MCPS Math Pathways Whitman Cluster Parent Meeting March 8, 2018 Sheila Berlinger, supervisor elementary mathematics Darrian McCarter, supervisor secondary mathematics
Rigor in Math: Key Messages 1. Rigor is the expectation for ALL students. 2. Rigorous tasks may not always have a direct path towards a solution and can have multiple access points for solving. 3. Rigorous instruction builds students deep and conceptual understanding of mathematics. 4. Rigor requires students to do the reasoning about mathematics for themselves. Productive struggle helps students to make sense of the mathematics. 2
Key Enrichment Messages Infuse enrichment throughout math instruction on all levels for all students Use enrichment as an instructional pathway for students who have already mastered grade level benchmarks Implement enriched tasks with an emphasis on differentiation and discourse 3
Pathways 4
Acceleration Core Principles 1. When students are challenged with a rigorous mathematics program and supported, they meet or exceed the expectations. 2. The MCPS curriculum is designed for all students to reach the goal of success in Algebra 1 or higher by Grade 8, and there will be options in every school for students to reach courses beyond Algebra 1 by Grade 8. 3. MCPS will broaden access to math acceleration for all students. 4. There will be no barriers to participation in accelerated curriculum. 5
Essential Understandings: Math 4/5 Math 4/5 and Math 5/6 are accelerated math courses which follow a different pacing schedule to allow the complete instruction of Math 4, Math 5 and Math 6 over 3 years. Math 4 and Math 5 do not parallel the instructional sequence and offer different level of exposures to enrichment unique to this class. 6
Secondary Pathways 7
MCPS Mathematics Graduation Requirements Math Credits: 4 credits: 1 full-year (A/B) algebra credit or subsequent mathematics courses which algebra I is a prerequisite and 1 geometry credit required. Students who successfully complete a calculus course may be exempted from this 4-credit requirement. Math Assessment: Pass Algebra 1 PARCC: 725 current 7th graders and above 750 current and subsequent 6th grade students 8
MSDE Mathematics Enrollment Requirements NEW STATE REQUIREMENT FOR STUDENTS GRADUATING IN 2018 AND LATER: Students graduating in 2018 and later must be enrolled in a math course in each year of high school. This may result in students earning more than 4 credits in math for graduation. 9
The University System of Maryland (USM) (USM) Requirement The coursework must include Algebra I, Geometry, and Algebra II. Students who complete Algebra II before their senior year must also complete the fourth-year math requirement. They can do so by taking a course during their senior year that utilizes non-trivial algebra. MCPS Course Offerings Statistics and Mathematical Modeling Quantitative Literacy Precalculus AP Statistics Calculus w/ Application AP Calculus Multivariable Calculus and Differential Equations 10
General Questions/Answers Can a student repeat a math class in high school? If so, how does a repeated course affect GPA and credits? Why is math the only official MCPS subject matter to offer formal, data- driven screening and acceleration at the ES level? Why doesn t MCPS formally screen for other subject areas when AP course offerings at the HS level require an equal amount of rigor and preparation? How do we promote a better dialogue around acceleration beyond mathematics? 11
Additional Questions
Grade 4 Mathematics Concepts and Topics Week Marking Period 1 Marking Period 2 Marking Period 3 Marking Period 4 1 Place value (to one million): relationships among places in the base ten system Reading & writing numbers to one million: numerals, number names, expanded form 2 Place value (to one million): relationships among places in the base ten system Reading & writing numbers to one million: numerals, number names, expanded form Comparison: multi-digit numbers (<,>,=) 3 Comparison: multi-digit numbers (<,>,=) Rounding (within one million): nearest 10 or 100 Multiplication (2-digit 1-digit): equations, rectangular arrays, area models, place value strategies, properties of operations Multiplication (3- and 4-digit 1-digit): equations, rectangular arrays, area models, place value strategies, properties of operations Multiplication (up to 4-digit 1-digit): equations, area models, place value strategies, properties of operations Area & perimeter formulas (rectangles): word problems, including missing side lengths 4 Rounding (within one million): to any place Multiplication (up to 4-digit 1-digit): equations, area models, place value strategies, properties of operations Multiplicative reasoning: converting measurement units (larger to smaller) 5 Addition & subtraction fluency within one million (without decomposing across zeroes): standard algorithm 6 Addition & subtraction fluency within one million (including decomposing across zeroes): standard algorithm 7 Multi-step word problems: addition & subtraction, assess reasonableness Division with & without remainders (2-digit 1-digit): equations, rectangular arrays, area models, place value strategies, properties of operations Division with & without remainders (3-and 4- digit 1-digit): equations, place value strategies, properties of operations Division with & without remainders (3-and 