utilize Properties of Operations in order to rewrite expressions in different forms•Ability to develop understanding of equivalent forms of numbers, their various uses and relationships, and how they apply to

a problem

SUPPORTS FOR TEACHERSCritical Background Knowledge

Identifying patterns in number and geometry Developing operation algorithms for fractions, decimals and percents

Academic VocabularyPercent of change, percent of errorSuggested Instructional Strategies

Introduce by comparing one object to another. Then change which object is compared to the other.

The concept of which is the whole or 100% is critical to understand

Resources Textbook Correlation

Algebra 1 Foundation SeriesChapter One Section 2

MARS Taskso Short tasks Expressions and Equations

Texas Instrument Lessono Scavenger Hunt

Sample Formative Assessment TasksSkill-based task

54 is what percent of 50? 50 is what percent of 54?

Problem TaskIf a pizza is purchased and then paid for with a sales tax of 5.5% and then tip is added of 20% and the total paid, including the tip is $12.66 how much did the pizza originally cost?

CORE CONTENTCluster Title: Analyze proportional relationships and use them to solve real-world and mathematical problems. Standard 7.RP.2: Recognize and represent proportional relationships between quantities. Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for AlgebraConcepts and Skills to Master• Ability to recognize in a given proportional situation that the two “between ratios” and the two “within ratios” are the same • Ability to distinguish between additive and multiplicative situations • Ability to recognize that two equal ratios represent a proportion • Ability to recognize and represent the connection between equivalent ratios, values in a table, and graphed orderedpairs• Ability to express unit rates using a variety of representations, given a contextual situation SUPPORTS FOR TEACHERSCritical Background Knowledge

Understand what a variable is and the importance of defining the variable in an expression or equation. Understand that a variable has some value and the same rules that apply to numbers also apply to variables Understand the concept of an independent and dependent variable Understand discrete versus continuous data. Plot points on a graph Construct graphs and tables

Academic VocabularyProportional relationships; constant; unit rate; equivalent ratiosSuggested Instructional Strategies

Introduce the lesson by allowing students to identify patterns through the use of tables.

Explore various ways to represent equations (describe what made it easier for you to connect the concepts of tables and graphs to actual equations.)

Resources Textbook Correlation

Algebra 1 Foundation Series – Ch 1 Section 9 MARS TASKS

o Short Task for Ratios and Proportionso Short Task Answers for Ratios and Proportionso E02 Counting Treeso A12 Fencingo A21: Sale!o A23:T-Shirt Saleo A01: 25% Sale

Sample Formative Assessment TasksSkill-based taskThe school needs to purchase TI-84 calculators. Each

Problem TaskOne cellular phone carrier charges $26.50 a month plus $0.15 a

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebracalculator is sells for $125.00. Part A. How many calculators can be purchased with $5000? calculatorsPart B. Explain how you determined the number of

calculators can be purchased. Use an equation, graph and table in addition to words, numbers, and/or symbols in your explanation.

minute for local calls. Another carrier charges $14.50 a month and $0.25 a minute for local calls.

Part A. For how many minutes is the cost of the plans the same?

minutes

Part B. Use a table, graph and equation to justify your answer.

CORE CONTENTCluster Title: Solve real-life mathematical problems using numerical and algebraic expressions and equations. Standard 7.EE.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebraand inequalities to solve problems by reasoning about the quantities. Standard 7.EE.4a. Solve word problems leading to 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. Concepts and Skills to Master

Ability to differentiate between algebraic solution and an arithmetic solution Ability to solve double sided equations Ability to create three representations to represent linear situations

SUPPORTS FOR TEACHERSCritical Background Knowledge

Understanding constant rate of change and how to determine slope in real world situations. Understanding the connection between different representations of linear situations. Ability to solve double sided equations with and without distribution. Ability to isolate the variable, when an unknown variable is specified in the formula. Ability to construct patterns in a table and graph linear patterns. Ability to use words to describe the change in dependent and independent variables.

Academic VocabularySlope, rise, run, y-intercept, horizontal change, vertical change, x-intercept, intersecting lines, scaleSuggested Instructional Strategies

Model multiple representations of the solutions. Prior to expecting students to respond to performance based tasks model problem solving using all three representations to determine solutions. Use the DVD Task as a preliminary task http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-comparing-linear-functions/274-comparing-linear-functions-faculty-debrief?

