ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT Math 6-8 Curriculum Guide

ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT Math 6-8 Curriculum Guide BOE Approval: 02/12/2015

Math 6-8 Curriculum Guide Table of Contents DTSD Mission Statement 3 Department Vision 3 Affirmative Action Compliance Statement 3 Curriculum and Planning Guides Grade 6 Units 4-18 Grade 7 Units 19-39 Grade 8 Units 40-50 STANDARDS FOR MATHEMATICAL PRACTICE The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices are integrated throughout our curriculum at all grade levels. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate Tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. INTERDISCIPLINARY THEMES Planned interdisciplinary activities can help students to make sensible connections among subjects, while limiting the specialist's tendency to fragment the curriculum into isolated pieces. Such activities provide students with broader personal meaning and the integrated knowledge necessary to solve real-world problems. Teachers are encouraged to independently and cooperatively develop lessons which cover multiple areas simultaneously. 2

MISSION STATEMENT The Rochelle Park School District s envisions an educational community which inspires and empowers all students to become self-sufficient and thrive in a complex, global society DEPARTMENT VISION It is the firm belief of the Rochelle Park Township School District that mathematics provides students with a common language that allows them to actively participate in collaborative problem solving scenarios. This common language will provide our students with a foundation of a deeper understanding of their future fiscal responsibilities within the global economy they participate in. We encourage our students to advocate for their communities by acting as a driving force, so that we may build a more sustainable economy in the future. This guide is to provide focus for the learning that will take place in this course, but is completely modifiable based upon the needs and abilities of the students and their Individual Education Plans. Curriculum implementation follows best practice and adheres to the New Jersey Core Content Standards. At the same time, for students with disabilities, the Individual Education Plan, specifically the Goals and Objectives of the plan, supersede any curricular adherence or suggestion. 21 ST CENTURY THEMES & SKILLS Embedded in much of our units of study and problem based learning projects are the 21 st Century Themes as prescribed by the New Jersey Department of Education. These themes are as follows: Global Awareness Financial, Economic, Business, and Entrepreneurial Literacy Civic Literacy Health Literacy AFFIRMATIVE ACTION COMPLIANCE STATEMENT The Rochelle Park Township Public Schools are committed to the achievement of increased cultural awareness, respect and equity among students, teachers and community. We are pleased to present all pupils with information pertaining to possible career, professional or vocational opportunities which in no way restricts or limits option on the basis of race, color, creed, religion, sex, ancestry, national origin or socioeconomic status. 3

Grade: 6 Unit: Operations and Properties (1) Time Frame: 20.5 periods Estimation can be used to check the reasonableness of answers. Many mental math strategies use number properties that you already know to make equivalent expressions that may be easier to simplify. What is the Order of Operations and how does it help? How are exponents used to represent numbers and why? How do I use the commutative, associative, and distributive property to solve equations and expressions? KNOWLEDGE SKILLS STANDARDS dividing multi-digit numbers can be done using the standard algorithm. use the order of operations. use properties to find numerical expressions can be written using whole number equivalent expressions. exponents. (2) CC.6.NS.2 in expressions, letters stand for numbers. properties of operations can be used to generate equivalent expressions. expressions can be evaluated with specific values for variables using the conventional order of operations. different strategies to find the greatest common factor and least common multiple of two whole numbers. the sum of two whole numbers can be expressed with a common factor as a multiple of a sum of two whole numbers with no common factor using the distributive property. (1) estimate with whole numbers. (2) use the algorithm for division and interpret the quotient and remainder in a real world setting. (3) represent numbers by using exponents. (4L)-use a graphing calculator to explore the order of operations. (4) use the order of operations. (5) use number properties to compute mentally. (3) CC.6.EE.1 (4L) CC.6.EE.2,2c 8.1.8.A.5 (4) CC.6.EE.2,2c (5) CC.6.EE.3 CC.6.NS.4 VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT estimate, compatible number, underestimate, overestimate, dividend, divisor, exponent, base, exponential form, numerical expression, simplify, order of operations, commutative property, associative property, distributive property Holt McDougal Mathematics 6: Chapter 1 HMM 6 Lab Activities WB (3) graphing calculator (4L) number cubes (5) Quiz 1A Quiz 1B Chapter 1 Test 4

Grade: 6 Unit: Introduction to Algebra (2) Time Frame: 28 periods An equation is a mathematical statement that two expressions are equal. Multiplication and division are inverse operations as addition and subtraction are inverse operations. Why should we study Algebra? What are mathematical expressions and equations? What is the difference? How do I determine whether a solution to an equation is correct? KNOWLEDGE SKILLS STANDARDS in expression, letters stand for numbers. write expressions and equations for given situations. parts of expressions can be identified evaluate expressions. using mathematical parts and one or solve one-step equations. more parts can be viewed as a single (1) CC.6.EE.2,2b entity. operations with numbers and/or variables can be written as expressions. (2) CC.6.EE.2,2a,2b (3) CC.6.EE.2,2a solving an equation or inequality is a process of answering the question which values from a specified set, if any, make the equation or inequality true? methods to identify when two expressions are equivalent. real world and mathematical problems can be solved by writing and solving equations of the form x + p = q and px = q where p,q, and x are all nonnegative rational numbers. variables can be used to represent an unknown number or a number in a specified set and that expressions can be written when solving a real-world or mathematical problem. algebraic expression, constant, equation, evaluate, inverse operations, solution, variable (1) identify and evaluate expressions. (2) translate between words and math. (3) write expressions for tables and sequences. (3L)- use grid paper to model the area and perimeter of different rectangles. (4) determine whether a number is a solution of an equation. (5) solve whole number addition equations. (6) solve whole number subtraction equations. (7) solve whole number multiplication equations. (8) solve whole number division equations. (3L) CC.6.EE.2,3 (4) CC.6.EE.4,5 (5) CC.6.EE.6,7 (6) CC.6.EE.6 (7) CC.6.EE.6,7 (8) CC.6.EE.6 VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT Holt McDougal Mathematics 6: Chapter 2 HMM 6 Lab Activities WB Quiz 2A (1,5,7) Quiz 2B grid paper (3L), scissors (3L), balance scales (4,6), algebra Chapter 2 Test tiles/counters(5), index cards (8) 5