4- digit 1-digit): equations, place value strategies, properties of operations 8 Multiplication as comparison Word problems involving measurement (whole numbers): four operations involving distances, intervals of time, masses of objects, money 9 Multiplication & division word problems: comparison (1-digit factors) Distinguishing multiplicative comparison from additive comparison Four operation word problems (whole numbers): multi-step Area & perimeter formulas (rectangles): word problems, including missing side lengths Factor pairs & multiples (1-100) Prime & composite Word problems involving measurement: converting from larger units of time to smaller units Fractions equivalent to ½: relate visual models to multiplicative reasoning Comparison of fractions to benchmarks (0, ½, 1) Fractions equivalent beyond ½: relate visual models to multiplicative reasoning Comparison of fractions (Grade 4 limited to denominators of 2,3,4,5,6,8,10,12,100): different numerator or denominator Fractions: decomposing Addition & subtraction of fractions (like denominators, including mixed numbers) 1-step word problems: addition & subtraction of fractions with like denominators Fractions: decomposing Addition & subtraction of fractions (like denominators, including mixed numbers) 1-step word problems: addition & subtraction of fractions with like denominators Measurement data: line plots (halves, fourths, eighths) Multiplication of a fraction by a whole number, including word problems Multiplication of a fraction by a whole number, including word problems Word problems involving measurement (fractions): addition, subtraction, & multiplication involving distances, intervals of time, masses of objects Fraction with denominator 10 as equivalent fraction with denominator 100 Addition of fractions with unlike denominators (10 & 100) Decimal notation (fractions with denominators 10 or 100) Word problems involving measurement (including decimals as fractions): distances, liquid volumes, intervals of time Decimal notation (fractions with denominators 10 or 100): meter stick, number line Comparison of decimals (to hundredths) Multiplication (2-digit 2-digit): equations, rectangular arrays, area models, place value strategies, properties of operations Multiplication (4-digit 1-digit, 2-digit 2- digit) & division (4-digit 1-digit): equations, rectangular arrays, area models, place value strategies, properties of operations Lines, line segments, perpendicular & parallel lines: drawings, identification in twodimensional figures Lines of symmetry Geometric measurement: angle concepts & measurement Geometric measurement: angle concepts & measurement Classification of 2-dimensional shapes: parallel lines, perpendicular lines, angles of specified size Geometric measurement: angle concepts & measurement Classification of triangles: sides and angles Addition & subtraction fluency within one million: standard algorithm Four operation word problems (whole numbers): multi-step Number & shape patterns Montgomery County Public Schools, Maryland Curriculum 2.0 July 2016 B9
Grade 4/5 Compacted Mathematics Concepts and Topics Week Marking Period 1 Marking Period 2 1 Place value (to one million): relationships among places in the base ten system Reading & writing numbers to one million: numerals, number names, expanded form Comparison: multi-digit numbers (<,>,=) 2 Comparison: multi-digit numbers (<,>,=) Rounding (within one million): to any place Factor pairs & multiples (1-100) Prime & composite Word problems involving measurement: converting from larger units of time to smaller units Fractions equivalent to ½: relate visual models to multiplicative reasoning Comparison of fractions to benchmarks (0, ½, 1) 3 Addition & subtraction fluency within one million: standard algorithm Fractions equivalent beyond ½: relate visual models to multiplicative reasoning Comparison of fractions (Grade 4 limited to denominators of 2,3,4,5,6,8,10,12,100): different numerator or denominator 4 Multi-step word problems: addition & subtraction, assess reasonableness Fractions: decomposing Multiplication & division word problems: comparison (1-digit factors) Addition & subtraction of fractions (like denominators, including mixed numbers) Distinguishing multiplicative comparison from additive comparison 1-step word problems: addition & subtraction of fractions with like denominators Measurement data: line plots (halves, fourths, eighths) B13 5 Multiplication (up to 4-digit 1-digit): equations, area models, place value strategies, properties of operations 6 Multiplication (up to 4-digit 1-digit): equations, area models, place value strategies, properties of operations Area & perimeter formulas (rectangles): word problems, including missing side lengths Multiplicative reasoning: converting measurement units (larger to smaller) 7 Division with & without remainders (up to 4-digit 1-digit): equations, rectangular arrays, area models, place value strategies, properties of operations 8 Division with & without remainders (up to 4-digit 1-digit): equations, place value strategies, properties of operations 9 Four operation word problems (whole numbers): multi-step Word problems involving measurement (whole numbers): four operations involving distances, intervals of time, masses of objects, money Area & perimeter formulas (rectangles): word problems, including missing side lengths Multiplication of a fraction by a whole number, including word problems Multiplication of a fraction by a whole number, including word problems Word problems involving measurement (fractions): addition, subtraction, & multiplication involving distances, intervals of time, masses of objects Lines, line segments, perpendicular & parallel lines: drawings, identify in 2-D figures Lines of symmetry Geometric measurement: angle concepts & measurement Geometric measurement: angle concepts & measurement Classification of 2-dimensional shapes: parallel lines, perpendicular lines, angles of specified size Classification of triangles: sides and angles Geometric measurement: angle concepts & measurement Montgomery County Public Schools, Maryland Curriculum 2.0 July 2016
