Grade 6 Mathematics 621/622

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Berenice Spencer
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1 Sept/Oct UNIT 1- OPERATIONS AND EXPRESSIONS: How do you write and evaluate numerical and algebraic expressions? Elementary School Math Concepts: *Previously-learned (review of summer work) Multi- digit sums, differences, multiplication, and division Round Estimate Order of operations review Statistical measures of central tendency Analyze histogram Unit 1 Concepts: Order of operations with numerical and algebraic expressions Divisibility Prime factorization Translating with algebra Properties of Real Numbers Evaluate expressions sum, difference, product, quotient, mean, median, mode, max, min, range, algebraic expression, base, divisible, numerical expression, factor, prime factorization, term, variable, whole number,distribute, translate, evaluate, inequality, commutative, associative 6.EE.1 6.EE.2a 6.EE.2b 6.EE.2c 6.EE.3 6.EE.4 6.EE.6 5.OA.1,2 Fundamental for Secondary Mathematics: Apply previously learned skills and concepts to more sophisticated mathematical techniques. - Summer Work Demonstrate mastery of basic skills Demonstrate fluency with simplifying multidigit sums, differences, multiplication and division. Round from hundredths to hundreds and estimate values to whole numbers. Utilize the order of operations to correctly simplify numerical expressions Compare real numbers and expressions with inequalities and equalities. Find measures of central tendency Analyze histogram with measures of central tendency and range Operations and Expressions: Represent repeated factors with exponents Find the values of numerical expressions written with exponents Apply divisibility rules to solve problems Break down numbers into its primes and rewrite with exponents Incorporate more sophisticated order of operation problems into the simplification of numerical expressions, and utlize in problem solving situations Apply properties of real numbers Translate problem solving situations into algebra Evaluate algebraic expressions by applying order of operations Identify and combine like terms in algebraic expressions by applying properties of real numbers Problem Solving Technique: Working Backwards 1. Big Idea Project: Sweet Success 2. Cross Curricular: Bacterial Growth p.8 p.11, p.23, p Extentions: s Practice Reteach Enrich Exponents and Geometry 4. Literature: Fabulous Fibonacci Numbers Math Detective with Carmen Sandiego: Divisibility SMART Grade 6 slides- Algebraic Expressions RtI Tiers 1, 2, 3 activities Problem of the Day World Written unit UNIT 1 common

2 Oct./ Nov. UNIT 2- DECIMAL OPERATIONS: How do you solve real-world problems involving decimals? Rounding Decimals Long division with traditional algorithm (multidigit) Unit 2 Concepts: Place values (thousandths to thousands) Estimating sum/difference of decimals Add and Subtract decimals with borrowing Decimal multiplication with traditional algorithm Divide decimals by whole numbers Divide decimals by decimals Evaluate algebraic expressions with decimals (addition/subtraction) Compatible numbers, decimal, dividend, divisor, quotient, thousandth, round 6.NS.2 6.NS.3 5.NBT.5, 6, 7 Round decimals to whole number values. Use traditional long division methods to simplify numerical expressions. Identify preview words in a graphic organizer Decimal Operations: Correctly name place values from the thousandths to the thousands. Estimate the sum, difference, product and quotient of decimals by estimating each number first. Add, subtract, multiply and divide decimals by utilizing traditional algorithms, including long division. Evaluate algebraic expressions with decimals Problem solve with real life applications involving decimals. Read, write and solve to solve problems with decimals Make connections between math and science, and math and business using decimals Comparing Eggs p.52 p.51, p.59, p.37, Amoebas p.74, p.77 s Practice 2.1, 2.3, Reteach 2.1, 2.3, 2.6, 2.7 Enrich 2.1, 2.3, 2.6, 2.7 Real World Video, Ch2 Destination Math itools SMART Gallery Grade 6 Slides Problem Solving Technique: Solve a simpler problem Algebra Technique: Use algebraic expressions to model real life applications. Evaluate with decimals. activities Problem of the Day World: Currency Exchange Rates, Pose a Problem Written unit UNIT 2 common