Resources Textbook Correlation:

Algebra 1 Foundation SeriesChapter One Section 2

MARS: Fencing

Sample Formative Assessment TasksSkill-based taskYour parents are willing to purchase movie passes and dinner for each friend that attends your birthday party. The movie tickets are

Problem TaskEnvironmental Connection: Did you know that every drop of water that runs down the drain ends up flowing

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebra$7.50 for all ages and the dinner will cost $14.50 for each guest. If both parents and the birthday person attends what is the maximum number of guests that are allowed to attend. Write an inequality or equation to represent the situation.

into the sewage system? Sending clean water down the drain fills up the sewer and allows dirty water and waste overflow into the streams and oceans. Polluted water can harm, and even kill, animals that drink it and live in the water. What can you do? www.futurefriendly.com Water Saving Tip - Turn off water when brushing your teeth. The average bathroom faucet runs at 2 gallons per minute. Turning it off when you brush your teeth is one of the easiest ways to save water. Use the number of members your household to write and equation and construct a linear representation of how much water could be saved in two weeks. Explain your linear representation and describe the variables used to support your explanation.

CORE CONTENTCluster Title: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.Standard 7.NS.1.a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebracharge because its two constituents are oppositely charged.Standard 7.NS.1.b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.Standard 7.NS.1.c Understand subtraction of rational numbers a adding the additive inverse, p – q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Standard 7.NS.1.d Apply properties of operations as strategies to add and subtract rational numbers.Concepts and Skills to Master

Ability to build on prior experience with positive and negative rational numbers Ability to identify additive inverses using rational numbers. Ability to apply knowledge of positive or negative values for fractions and decimals. Ability to develop and apply the following properties: Commutative Property of Addition, Associative Property of Addition,

Identify Property of Addition, and the Distributive Property.SUPPORTS FOR TEACHERSCritical Background Knowledge

Understand how to model addition and subtraction of integers using distance/direction on a number line and using chips. Understand that the Commutative Property holds for addition of rational numbers. Understand and use the relationship between addition and subtraction to simplify computation by changing subtraction problems to

addition and vice versa. Understand and use the relationship between addition and subtraction found in fact families. Develop algorithms for adding and subtracting integers. Recognize and solve problems involving addition and subtraction of integers. Use the Distributive Property to solve problems. Solve simple equations with missing facts by using fact families.

Academic VocabularyAdditive inverse, rational numbersSuggested Instructional Strategies

To introduce students to adding integers, discuss examples of saving and spending.

Resources Textbook Correlation:

o Algebra 1 Foundation Series

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebra Start the lesson by showing students the addition of two positive

numbers. Then show that addition of two negative numbers follow a similar pattern. Focus your presentation on integers with different signs. Use the number line to model.

To introduce students to subtracting integers, ask them to explain how they would subtract a greater number from a lesser number.

To introduce subtraction of integers, relate negative integers to borrowing money to buy something you do not have enough money for.

Chapter One Sections 3,4,5,6 and 8 MARS Task:

A11: Division E03: A Day Out E11: Taxi Cabs

Texas Instruments Lessons:Adding Integers – A Modeling ApproachAdding Integers ExplorationGetting NegativeInteger Subtraction – What’s the Difference?IntegersNumber Line Activity – Adding Integers

Other Resources:http://mathstar.lacoe.edu/lessonlinks/integers/integers_adding_main.html http://mathstar.lacoe.edu/lessonlinks/integers/integers_subtracting_main.htmlhttp://www.uen.org/Lessonplan/preview?LPid=23406

Sample Formative Assessment TasksSkill-based taskA research team aboard an underwater research vesseldescends 1,500 feet beneath the surface of the water. They then rise 525 feet and descend again 350 feet. Write anaddition expression to represent this situation. Then find the sum.

If the overnight temperature at the Arctic Circle was -14°F, but the temperature rose to 8°F during the day, what was the difference between these high and low temperatures?

Problem TaskExplain how you can tell without calculating the sum of a positive number and a negative number will be positive, negative, or zero.

CORE CONTENTCluster Title: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.Standard 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for AlgebraStandard 7.NS.2.a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.Standard 7.NS.2.b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then: -(p/q) = -p/q = p/-q Interpret quotients of rational numbers by describing real-world contexts.Standard 7.NS.2.c Apply properties of operations as strategies to multiply and divide rational numbers.Concepts and Skills to Master

Ability to identify and apply the following properties: Multiplicative Inverse, Commutative Property of Multiplication, Associative Property of Multiplication, Identity Property of Multiplication.