Grade 4/5 Compacted Mathematics Concepts and Topics Week Marking Period 3 Marking Period 4 1 Fraction with denominator 10 as equivalent fraction with denominator 100 Addition of fractions with unlike denominators (10 & 100) Decimal notation (fractions with denominators 10 or 100) Word problems involving measurement (including decimals as fractions): distances, liquid volumes, intervals of time 2 Decimal notation (fractions with denominators 10 or 100): meter stick, number line Comparison of decimals (to hundredths) Multiplication (2-digit 2-digit multiples of 10): equations, rectangular arrays, area models, place value strategies, properties of operations 3 Multiplication (4-digit 1-digit, 2-digit 2-digit) & division (4-digit 1-digit): equations, rectangular arrays, area models, place value strategies, properties of operations 4 Addition & subtraction fluency within one million: standard algorithm Four operation word problems (whole numbers): multi-step Number & shape patterns Division (up to 4-digit 2-digit multiple of ten): equations, rectangular arrays, area models, place value strategies, properties of operations Division (up to 4-digit 2-digit): equations, place value strategies, properties of operations Addition & subtraction of fractions (related denominators, including 2, 4, & 8; 3 & 6): equivalent fractions as a strategy, word problems, estimation & reasonableness of answers Addition & subtraction of fractions (denominators with a common factor, including 6 & 9): equivalent fractions as a strategy, word problems, estimation & reasonableness of answers **************************END OF GRADE 4 CONTENT******************************* B14 5 Multiplication: standard algorithm (multi-digit whole numbers) Addition & subtraction of fractions (1-digit denominators with no common factors, including 3 & 4): equivalent fractions as a strategy, word problems, estimations & reasonableness of answers 6 Volume (right rectangular prisms): counting unit cubes (cubic cm, cubic in, cubic ft, & improvised units), relationship to multiplication, problem solving Addition & subtraction of fractions: equivalent fractions as a strategy, word problems, estimation & reasonableness of answers 7 Volume (right rectangular prisms): formulas for rectangular prisms, additive properties, problem solving Numerical expressions with parentheses, brackets, braces 8 Place value relationships among places in the base ten system Place value patterns: multiplication or division by powers of 10, whole number exponents Decimals (thousandths): read, write, compare, & round 9 Addition & subtraction of decimals (tenths & hundredths as addends): concrete models, drawings, written method, place value strategies, properties of operations, relationship between addition & subtraction Ordered pairs on a coordinate plane Numerical patterns using two given rules: relationships between corresponding terms Classification of two-dimensional figures: properties Classification of two-dimensional figures: properties Montgomery County Public Schools, Maryland Curriculum 2.0 October 2014
Week Marking Period 1 Marking Period 2 Marking Period 3 Marking Period 4 Grade 5 Mathematics Concepts and Topics B11 1 Multiplication: standard algorithm (multi-digit whole numbers) 2 Volume (right rectangular prisms): counting unit cubes (cubic cm, cubic in, cubic ft, & improvised units), relationship to multiplication, problem solving 3 Volume (right rectangular prisms): formulas for rectangular prisms, additive properties, problem solving Numerical expressions with parentheses, brackets, braces: evaluating 4 Numerical expressions: evaluating, interpreting without evaluating 5 Place value relationships among places in the base ten system Place value patterns: multiplication or division by powers of 10, whole number exponents Decimals (thousandths): read & write 6 Comparison of decimals (to thousandths) Rounding decimals 7 Addition & subtraction of decimals (tenths or hundredths as addends): concrete models, drawings, written method, place value strategies, properties of operations, relationship between addition & subtraction 8 Addition & subtraction of decimals (tenths & hundredths as addends): concrete models, drawings, written method, place value strategies, properties of operations, relationship between addition & subtraction 9 Division (2- or 3-digit 2-digit multiple of ten): equations, rectangular arrays, area models, place value strategies, properties of operations Division (up to 4-digit 2-digit multiple of ten): equations, rectangular arrays, area models, place