3 Nov. UNIT 3- FRACTION AND DECIMALS: How do you work with fractions, decimals and mixed numbers? Common factors of two numbers (GCF) Add and subtract like fractions Unit 3 Concepts: Compare and order fractions and decimals Add and subtract unlike fractions Multi-step problems with fractions, mixed numbers and decimals Estimate fractions Least common denominator, mixed number, repeating decimal, terminating decimal, unlike fractions, least common multiple 6.NS.4 5.NF.1, 2 Compare and order whole numbers. Model fractions using visual diagrams. Find the sum and difference of fractions with common denominators. Fractions and Decimals: Convert simple decimals to fractions and mixed numbers, and fractions to decimals with long division. Simplify fractions by applying GCF and division Compare and order unlike fractions and mixed numbers by modeling, by using a 3-step method, and by utilizing inequalities and equalities. Estimate the sum and difference of two unlike fractions/mixed numbers Write equivalent fractions to add and subtract by using the LCD Apply properties of real numbers to simplify expressions Evaluate algebraic expressions with fractions Problem solve with real life applications involving fractions and mixed numbers Problem solve by finding What s the error? Choose an operation to solve a problem involving mixed numbers and fractions Problem Solving Technique: Choose an operation Algebra Technique: Use algebraic expressions to model real life applications. Evaluate with fractions and mixed numbers. ps. 95, 99, 109 s Practice Reteach Enrich Real World Video, Ch3 p.91: Ordering fractions and decimals p.105: Multiple ways to rename Math Detective with Carmen SanDiego: p.83 SMART Gallery Grade 6 Slides: GCF, LCM Problem of the Day World: Ozark Trail Hiking Club, Snowfall chart, rock climbing walls Written unit UNIT 3 common

4 Nov/Dec UNIT 4- MULTIPLYING AND DIVIDING FRACTIONS: How can you use products and quotients of fractions to solve problems? Estimate fractions Estimate products of whole numbers Unit 4 Concepts: Model fractions Estimate fraction products/quotients Multiply/divide fractions and mixed numbers Choose operation Multiplicative inverse, reciprocal, reasonable, compatible numbers 6.NS.1 5.NF.3,4,5,6,7 Relate mixed numbers and fractions greater than one. Estimate fractions, and products of two and three digit numbers Solve contextual problems involving multiplication and division of whole numbers Fraction Operations: Model the multiplication of fractions Estimate fraction products and quotients by first estimating each factor separately Multiply and divide fractions and mixed numbers by using the traditional algorithm and by writing answers in simplest form. Apply the Distributive Property to multiply fractions and mixed numbers Evaluate algebraic expressions with fractions by using order of operations Problem solve with real life applications involving fractions and mixed numbers Problem solve by finding What s the error? Choose an operation to solve a problem involving mixed numbers and fractions Problem Solving Technique: Choose operation Algebra Technique: Use algebraic expressions to model real life applications. Evaluate with fractions and mixed numbers. p.127, Connect to Health p.132, p.145, 153 s Practice , Reteach , Enrich , Real World Video, Ch4 Powers of Fractions p.131 Evaluating Algebraic Expressions with Mixed Numbers p Literature: Fair Share SMART Gr 6 and 7 slides World: Speed skating, Tree house UNIT 4 common

