Math Pacing Guide 6 Unit 1 - Lorain City School District / …€¦ · ·...

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Lorain City School District Scope, Sequence and Pacing Guides

Ohio’s New Learning Standards: 6th Grade SpringBoard

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Math-‐6th Grade SpringBoard Unit 1 Number Concepts

Days: 33 days Essential Question: Why is it important to be able to use whole numbers, fractions, and decimals to solve problems? How can you use visualization and estimation to solve problems?

Learning Target Materials Ohio’s New Learning Standards Daily “Clear Learning Targets” should reflect the more detailed “Learning Targets” included in the SpringBoard text.

-‐Fraction strips -‐Number cubes

6. NS.B.2 Fluently divide multi-‐digit numbers using the standard algorithm. 6. NS.B.3 Fluently add, subtract, multiply, and divide multi-‐digit decimals using the standard algorithm for each operation. 6. NS.C.7 Understand ordering and absolute value of rational numbers. 6. NS.C.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 6. NS. C.7b Write, interpret, and explain statements of order for rational numbers in real-‐world contexts. 6. EE. A.1 Write and evaluate numerical expressions involving whole-‐number exponents. 6. NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two numbers less than or equal to 12. 6. NS. A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Pacing (based on a 45-‐minute class period) Vocabulary Unit overview/Getting Ready –(1 day) Unpacking Assessment –(1 day) Activity 1-‐ (7 days) Embedded Assessment 1-‐(1 day) Unpacking Assessment – (1 day) Activity 2-‐ (2 days) Activity 3 – (3 days) Embedded Assessment 2 – (1 day) Unpacking Assessment –(1 day) Activity 4-‐ (7 days) Activity 5-‐ (3-‐4 days) Activity 6-‐(3-‐4 days) Embedded Assessment 3 ( 1 day)

Academic Vocabulary: Annex Algorithm Conjecture Simulate Math Terms: Factor Visual representation Composite Number Prime number Greatest Common Factor Evaluate Least Common Denominator Least Common Multiple Improper Fraction Proper Fraction Reciprocal Mixed Number



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Approximately 33 days

Approved Resource Additional Resources SpringBoard Unit 1

MathCore2K (mathcore2k.com) SpringBoard Digital Resources

Assessments

Embedded Assessments: These assessments, following Activities 1,3 and 6, will give you an opportunity to demonstrate how you can use your understanding of number concepts to solve mathematical and real-‐world problems. Embedded Assessment 1: Comparing and Computing with Whole Numbers and Decimals p. 25 Embedded Assessment 2: Prime Factorization, Exponents, GCF, and LCM p. 43 Embedded Assessment 3: Multiplying and Dividing Fractions and Mixed Numbers p. 79

Mini-‐ Lessons: Compatible Numbers (TE-‐ 16) Divisibility Rules (TE-‐28)



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Math-‐6th Grade SpringBoard Unit 2 Integers

Days: 20 days Essential Question: -‐How can integers be represented visually and how can operations with integers be represented with models? -‐How are positive and negative numbers used in real-‐world situations?


-‐Two-‐color counters -‐Graph paper

6. NS.C.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. 6. NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6. NS.C.6a Recognize opposite signs of numbers as indicating locating on opposite sides of 0 on the number line. 6. NS. C. 6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 6. NS.C. 6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 6. NS.C.7 Understand ordering and absolute value of rational numbers. 6. NS. C. 7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 6. NS.C.7b. Write, interpret, and explain statements of order for rational numbers in real-‐world contexts. 6. NS. C. 7c Understand the absolute value of a rational number as its distance from 0 on the number line: interpret absolute value as magnitude for a positive or negative quantity in a real-‐world situation. 6. NS. C. 7d Distinguish comparisons of absolute value from statements about order.

Pacing (based on a 45-‐minute class period) Vocabulary Unit overview/Getting Ready –(1 day) Unpacking Assessment –(1 day) Activity 7-‐ (2 days) Activity 8-‐ (5 days) Embedded Assessment 1-‐(1 day) Unpacking Assessment – (1 day) Activity 9-‐ (3 days) Activity 10 – (3 days) Embedded Assessment 2 – (1 day) Approximately 20 days

Academic Vocabulary: elevation Math Terms: Absolute value Origin Integer Quadrants Opposite Reflection Additive inverse Coordinate plane Ordered pair



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Assessments

Embedded Assessments: These assessments, following Activities 8 and 10, will give you an opportunity to demonstrate how you can use your understanding of number concepts to solve mathematical and real-‐world problems. Embedded Assessment 1: The Number Line and Adding and Subtracting Integers p. 107 Embedded Assessment 2: Coordinate Plane and Multiplying and Dividing Integers p. 127

Mini-‐ Lessons: Integers (TE page 85) Plotting Points ( TE page 110) Reflections in the Plane (TE 114)



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Math-‐6th Grade SpringBoard Unit 3 Expressions and Equations

Days: 33 days

Essential Question: -‐Why are tables, graphs, and equations useful for representing relationships? -‐How can you use equations to solve real-‐world problems?