Grade: 6 Unit: Decimals (3) Time Frame: 29.5 periods Decimal numbers represent combinations of whole numbers and numbers between whole numbers. Equations with decimals can be solved using inverse operations just as equations with whole numbers can be solved using inverse operations. How can I add, subtract, multiply and divide decimals fluently? How do decimal numbers impact multiplication and division? How do I estimate with decimals? KNOWLEDGE SKILLS STANDARDS adding, subtracting, multiplying, and dividing decimals can be done using the standard algorithm for each operation. use common procedures to multiply and divide decimals. evaluate expressions and solve equations with decimals. real world and mathematical problems can be solved by writing and solving equations of the form x + p = q and px=q where p, q, and x are all nonnegative rational numbers. variables can be used to represent an unknown number or a number in a specific set and that expressions can be written when solving a real world or mathematical problem. clustering, front-end estimation (1) write, compare, and order decimals using place value and number lines. (2) estimate decimal sums, differences, products, and quotients. (3L) use decimal grids to model addition and subtraction of decimals. (3) add and subtract decimals. (4L) use decimal grids to model multiplication and division of decimals. (4) multiply decimals by whole numbers and by decimals. (5) divide decimals by whole numbers. (6) divide whole numbers and decimals by decimals. (7) solve problems by interpreting the quotient. (8) solve equations involving decimals (3L) CC.6.NS.3 (3) CC.6.EE.7 CC.6.NS.3 (4L) CC.6.NS.3 (4) CC.6.EE.7 CC.6.NS.3 (5) CC.6.NS.3 (6) CC.6.NS.3 (7) CC.6.NS.3 (8) CC.6.EE.6,7 VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT Holt McDougal Mathematics 6: Chapter 3 HMM 6 Lab Activities WB (3,6,8) Quiz 3A Quiz 3B decimal grids/grid paper (3L, 4L), colored pencils (4L), transparency grids (4L), graph paper (5), index Chapter 3 Test cards (6) 6

Grade: 6 Unit: Number Theory & Fractions (4) Time Frame: 29.5 periods You can use factors to write a number in different ways. Algebraic expressions can be factored using GCF and the distributive property. Decimals and fractions can often be used to represent the same number. How can we develop and apply number theory concepts in problem solving situations? What do the factors and multiples of a number tell me? How do we identify and demonstrate knowledge of fractions? KNOWLEDGE SKILLS STANDARDS the greatest common factor of two whole numbers less than or equal to 100 can be found and the sum of two whole numbers 1-100 can be expressed using the distributive property. expressions can be identified as equivalent when they are named the same number regardless of the value substituted into them. rational numbers can be ordered and also have an absolute value. view a fraction as parts of a whole. use multiplication and division to determine equivalent fractions. (1) write prime factorizations of composite numbers. (2) find the greatest common factor (GCF) of a set of numbers. (2L) use a graphing calculator to find the greatest common factor (GCF) of two or more numbers. (3) factor numerical and algebraic expressions and write equivalent numerical and algebraic expressions. (4L)use decimal grids to show the relationship between decimals and fractions. (4) convert between decimals and fractions. (5L) use pattern blocks to model equivalent fractions. (5) write equivalent fractions. (6) covert between mixed numbers and improper fractions. (7) use pictures and number lines to compare and order fractions. (2) 6.NS.4 (2L) 6.NS.4 8.1.8.A.5 (3) 6.EE.4 (7) 6.NS.7 7

VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT common denominator, coefficient, equivalent expressions, equivalent fractions, factor, greatest common factor, improper fraction, like fractions, mixed numbers, prime factorization, proper fraction, repeating decimal, simplest form, term, terminating decimal, unlike fractions Holt McDougal Mathematics 6: Chapter 4 HMM 6 Lab Activities WB (6,7) graphing calculator (2L), decimal grids/grid paper (4L), fraction bars (4L, 5L, 6, 7), pattern blocks (5L), number cubes (5L), customary rulers (5L, 6), transparency ruler (5L) Quiz 4A Quiz 4B Chapter 4 Test 8