5 Jan. UNIT 5- RATIOS, RATES AND PROPORTIONAL REASONING: How can you use ratios to express relationships and solve problems? Proportional reasoning Multiply/divide equivalent fractions Convert decimals/fractions Compare fractions/decimals/percents Unit 5 Concepts: Unit rate and rate applications Proportions and equivalent ratios Conversions Proportional reasoning in application Percent understanding Ratio, equivalent ratios, rate, unit rate, proportion, percent, denominator 6.RP.1 6.RP.2 6.RP.3a 6.RP.3b 6.RP.3c 6.RP.3d MA.3.e Solve problems using proportional reasoning Convert between fractions, decimals and percents using place value and equivalent fractions Compare and order fractions, decimals and percents Ratios, Rates, Proportional Reasoning: Use ratio language to describe a ratio relationship between two quantities using words, using a fraction and using a colon. Understand the concept of a ratio by finding equivalent ratios, representing ratios in a table, and solving real world problems by using ratios Use rate language in the context of a ratio relationship by examining real world problems Understand the concept of a unit rate by solving problems with applicable units, and by simplifying to find equivalent ratios. Model proportions Introduce proportions as an equation with an unknown Use ratio and rate reasoning to solve real-world and mathematical problems involving tables and rates. Solve proportions by using cross-products and algebra Change percents to fractions by using %/100, and to decimals by using long division Solve word problems with part-whole-percent, and cross product methods. Use proportional reasoning to convert units, and solve problems that relate to real-word applications. Problem Solving Technique: Use a model Algebra Technique: Solve rational algebraic equations by setting up proportions, and utilizing the cross-product method. Subatomic Particles p.178, ps.169, 181, 191, Sand Sculpture p. 196, 207 s Practice Reteach Enrich Real World Video, Ch5 Multiple solution methods for proportions p.185 Renaming amounts to solve a problem p Math Detective: p Literature: The Missing Cup SMART Gr 6 activity: Scale on a Map, Rate and Unit Rate, 2 Color Counter Investigation Vocab bubble chart World: Bird House, Star Fruit Problem, video game UNIT 5 common

6 Feb. UNIT 6- INTEGERS: (Chapters 9,10 in Book) What do integers represent? Integers on a number line Integer context Unit 6 Concepts: Integers in real world Position of rational numbers on number line Coordinate plane graphing (4 quadrants) Absolute value Distance between integers Inequality statements Absolute value, additive inverse, integers, opposites 6.NS.5 6.NS.6a 6.NS.6b 6.NS.6c 6.NS.7a 6.NS.7b 6.NS.7c 6.NS.7d 6.NS.8 Locate and identify integers on a number line Express integers in context, including temperature Integers: Use positive and negative numbers to describe quantities having opposite directions or values Use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of zero Understand a rational number is a point on the number line Extend familiar number line diagrams and coordinate axes to represent negative number coordinates Find and position integers and other rational numbers on a number line and coordinate plane Write, interpret and explain statements of order for rational numbers in real-world contexts Understand the absolute value of a rational number as its distance from 0 on the number line, and interpret its value in real world context Interpret inequalities as statements of relative positions of 2 numbers on a number line Solve real world and math problems by graphing coordinate pairs in all 4 quadrants. Find distance between points with same x or y coordinates. p.327 s Practice 9.1, 10.9 Reteach 9.1, 10.9 Enrich 9.1, 10.9 Comparing and Ordering positive and negative numbers p.323 Horizontal and Vertical distances p Math Detective: p Literature: How much should it cost? SMART Gr 6 and 7 slides: Comparing and ordering integers, absolute value, coordinate plane Problem Solving Technique: Write math to explain concept Algebra Technique: Solve rational algebraic equations by setting up proportions, and utilizing the cross-product method. World: Average surface temperature of planets, Downtown Philly Unit 6 common

7 Mar. UNIT 7- SOLVE ONE-STEP EQUATIONS: How do we represent and solve for unknowns given a real-world situation? (Chapter 10 in the book) Equations Inequalities Function Rule Numerical sequences Unit 7 Concepts: Substitute Equation solving (x + p = q, px = q) Two- variable equations Two- variable situation with graph/table Equation, function, inequality, inverse operations, linear equation,ordered pair, origin, sequence, term 6.EE.5 6.EE.6 6.EE.7 6.EE.8 6.EE.9 Use models and inverse operations to solve equations and inequalities Recognize, describe, extend and analyze numerical sequences Determine a functional rule from a table or a graph One-Step Equation Solving: Write addition, subtraction, multiplication and division equations with algebra to solve a problem Solve equations and inequalities involving addition, subtraction, multiplication and division by using models, substitution and algebra. Solve real world and algebraic equations of the form x + p = q by using inverse operations where p, q and x are all non-negative rational numbers. Solve real world and algebraic equations of the form px = q by using inverse operations where p, q and x are all non-negative rational numbers. Represent real world situations with two variables that change inrelationship to each other Analyze a two-variable situation with graphs and tables, and relate these to the equation. Problem Solving Technique: Work backwards Algebra Technique: Write and solve algebraic equations using inverse operations. Represent problems with algebra in two variables. p. 391, 397 s Practice , 10.7, 10.8 Reteach , 10.7, 10.8 Enrich , 10.7, 10.8 Connect to Reading p Math Detective: p Literature: Input should equal output SMART Gr 6 slides: Solving equations Macbook Airs: Vocab tree diagram World: Fuel efficiency, Zoo animals, Olympic games Unit 7 common