6. EE. A. 1 Write and evaluate numerical expressions involving whole-‐number exponents. 6. EE. A. 2 Write, read, and evaluate expressions in which letters stand for numbers. 6. EE. A. 2a Write expressions that record operations with numbers and with letters standing for numbers. 6. EE. A. 2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) 6. EE. A. 2c 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. 6. EE. A. 3 Apply the properties of operations to generate equivalent expressions. 6. EE. A. 4 Identify when two expressions are equivalent. 6. EE. B. 6 Use variables to represent numbers and write expressions when solving a real-‐world or mathematical problem.

Pacing (based on a 45-‐minute class period) Vocabulary Unit overview/Getting Ready –(1 day) Unpacking Assessment –(1 day) Activity 11-‐ (6-‐7 days) Activity 12-‐ (2-‐3 days) Embedded Assessment 1-‐(1 day) Unpacking Assessment – (1 day) Activity 13-‐ (6 days) Activity 14 – (4 days) Activity 15-‐ (2 days) Activity 16-‐ (2-‐4) Embedded Assessment 2 – (1 day) Approximately 33 days

Academic Vocabulary: Compare Contrast Math Terms: Numerical expression Solution Variable Inverse operations Coefficient Inequality Algebraic expression Rate of change Term Ordered Pair Unit rate Independent variable Equation Dependent variable



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MathCore2K (mathcore2k.com)

Assessments

Embedded Assessments: These assessments, following Activities 12 and 16, will give you an opportunity to demonstrate how you can use your understanding of number concepts to solve mathematical and real-‐world problems. Embedded Assessment 1: Order of Operations and Expressions p. 157 Embedded Assessment 2: Expressions and Equations p. 211

Mini-‐ Lessons for intervention, differentiation and prerequisite skills: Points on a Number Line p. 201



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Math-‐6th Grade SpringBoard Unit 4 Ratios

Days: 25 days

Essential Question: -‐Why is it important to understand calculations with ratios, rates, and percents? -‐Why are proportional relationships important in mathematics?


6. RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6. RP.A. 2 Understand the concept of a unit rate. 6. RP. A. 3 Use ratio and rate reasoning to solve real-‐world and mathematical problems, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 6. RP.A. 3a Make tables of equivalent ratios relating quantities with whole-‐number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios 6. RP. A. 3b Solve unit rate problems including those involving unit pricing and constant speed. 6. RP.A. 3c Find a percent of quantity as a rate per 100 6. RP.A.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. 6. EE.C. 9 Use variables to represent two quantities in a real-‐world problem that change in relationship to one another, write an equation to express one quantity, thought of as the dependent variable.

Pacing (based on a 45-‐minute class period) Vocabulary Unit overview/Getting Ready –(1 day) Unpacking Assessment –(1 day) Activity 17-‐ (2 days) Activity 18-‐ (4 days) Activity 19-‐ (4 days) Embedded Assessment 1-‐(1 day) Unpacking Assessment – (1 day) Activity 20-‐ (6 days) Activity 21 – (3 days) Embedded Assessment 2 – (1 day) Approximately 25 days

Academic Vocabulary: benchmark Math Terms: Ratio Equivalent ratios Rate Dimensional analysis Conversion factor Unit rate Unit price Proportion average



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Assessments

Embedded Assessments: These assessments, following Activities 19 and 21, will give you an opportunity to demonstrate how you can use your understanding of number concepts to solve mathematical and real-‐world problems. Embedded Assessment 1: Ratios and Rates p. 245 Embedded Assessment 2: Understanding and Applying Percents p. 273

Mini-‐ Lessons for intervention, differentiation and prerequisite skills: Solving Proportions p. 229 Unit Rates p. 234 Solving Proportions p. 238 Benchmark Percents Less Than 100 p. 249 Converting Among Decimals , Fractions, and Percents p. 251 Discount p. 266



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Math-‐6th Grade SpringBoard Unit 5 Geometry Concepts

Days: 23 days Essential Question: -‐In what ways are geometric figures used in real life? -‐Why is it important to understand the characteristics of two-‐and three-‐dimensional figures?


