Course Syllabus

6th Grade Common Core Mathematics 2014-2015 Pacing Guide

6--2014

1st Nine Weeks

July 31 – October 2

September 1 (Labor Day Holiday)

Unit 1: Number System Fluency ( 4 weeks; July 31- August 29)

Compute fluently with multi-digit numbers and find common factors and multiples.

CC.6.NS.4 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.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

CC.6.NS.1 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.

Compute fluently with multi-digit numbers and find common factors and multiples.

CC.6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

CC.6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for

each operation.

Unit 2: Rate, Ratio, & Proportional Reasoning (MODELS) ( 4 weeks; September 3 – October 2)

Understand ratio concepts and use ratio reasoning to solve problems.

CC.6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between

two quantities.

CC.6.RP.2 Understand the concept of a unit rate associated with a ratio with (b not equal to zero), and use

rate language in the context of a ratio relationship.

CC.6.RP.3 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.

3b. Solve unit rate problems including those involving unit pricing and constant speed. (MODELS)

3c. 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. Explore and

model percents using multiple representations. (MODELS)

6th Grade Common Core Mathematics 2014-2015 Pacing Guide

6--2014

2nd Nine Weeks

October 3 – December 19

October 6-9 (Fall Holiday); October 13 (Student Holiday); October 20-24 (ITBS);November 11 (Veteran’s

Day); November 24-28 (Thanksgiving Holiday)

Unit 3: Expressions ( 4 weeks; October 3 – November 7)

Apply and extend previous understandings of arithmetic to algebraic expressions.

CC.6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.

CC.6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

2a. Write expressions that record operations with numbers and with letters standing for numbers. For

example, express the calculation “Subtract y from 5” as –. Translate verbal phrases to algebraic

expressions Use variables, such as x or y, for unknown quantities in algebraic expressions

2b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient,

and coefficient); view one or more parts of an expression as a single entity. For example, describe

the expression as a product of two factors; view as both a single entity and a sum of two terms.

2c. Evaluate expressions at specific values for their variables. Include expressions that arise from

formulas 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).

CC.6.EE.3 Apply the properties of operations to generate equivalent expressions. Simplify algebraic

expressions, using commutative, associative, and distributive properties as appropriate.

CC.6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same

number regardless of which value is substituted into them).

Unit 4a: Equations & Inequalities ( 4 weeks; November 12 – December 16)

Reason about and solve one-variable equations and inequalities.

CC.6.EE.5 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.

CC.6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or

mathematical problem; understand that a variable can represent an unknown number, or, depending on

the purpose at hand, any number in a specified set. Given a problem, define a variable, write an

equation.

CC.6.EE.7 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 non-negative rational numbers.

Understand ratio concepts and use ratio reasoning to solve problems.

CC.6.RP.3 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. (Connect

models to equations.)

3b. 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?

3c. 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. Explore and

model percents using multiple representations

3d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately

when multiplying or dividing quantities. Students will convert from one unit to another within one

system of measurement (customary or metric) by using proportional relationships. (length,

capacity/volume, and mass

6th Grade Common Core Mathematics 2014-2015 Pacing Guide

6--2014

3rd Nine Weeks

January 6 – March 13

January 19 (MLK Holiday); February 16 (President’s Day Holiday); February 17 (Student Holiday)

Unit 4b: Equations & Inequalities ( 2.5 weeks; January 7 – January 22)

CC.6.RP.3 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.

3a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing

values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare

ratios. Analyze and describe patterns arising from mathematical rules, tables, and graphs

CC.6.EE.9 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.

Reason about and solve one-variable equations and inequalities.

CC.6.EE.5 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.

CC.6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld

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. Include inequalities of

the form x c and x c.

Unit 5: Area & Volume ( 3 weeks; January 23 – February 13)

Solve real-world and mathematical problems involving area, surface area, and volume.

CC.6.G.1 Find 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. Find the area of a polygon (regular and irregular) by

dividing it into squares, rectangles, and/or triangles and find the sum of the areas of those shapes.

CC.6.G.2 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 = lwh and V = Bh to find

volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and

mathematical problems.

CC.6.G.4 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.

Unit 6: Exploring Rationals: Numbers & their Opposites (≈ 3 weeks; February 18 – March 13)

Apply and extend previous understandings of numbers to the system of rational numbers.

CC.6.NS.5 Understand that positive and negative numbers are used together to describe quantities having

opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level,

debits/credits, positive/negative electric charge); use positive and negative numbers to represent

quantities in real-world contexts, explaining the meaning of 0 in each situation.

Students will understand the meaning of positive and negative rational numbers

CC.6.NS.6 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.

6th Grade Common Core Mathematics 2014-2015 Pacing Guide

6--2014

6a. 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.

6b. 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.

Given a point in the coordinate plane, determine the coordinates resulting from a reflection.

6c. 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.

CC.6.NS.7 Understand ordering and absolute value of rational numbers.

7a. Interpret statements of inequality as statements about the relative position of two numbers on a

number line diagram. For example, interpret –– as a statement that –3 is located to the right of –7 on a

number line oriented from left to right.

7b. Write, interprets, and explains statements of order for rational numbers in real-world contexts. For

example, write –3°C > –7°C to express the fact that –3°C is warmer than –7°C.

7c. 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.

7d. 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.

CC.6.NS.8 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.

CC.6.G.3 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.

4th Nine Weeks

March 16 – May 22

March 30-April 3 (Spring Break)

Unit 7: Statistics (≈ 2 weeks; March 16– March 27)

Develop understanding of statistical variability.

CC.6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the

question and accounts for it in the answers.

CC.6.SP.2 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.

CC.6.SP.3 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.

6th Grade Common Core Mathematics 2014-2015 Pacing Guide

6--2014

Summarize and describe distributions.

CC.6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

CC.6.SP.5 Summarize numerical data sets in relation to their context, such as by:

a. Reporting the number of observations. Analyze categorical data using frequencies of

categories or proportions of categories

b. Describing the nature of the attribute under investigation, including how it was measured

and its units of measurement. Students summarize numerical data by providing background

information about the attribute being measured, methods and unit of measurement, and the

context of data collection activities

c. 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 was gathered.

Analyze numerical data using the appropriate measure of central tendency (mean and/or median).

Analyze data with respect to the appropriate measures of variation (range, interquartile range,

and/or mean absolute deviation). The choice of summary measures to report is related to the shape

of the distribution (symmetry versus skewed to the higher values or skewed to the lower values)

d. Relating the choice of measures of center and variability to the shape of the data distribution and

the context in which the data was gathered.