8 April UNIT 8- GEOMETRY AND MEASUREMENT: (Chapters 11, 12, 13) How do we use Geometry in the real-world? Polygon identification Dimension identification Perimeter Coordinate pair graphing Unit 8 Concepts: Area of irregular shapes Volume of rectangular prisms Length of sides in coordinate plane Area and circumference of circle Real- world problems Area, volume, radius, diameter, center, length, width, height, right triangle, right rectangular prism, regular polygon, coordinate plane, coordinate pair, vertices, surface area, net, circumference, pi, perimeter, quadrilateral, trapezoid, dimensions, unit cube, formula, angle, composite figure, parallelogram, solid figure 6.G.1 6.G.2 6.G.3 6.G.4 Identify regular shapes and solids, including the dimensions of each figure Graph coordinate pairs in a four-quadrant plane Find the perimeter of two- dimensional figures Geometry and Measurement: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles, triangles or other shapes. Solve real-world problems by finding the area of figures (above) Find circumference and area by using relationships among radius, diameter, and center of a circle Find the volume of a right rectangular prism by packing it with unit cubes Apply formulas V = lwh and V=bh to find volumes of right rectangular prisms with fractional edge lengths in the context of real-world situations Draw polygons in the coordinate plane given coordinates for the vertices Use coordinates to find the length of sides of a polygon on a coordinate plane with first same coordinates and second same coordinates. Represent 3D figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures, and apply these techniques to the real world Problem Solving Technique: Break down complex area problems into simpler ones Algebra Technique: Utilize and evaluate formulas to find the perimeter, area or volume of figures. 1.Cross Curricular: Ch. 11 pg 439,444, 457. Ch 12 pg 471, 484. Ch 13 pg 527, 537 s Practice , , Reteach , , Enrich , , Literature: If I designed a zoo SMART Gr 6 slides: Area of a parallelogram, triangle, irregular shape, circle; circumference of a circle,volume of rectangular prisms, 3D figures, nets and surface areas(includes faces, vertices and edges) Unit 8 common

9 May/ June UNIT 9- STATISTICS:. How do we measure observations, and what do they mean? (Chapter 7 in the book) Measures of central tendency Variability measurements Gather data Unit 9 Concepts: Statistical questions Measures of statistics Display data Summarize data Explain outcomes of data Mean, median, mode, interquartile range, variability, data, tally, histogram, central tendency, box plot, line plot, circle graph 6.SP.1 6.SP.2 6.SP.3 6.SP.4 6.SP.5 Calculate mean, median, mode and range Gather data from histograms, line plots, box plots and circle graphs Tally data given an experiment Statistics: Recognize statistical understanding as one that anticipates more than one answer Understand that a set of data collected to answer a statistical question has a spread, size and overall shape. Understand what mean, median and mode represent for the set of data, and that range represents the variable of the data. Display numerical data with a number line (line plot), histograms, box plots and circle graphs. Summarize data by reporting the number of observations, the units of measure, using mean, median, mode, and interquartile range, and describing overall patterns. Choose a measure of central tendency to accurately describe the context of the data. Problem Solving Technique: Analyze data in a variety of forms 1. Cross Curricular p 280 practice and reteach are both from ch Enrich is the same SMART Gr 6 slides: Measures of Central Tendency, Line Plots, Stem-and-leaf, pictograph and bar graph, circle graphs World: Unit 9 common Note: Courses 621 and 622 will move at different paces. Time allotments may change as the year continues. All s may not be given. Administration of these are based on the needs of the students.

Calculate the area of right triangles and other types of triangles. 6.G.1

Calculate the area of right triangles and other types of triangles. 6.G.1 Name of Student 6 th Grade Domain and Cluster Solve real-world and Mathematical problems involving area, surface area, and volume. Mastered Y/N Common Core Math Standards Portfolio Tracking Sheet Geometry