Extended Algebra Curriculum Guide

Transcription

1 Unit 1: Numeracy and Expressions (Approximate number of days - Extended: 11 days Algebra: 11 days) (FYI, last day of 1 st quarter is Day 42, October 30) Connections to Previous Learning: Students use the properties of arithmetic learned in middle school to build and transform algebraic expressions of continued complexity. Exponent rules and square roots and cube roots where taught in 8 th grade. Focus within the Grade Level: Students understand that complex expressions are built of the basic operations; sums of terms and products of factors. Students will give precise attention to units when applying these skills to real world situations. Connections to Subsequent Learning: Students apply the properties of operations to algebraic expressions and extend these properties to functions such as square root, exponential, and trigonometric. Unit 1 Clover Park School District 6/01/15 Page 1

2 Common Core Standards in this unit: Reason quantitatively and use units to solve problems. N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Interpret the structure of expressions. SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. SSE. 3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. c. Use the properties of exponents to transform expressions for exponential functions. (will build on in Unit 4) Perform arithmetic operations on polynomials APR.1 Understand that polynomials form a system analogous to the integers, namely they are closed under the operation of addition, subtraction, and multiplication; Add, subtract, multiply polynomials. (multiply polynomials will build on in Unit 3) Mathematical Practices Estimated Days on the Unit days 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make sure of structure. 8. Look for and express regularity in repeated reasoning. Unit 1 Clover Park School District 6/01/15 Page 2

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6 Students will be able to independently use their learning to Stage 1 Desired Results Transfer Goals Apply concepts and procedures involving expressions to solve to real world examples. Reason quantitatively and use units to solve problems. Interpret the structure of expressions. Meaning Goals UNDERSTANDINGS Students will understand that Every number has a decimal expansion. The value of any real number can be represented in relation to other real numbers such as with decimals converted to fractions, scientific notation and numbers written with exponents (8 = 2 3 ). Properties of operations with whole and rational numbers also apply to all real numbers. ESSENTIAL QUESTIONS When is it advantageous to represent relationships between quantities symbolically? numerically? graphically? Why are procedures and properties necessary when manipulating numeric or algebraic expressions? How can the structure of expression help determine equivalent expressions? Acquisition Goals Students will know Decimals that terminate actually repeat the digit zero. (2.5 = ) Numbers that repeat in their decimal form are called rational. Numbers that do not repeat in their decimal form are called irrational. Exponent operation properties. Students will be skilled at Identify the different parts of the expression and explain their meaning within context. (i.e. terms, factors, coefficients, constants, exponents). Define, explain and describe the components of a complicated expression using decomposition. Unit 1 Clover Park School District 6/01/15 Page 6

7 Stage 1 Established Goals: Common Core State Standards for Mathematics Students will be able to independently use their learning to Reason quantitatively and use units to solve problems. N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Explanations, Examples, and Comments N.Q.1 Include word problems where quantities are given in different units, which must be converted to make sense of the problem. For example, a problem might have an object moving 12 feet per second and another at 5 miles per hour. To compare speeds, students convert 12 feet per second to miles per hour: Graphical representations and data displays include, but are not limited to: line graphs, circle graphs, histograms, multi line graphs, scatterplots, and multi bar graphs. Stage 3 MATERIALS BY STANDARD(S): Teacher should use assessment data to determine which of the materials below best meet student instructional needs. All materials listed may not be needed. These standards are looked at throughout the unit and in additional units. N.Q.2 What type of measurements would one use to determine their income and expenses for one month? How could one express the number of accidents in Arizona? N.Q.3 The margin of error and tolerance limit varies according to the measure, tool used, and context. Unit 1 Clover Park School District 6/01/15 Page 7