Ability to recognize that rules for multiplying signed numbers remain the same for all rational numbers. Ability to explore and justify the result of division by 0. Ability to apply and extend knowledge of addition and subtraction of integers (i.e., two color counters, arrows on a number line) to extend to

multiplication and division. Ability to use patterns and concrete models to devise a general rule for dividing integers. Ability to identify and apply the following properties: Distributive Property, Associative Property, Commutative Properties, and Identity

Properties.SUPPORTS FOR TEACHERSCritical Background Knowledge

Understand how to use a number line/motion model to develop the relationship between repeated addition and multiplication with integers.

Understand and use the relationship between multiplication and division found in fact families. Develop and use algorithms for multiplying and dividing integers. Examine number patters to confirm the algorithm for multiplication. Recognize and solve problems involving multiplication and division of integers.

Academic VocabularyAdditive Inverse, Algorithm, Commutative Property, Distributive Property, Integers, Negative Numbers, Order of Operation, Positive Numbers, Rational NumbersSuggested Instructional Strategies

Put the following problems on the board. Resources

Textbook Correlation:

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebra3 x -9 = -27-2 x 5 = -10-6 x 0 = 0-3 x -9 = 27-2 x -5 = 10-20 ÷ 5 = -4-9 ÷ -3 = 320 ÷ -5 = -49 ÷ 3 = 3

Ask the students if they can spot any patterns. Have students write their answers on the board.

Then, ask students if they can determine the rules for multiplying and dividing integers?

o Algebra 1 Foundation SeriesChapter One Sections 3,6 and 8

MARS Task: A11: Division E03: A Day Out E11: Taxi Cabs

Texas Instruments Lessons:Dividing FractionsDividing NotesDivision of IntegersIntegersMultiplication of Integers

Other Resources:On line game: http://www.math-play.com/multiplying-and-dividing-integers-game.htmlYou Tube Video: http://www.youtube.com/watch?v=GkbXbptFnnw

Sample Formative Assessment TasksSkill-based taskA sky diver’s elevation changes by -3600 feet in 4 minutes after the parachute opens. What is the average change in the sky diver’s elevation each minute?

Problem TaskA farmer has 120 bushels of beans for sale at a farmer’s market. He sells and average of 15 ¾ bushels each day. After 6 days, what is the change in the total number of bushels the farmer has for sale

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebra

The formula F = 9/5C + 32 changes a temperature reading from the Celsius scale C to the Fahrenheit scale F. What is the temperature measured in degrees Fahrenheit when the Celsius temperature is -25°C?

at the farmer’s market? How does the number of bushels the farmer has change each day? Should the change be a positive or a negative number? How do you know? What expression represents the total number of bushels sold in 6 days? Evaluate your expression to determine the change in the total number of bushels the farmer has for sale at the farmer’s market. Is your answer reasonable? Explain why or why not.

CORE CONTENTCluster Title: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.Standard 7.NS.2.d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for AlgebraConcepts and Skills to Master

Ability to recognize that a terminating decimal or repeating decimal is a rational number. Ability to recognize that when rational numbers in fractional form are converted to decimals, they either terminate or

repeat.SUPPORTS FOR TEACHERSCritical Background Knowledge

Understand the connection between decimals and fractions. Understands how to make connections between decimals and fractions represented in real world situations. Understand terminating and repeating decimals. Understand rational and irrational numbers. Ability to convert fractions to decimals. Ability to convert decimals to fractions. Ability to apply algorithms for dividing integers.

Academic VocabularyTerminating decimals, repeating decimals, irrational numbers, rational numbers, positive numbers, negative numbersSuggested Instructional Strategies

Before beginning this investigation, you may want to review: the difference between irrational and rational numbers; the difference between a terminating and a repeating decimal; how to change a fraction to a decimal and vice versa.

Resources Textbook Correlation:

Algebra 1 Foundation Series – Ch1 – Sec: 3, 6, & 8 MARS Task:

E11: Taxi Cabs; A12: Fencing Texas Instruments Lessons:

Repeating Decimals and FractionsFractions to Decimals Form

Sample Formative Assessment TasksSkill-based taskWrite 2

7 as a decimal.Which is greater? -18/25 or -0.72727272…

Problem TaskYou are tutoring a younger student. How would you explain rational numbers, irrational numbers, and how are they different?