Grade: 6 Unit: Fraction Operations (5) Time Frame: 26.5 periods You can use any common denominator or the least common denominator to add and subtract unlike fractions. Reciprocals are necessary to divide by fractions. How do I add, subtract, multiply, and divide fractions fluently? How can I solve equations with fractions? KNOWLEDGE SKILLS STANDARDS word problems can be solved using division of fractions. the greatest common factor of two whole numbers less than or equal to 100 can be found and the sum of two whole numbers 1-100 can be expressed using the distributive property. real world problems can be solved by writing and solving equations in the form x+p=q and px=q where all values are nonnegative rational numbers. understand the procedures for multiplying dividing fractions. evaluate expressions and solve equations with fractions. (1) find the least common multiple (LCM) of a group of numbers. (2) add and subtract fractions with unlike denominators. (3) Regroup mixed numbers to subtract. (4) Solve equations by adding and subtracting fractions. (5) Multiply mixed numbers. (5L) use grids to model division of Fractions. (5L) use fraction bars to model the division of fractions in world problems. (6) divide fractions and mixed numbers. (7) solve equations by multiplying and dividing fractions. (1) 6.NS.4 (4) 6.EE.7 (5L)6.NS.1 (5L)6.NS.1 (6) 6.NS.1 (7) 6.EE.7 6.NS.1 VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT least common denominator, least common multiple, reciprocals, multiplicative inverse Holt McDougal Mathematics 6: Chapter 5 HMM 6 Lab Activities WB (1,2) spinners (1), fraction bars (2,3), grid paper (2, 3, 5L), fraction bar transparency (2,3), transparency grid (5L) Quiz 5A Quiz 5B Chapter 5 Test 9

Grade: 6 Unit: Data Collection and Analysis (6) Time Frame: 29.5 periods Descriptions of a set of data are called mean, median, mode, and range. Data can be displayed on various plots. How can data be described using mean, median, mode, and range? Which representation is best for analyzing the distribution of data? How can I use the appropriate measure of central tendency or variability to analyze or describe a data set? KNOWLEDGE SKILLS STANDARDS a statistical question anticipates variability in data related to the question and that it needs to be accounted for in answers. use mean, median, mode, and range to summarize data sets. make and interpret a variety of graphs. data collected to answer a statistical question has a distribution which can be described in various different ways. (1L) 6.SP.2 a measure of accentor 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. the numerical data can be displayed in plots on a number line, including dot plots, box plots, and histograms. (1L) collect data and use counters to find the mean of a set of data. (1) find the range, mean, median and mode of a set of data. (2) learn the effect of additional data and outliers. (3) calculate, interpret, and compare measures of variation in a data set. (4) organize data in line plots, frequency tables and histograms. (4L) use a survey to collect and organize data into a table. (4E) describe the frequency distribution of a data set and make a cumulative frequency table and histogram. (5) describe and compare data distributions by their center, spread, and shape, using box and whisker plots or dot plots. (1) 6.SP.3 6.SP.2 (2) 6.SP.3 (3) 6.SP.1 6.SP.3 6.SP.4 (4) 6.SP.4 (4L) 6.SP.5 (4E) 6.SP.5 numerical data sets can be 6.SP.2 summarized in relation to their (5) 6.SP.5 context. 6.SP.2 6.SP.3 6.SP.4 VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT box and whisker plot, frequency, frequency table, histogram, interquartile range (IQR), line plot, mean, median, mode, outlier, quartiles, range, variation Holt McDougal Mathematics 6: Chapter 6 HMM 6 Lab Activities WB (1,4) counters (1L) magazines/newspapers (2) graph paper (6L) Quiz 6A Quiz 6B Chapter 6 Test 10

Grade: 6 Unit: Proportional Relationships (7) Time Frame: 32.5 periods Scale models use proportional relationships to make smaller versions of large objects and larger versions of small objects. Ratios can be written to compare a part to a part, a part to the whole, or the whole to a part. Ratios in tables can be used to make estimates or predictions. One number can be represented in three different forms: fraction, decimal, and percent. How are ratios and rates connected? How are fractions, decimals, and percents related? What techniques can be used to find fraction, decimal or percent names for the same quantities? KNOWLEDGE SKILLS STANDARDS a unit rate can be associated with a ratio a:b and that rate language can be used in the context of a ratio relationship. real-world and math problems can be solved using rate and ratio reasoning through tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a rational number is a point on a number line and that number line diagrams and coordinate axes can be extended with negative number coordinates. integers and other rational numbers can be positioned on a horizontal or vertical number line diagram and on a coordinate plane. the relationship between two quantities can be described by using a ratio and ratio language. a percent of a quantity can be found as a rate per 100 and that problems can be solved given a part and the percent when being asked to find the whole. use tables to determine whether quantities are in equivalent ratios. Use proportional reasoning to solve rate and ratio problems. (1) write ratios and rates and find rates. (2) use a table to find equivalent ratios and rates. (3) graph ordered pairs on a coordinate grid. (3E) graph equivalent ratios on the coordinate plane. (4L) use counters to model equivalent ratios. (4) write and solve proportions. (5L) use a 10 by 10 grid to model a percent. (5) write percents as decimals and fractions. (6) write decimals and fractions as percents. (7) find the percent of a number. (8) solve problems involving percents. (1) 6.RP.2 (2) 6.RP.3 (3) 6.NS.6 6.NS.6c (3E)6.RP.3 (4L)6.RP.1 (4) 6.RP/1 (5L)6.RP.3c (5) 6.RP.3c (6) 6.RP.3c 8.1.8.A.5 (7) 6.RP.3 6.RP.3c (8) 6.RP.3 11

VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT coordinate grid, equivalent ratios, ordered pair, percent, proportion, rate, ratio, unit rate Holt McDougal Mathematics 6: Chapter 7 HMM 6 Lab Activities WB (3,5,7) graphing calculator (6) colored pencils (2) graph paper (3, 5L, 7) road maps (3) two color counters (4L) 10 by 10 grids (5L) number cubes (5) media advertisements involving percents (7) Quiz 7A Quiz 7B Chapter 7 Test 12