8 Stage 1 Established Goals: Common Core State Standards for Mathematics Students will be able to independently use their learning to Part A Interpret the structure of expressions. SSE.1 Interpret expressions that represent a quantity in terms of its context. d. Interpret parts of an expression, such as terms, factors, and coefficients. e. Interpret complicated expressions by viewing one or more of their parts as a single entity. SSE. 3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. f. Use the properties of exponents to transform expressions for exponential functions. Perform arithmetic operations on polynomials APR.1 Understand that polynomials form a system analogous to the integers, namely they are closed under the operation of addition, subtraction, and multiplication; Add, subtract, multiply polynomials. Explanations, Examples, Comments, and Pre-requisite Material Explanation: - Interpret the structure of expressions. Limit to linear expression and to exponential expressions with integer exponents. - Students should understand the vocabulary for the parts that make up the whole expression and be able to identify those parts and interpret their meaning in terms of a context. - Variables, Expressions, Exponents are review from 8 th grade curriculum. Vocabulary CARDS - Real Numbers - Rational and Irrational Numbers - Integers, Whole, Natural - Expansion - Value - Approximation - Estimate - Number line - Square Root - Numerical Expression - Algebraic Expression - Variable - Constant Extended Algebra Stage 3 MATERIALS BY STANDARD(S): Book Resources Holt Algebra 1: 1-1Variables and Expressions Holt Course 3: 1-3 Integers and Absolute Value Holt Course 3: 1-4 Adding Integers Holt Course 3: 1-5 Subtracting Integers Holt Course 3: 2-1 Rational Numbers Holt Course 3: 2-2 Comparing and Ordering Rational Numbers Holt Course 3: 2-3 Adding and Subtracting Rational Numbers Holt Course 3: 2-3 Multiplying Rational Numbers Algebra Stage 3 MATERIALS BY STANDARD(S): Teacher should use assessment data to determine which of the materials below best meet student instructional needs. All materials listed may not be needed. Book Resources Holt Algebra 1: 1-7 Simplifying Expressions Holt Algebra 1: 7-1 Integer Exponents Holt Algebra 1: 7-3 Multiplication Properties of Exponents Holt Algebra 1: 7-4 Division properties of Exponents Holt Algebra 1: 7-5 Polynomials Holt Algebra 1: 7-6 Add/Subtract Polynomials (Combining Like Terms ) Holt Algebra 1: 7-7 Multiplying Polynomials Holt Algebra 1: 7-8 Special Products of Unit 1 Clover Park School District 6/01/15 Page 8

9 - Evaluate - Term - Like-Terms - Coefficient - Perfect Square Trinomials Pre-requisite skills: (Extended) Vocabulary Cards - Place value - Adding integers - Subtracting integers - Multiplying integers - Dividing integers - Rounding - Order of operation - Combine like terms - Distributive property Fraction review (Extended) - Fraction awareness - Equivalent fractions - Multiply fractions - Divide fractions - Add and subtract fractions SSE.2 Examples: 1. Holt Course 3: 2-4 Dividing Rational Numbers Holt Course 3: 1-6 Multiplying and Dividing Integers Holt Course 3: 4-7 The Real Numbers Holt Algebra 1: 1-2 Adding and Subtracting Real Numbers Holt Algebra 1: 1-3 Multiplying and Dividing Real Numbers Holt Course 2: 1-2 Exponents Holt Course 3: 4-1 Exponents Holt Course 3: 4-3 Properties of Exponents Holt Algebra 1: 1-4 Powers and Exponents Holt Course 3: 4-5 Squares and Square Roots Holt Course 3: 4-6 Estimating Square Roots Holt Algebra 1: 1-5 Square Roots and Real Numbers Holt Course 2: 1-5 Order of Operations Holt Algebra 1: 1-6 Order of Operations Holt Course 2: 1-7 Variables and Algebraic Expressions Holt Course 2:1-8 Translate Words into Math Holt Course 2:1-9 Simplifying Algebraic Expressions Binomials Holt Algebra 1: 11-6 Radical Expressions Holt Algebra 2: 1-4 Simplifying Algebraic Expessions Holt Algebra 2: 1-5 Properties of Exponents Additional Resources Rational and Irrational: Lesson, PowerPoint may need to change ( + )( + ) Evaluate Rational and Irrational: Lesson, PowerPoint may need to change ( + )( + ) Fractional Exponents Lesson Exploring Rational Exponents Checkerboard Borders: Develop Understanding Task page 4 (multiply polynomials) Building More Checkerboard Borders: Develop Understanding Task page 9 (multiply polynomials) Algebraic Expression Card Match Exploring Exponents TI Activity - Student papers - Teacher papers Exponent Rules TI Activity - Student papers Teacher papers Algebraic Expressions with Some Unit 1 Clover Park School District 6/01/15 Page 9

10 APR.1 Examples: 1. Additional Resources Once Upon a Time (Noyce Foundation) Place Value Rounding Fraction review - Fraction awareness - Equivalent fractions - Multiply and Divide fractions - Add and subtract fractions Holt Course 2: Estimate with Fractions Holt Course 2: Adding and Subtracting Fractions Holt Course 3: 2-6 Adding and Subtracting with unlike denominators Geometry: Lesson and Worksheets Simplify Algebraic Expressions with Some Geometry: Worksheets Algebraic Expressions with Some Geometry: Worksheets Unit 1 Clover Park School District 6/01/15 Page 10

