4. Send edits/suggestions to David Harris based on planning and results. This is how we will make this document responsive to classroom needs.

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1 6 th Grade Pacing Guide Cover Sheet In the organization of the pacing guide there are some things left unwritten. It is assumed that teachers will read the standards related to the big ideas when planning. Some text sections are merely support for the standards and some are aimed directly at them. Here is the order of planning in this design: 1. Start with the Content Map. Read the big ideas, ask yourself the essential questions. a. Read the standards listed on the map (sorted by Benchmarks). Ask yourself if they are represented well in the mapping. b. Write an assessment question or two for each question set that gives the student a chance to show understanding of the main ideas. Consider the type of thinking (look at MR standards) when writing. c. Consider the cognitive demand of the question(s). 2. Go to pacing guide and look over the suggested text pages. a. Are the essential questions answered there? b. Does the type of thinking (MR standards) that you discussed in the content map exist in the work students do in the text? c. Are there various levels of demand? 3. Plan and supplement or supplant text materials as needed. 4. Send edits/suggestions to David Harris based on planning and results. This is how we will make this document responsive to classroom needs. Notes on Pacing Guide 1. Right hand column differentiates for advanced/regular 6 th grade math. Topics that are supportive but pre requisite (not essential grade level standards) are noted as support topics. Topics that are extensions but not essential grade level standards are listed as extension topics. Below is how the two classes will differentiate. 6 th Grade Math: May need to pay attention to support topics and not investigate some extension topics. Advance 6 th Grade Math: Support topics (review) may or may not be done to diagnose areas where review is needed. The extension topics are one way in which this course is different than the regular course, as opposed to simple acceleration of instruction. Enrichment sections of the ancillary materials may also provide added depth or ideas for how to go deeper. 2. Left hand column time is written for 6 th Grade regular class. Adjustments through site planning (for advanced and Regular classes) should keep the integrity of Benchmark sets in place. 3. Key standards are in Bold EUSD Power standards are denoted with (PWR).

2 th Grade (Including Advanced) Math Pacing Guide See cover page for notes on pacing guide structure. Big Idea(s): Algebra is distinguished from arithmetic by the systematic use of symbols for values. Writing and evaluating expressions with algebraic notation follows the same rules/properties as in arithmetic expressions. These expressions and equations can be used to model real world situations. August 24 Sept. 18 (19 days) Includes time for diagnostic and review, if needed. Essential Questions Set #1 Holt: Text 1 2 to 1 4 How do we use math to help us describe and understand patterns? How are numerical expressions simplified? How do the basic properties help us understand simplifying expressions? Concepts expressing numerical patterns Order of operations Using exponents Commutative, associative, identity properties Standards: AF 1.2(PWR), AF 1.3, AF1.4 Essential Questions Set #2 Holt: Text 1 5 to 1 11 What algebraic tools do we use to help us describe and understand the world? How are expressions different than equations? How are algebraic expressions simplified? How do we solve algebraic equations? Concepts/Skills Writing expressions Evaluating expressions Making conjectures Drawing a diagram or chart modeling equations Solving equations with addition Solving equations with multiplication Standards: AF1.1(PWR), AF1.2(PWR), AF1.3, 1 1 Math expressions 1 2 Properties of addition & multiplication 1 3 Inverse operations (more properties) 1 4 Distributive property 3 1 (exponents) also E5 1 5 Order of operations A problem solving model is suggested 1 6 and Writing Expressions 2 2Writing Equations 2 4 solving equations (skip inequalities) 2 5 More solving equations 2 6 Using expressions in problem solving 8 1 Equations and Variables 8 2 Equations: Addition and Subtraction 8 3 Equations: Multiplication and Division 2