value strategies, properties of operations Division (up to 4-digit 2-digit): equations, rectangular arrays, area models, place value strategies, properties of operations Division (up to 4-digit 2-digit): equations, place value strategies, properties of operations Addition & subtraction of fractions (related denominators, including 2, 4, & 8; 3 & 6): equivalent fractions as a strategy, word problems, estimation & reasonableness of answers Addition & subtraction of fractions (denominators with a common factor, including 6 & 9): equivalent fractions as a strategy, word problems, estimation & reasonableness of answers Addition & subtraction of fractions (1-digit denominators with no common factors, including 3 & 4): equivalent fractions as a strategy, word problems, estimations & reasonableness of answers Addition & subtraction of fractions: equivalent fractions as a strategy, word problems, estimation & reasonableness of answers Multiplication of a whole number and a fraction (partitive, whole number products): problem solving, length models, number line models, set models Multiplication of a fraction by a fraction (numerator of one factor is a multiple of the denominator of the other factor): problem solving Multiplication fluency: standard algorithm Multiplication of a fraction by a fraction (both factors <1): problem solving, area models Multiplication of a fraction by a fraction (one factor >1): problem solving, area models Multiplication of a fraction by a fraction (both factors >1): problem solving, area models Multiplication of a fraction by a fraction (both factors >1, including mixed numbers): problem solving, area models Area: rectangles with fractional side lengths Multiplication of a whole number and a fraction (partitive, fraction products) Division of a unit fraction by a non-zero whole number or a whole number by a unit fraction: visual fraction models, relationship between multiplication and division, equations, word problems Division of a unit fraction by a non-zero whole number or a whole number by a unit fraction: visual fraction models, relationship between multiplication and division, equations, word problems Fractions as division of numerator by denominator: visual fraction models, equations, word problems Measurement data: line plots (12, 14, 18 of a unit) Multiplication fluency (multi-digit whole numbers): standard algorithm Multiplication of decimals (to hundredths): models, drawings, written method, place value strategies, properties of operations Division of decimals (to hundredths): place value strategies, properties of operations Division of decimals (to hundredths): place value strategies, properties of operations Word problems (multi-step): conversion of measurement units (within a given measurement system) Addition, subtraction, multiplication, division of decimals (to hundredths): place value strategies, properties of operations Word problems (multi-step): conversion of measurement units (within a given measurement system) Ordered pairs on a coordinate plane Ordered pairs on a coordinate plane Numerical patterns using two given rules: relationships between corresponding terms Classification of two-dimensional figures: properties Classification of two-dimensional figures: properties Classification of two-dimensional figures: properties Montgomery County Public Schools, Maryland Curriculum 2.0 October 2014
Grade 5/6 Compacted Mathematics Concepts and Topics B15 Week Marking Period 1 (Grade 5 Content) 1 Multiplication of a whole number and a fraction (partitive, whole number products): problem solving, length models, number line models, set models 2 Multiplication of a fraction by a fraction (numerator of one factor is a multiple of the denominator of the other factor): reasoning, problem solving Multiplication fluency (multi-digit whole numbers): standard algorithm 3 Multiplication of a fraction by a fraction (both factors <1; one factor >1):: problem solving, area models 4 Multiplication of a fraction by a fraction (both factors >1, including mixed numbers): problem solving, area models 5 Area: rectangles with fractional side lengths Multiplication of a whole number and a fraction (partitive, fraction products) 6 Division of a unit fraction by a non-zero whole number or a whole number by a unit fraction: visual fraction models, relationship between multiplication and division, equations, word problems 7 Division of a unit fraction by a non-zero whole number or a whole number by a unit fraction: visual fraction models, relationship between multiplication and division, equations, word problems Fractions as division of numerator by denominator: visual fraction models, equations, word problems Measurement data: line plots (,, of a unit) 8 Multiplication of decimals (to hundredths): models, drawings, written method, place value strategies, properties of operations Division of decimals (to hundredths): place value strategies, properties of operations 9 Division of decimals (to hundredths): place value strategies, properties of operations Addition, subtraction, multiplication, division of decimals (to hundredths): place value strategies, properties of operations Word problems (multi-step): conversion of measurement units (within a given measurement system) Marking Period 2 (Grade 6 Content) Understanding Ratios and Rates o Describe, recognize, and represent