Unit Standard 6NS1 1 Operations w/rational numbers excluding integers 6NS2 6NS3 1st Quarter (9 weeks) Standard Description -Interpret and compute quotient of fractions, and solve word problems involving division of fractions by using visual fraction models and equations to represent the problem. -Fluently divide multi-digit numbers, using standard algorithm -Fluently add, subtract, multiply and divide decimals Content Focus Understanding dividing fractions Interpret and compute quotients of fractions Solve real-world problems involving division of fractions Solve real-world problems involving multiplication and division of fractions. Estimate with fractions and decimals. Understanding dividing multi-digit numbers Estimating and determining reasonable quotients Computation Word problems Understanding decimals using all four operations to solve problems. Estimate reasonable answers Solve real-word problems Write decimal in expanded form Converting terminating decimals, repeating decimals and percents to fractions and mixed numbers Comparing rational numbers written as fractions, decimals, mixed numbers and percents. Apply the distributive property to compute with decimals. 6NS4 15 days -Find the greatest common factor (GCF) of two whole numbers less than or equal to 100 -Find the least common multiple (LCM) of two whole numbers less than or equal to 12. - Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Ex. 36 + 8 as 4(9+2) Find the GCF and LCM of two whole numbers Apply the distributive property to rewrite a simple addition problem when the addends have a common factor Add/Subtract fractions with unlike denominators including mixed numbers. Teacher Resources Go Math! Chapters 1 & 2 Investigations – Prime Time Bits & Pieces 1 NLVM website Khan Academy: Unit 2 Integers and the coordinate plane Standard 6NS5 6NS7b 6NS6b,c 6NS8 6NS6a 6NS7b 6NS7d 6G3 Standard Description -Understanding that positive and negative numbers are used together to describe quantities having opposite directions or values -Write, Interpret and explain statements of order for rational numbers -Understanding a rational number as a point on the number line. -Understand signs of numbers in ordered pairs as indicating location in quadrants of the coordinate plane -Find and position pairs of integers and other rational numbers on a coordinate plane -Recognize opposite signs of numbers -Understand that absolute value of a rational number as its distance from 0 on the number line in real-world context -Distinguish comparisons of absolute value from statements about order -Draw polygons in the coordinate plane given coordinates for the vertices -Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate using realworld context Content Focus Understanding positive and negative numbers Use them to represent real-world quantities Compare and order integers in realworld context Using integers and other rational numbers with the coordinate plane Extend the number line to include negative numbers Graph ordered pairs of rational numbers on a coordinate plane Understanding absolute value Find the absolute value of rational numbers Interpret the absolute value of rational numbers. Compare the absolute value of rational numbers Use absolute value to find the distance between two points Using rational numbers/coordinates to draw polygons in the coordinate plane Apply these techniques in the context of solving real-world and mathematical problems Identify two-dimensional and threedimensional figures based on attributes, properties and component parts. Identify line and rotational symmetries of polygons. (rotation, reflection, transitions and dilations) 10 days Classify angles as right, acute, obtuse and straight. Teacher Resources Go Math! Chapter 3 Go Math! Chapter 10.9 Investigations – Data About Us Bits & Pieces II Khan Academy: Unit 3 Expressions Standard 6EE1 6EE2 6EE2a,b Standard Description Content Focus -Write, read and evaluate expressions in which letters stand for numbers -Write expressions that record operations with numbers and with letters standing for numbers -Identify parts of an expression using mathematical terms -Apply the properties of operations to generate equivalent expressions Write equivalent expressions using properties of operations -Identify when two expressions are equivalent Identify equivalent expressions Parts of an expression Write an expression Read an expression Evaluate an expression Teacher Resources Go Math! Chapter 7 NLVM website Khan Academy: 6EE3 15 days Unit 6EE4 Standard 4 Solving Equations 6EE7 6EE2c 10 days (Continues into 2nd quarter) Standard Description Content Focus Before starting this unit it is important that students understand: o How do you use the order of operations to problems? o Why do we need an order of operations? Apply order of operations correctly to solve one-step equations -Solve real-world and mathematical problems by writing and solving equations of the form x + p=q and px +q for cases which p, q, x are all nonnegative rational numbers -Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Write, solve and use equations in real-world and mathematical problems Teacher Resources Go Math! Chapter 7.1 and 7.2 Go Math! Chapter 8 InvestigationsCovering and Surrounding I Unit 5 Inequalities Standard 6NS7a 6NS7b 6NS7d 2nd Quarter (9 weeks) Standard Description -Interpret statements of inequality as statements about relative position of two numbers on a number line. -Understand solving an equation or inequality as a process of 6EE5 20 days Unit 6 Ratio and Proportional Reasoning -Write an inequality of the form x>c or x<c to represent a constraint or Standard 6RP1 Standard Description 20 days condition in real-world or mathematical problems. -Understand the concept of ratio and use ratio language to describe a ratio relationship between two quantities. 6RP3c Graph inequality on a number line. Write an inequality to model a situation. answering a question: which values from a specific set, if any, make the equation or inequality true. 6NS8 6RP2 6RP3b Content Focus Using inequalities to solve realworld and mathematical problems. Distinguish the difference between an equation and inequality. Content Focus Understanding ratios. Explain what a ratio is Write a ratio three ways Read a ratio correctly -Understand the concept of unit rate -Solve unit rate problems including those involving unit pricing and constant speed Use ratio and rate reasoning to solve real-world and mathematical problems. Relationships between ratios and unit rates Solve problems using unit rates -Find a percent a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent. Understanding percents. Write a percent as fraction and decimal Write fractions and decimals as percents Find a percent of a quantity Find the whole given a part and a percent Solve percent word problems Solve problems involving percents (sales tax, gratuity, simple interest Teacher Resources Go Math! Chapter 8 Teacher Resources Go Math! Chapters 4, 5 & 6 Investigations: Bits and Pieces 1 &3 Shapes and Designs (reinforced; applied investigation) and percent of change) Compare rational numbers written as fractions, decimals, mixed numbers and percents. 