|MS6||MA||EE||01||00*||0||MS6-MA-EE.01.00*.0||Write and evaluate numerical expressions involving whole-number exponents.||Number Sense & Operations: Use place value, write numbes in standard, expanded and exponential form|
|MS6||MA||EE||02||00*||0||MS6-MA-EE.02.00*.0||Write, read, and evaluate expressions in which letters stand for numbers.||Algebraic Patterns and Connections: use expressions and equations to model situations|
|MS6||MA||EE||02||A||0||MS6-MA-EE.02.A.0||Write expressions that record operations with numbers and with|
letters standing for numbers. For example, express the calculation
“Subtract y from 5” as 5 – y.
|Algebraic Patterns and Connections|
|MS6||MA||EE||02||B||0||MS6-MA-EE.02.B.0||Identify parts of an expression using mathematical terms (sum,|
term, product, factor, quotient, coefficient); view one or more
parts of an expression as a single entity. For example, describe the
expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
|Number Sense & Operations: Describe and Apply properties of numbers|
|MS6||MA||EE||02||C||0||MS6-MA-EE.02.C.0||Evaluate expressions at specific values of their variables. Include|
expressions that arise from formulas used in real-world problems.
Perform arithmetic operations, including those involving wholenumber
exponents, in the conventional order when there are no
parentheses to specify a particular order (Order of Operations).
For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.
|Number Sense & Operations: Demonstrate Ways of performing operations|
|MS6||MA||EE||03||00||0||MS6-MA-EE.03.00.0||Apply the properties of operations to generate equivalent expressions. (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.||Number Sense & Operations: Demonstrate Ways of performing operations|
|MS6||MA||EE||04||00||0||MS6-MA-EE.04.00.0||Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). (e.g., the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.||Algebraic Patterns and Connections: Use and interpret operational and relational symbols|
|MS6||MA||EE||05||00||0||MS6-MA-EE.05.00.0||Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.||Algebraic Patterns & Connections: Solve Equations & Inequalities|
|MS6||MA||EE||06||00*||0||MS6-MA-EE.06.00*.0||Use variables to represent numbers and write expressions when solving a real-world or mathematical problems.||Algebraic Patterns and Connections: use expressions and equations to model situations|
|MS6||MA||EE||07||00||0||MS6-MA-EE.07.00.0||Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.||Algebraic Patterns & Connections: Solve Equations & Inequalities|
|MS6||MA||EE||08||00||0||MS6-MA-EE.08.00.0||Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.||Algebraic Patterns & Connections: Solve Equations & Inequalities|
|MS6||MA||EE||09||00||0||MS6-MA-EE.09.00.0||Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., in a problem involving motion at constant speed, list and graph ordered airs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.||Data Analysis, Probability & Statistics|
|MS6||MA||G||01||00*||0||MS6-MA-G.01.00*.0||Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.||Geometry|
|MS6||MA||G||02||00||0||MS6-MA-G.02.00.0||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. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.||Geometry|
|MS6||MA||G||03||00||0||MS6-MA-G.03.00.0||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. Apply these techniques in the context of solving real-world and mathematical problems.||Geometry|
|MS6||MA||G||04||00||0||MS6-MA-G.04.00.0||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 real-world and mathematical problems.||Geometry|
|MS6||MA||NS||01||00*||0||MS6-MA-NS.01.00*.0||Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.||Not on IA: Division of Fractions|
|MS6||MA||NS||02||00*||0||MS6-MA-NS.02.00*.0||Divide multi-digit numbers using the standard algorithm.||Compute with Whole Numbers|
|MS6||MA||NS||03||00*||0||MS6-MA-NS.03.00*.0||Add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.||Compute with Decimals|
|MS6||MA||NS||04||00||0||MS6-MA-NS.04.00.0||Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple 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. (e.g., express 36 + 8 as 4 (9 + 2).||Compute with Fractions|
|MS6||MA||NS||05||00*||0||MS6-MA-NS.05.00*.0||Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.||Number Sense and Operations|
|MS6||MA||NS||06||00||0||MS6-MA-NS.06.00.0||Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.||Not on IA|
|MS6||MA||NS||06||A||0||MS6-MA-NS.06.A.0||Recognize opposite signs of numbers as indicating locations|
on opposite sides of 0 on the number line; recognize that the
opposite of the opposite of a number is the number itself, e.g.,
–(–3) = 3, and that 0 is its own opposite.
|Not on IA|
|MS6||MA||NS||06||B||0||MS6-MA-NS.06.B.0||Understand signs of numbers in ordered pairs as indicating|
locations in quadrants of the coordinate plane; recognize that
when two ordered pairs differ only by signs, the locations of the
points are related by reflections across one or both axes.