Grade: 6 Unit: Measurement & Geometry (8) Time Frame: 29.5 periods Conversion factors are an efficient tool for converting units. In the same way that the area of a plane figure is the number of non-overlapping unit squares needed to cover the figure, the volume of a threedimensional figure is the number of nonoverlapping unit cubes needed to fill the figure. What attributes of a shape are important to measure? How do I determine a basic shape and the appropriate formula to find area, perimeter, and volume? What am I finding when I find area and perimeter? KNOWLEDGE SKILLS STANDARDS ratio reasoning can be used to convert measurement units and that units can be appropriately manipulated or transformed when multiplying or dividing quantities. the area of right triangles, other triangles, special quadrilaterals, and polygons can be found by composing into rectangles or decomposing into triangles and other shapes and that these techniques can be used to solve real world and mathematical problems. expressions can be evaluated at specific values of their variables including expressions that arise from formulas used in real world problems. arithmetic operations should be performed in the conventional order when there are no parentheses to specify a particular order. volume of a right rectangular prism with fractional edge lengths can be found by packing it with unit cubes of the appropriate unit fraction edge lengths and that the volume is the same as would be found by solve problems that involve lengths, areas, and volumes. use fractions and decimals to solve measurement problems. (1) convert customary units of measure. (2) convert metric units of measure. (3) estimate the area of irregular figures and find the area of rectangles and parallelograms. (3L) use grid paper to discover the relationship between the area of a square and its side length. (4) find the area of triangles and trapezoids. (4L) use geometry software to explore area. (5) break a polygon into simpler parts to find its area. (6L) use centimeter cubes to explore the volume of prisms. (6) estimate and find the volumes of rectangular prisms and triangular prisms. (7L) use a net to build a threedimensional figure. (7) find the surface areas of prisms, pyramids, and cylinders. (1) 6.RP.3d (2) 6.RP.3d (3) 6.G.1 6.EE.2c (4) 6.G.1 (4L) 8.1.8.A.5 (5) 6.G.1 (6L) 6.G.2 (6) 6.G.2 6.EE.2c (7L) 6.G.4 (7) 6.G.4 13

multiplying the edge lengths of the prism. real world and mathematical problems involving volume can be solved by applying the rectangular prism volume formula. that three dimensional figures can be represented using nets made up of rectangles and triangles and that these nets can be used to find the surface area which can be applied to realworld and mathematical problems. VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT area, net, surface area, volume Holt McDougal Mathematics 6: Chapter 8 HMM 6 Lab Activities WB (1,2,4,6,7) geometry software (4L) map of Australia (3L) graph paper (3, 7L) grid paper (3L) centimeter cubes (6L) centimeter graph paper (6L) prism models (6) scissors (7L) tape (7L) Quiz 8A Quiz 8B Chapter 8 Test 14

Grade: 6 Unit: Integers & the Coordinate Plane (9) Time Frame: 20.5 periods Integers and their absolute values are useful in finding and comparing distances. Understanding a coordinate plane can prove useful in everyday life. For example, we use a coordinate system on Earth to find exact locations. What ordered pair corresponds to a given point on a graph? How does reversing the order of the numbers affect the location of the point? What is absolute value? Where do we see integers in the real world? KNOWLEDGE SKILLS STANDARDS positive and negative numbers are used together to describe quantities having opposite directions or values and that positive and negative numbers can be used to represent quantities in real world contexts. use negative numbers in everyday contexts. draw and transform figures in the coordinate plane. the order and absolute value of rational numbers. statements of inequality can be interpreted as statements about the relative position of two numbers on a number line diagram. statements of order for rational numbers can be written, interpreted, and explained in real world contexts. a rational number is a point on a number line and that number line diagrams and coordinate axes can be extended with negative number coordinates. integers and other rational numbers can be positioned on a horizontal or vertical number line diagram and on a coordinate plane. polygons can be drawn in the coordinate plane given coordinates for the vertices and that coordinates can be used to find the length of a side joining (1) identify and graph integers and find opposites. (2) compare and order integers. (2E) compare and order negative rational numbers. (3) locate and graph points on the coordinate plane. (4) draw polygons in the coordinate plane and find the lengths of their sides. (5) use translations, reflections, and rotations to change the positions of figures in the plane. (1) 6.NS.5 (2) 6.NS.7 6.NS.7a 6.NS.7b (2E) 6.NS.6 6.NS.6c (3) 6.NS.6 (4) 6.G.3 6.NS.6 6.NS.6c 6.NS.8 (5) 6.NS.8 6.NS.6b 6.NS.6c 15

points with the same first or second coordinate. real world and mathematical problems can be solved by graphing points in all four quadrants of the coordinate plane and that coordinates and absolute value can be used to find distances between points with the same first or second coordinate. signs of numbers in ordered pairs are indicating locations in quadrants of the coordinate plane and that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT absolute value, axes, coordinate plane, coordinates, integer, linear equation, negative number, opposites, origin, positive number, quadrants, x-axis, x-coordinate, y- axis, y-coordinate Holt McDougal Mathematics 6: Chapter 9 HMM 6 Lab Activities WB (2,3) two colored counters (1) large sticky notes (2) graph paper (3) state maps (3) grid paper (5) pattern blocks (5) Quiz 9A Quiz 9B Chapter 9 Test 16