ratio relationships in a variety of representations o Explain and classify different types of ratios, including rate and unit rate Understanding Ratios and Rates o Interpret problems with ratios, including unit rates Application of Ratios and Rates o Create, interpret, and find missing values in tables of equivalent ratios o Display a series of equivalent ratios on a coordinate grid Application of Ratios and Rates o Solve rate and ratio problems, including unit rate, using multiple representations o Convert customary and metric units using ratio reasoning Application of Ratios and Rates o Describe and compare ratios as a fraction, decimal, and percent o Solve percent problems involving finding the part or the whole Division of Fractions o Divide fractions by whole numbers Division of Fractions o Divide whole numbers by fractions o Divide fractions by unit fractions o Divide a fraction by a fraction Division of Fractions o Reason about the inverse relationship between division and multiplication of fractions o Use reasoning about the unit rate to develop understanding of the standard algorithm for dividing fractions Multi-Digit Computation o Apply place value understanding to develop understanding of the standard algorithm for division o Solve word problems using the standard algorithm for division Multi-Digit Computation o Multiply decimals using fractions and the standard algorithm o Divide decimals by reasoning about place value and using the standard algorithm Multi-Digit Computation Montgomery County Public Schools, Maryland Curriculum 2.0 October 2014
Grade 5/6 Compacted Mathematics Concepts and Topics B16 Week Marking Period 3 (Grade 6 Content) 1 Extending the Number Line o Understand that positive and negative integers are used together to describe quantities and values o Recognize that positive and negative rational numbers are used together to describe quantities having opposite directions or values, and reason about the meaning of 0 in real-world contexts o Recognize and position a number, its opposite, and the opposite of the opposite on a horizontal and vertical number line diagram 2 Order and Absolute Value oorder rational numbers and interpret comparisons on a number line o Describe absolute value of a rational number as the distance from 0 on a number line and interpret the magnitude of a number by absolute value odistinguish comparisons of absolute value from statements about order 3 Coordinate Relationships o Identify parts of the coordinate plane and name and locate points using ordered pairs on the coordinate grid o Reason about the relationship between coordinates reflected over the x- and y- axes o Find horizontal and vertical distances on the coordinate plane using absolute value 4 Coordinate Relationships ouse the coordinate plane to graph geometric shapes Multi-Digit Computation ofluently add, subtract, multiply, and divide multi-digit decimals 5 Exponents o Identify and model the relationship between exponents and repeated multiplication owrite and evaluate numerical expressions involving whole-number exponents Introducing Algebraic Expressions ocreate, interpret, and evaluate numerical expressions using order of operations 6 Introducing Algebraic Expressions oreason about situations to interpret, create, and evaluate algebraic expressions ocreate and evaluate an expression for an unknown based on a context 7 Properties and Equivalency o Identify common factors and common multiples of a pair of numbers; including the greatest common factor and least common multiple o Identify the common factors from two whole numbers and rewrite the sum using the greatest common factor ocreate multiple representations of equivalent algebraic expressions 8 Equations and Inequalities o Reason about the role of the variable by examining the structure of equivalent expressions o Solve equations, precisely state the meaning of the variable, and represent Marking Period 4 (Grade 6 Content) Relationships between Variables o Analyze the relationship between two variables to choose an independent variable and dependent variable o Reason about equations in two variables and the solutions o Represent the relationship between the independent and dependent variables on a table and a graph Relationships between Variables o Write equations to model real-world situations Relating Area and Volume o Explore rectangles and the attributes of other two-dimensional figures o Develop the area formulas for right triangles, parallelograms, and triangles Relating Area and Volume o Determine the area of special quadrilaterals, polygons, and composite figures using decomposition and composition o Model volume Relating Area and Volume o Examine the relationship between the area of the base and the height of a prism to derive a formula for volume o Reason about and apply the volume formula Surface Area o Construct three-dimensional figures using nets Surface Area o Use nets to determine the surface area of three-dimensional figures Multi-Digit Computation o Use the standard algorithm to fluently add, subtract, multiply, divide multi-digit decimals and divide whole numbers Statistical Questions o Explore and reason about data displays o Distinguish between statistical and non-statistical questions Statistical Questions o Write examples of statistical questions Analyzing Data Distributions o Reason about and determine measures of center and spread using data sets Analyzing Data Distributions o Explore the mean absolute deviation o Construct and interpret histograms and box plots to analyze a data set the solution 9 Equations and Inequalities Analyzing Data Distributions o Identify the data display that best describes measures of center, spread, and the overall shape of the distribution Montgomery County Public Schools, Maryland Curriculum 2.0 October 2014