|Not on IA|
|MS6||MA||NS||06||C||0||MS6-MA-NS.06.C.0||Find and position integers and other rational numbers on a|
horizontal or vertical number line diagram; find and position pairs
of integers and other rational numbers on a coordinate plane.
|Not on IA|
|MS6||MA||NS||07||00||0||MS6-MA-NS.07.00.0||Understand ordering and absolute value of rational numbers.||Number Sense & Operations: Represent Compare and Order Numbers|
|MS6||MA||NS||07||A||0||MS6-MA-NS.07.A.0||Interpret statements of inequality as statements about the relative|
position of two numbers on a number line diagram. For example,
interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.
|Number Sense & Operations|
|MS6||MA||NS||07||B||0||MS6-MA-NS.07.B.0||Write, interpret, and explain statements of order for rational|
numbers in real-world contexts. For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC.
|Number Sense and Operations / Algebraic Pattens and Connections|
|MS6||MA||NS||07||C||0||MS6-MA-NS.07.C.0||Understand the absolute value of a rational number as its distance|
from 0 on the number line; interpret absolute value as magnitude
for a positive or negative quantity in a real-world situation. For
example, for an account balance of –30 dollars, write |–30| = 30 to
describe the size of the debt in dollars.
|Not on IA|
|MS6||MA||NS||07||D||0||MS6-MA-NS.07.D.0||Distinguish comparisons of absolute value from statements about|
order. For example, recognize that an account balance less than –30
dollars represents a debt greater than 30 dollars.
|Not on IA|
|MS6||MA||NS||08||00*||0||MS6-MA-NS.08.00*.0||Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.||Not on IA|
|MS6||MA||RP||01||00*||0||MS6-MA-RP.01.00*.0||Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.||Measurement|
|MS6||MA||RP||02||00||0||MS6-MA-RP.02.00.0||"Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1"||Measurement|
|MS6||MA||RP||03||00||0||MS6-MA-RP.03.00.0||Use ratio and rate reasoning to solve real-world and mathematical|
problems, e.g., by reasoning about tables of equivalent ratios, tape
diagrams, double number line diagrams, or equations.
|MS6||MA||RP||03||A||0||MS6-MA-RP.03.A.0||Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.||Measurement|
|MS6||MA||RP||03||B||0||MS6-MA-RP.03.B.0||Solve unit rate problems including those involving unit pricing and|
constant speed. For example, if it took 7 hours to mow 4 lawns, then
at that rate, how many lawns could be mowed in 35 hours? At what
rate were lawns being mowed?
|Measurement: Understand and Apply Rate|
|MS6||MA||RP||03||C||0||MS6-MA-RP.03.C.0||Find a percent of a quantity as a rate per 100 (e.g., 30% of a|
quantity means 30/100 times the quantity); solve problems
involving finding the whole, given a part and the percent.
|Number Sense & Operations / Algebraic Patterns & Connections|
|MS6||MA||RP||03||D||0||MS6-MA-RP.03.D.0||Use ratio reasoning to convert measurement units; manipulate|
and transform units appropriately when multiplying or dividing
|Measurement / Fractions|
|MS6||MA||SP||01||00||0||MS6-MA-SP.01.00.0||Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.||Data Analysis, Probability & Statistics|
|MS6||MA||SP||02||00||0||MS6-MA-SP.02.00.0||Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.||Data Analysis, Probability & Statistics|
|MS6||MA||SP||03||00||0||MS6-MA-SP.03.00.0||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.||Data Analysis, Probability & Statistics|
|MS6||MA||SP||04||00||0||MS6-MA-SP.04.00.0||Display numerical data in plots on a number line, including dot plots, histograms, and box plots.||Data Analysis, Probability & Statistics|
|MS6||MA||SP||05||00||0||MS6-MA-SP.05.00.0||Summarize numerical data sets in relation to their context, such as by:||Data Analysis, Probability & Statistics|
|MS6||MA||SP||05||A||0||MS6-MA-SP.05.A.0||Reporting the number of observations.||Data Analysis, Probability & Statistics|
|MS6||MA||SP||05||B||0||MS6-MA-SP.05.B.0||Describing the nature of the attribute under investigation,|
including how it was measured and its units of measurement.
|Not on IA|
|MS6||MA||SP||05||C||0||MS6-MA-SP.05.C.0||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 deviations
from the overall pattern with reference to the context in which the
data were gathered.
|Data Analysis, Probability & Statistics|
|MS6||MA||SP||05||D||0||MS6-MA-SP.05.D.0||Relating the choice of measures of center and variability to the|
shape of the data distribution and the context in which the data
|Data Analysis, Probability & Statistics|