Grade: 6 Unit: Functions (10) Time Frame: 17.5 periods A function is one way of using mathematics to describe an observable event. Functions, which show how different values are related, can be used in math to describe the real world. How do variables relate to functions? How do I graph a linear equation or inequality? KNOWLEDGE SKILLS STANDARDS variables can be used to represent two quantities in a real-world problem that change in relationship to one another and use equations to describe relationships shown in a table. write inequalities to describe that an equation can be written to express one quantity thought of as the dependent variable, in terms of the other quantity thought of as the independent variable. Also, that graphs and tables can be used to analyze the relationship between the dependent and independent variables. certain situations. (1) 6.EE.9 (2) 6.EE.9 (2E) 6.EE.9 real world and math problems can be solved using rate and ratio reasoning through tables of equivalent ratios, tape diagrams, or equations. tables can be made of equivalent ratios relating quantities with whole number measurements and that once the missing values are found in the tables, they can then be plotted on the coordinate plane. an inequality in the form of x>c or x<c can be written to represent a constraint or condition in a realworld or mathematical problem and that inequalities of the form x>c or x<c have infinitely many solutions which can be represented on number line diagrams. (1) use data in a table to write an equation for a function and use the equation to find a missing value. (2) represent linear functions using ordered pairs and graphs. (2E) identify the independent and dependent variables in a real world situation. (3) find rates of change and slope. (4) read and write inequalities and graph them on a number line. (3) 6.RP.3 6.RP.3a (4) 6.EE.8 17

VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT algebraic inequality, compound inequality, function, inequality, input, linear equation, output, rate of change, slope, solution of an inequality Holt McDougal Mathematics 6: Chapter 10 HMM 6 Lab Activities WB (1,2,3) graph paper (2) square tiles (3) graph paper (3) uncooked spaghetti (3) Chapter 10 Test 18

Grade: 7 Unit: Algebraic Reasoning (1) Time Frame: 18 periods Just as the order of the words in a sentence is important to the sentences meaning, the order of operations is essential to the meaning or value of a mathematical expression. The Commutative Property and the Associative Property are cornerstones for the study of Mathematics. How is thinking algebraically different from thinking arithmetically? How do I use the rules for Order of Operations to solve expressions? KNOWLEDGE SKILLS NJCCCS a horizontal or vertical number line diagram can be used to add and subtract rational numbers. strategies to add and subtract rational numbers such as operational properties. strategic tools to solve multistep, real life and mathematical problems posed with positive and negative rational numbers. that re-writing expressions in different forms can shed light on a problem and how the quantities in it are related. variables can be used to represent real-world or mathematical problems. strategies to add, subtract, factor and expand linear expressions with rational coefficients. use of properties of arithmetic and properties of equality. write and simplify expressions to solve problems. (1) use the order of operations to simplify numerical expressions. (1L) use a graphing calculator to evaluate expressions with exponents. (2) identify properties of rational numbers and use them to simplify numerical expressions. (3) evaluate algebraic expressions. (4) translate words into numbers, variables, and operations. (5) simplify algebraic expressions. (1L) 8.1.8.A.5 (2) CC.7.NS.1,1d CC.7.EE.3 (4) CC.7.EE.2,4 (5) CC.7.EE.1,4 VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT Holt McDougal Mathematics 7: Chapter 1 HMM 7 Lab Activities WB (1,5) Quiz 1A Quiz 1B scientific/graphing calculator (1L) algebra tiles (5) numerical expression, order of operations, communicative property, associative property, identity property, distributive property, variable, constant, algebraic expression, evaluate, term, coefficient Chapter Test 1 19

Grade: 7 Unit: Integers and Rational Numbers (2) Time Frame: 31 ½ periods The sign of an integer tells its direction, and the absolute value tells its magnitude. Integers are closed under the operations of addition and subtraction, which means that adding or subtracting any two integers, will produce another integer. The Properties of Equality are used to transform an equation into an equivalent equation whose solution can be easily seen. What are integers? What are rational numbers? How is the understanding of positive and negative rational numbers, their representations, and relationships essential in problem solving? KNOWLEDGE SKILLS NJCCCS extensions of previous understanding of addition and subtraction to add and subtract rational numbers. that real world and mathematical problems can be solved with the four operations involving rational numbers. p+q as the number located a distance /q/ from p, in the positive or negative direction depending on whether q is positive or negative. a number and its opposite have a sum of zero. real-world contexts can be described by sums of rational numbers. strategic tools to solve multistep, real-life and mathematical problems posed with positive and negative rational numbers. situations in which opposite quantities combine to make zero. subtraction of rational numbers as adding the additive inverse p q = p + (-q). add, subtract, multiply, and divide integers. express fractions as decimals. (1) compare and order integers and determine absolute value. (2L) use integer chips to model integer addition. (2) add integers. (2E) use additive inverses and absolute value in real-world situations. (3L) use integer chips to model integer subtraction. (3) subtract integers. (4L) use integer chips to model integer multiplication and division. (4) multiply and divide integers. (5L) use algebra tiles to model and solve equations that contain integers. (5) solve one-step equations that contain integers. (6) write fractions as decimals, and vice versa, and determine whether a decimal is terminating or repeating. (7) compare and order fractions and decimals. (2L) CC.7.NS.1,3 (2) CC.7.NS.1,1b,3 CC.7.EE.3 (2E) CC.7.NS.1,1a,1b (3L) CC.NS.1,3 (3) CC.7.NS.1,1c (4L) CC.7.NS.2,3 (4) CC.7.NS.2 CC.7.EE.2 (5L) CC.7.EE.4 (5) CC.7.EE.4 CC.7.NS.1b (6) CC.7.NS.2c, 3 (7) CC.7.NS.2c, 3 20