3 Big Idea(s): The rational numbers include integers. These numbers can be manipulated and represented on the number line. Computation with signed numbers adds extra complexity to whole number computation. Sept. 21 Oct Days Essential Questions Set #3 Holt Text: 2 1 to 2 5 How is the integer number line made? How does computing with all integers differ from just the whole numbers. How is it the same? How does solving equations change when using all integers and not just positive numbers? Concepts/Skills Computing with all integers Absolute value Using models to demonstrate computing with integers solving equations with all integers Standards: NS2.3 (PWR), Supportive Topics This section may require less time for the advanced class. Possibly supplement by investigating essential Question Sets#4 and # Negative Numbers 11 2 Adding Integers 11 3 Subtracting Integers 11 4 Products w/ Negative Factors 11 5 Products w/ several Negative factors 11 6 Quotients of Integers 11 7 Solving Equations Big Idea(s): Equations in two variables represent a relationship. This relationship can be represented as a set of points on a coordinate grid. Optional: (sections 2 6 to 2 8) Essential Questions Set #4 (optional) Holt Text 2 6 What does a point on a coordinate grid represent? How do we use the coordinate grid system to describe the relationship between two variables? Concepts/Skills Graphing points in the coordinate plane Graphing a function on the coordinate plane Standards: Prep for AF 1.0/ Extensions of AF 2.0 Extension Topics: 6 th Grade Standards do not specifically mention graphing equations in two variables. This big idea is therefore an extension of AF 2.0 and preparatory for 7 th grade. (Questions sets 4&5) 11 8 Graphs of Ordered Pairs 11 9 Graphs of Equations 3

4 Essential Question Set #5 (optional) Holt Text: 2 7 to Lab What tools do we use to find solutions to equations in 2 variables? How do we generate points for an x y graph of an equation? How does a line on a graph relate to an algebraic equation? Concepts/Skills Using a t table Generating x y values for an equation in 2 variables Generating x y coordinates from a linear equation Graphing the line that represents a linear function Standards: AF 1.0 (graph & interpret results) Big Idea(s): The fundamental theorem of arithmetic states that any integer greater than 1 can be written as a unique product (up to ordering of the terms) of prime numbers. Exponents allow the representation of the product of the same factor more than once as a base and a power. 4

5 Oct (8 days) Essential Questions Set #6 Holt text: 3 1 to 3 3 How does factorization show us more than one way to represent a number? How is prime factorization different than factorization? What is the greatest common factor of any two numbers? What is the least common multiple of any two numbers? What does x y mean? Concepts/Skills Factoring a whole number into primes Factoring a whole number into sets of factor pairs Exponents Standards: NS2.4(PWR) 5 1 Factors and Multiples 5 2 Tests for Divisibility 5 3 Square numbers and Square Roots 5 4 Primes and Composites 5 5 GCF 5 6 LCM May need to see E5 or section 3 1 for more exponent examples. Big Idea(s): Any rational number can be represented as a fraction or a decimal. All rational numbers can be compared and ordered. Computation with rational numbers that are not whole numbers may require an extra step for conversion to like terms (place value, denominator). Oct. 26 Nov. 3 (7 days) Essential Questions Set #7 Holt text: 3 4 to 3 6 How do you compare and order fractions? How do you compare and order decimals? How do you convert between decimals and fractions? What does simplify a fraction mean? How do you define a rational number? Comparing and ordering fractions Converting between decimal and fraction 6 1 Fractions 6 2 Equivalent Fractions 6 3 Fractions & Mixed Numbers 6 4 Comparing Fractions 6 5 Changing a Fraction to a Decimal 6 6 Changing a Decimal to a Fraction Need to supplement for definition of rational number. 5