Marking Period 1 Sept Sept/ Oct Oct Marking Period 2 Nov Dec/ Jan Jan MCPS 2015 Mathematics 6 At-a-Glance Ratios, Fractions, and Decimals Topic 1: Understanding Ratios and Rates Students investigate the concepts of ratio and rate. They use multiple forms of ratio language and ratio notation and make connections between ratios and fractions. Students relate their understanding of ratios to explain and classify different types of ratios; including rate and unit rate. They use reasoning about multiplication and division to solve ratio and rate problems about quantities. Topic 2: Application of Ratios and Rates Students apply reasoning when solving collections of ratio problems in real world contexts using various tools. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in a table, students connect their understanding of multiplication and division with ratios and rates. Students solve a wide variety of problems involving ratios and rates, discovering that a percent of a quantity is a rate per 100. Although it is traditional to move students quickly to solving proportions by cross multiplying, it is imperative for students to reason multiplicatively with ratios to aid their understanding of future mathematics. Topic 3: Division of Fractions Students conclude the work with fraction operations from previous grade levels by computing quotients of fractions. Students investigate two interpretations of division: measurement and sharing. They can use story contexts and visual models to develop an understanding of computing quotients of fractions, and begin to move to using the relationship between division and multiplication to determine the standard algorithm of dividing fractions. Topic 4: Multi-Digit Computation (dividing whole numbers and adding/subtracting decimals) Students are expected to demonstrate fluency in two computation standards by the end of Grade 6. During the first marking period, students divide multi-digit numbers using the standard algorithm. They also add and subtract multidigit decimals using the standard algorithm. Students use estimation and place-value understandings to explain computation with the standard algorithms. The standard algorithms become parts of a repertoire of strategies used throughout the year. A spectrum of multi-step word problems of varying complexity levels are purposefully incorporated throughout the year as new learning is developed and applied. Number Relationships Topic 1: Multi-Digit Computation (multiplying and dividing decimals) Students use their knowledge of equivalent fractions to fluently multiply and divide multi-digit decimals using the standard algorithm. A spectrum of multi-step word problems of varying complexity levels are purposefully incorporated throughout the year as new learning is developed and applied. Topic 2: Extending the Number Line Students are focused on developing an understanding of the meaning of negative numbers in real-world contexts. Students extend their previous understandings of number and ordering of numbers to the rational number system, which includes negative rational numbers. Topic 3:Order and Absolute Value The number line serves as a model for students to relate integers and other rational numbers to statements of order in real-world contexts. Students describe the relationship between rational numbers in real-world scenarios with respect to numbers positions on the number line. Students use the concept of absolute value and its notation to show a number s distance from zero on the number line and recognize that opposite numbers have the same absolute value. Using real-world scenarios, students interpret absolute value. They apply their understanding to distinguish comparisons of absolute value from statements about order. Topic 4: Coordinate Relationships Students extend their understanding of the ordering of rational numbers on a number line to the coordinate plane. Students determine the relationship between the signs of numbers in an ordered pair in relation to the location of the point. They build upon their foundational understanding of plotting points in the first quadrant and transition to locating points in all four quadrants. Topic 5: Multi-Digit Computation (divide whole numbers and decimal operations) Students use their knowledge of equivalent fractions to fluently multiply and divide multi-digit decimals using the standard algorithm, including multi-step word problems of varying complexity levels. Topic 6: Exponents Students apply prior knowledge of place value and powers of ten and extend this knowledge to any positive rational number using repeated multiplication. Students develop the conceptual understanding that a whole number exponent is equivalent to repeated multiplication. In order to develop this conceptual understanding, students write and evaluate numerical expressions that are limited to whole number exponents.