the distance between two rational numbers on the number line is the absolute value of their difference and this principle as it applies in real world contexts. extensions of previous understanding of multiplication and division and of fractions to multiply and divide rational numbers. expressions in different forms can shed light on a problem and how the quantities in it are related. variables can be used to represent quantities in a realworld or mathematical problem. simple equations and inequalities can be constructed to solve problems by reasoning about the quantities. properties of operations as strategies to multiply and divide rational numbers. VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT absolute value, additive inverse, integer, opposite, rational number, repeating decimal, terminating decimal Holt McDougal Mathematics 7: Chapter 2 HMM 7 Lab Activities WB (4,6,7) integer chips (1, 2L, 3L, 4L) algebra tiles (5L) colored pencils (5L) Quiz 2A Quiz 2B Chapter 2 Test 21

Grade: 7 Unit: Applying Rational Numbers (3) Time Frame: 27 periods Many statistics are recorded as decimals. By using operations with decimals you can determine those statistics. When there are different denominators, the fractions cannot be directly combined because they are different parts of a whole. How do I evaluate rational numbers using various operations? How does understanding the properties of operations on positive and negative rationals provide a basis for understanding more complex mathematical concepts? KNOWLEDGE SKILLS NJCCCS extensions of previous understanding of addition and subtraction to add and subtract rational numbers. p+q as the number located a distance /q/ from p, in the positive or negative direction depending on whether q is positive or negative. subtraction of rational numbers as adding the additive inverse, p q = p + (-q) real-world and mathematical problems can be solved with the four operations involving rational numbers. extensions of previous understanding of addition and subtraction to add and subtract rational numbers. multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1)=1 and the rules for multiplying singed numbers. add, subtract, multiply, and divide rational numbers. solve equations containing fractions. (1) add and subtract decimals. (2) multiply decimals. (3) divide decimals. (4) solve one-step equations that contain decimals. (5) add and subtract fractions. (6) multiply fractions and mixed numbers. (7) divide fractions and mixed numbers. (8) solve one-step equations that contain fractions. (1) CC.7.NS.1,1b,1c,3 (2) CC.7.NS.1,2,2a,3 (3) CC.7.NS.2,2b (4) CC.7.EE.4 CC.7.NS.2 (5) CC.7.NS.1,1b,1c,3 (6) CC.7.NS.1,2,2a,3 (7) CC.7.NS.2,2b,3 (8) CC.7.EE.4 22

products of rational numbers can be described in real-world contexts. integers can be divided, provided that the divisor is not zero and every quotient of integers is a rational number. If p and q are integers, then (p/q) = (-p)/q = p/(-q). quotients of rational numbers can be described in real-world contexts. variables can be used to represent quantities in a real-world or mathematical problem. simple equations and inequalities can be constructed to solve problems by reasoning about the quantities. VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT multiplicative inverse, reciprocal Holt McDougal Mathematics 7: Chapter 3 HMM 7 Lab Activities WB (1,6,7) decimal grids (2) grid transparencies (2) graph paper (3,4) measuring tape (3) colored pencils (6) grids (6) Quiz 3A Quiz 3B Chapter 3 Test 23

Grade: 7 Unit: Proportional Relationships (4) Time Frame: 24 periods Proportions can be used to solve real-world problem situations such as: finding the heights of objects that are too tall to measure directly, scaling a recipe, converting between different units of measurement. Arithmetically, ratios look and behave like fractions, but they are not the same as fractions. A dilation is a proportional shrinking or enlargement of a figure. What does it mean to be in a ratio of 3/5? How can I distinguish between situations that are proportional or not proportional and use proportions to solve problems? How can I apply proportionality to measurement in multiple contexts, including scale drawings? KNOWLEDGE SKILLS NJCCCS unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. proportional relationships between quantities the constant of proportionality (unit rate) from tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships whether two quantities are in a proportions relationship by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. that real world and mathematical problems can be solved with the four operations involving rational numbers. proportional relationships can be represented by equations of the form t = pn or y = kx. that scale drawings of geometric figures can be used to compute actual lengths and areas as well as to reproduce a use proportionality to solve problems, including problems involving similar objects, units of measurement, and rates (1) find and compare unit rates, such as average speed and unit price (2) find equivalent ratios and identify proportions (3) solve proportions using cross products (4) use ratios to determine if two figures are similar (5) use similar figures to find unknown side lengths (6) understand ratios and proportions in scale drawings, and use ratios and proportions with scale (6L1) use graph paper to make scale drawings and scale models (6L2) use scale drawings to find actual measures of objects and to create a new drawing of the object in a different scale (1) CC.7.RP.1,2,2b (2) CC.7.RP.2,2a CC.7.NS.3 (3) CC.7.RP.1,2,2c (4) CC.7.RP.2,2c CC.7.NS.3 (5) CC.7.G.1 CC.7.RP.2c CC.7.EE.2 (6) CC.7.G.1 CC.7.NS.3 (6L1) CC.7.G.1 (6L2) CC.7.G.1 24

scale drawing at a different scale. expressions in different forms can shed light on a problem and how the quantities in it are related. VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT corresponding angles, corresponding sides, cross product, equivalent ratios, indirect measurement, proportion, rate, scale, scale drawing, scale factor, scale model, similar, unit rate Holt McDougal Mathematics 7: Chapter 4 HMM 7 Lab Activities WB (2,3,4,5,6) measuring tape (3) customary rulers (5) social studies/reference books (6) measuring tape (6L1) Quiz 4A Quiz 4B Chapter 4 Test 25