6 Nov. 9 Dec. 11 (19 days) Simplifying fractions Standards: NS1.1(PWR) Benchmark: Essential Question Set #1, 2, 3, 6, 7 window: Oct.4 6/ Due into Edusoft 11/6 Trimester 1 ends 11/13 Essential Questions Set #8 Holt text: 4 1 to 4 5 How is estimating with fractions different than estimating with whole numbers? How do you model the addition of fractions and mixed numbers? What do you need to know to be able to add and subtract fractions correctly? What do you need to know to correctly multiply fractions? What do you need to know to correctly divide fractions? Estimating sums of fractions Modeling addition & subtraction of fractions Adding & subtracting fractions Multiplying and dividing fractions for follow up to Benchmark #1 is built into this long section, if needed. 7 1 Addition/Subtraction of Fractions 7 2 Addition/Subtraction of Mixed Numbers 7 3 Multiplication of Fractions 7 4 Division of Fractions 7 5 Multiplication And Division of Mixed Numbers Standards: NS 2.1, NS2.2 Big Idea(s): Solving equations with fractions utilizes the same algebraic rules as with whole numbers. Dec (5 days) Essential Question Set #9 Holt Text: 4 6 What are the steps to solving an equation that contains an addition expression? What are the steps to solving an equation that contains a fractional coefficient? Concepts/Skills Solving equations containing fractions Extension Topic: Apply the models for computing fractions developed by students to equations and word problems. 8 4 Equations Decimals and Fractions Standards: NS2.1 and AF 1.1(PWR) Big Idea(s): Place value is critical for accurate computation with decimal 6

7 numbers. Solving equations with decimals follows the same rules and procedures as in whole numbers and fractions. Jan. 4 6 (3 days) Essential Questions Set #10 Holt text: 4 7 to 4 10 How does addition and subtraction of decimal numbers differ from whole numbers? What do you need to consider or do when multiplying or dividing with decimal numbers? Computing with decimals Not grade level Standards except solving equations: AF1.1(PWR) Supportive Topics: This section is a skills review for subsequent sections, especially rate, percent and interest. Length of time spent is to be determined at the site level. These questions will not be tested specifically but embedded in the afore mentioned standards questions. It may also simply be an extension of the equation work from the fraction sections. Resource: 3 3 Decimals 3 4 Comparing Decimals 3 5 Rounding 3 6 Adding and Subtracting Decimals 3 7 Multiplying or Dividing by powers of Multplying Decimals 3 9 Dividing Decimals 3 10 Using Estimation Big Idea(s): Proportionality is a mathematical relation between two quantities. Ratios are used in various contexts to describe the relative size of two quantities. Two equivalent ratios form a proportion. Proportions can be used to solve for unknown quantities where a ratio or rate remains equal. Jan.7 22 (11 days) Essential Questions Set #11 Holt text: 5 1 to 5 2 What are the three ways a ratio can be represented? Ratios Extension Topics: Slope

8 What is the difference between a ratio and a rate? How does knowing a rate allow us to find one quantity of the rate if we know the other? Rates and ratio Apply rates to solve problems is a rate. Activities where students analyze graphs of the form y = mx + b are appropriate if Essential question set #4 was taught. Standards: AF2.2(PWR), AF2.3(PWR) Essential Questions Set #12 Holt text: 5 3 to 5 5 How do you prove two ratios form a proportion? How do you solve for an unknown element of a proportion? How can proportions be used to convert between customary and metric units? Ratios and rates Converting between units of measure Solving a proportion 7 7 Proportions 7 8 Using Proportions Need to supplement for converting between customary and metric Standards: AF2.2(PWR), AF2.1, NS1.3(PWR) Big Idea(s): Application of proportion utilize formulas and geometric relationships to describe, model and design to scale. 8

9 Jan (5 days) Essential Questions Set #13 Holt text: 5 6 to 5 8 Mathematically, what does it mean to say two figures are similar? How do scale models utilize the concept of similar figures and proportionality? Solve similar figures Solve problems involving scale and proportion Standards: NS1.2 and NS1.3(PWR) Suggestion: Excellent time for problems that foster the thinking in standard set MR2.0 Need to supplement for lessons on similarity 7 9 Scale Drawing Big Idea(s): Percents are a special proportion where the ratio (relative size) is always described as a part of 100. Percents can be applied to many everyday uses such as percent of change, simple interest and tips. Feb (13 days) Essential Questions Set #14 Holt text: 6 1 to 6 5 What does a percent of a quantity mean? How do you convert from a fraction or decimal part of a quantity to percent? How do you find the percent of a quantity? How do we use proportions to solve for unknown amounts in percent problems? Percent Converting between decimals, fractions, percents Using proportions to solve for percents or missing amounts when percent is known Using equations to solve for parts or percents. Standards: NS1.4(PWR) Essential Questions Set #15 Holt text: 6 6 to 6 7 What does percent of change mean and how is it calculated? How do you find simple interest? How do you figure the tip at a restaurant? Calculating percent of change Calculating simple interest Calculating the tip. Standards: NS1.4(PWR) 9 1Percents & Fractions 9 2 Percents & Decimals 9 3 Computing with Percents 9 4 Percent of Change 9 5 Discount and Markup 9 6 Commission and Profit 9 7 Simple Interest Extension Topic: 9 8 Compound Interest 9