-‐3 number cubes per group -‐segment models -‐protractors -‐rulers -‐scissors -‐graph paper -‐unit cubes -‐tape

6. G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-‐world and mathematical problems. 6. G.A.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. 6. G.A.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 6. G.A. 4 Represent three-‐dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface are of these figures.

Pacing (based on a 45-‐minute class period) Vocabulary Unit overview/Getting Ready –(1 day) Unpacking Assessment –(1 day) Activity 22-‐ (4 days) Activity 23-‐ (5 days) Activity 24-‐ (2 days) Embedded Assessment 1-‐(1 day) Unpacking Assessment – (1 day) Activity 25-‐ (3 days) Activity 26 – (3 days) Embedded Assessment 2 – (1 day) Approximately 23 days

Academic Vocabulary: composite Math Terms: Theorem Equiangular Polygon Quadrilateral Consecutive angles Perimeter Area Altitude



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Assessments

Embedded Assessments: These assessments, following Activities 24 and 26, will give you an opportunity to demonstrate how you can use your understanding of number concepts to solve mathematical and real-‐world problems. Embedded Assessment 1: Geometric Concepts p. 315 Embedded Assessment 2: Surface Area and Volume of Prisms

Mini-‐ Lessons for intervention, differentiation and prerequisite skills: Measuring with a Protractor (TE 281)



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Math-‐6th Grade SpringBoard Unit 6 Data Analysis

Days: 23 days

Essential Question: -‐How is data organized and presented in real-‐world situations? -‐What are ways you can summarize data both numerically and graphically?


-‐calculator -‐graph/grid paper -‐rulers/tape measures

6. SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. 6. SP. A. 2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6. SP. A. 3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6. SP.B. 5 c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 6. SP. B. 4 Display numerical data in plots on number line, including dot plots, histograms, and box plots. 6. SP. B.5 Summarize numerical data sets in relation to their context, such as by: 6. SP. B.5a Reporting the number of observations 6. SP. B.5b Describing the nature of the attribute under investigation, including how it was measured 6. SP. B. 5c Giving quantitative measure of center 6. SP. B. 5d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Pacing (based on a 45-‐minute class period) Vocabulary Unit overview/Getting Ready –(1 day) Unpacking Assessment –(1 day) Activity 27-‐ (4 days) Activity 28-‐ (3 days) Embedded Assessment 1-‐(1 day) Unpacking Assessment – (1 day) Activity 29-‐ (4 days) Activity 30 – (5 days) Embedded Assessment 2 – (1 day) Approximately 23 days

Academic Vocabulary: Uniform Range Math Terms: Statistical question Outliers Stem plot Variability Median Frequency table Distribution Mean absolute deviation Mean Bar chart Interquartile range Class intervals Mode Quartiles Skewed Dot Plot Five-‐number summary Histogram Symmetrical Box plot



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Assessments

Embedded Assessments: These assessments, following Activities 28 and 30, will give you an opportunity to demonstrate how you can use your understanding of number concepts to solve mathematical and real-‐world problems. Embedded Assessment 1: Types of Variables and Measures of Center p. 377 Embedded Assessment 2: Measures of Variability and Numerical Graphs p. 407

Mini-‐ Lessons for intervention, differentiation and prerequisite skills: Data Analysis (TE 353) Measures of Data (TE 380) Mean Absolute Deviation (TE 385) Median and Quartiles (TE 389)



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Math-‐6th Grade SpringBoard Unit 7 Personal Financial Literacy

Days: 5 days Essential Question: -‐How can you build a good credit history? -‐How can being financially literate help you plan for college and your future?


-‐optional fee schedules from local financial institutions, -‐sample credit report

Pacing (based on a 45-‐minute class period) Vocabulary Unit overview/Getting Ready –(1 day) Unpacking Assessment –(1 day) Activity 31-‐ (3 days) Approximately 5 days

Academic Vocabulary: Savings account Checking account Debit card Deposit Withdrawal Transfer Credit card Credit report



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Assessments

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Math Pacing Guide 6 Unit 1 - Lorain City School District / …€¦ · ·...

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