Grade: 7 Unit: Graphs (5) Time Frame: 18 periods Graphs can be used to analyze countless real-world phenomena, such as speed, time, and distance. A graph is an efficient way of conveying a great deal of information. A rate of change is a ratio that compares the amount of change in a dependent variable to the corresponding amount of change in and independent variable. What story does a line tell? What makes a pattern linear? How can I apply proportionality to measurement in multiple contexts, including speed? KNOWLEDGE SKILLS NJCCCS unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. proportional relationships between quantities whether two quantities are in a proportions relationship by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. the constant of proportionality (unit rate) from tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships proportional relationships can be represented by equations of the form t = pn or y = kx. that a point (x,y) on the graph of a proportional relationship means in terms of a situation with special attention to the points (0,0) and (1, r) where r is the unit rate. a horizontal or vertical number line diagram can be used to add and subtract rational numbers. graph linear relationships and identify the slope of the line. identify proportional relationships (y =kx) (1) plot and identify ordered pairs on a coordinate plane (2) relate graphs to situations (3L) graph proportional relationships on the coordinate plane and use the graph to determine equivalent ratios and rates. (3) determine the slope of a line and recognize constant and variable rates of change. (4) identify, write, and graph an equation of direct variation. (3L) CC.7.RP.1,2, 2a,2b,2c (3) CC.7.RP.1,2d (4) CC.7.RP.2,2a CC.7.NS.1 26

VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT constant of variation, coordinate plane, direct variation, ordered pair, origin, quadrant, rate of change, slope, x-axis, y-axis Holt McDougal Mathematics 7: Chapter 5 HMM 7 Lab Activities WB (1,3) graph paper (1, 2, 3L) media advertisements w/ graphs (2) Quiz 5A Quiz 5B Chapter 5 Test 27

Grade: 7 Unit: Percents (6) Time Frame: 22½ periods Percents are commonly used to express and compare ratios. Percent means per hundred. Understanding how to calculate percents has real world applications in such things are determining discounts and interest. Why are fraction, decimal, and percent equivalencies important? How can I solve percents problems, involving discounts, simple interest, taxes, tips and percents of increase or decrease? KNOWLEDGE SKILLS NJCCCS strategic tools to solve multistep, real life and mathematical problems posed with positive and negative rational numbers. expressions in different forms can shed light on a problem and how the quantities in it are related. properties of operations as strategies to add and subtract rational numbers. multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1)=1 and the rules for multiplying singed numbers. integers can be divided, provided that the divisor is not zero and every quotient of integers is a rational number. If p and q are integers, then (p/q) = (-p)/q = p/(-q). properties of operations as strategies to multiply and divide rational numbers. that proportional relationships work with proportions involving percents solve a wide variety of percent problems (1) write decimals and fractions as percents (2) estimate percents (3) use properties of rational numbers to write equivalent expressions and equations. (4) solve problems involving percent of change (5) find commission, sales tax and withholding tax (6) compute simple interest (6L) use a calculator to compute compound interest (1) CC.7.EE.3 (2) CC.7.EE.3 (3) CC.7.EE.2,3 CC.7.NS.1d,2a,2b,2c (4) CC.7.RP.3 CC.7.EE.2,3 (5) CC.7.RP.3 (6) CC.7.RP.3 (6L) CC.7.RP.3 8.1.8.A.5 28

can be used to solve multistep ratio and percent problems. that re-writing expressions in different forms can shed light on a problem and how the quantities in it are related. strategic tools to solve multistep, real life and mathematical problems posed with positive and negative rational numbers; mental computation and estimation strategies to convert between forms and assess the reasonableness of answers. VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT commission, commission rate, interest, percent of change, percent of decrease, percent of increase, principal, rate of interest, simple interest Holt McDougal Mathematics 7: Chapter 6 HMM 7 Lab Activities WB (2,4,5) dictionaries (1) toy money (4) advertisements w/ interest (6) number cubes (6) Quiz 6A Quiz 6B Chapter 6 Test 29

Grade: 7 Unit: Collecting, Displaying, and Analyzing Data (7) Time Frame: 15 periods Sampling is the area of statistics concerned with choosing a subset of a population in order to make statistical inferences about the population as a whole. There are various ways of presenting/representing data both numerically and graphically. How do I use data to make decisions? How do I determine the appropriate data display to organize and communicate findings? KNOWLEDGE SKILLS STANDARDS a random sample can be used to draw inferences about a population with an unknown characteristic of interest and to generate multiple samples (or simulated samples) of the same make and interpret graphs, such as box-and-whisker plots make estimates relating to a population based on a sample size to gauge the variation in (2) CC.7.SP.2,4 estimates or predictions. measures of center and measures of variability for numerical data from random samples can be use to draw informal comparative inferences about two populations. statistics can be used to gain information about a population by examining a sample of the population and that generalizations about a population are valid only if the sample is representative of that populations. Students will also understand that random sampling tends to produce representative samples and support valid inferences. the degree of visual overlap of two numerical data distributions with similar variabilities, can be informally assessed by measuring the difference between the centers by expressing it as a multiple of a measure of variability. (1) find the mean, median, mode and range of a data set (2) display and analyze data in a box-and-whisker plots (2L) use a graphing calculator to analyze data in box-andwhisker plots (3) compare and analyze sampling methods (3L1) use a sampling method, collect data, and summarize the results (3L2) use random sampling to make predictions about populations. (2L) CC.7.SP.4 8.1.8.A.5 (3) CC.7.SP.1 (3L1) CC.7.SP.1,2 (3L2) CC.7.SP.1,2,3 8.1.8.A.5 30

VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT biased sample, box-and-whisker plot, convenience sample, interquartile range, lower quartile, mean, median, mode, outlier, population, random sample, range, sample, upper quartile Holt McDougal Mathematics 7: Chapter 7 HMM 7 Lab Activities WB (1) graph paper (2) index cards (2) graphing calculator (2L, 3) Chapter 7 Test 31

Grade: 7 Unit: Geometric Figures (8) Time Frame: 28 ½ periods Geometric figures are an integral part of architecture, industrial design, and construction. When three side lengths are given, either exactly one triangle can be formed, or no triangle is possible. There are several ways to prove that two triangles are congruent. How do we use geometry to make sense of the real world? What is the relationship between plane states and solid states? What happens to a figure on a coordinate plane when its vertices are transformed? KNOWLEDGE SKILLS STANDARDS facts about supplementary, complementary, vertical and adjacent angles to write and solve simple equations for an unknown angle in a figure. that proportional relationships can be represented by equations. various tools/techniques to draw geometric shapes with given conditions, while focusing on the conditions that determine a unique triangle, more than one triangle or no triangle when constructing triangles from three angle measures or sides. use facts about distance and angles to analyze figures find unknown measures of angles (1) identify and describe geometric figures (2L) use a protractor to explore complementary and supplementary angles. (2) identify angles and angle pairs. (3L1) use a protractor and a straightedge to find relationships among the angles formed by parallel lines and transversals. (3) identify parallel, perpendicular, and skew lines, and angles formed by a transversal (3L2) use a compass and a straightedge to bisect a line segment, bisect an angle, and construct congruent angles. (4) find the measures of angles in polygons (5L1) use geometry software to determine if three given angles of a triangle determine a unique triangle, several different triangles or no triangle. (5) identify congruent figures and use congruence to solve problems (2L) CC.7.G.5 (2) CC.7.G.5 (3L1) CC.7.G.5 (3) CC.7.G.5 (3L2) CC.7.G.5 (4) CC.7.G.5 CC.7.RP.2c (5L1) CC.7.G.2 8.1.8.A.5 (5) CC.7.G.2 32

(5L2) use geometry software to translate and rotate polygons. (5L3) use geometry software to determine if three given lengths of a triangle determine a unique triangle, several different triangles, or no triangle. (5L2) CC.7.G.2 8.1.8.A.5 (5L3) CC.7.G.2 8.1.8.A.5 VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT acute angle, acute triangle, adjacent angles, angle, complementary angles, congruent, diagonal, line, line segment, obtuse angle, parallel lines, plane, point, ray, right angle, Side-Side-Side Rule, skew lines, straight angle, supplementary angles, transversal, vertex, vertical angles Holt McDougal Mathematics 7: Chapter 8 HMM 7 Lab Activities WB (1,2,3,4) dot paper (1) protractors (2, 3L1, 3L2) cereal/shoe boxes (2) compasses (3L2) geometry software (5L1,2,3) Quiz 8A Quiz 8B Chapter 8 Test 33

Grade: 7 Unit: Measurement and Geometry (9) Time Frame: 25½ periods Perimeter and area of a given space can be determined by measuring their dimensions and then using a formula. For example, landscapers rely heavily upon these formulas. The volume of a three-dimensional figure represents the amount of space it contains. Conversion factors can be used to convert one unit of volume to another. How many ways can an object be measured? What does what we measure affect how we measure? How are surface area and volume like and unlike each other? How do I use a formula to determine surface area and volume? KNOWLEDGE SKILLS STANDARDS formulas for the area and circumference of a circle and use them to solve problems; an informal derivation of the relationship between the circumference and area of a circle. that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. techniques to solve real-world and mathematical problems involving area, volume and surface area of two- and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. the two-dimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. solve problems involving area and circumference of circles investigate cross sections and surface area (1L) use loops of string to explore perimeter and circumference (1) find the perimeter of a polygon and the circumference of a circle (2) find the area of the circles (3) find the area of irregular figures. (4) identify various threedimensional figures. (4E) sketch and describe cross sections of three-dimensional figures. (5L) use centimeter cubes to model and find the volume of prisms and cylinders. (5) find the volume of prisms and cylinders. (6L) use graph paper to create two-dimensional nets for three dimensional figures. (6) find the surface area of prisms and cylinders. (1L) CC.7.G.4 CC.7.EE.2 (1) CC.7.G.4 (2) CC.7.G.4 8.1.8.A.5 (3) CC.7.G.6 (4E) CC.7.G.3 (5L) CC.7.G.6 (5) CC.7.G.6 (6L) CC.7.G.6 (6) CC.7.G.6 34