10 Big Idea(s): Data can be collected, organized and described using mathematical tools such as measures of central tendency and statistical graphs. Feb. 22 Mar. 3 (8 days) Essential Questions Set #16 Holt text: 7 1 to 7 5 Why do we compute measures of central tendency such as mean, median, mode? How do we know which measure is the best to describe data? How do graphs and tables help us to organize and analyze data? Calculating Mean, median, mode Reading graphs and tables Making graphs and tables Additional Data and outliers Standards: SDAP1.1 SDAP1.2, SDAP1.3, SDAP1.4 Essential Questions Set #17 Holt text: 7 6 to 7 8 How does the way data is collected affect how accurately the data describes or predicts phenomena? Data collection: Convenience sampling, responding to a survey, etc. Standards: SDAP1.2, SDAP2.2(PS), SDAP2.3, SDAP2.4, SDAP2.5 Support/Extension Topics: Mean, median, mode is a review of 4 th and 5 th grade standards. A good time for differentiating between those who need a review and those who could do an extension with percent/scale models or graphing data Picturing Data 12 2 Pictographs and Circle Graphs 12 3 Mean, Median, Mode 12 5 Stem&Leaf Plots 12 6 Box & Whisker Plots 12 7 Histograms optional Extension Topic: 12 4 Frequency Distributions Not covered in McDougal Little Text Benchmark: Essential Question Sets #8 17 (except #10), Window: March 3 5/ Due in Edusoft March 5 Trimester 2 ends March 5 10

11 Big Idea(s): The likelihood of an event occurring is called probability. Probability can be determined theoretically, through mathematical models or experimentally, through controlled trials. March 8 23 (12 days) Essential Questions Set #18 Holt text: 8 1 to 8 4 What does probability measure? What is the difference between theoretical and experimental probability? How do we use trials and probability to predict likelihoods of an event occurring? representing probability as a ratio or percent Counting/diagrams for possible outcomes Calculating experimental probability Calculating theoretical probability Standards:PS3.1(Pwr), PS3.2, PS3.3(Pwr), Essential Questions Set #19 Holt text: 8 5 to 8 7 What is a disjoint event? What is the different between dependent and independent events? How do we use samples to predict? Dependent and independent events Using samples to predict Standards: PS3.4, PS Probability of an Event 12 9 Probability & Odds Combined Probabilities Extension Topics: Theoretical versus Experimental Probability. Not Covered in McDougal Text Big Idea(s): Plane Geometry is the study of points, lines and planes. Angles and geometric figures are made with connected combinations of these basic elements. Angles are classified by their measure. Mar (3 days) Essential Questions Set #20 Holt text: 9 1 to 9 4 What are the three basic elements in plane geometry? What does it mean for two angles to be complementary? What does it mean for two angles to be supplementary? Point, line, plane Supplementary Angles Complementary Angles Standards: MG2.1, MG2.2(PS), 4 1 Points, Lines, Planes 4 2 Measuring and Segments 4 3 Angles and Angle Measure 11