Marking Period 3 Jan/ Feb Feb Feb/ Mar Mar Marking Period 4 Apr Apr/ May May Jun Mathematics 6 At-a-Glance Expressions and Equations Topic 1: Introducing Algebraic Expressions Students begin working systematically with algebraic expressions and use mathematical terms to clarify parts of an expression. They write, evaluate, and interpret expressions that correspond to given situations. Students use variables or letters to stand for unknowns to write expressions. When given the value of the variable, students use the Order of Operations to evaluate expressions. Students write expressions by abstracting patterns thus summarizing a calculation that can be carried out repeatedly with different numbers. They recognize how one part of the expression can impact the other parts and they view those parts as a single entity. Topic 2: Properties and Equivalency Students now consider common factors and multiples and find greatest common factors and least common multiples. Students apply their knowledge of common factors and multiples by using the distributive property. Students use previous understandings of equivalent numerical expressions to algebraic expressions. Students extend their work with properties of operations from arithmetic to algebra. Topic 3: Equations and Inequalities Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations and inequalities. Students understand the solution of an equation is the value of the variable that makes the equation true. It is important for students to state precisely the meaning of variables they use when setting up equations. Students solve real-world problems and represent inequalities on number line diagrams. Topic 4: Relationships Between Variables In addition to constructing and solving equations in one variable, students will use equations in two variables to express relationships between two quantities that vary together. As they work with two-variable equations, students begin to develop a dynamic understanding of variables and an appreciation that they can stand for any number from some domain. Students solve equations in real-world, contextual problems. Students will construct tables of independent and dependent values in order to analyze equations with two variables from real-life contexts. They will represent equations by plotting values from the tables on a coordinate grid. Geometric and Statistical Relationships Topic 1: Relating Area and Volume Students develop the formula for the area of triangles. They apply their knowledge of the area of triangular and/or rectangular regions to determine the area of quadrilaterals, polygons, and composite figures in real-life contexts. Students build on their understanding of how to find the volume of a right rectangular prism to include those with fractional edge lengths. They explore how the volume of a shape can be found by composing or decomposing shapes including when the edge lengths are fractional. Students apply formulas and use their previous experience with solving equations to find the values of missing volumes or missing dimensions. Topic 2: Surface Area Students deconstruct solid figures into nets to identify the measurement of the solids face edges and area. They use nets to develop, then apply the formula for surface area of prisms. Topic 3: Multi-Digit Computation (dividing whole numbers & decimals operations) During the fourth marking period, students use the standard algorithm to fluently operate with multi-digit numbers and decimals. A spectrum of multi-step word problems of varying complexity levels are purposefully incorporated in this topic as new learning is developed and applied. Topic 4: Statistical Questions Students differentiate between statistical and non-statistical types of questions. Statistical questions anticipate variability in the question which needs to be accounted for in the answer. Variability is explored in terms of the context, the statistical question being asked, measures of center and spread, and the display of the data. Topic 5: Analyzing Data Distributions Students 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. Students display numerical data in plots on a number line, including dot plots, histograms, and box plots. They learn to describe and summarize numerical data sets by identifying clusters, peaks, gaps, symmetry, skew, and outliers considering the context in which the data were collected. Exploring variation with the mean absolute deviation (MAD) sets the stage for introducing the standard deviation in later grades. MCPS 2015