11 Evaluative Criteria: SBAC Sample Items F-BF.2 (N.276) A-REI.3 (I.088) Stage 2 - Evidence SAMPLE Assessment Evidence CLASSROOM ACTIVITY/PERFORMANCE TASK(S): Kevin Durant vs. LeBron James Hexagons (Noyce Foundation) Formative assessments A.SSE.1 and APR.1: #1, #2, #3, #4, MC 1, MC 2 A.SSE.3: #1, #2, #3, #4, MC 1, MC 2 OTHER ASSESSMENT EVIDENCE: Stage 3 Learning Plan Sample Summary of Key Learning Events and Instruction that serves as a guide to a detailed lesson planning LEARNING ACTIVITIES: NOTES: A suggested guide to layout of unit by days when class meets every day in a block system Unit 1 Clover Park School District 6/01/15 Page 11

12 Extended Algebra Fractions review: throughout days 1-11 adding a few days Day 1: Variables and Expressions - Holt Algebra 1: 1-1Variables and Expressions - Your Name is worth/dollar words - Once Upon A Time Day 2: Integers, Rational Numbers, Real Numbers, and Absolute Value - Holt Course 3: 1-3 Integers and Absolute Value - Holt Course 3: 2-1 Rational Numbers - Holt Course 3: 4-7 The Real Numbers Day 3: Adding and Subtracting Real Numbers - Holt Course 3: 1-4 Adding Integers - Holt Course 3: 1-5 Subtracting Integers - Holt Course 3: Adding and Subtracting Rational Numbers - Holt Algebra 1: 1-2 Adding and Subtracting Real Numbers Day 4: Multiplying and Dividing Real Numbers - Holt Course 3: 2-3 Multiplying Rational Numbers - Holt Algebra 1: 1-3 Multiplying and Dividing Real Numbers Day 5: Square Roots - Holt Course 3: 4-5 Squares and Square Roots - Holt Course 3: Estimating Square Roots - Holt Algebra 1: 1-5 Square Roots and Real Numbers SSE.1, SSE.3, and APR.1 Algebra Day 1: Rational and Irrational - Lesson and PowerPoint - Holt Algebra 1: 1-5 Square Roots and Real Numbers Stage 3 Learning Plan Sample Unit 1 Clover Park School District 6/01/15 Page 12

13 Day 2: Evaluate Rational and Irrational - Lesson and PowerPoint - Holt Algebra 1: 10-6 Radical Expressions Stage 3 Learning Plan Sample Extended Algebra Day 1: Powers and Exponents - Holt Course 2: 1-2 Exponents - Holt Course 3: 4-1 Exponents - Exploring Exponents: TI Activity - Holt Algebra 1: 1-4 Powers and Exponents - Holt Algebra 1: 7-1 Integer Exponents Day 2: Order of Operations - Holt Course 2: 1-5 Order of Operations - Holt Algebra 1: 1-6 Order of Operations Day 3: Exponents - Holt Algebra 1: 7-3 Multiplication Properties of Exponents Day 4: Exponents - Holt Algebra 1: 7-4 Division properties of Exponents SSE.1, SSE.3, and APR.1 Algebra Day 1: Exponents Review - TI Activity: Rules of Exponents - Exponent Game - Laws of Powers Day 2: Exponents Review - Review Game - Review of All - Holt Algebra 2: 1-5 Properties of Exponents Unit 1 Clover Park School District 6/01/15 Page 13

14 Day 3 and 4: Rational Exponents - Lesson - Exploring Rational Exponents Stage 3 Learning Plan Sample Extended Algebra Day 1: Variables and Expressions - Holt Course 2: 1-7 Variables and algebraic Expressions - Holt Course 2: 1-8 Translate Words into Math - Holt Algebra 1: 1-1Variables and Expressions Day 2: Variables and Expressions - Holt Algebra 1: 1-7 Simplifying Expressions - Holt Course 2: 1-9 Simplifying Algebraic Expressions SSE.1, SSE.3, and APR.1 Algebra Day 1: Polynomials - Algebraic Expression Card Match - Holt Algebra 1: 7-5 Polynomials Day 2: Polynomials - Holt Algebra 1: 7-6 Add/Subtract Polynomials Day 3: Polynomials (Multiply) Can wait until Unit 3 - Checkerboard Borders - Holt Algebra 1: 7-7 Multiplying Polynomials Day4: Polynomials (Multiply) Can wait until Unit 3 - Building More Checkerboard Borders - Holt Algebra 1: 7-7 Multiplying Polynomials Day 5: Polynomials (Multiply) Can wait until Unit 3 - Holt Algebra 1: 7-8 Special Products of Binomials Unit 1 Clover Park School District 6/01/15 Page 14