12 Spring Break March 27 April 11 Big Idea(s): Closed plane figures made of line segments are called polygons. Polygons can be classified by number of sides as well as angle measure and relationships between sides (such as parallel or perpendicular). April (7 days) Essential Questions Set #21 Holt text: 9 5 to 9 9 How do you know that a figure is a polygon? Given a triangle, can you describe how you know if it is scalene, isosceles or equilateral? Given a triangle, can you describe how you know if it is acute, obtuse or a right triangle? Given the measure of two angles within a triangle, can you find the third angle s measure? Identifying polygons Classifying polygons Using the sum of a triangles angle to find an unknown angle measure Standards:MG2.3, MG2.2(Pwr) Chapter, Lesson, Notes 4 4 Triangles 4 5 Polygons 4 6 Circles 4 7 Congruent Figures Big Idea(s): Measurement of geometric shapes can be 1 dimensional (length/perimeter), 2 dimensional (area/surface area), or 3 dimensional (volume). April 21 May 14Continues on next page (18 days) Essential Questions Set #22 Holt text: 10 1 to 10 6 How do you find the perimeter of a polygon? How do you find the circumference of a circle? What is pi? How do you find the area of parallelograms? (including special ones such as rectangles and squares) How do you find the area of a circle? How do we use formulas for area and perimeter to solve for unknown measures of a figure? Finding the perimeter and area of polygons Finding the circumference and area of a circle Finding the are of composite/irregular figures Using algebra to represent geometric relationships Standards: MG1.1(Pwr), MG1.2, AF3.1, AF3.2 Chapter, Lesson, Notes Note: Application of AF3.1 and AF3.2 should be a deeper emphasis for advanced classes Areas of Rectangles and Parallelograms 10 2 Areas of Triangles and Trapezoids 10 3 Areas of Circles 10 4 Using Symmetry to find Areas 12

13 Essential Questions Set #23 Holt text: 10 7 to How is a polyhedron different than a polygon? In general, how do you find the volume of a polyhedron? What makes a prism, a prism? What defines a cylinder? How is surface area different than simple area? Finding the surface area of polyhedrons Finding the volume of polyhedrons Using algebra to represent geometric relationships Standards: MG1.3, AF3.1, AF3.2 CST Window is April 23 May 21. Note: Application of AF3.1 and AF3.2 should be a deeper emphasis for advanced classes Polyhedrons 10 6 Volumes of Prisms 10 7 Volumes of Cylinders 10 9 Surface Area May 17 June 16 Three possible areas of focus for during and Post CST are 1. Application of Mathematical Skills. See sample suggested focus below. 2. Extension Topics. See sample topic below. 3. Review/Remediation. Use benchmark #3 as a formative diagnostic. Differentiation in small groups for individual needs is recommended. Topics are listed as suggestions. Order and pacing is to be site determined. Big Idea(s): Solving inequalities and two step equations require the use of the basic properties for numbers and equations to isolate the variable. The solution can be checked in the original equation. Site Determined Essential Questions Set (Optional Extension) Holt text: 11 1 to 11 8 How do we use the basic properties to help us solve two step equations? In what ways is solving inequalities the same as solving equations? In what ways is solving inequalities different than solving equations? Solving two step equations Solving inequalities Standards extensions of AF1.0, AF2.0, MR2.0, MR3.0 Chapter, Lesson, Notes Extension Topics: (For Adv 6 th ) This questions set is an extension of 6 th grade standards and a pre teach for 7 th grade standards. 2 4 and 2 5 Solving Equations and Inequalities Two step equations will need to come from supplemental Materials Supportive Topics: One may choose to revisit standards from BM#3. During this time. 13

14 Application of Skills: Problems involving rates such comparative cost problems can be solved using algebraic analysis. For first year Algebra students, the focus will be on problem solving strategies and communication of method and solution through algebra. Simple system of linear equation problems are ideal for giving students practice using algebra and graphing to communicate methods and results of problem solving. Site Determined Essential Question Set (Application of Math) How is math used to solve applied problems? How are equations used to solve various types of applied problems? In what ways do models, such as drawings or physical models help us in problem solving or understanding a concept? How does a solution in math translate into a graphic representation? Applying algebra to word problems Accessing notes and other text based examples for use in problem solving Using models to solve problems Using graphs to explain a solution or solve a problem Standards: M.R. Standards Chapter, Lesson, Notes Site Planned Benchmark 3: Essential Question Sets #18 23 Due Edusoft June 11 Trimester 3 ends June 16 14

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