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebra

CORE CONTENTCluster Title: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.Standard 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.Concepts and Skills to Master

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebra Ability to describe and identify complex fractions. Ability to apply knowledge of Order of Operations.

SUPPORTS FOR TEACHERSCritical Background Knowledge

Understand the order of operations to order computation in problems. Ability to use the Distributive Property to solve problems.

Academic VocabularyDistributive Property, Integers, Negative Numbers, Order of Operation, Positive Numbers, Rational NumbersSuggested Instructional Strategies

Review with students the order of operations. Place the acronym on the board: PEMDAS. Have students come up with their own words to remember the acronym. Have students share with the class.

Resources Textbook Correlation:

Algebra 1 Foundation Series – Ch 1 Section 8 Texas Instruments Lessons:

o Number Senseo Oops! Order of Operations and the TI graphing

calculatoro Order Some Opso What’s Your Address?

Sample Formative Assessment TasksSkill-based taskWhat is the simplified form of (6² + 4) – 15?

Problem TaskConsider the expression (1 + 5)² - (18 ÷ 3). Can you perform the operations in different orders and still get the correct answer? Explain your reasoning.

CORE CONTENTCluster Title: Know that there are numbers that are not rational, and approximate them by rational numbers.Standard 8NS.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.Concepts and Skills to MasterSuccessive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebra Know that real numbers that are not rational are irrational. Understand that finite decimal expansions of irrational numbers are approximations. Show that rational numbers have decimal expansions that repeat eventually. Convert a decimal expansion, which repeats eventually, into a rational number.

SUPPORTS FOR TEACHERSCritical Background Knowledge

Understand the subsets of the real number system (natural numbers, whole numbers, integers, rational numbers). Convert rational numbers to decimals using long division (terminating and repeating) (7.NS.2d).

Academic VocabularyDecimal expansion, repeating decimal, termination decimal, rational, irrational, square root, , пSuggested Instructional Strategies Resources Use the Pythagorean Theorem with Letn = 0.1non-perfect squares tointroduceSo, 100n = 16.irrational numbers (8.G.7).Subtract - 10n = -1. Use the powers of ten technique:90n = 15 (explain to the right)÷90÷90

n =

Textbook Correlationo Algebra 1 Foundation Series

Chapter One Section 3

MARS Formative AssessmentLesson(MS) : Concept Development: Repeating Decimals

Texas Instrument 8.NS.1 Lessons: http://education.ti.com/calculators/downloads/US/Activities/Search/Standards

Sample Formative Assessment TasksSkill-based taskConvert 0.35 to a fraction.

Group the following numbers based on what you know about the number system: 5.3, 1. , , 2, 𝜋, 4.010010001…

Problem TaskSuppose you have a fraction with a denominator of 7. What is the longest string of non-repeating digits that will occur in the decimal expansions of the number? (Hint: Use the long division algorithm to show that for a denominator of n, there are only n possible remainders, 0 to n-1.)

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebra

CORE CONTENTCluster Title: Know that there are numbers that are not rational, and approximate them by rational numbers.Standard 8.NS.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., п2). 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. Concepts and Skills to MasterSuccessive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebra Compare and order irrational numbers. Place irrational numbers on a number line. Use approximations of irrational numbers to estimate the value of expressions. SUPPORTS FOR TEACHERSCritical Background Knowledge• Compare and place rational numbers on a number line. • Approximate irrational numbers as fractions or decimals.Academic Vocabularyrational, irrational, decimal expansion, square root, √, п, truncating, rounding Suggested Instructional Strategies Resources

Construct the Wheel of Theodorus to create physical lengths of the square roots of the counting numbers. Transfer those lengths onto a number line.

Find increasingly accurate estimations for square roots of numbers by guess- and-check with a calculator.

Textbook Correlation Algebra 1 Foundation Series

Chapter One Section 2

Wheel of Theodorus Project:

Texas Instrument 8.NS.2 Lessons: http://education.ti.com/calculators/downloads/US/Activities/Search/Standards

Sample Formative Assessment TasksSkill-based TaskPlace the following numbers on a number line: 5.3, 1.7…,√10, 2, п/2

Find between which two integers lies? 42

Problem TaskExplain when each approximation of п (3.14, 3, 22/7) is useful in calculating the circumference of a circle. Compare the answers you would get with each approximation. (Extension: Research how different cultures have approximated pi.)

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.

7th Grade Honors Unit 1 Foundations for Algebra

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.