6RP3d Unit 7 Linear Equations 20 days (continues into 3rd quarter Standard 6RP3a 6RP3b 6EE6 6EE9 -Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing. Standard Description -Make tables of equivalent ratios relating quantities, find missing values in the tables and plot pairs of values on the coordinate plane. -Use variables to represent numbers and write expressions when solving real-world or mathematical problem -Understand that a variable can represent an unknown number or any number in a specified set. -Use variables to represent two quantities in a real-world problem that change in relationship to one another -Analyze the relationship between the dependent and independent variables using graphs and tables and relate these to the equation. Converting units of measurement. Use ratio reasoning to convert from one unit of length, capacity and weight or mass to another Solve problems involving distance, rate and time. Content Focus Understanding linear equations in real-world and mathematical problems. Write equations to represent the relationship between an independent and dependent variable. Translate between equations and tables. Find patterns between two quantities Graph the relationships between two quantities Translate between equations and graphs Teacher Resources Go Math! Chapter 9 Unit Standard 6G1 8 Geometry 3rd Quarter (9 weeks) Standard Description -Find the area of triangles, special quadrilaterals and polygons by composing or decomposing into triangles and other shapes and apply these techniques to solve real-world and mathematical problems. 6G4 -Represent three-dimensional figures using nets made up of rectangles and triangles and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. 6G2 -Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. 20 days Content Focus Calculate the area of shapes. Right triangles/other triangles Special quadrilaterals Polygons Composite figures Understanding of composing and decomposing into triangles Solve problems involving perimeter of parallelogram and rectangles. Draw points, lines, line segments, rays, angles and perpendicular and parallel lines for two-dimensional shapes. Solve problems involving surface area in real-world and mathematical context. Use nets to represent three-dimensional figures Explain what the relationship between a net and the surface areas of a prism Find the surface areas of a prism, pyramid Solve problems involving volume in real-world and mathematical context. Relationship between the volume and edge lengths of prisms Find the volume of rectangular prism w/fractional edge length Teacher Resources Go Math! Chapter 10 & 11 Unit Standard 6SP1 9 Statistics Standard Description -Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for its answers. -Understand that a set of data collected to answer a statistical 6SP2 Content Focus Develop understanding of statistical variability. Identify a statistical question. question has a distribution which can be described by its center, spread, and overall shape. Describe the distribution of a data set collected to answer a statistical question Draw conclusions about a data set Find the probability of a simple event. 6SP3 -Recognize that a measure of center for a numerical data set summarizes all its values with a single number, while a measure of variation describes how it values vary with a single number. Express probabilities as ratios, percents and decimals. Explain what the measures of center and variability indicate about a data set.(mean, median, mode) 6SP4 -Display numerical data in plots on a number line, including dot plots, histograms and box plots. Use dot plots, frequency tables, histograms and box plots to display data. 6SP5a-d Draw a diagram to solve problems involving data Interpret information from bar graphs, line graphs and circle graphs. Teacher Resources Go Math! Chapters 12 & 13 Investigations: Data About Us -Summarize numerical data in relation to their context by reporting number observations and describing the nature of the attribute under investigation, including how it was measures and its units of measurement. -Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation) as well as describing any overall pattern and any striking deviation from the overall pattern. -Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Describe how a data set was collected. Describe a set of data using mean, median and mode. Describe how an outlier affects measures of center. Describe overall patterns in a data set. Calculate the mean absolute deviation of a data set Summarize a data set by using range, interquartile range and mean absolute deviation. Choose appropriate measures of center and variability to describe a data set 15 days Unit 10 Spiral Review for ARMT+ 5 days Standard Standard Description Content Focus Teacher Resources Unit 11 Transition Skills to 7th Grade 30 days Standard 7.NS.1 7.NS.2 7.NS.3 7.RP.1 7.RP.2 7.RP.3 4th Quarter (9 weeks) Standard Description Content Focus Build on integer concepts presented in Chapter 3 Use the number line to model addition and subtraction of integers. Evaluate order of operations with fractions and decimals Simplify complex fractions Identify proportional relationship Identify the constant of proportionality in proportional relationships Solve percent problems Involve percent problems involving discounts and sales tax. Find percent of change -Apply and extend previous understanding of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. -Apply and extend previous understanding of multiplication and division and of fractions to multiply and divide rational numbers. -Solve real-world and mathematical problems involving the four operations with rational numbers. -Analyze proportional relationships and use them to solve real-world and mathematical problems 7.EE.1 7.EE4 -Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Add algebraic expressions Solve two-step equations Solve inequalities 7.SP.1 7.SP.2 7.SP.5 7.SP.7 -Use random sampling to draw inference about a population. -Investigate chance processes and develop, use, and evaluate probability models. Taking a sample and leaning from it Use a sample to make a prediction Use probability to describe the likelihood of an event Write the probability of an event Calculate the experimental probability of an event Unit Standard Standard Description Content Focus Teacher Resources Go Math! Getting Ready for Grade 7 Teacher Resources