Curriculum Design Template

Content Area: Mathematics

Course Title: Math 6 Grade Level: 6

Number Expressions and Factors (1)

Fractions and Decimals (2)

Marking Period 1

Algebraic Expression and Properties (3)

Areas of Polygons (4)

Ratios and Rates (5)

Marking Period 2

Integers and the Coordinate Plane (6)

Equations and Inequalities (7)

Marking Period 3

Surface Area and Volume (8)

Statistical Measures (9)

Data Displays (10)

Marking Period 4

Date Created: July 2013

Board Approved on:

Unit Title Lessons to include Time Common Core Standards

Math

Numerical Expressions and Factors

1.1 Whole Number Operations

4 weeks 6.NS.2, 6.NS.4, 6.EE.1, 6.EE.2b

1.2 Powers and Exponents

1.3 Order of Operations

1.4 Prime Factorization

1.5 Greatest Common Factor

1.6 Least Common Multiple

Fractions and Decimals

2.1 Multiplying Fractions

4 weeks 6.NS.1, 6.NS.3

2.2 Dividing Fractions

2.3 Dividing Mixed Numbers

2.4 Adding and Subtracting Decimals

2.5 Multiplying Decimals

2.6 Dividing Decimals

Algebraic Expressions and Properties

3.1 Algebraic Expressions

3 weeks 6.NS.4, 6.EE.2a-c, 6.EE.3, 6.EE.4, 6.EE.6

3.2 Writing Expressions

3.3 Properties of Add and Multiplication

3.4 The Distributive Property

Area of Polygons

4.1 Areas of Parallelograms

2 weeks 6.G.1, 6.G.3 4.2 Areas of Triangles

4.3 Areas of Trapezoids

4.4 Polygons in the Coordinate Plane

Ratios and Rates

5.1 Rates

3 weeks 6.RP.1, 6.RP.2, 6.RP.3a-d

5.2 Ratio Tables

5.3 Rates

5.4 Comparing and Graphing Ratios

5.5 Percents

5.6 Solving Percent Problems

5.7 Converting Measures

Integers and the Coordinate Plane

6.1 Integers

3 weeks 6.NS.5, 6.NS.6a-c, 6.NS.7a-d, 6.NS.8

6.2 Comparing and Ordering Integers

6.3 Fractions and Decimals on the Number Line

6.4 Absolute Value

6.5 The Coordinate Plane

Equations and Inequalities

7.1 Writing Equations in One Variable

4 weeks 6.RP.3.a, 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8, 6.EE.9

7.2 Solving Eq Using Add or Sub

7.3 Solving Eq Using Mult or Div

7.4 Writing Equations in Two Variables

7.5 Writing and Graphing Inequalities

7.6 Solving Inequalities Using Add/Sub

7.7 Solving Inequalities Using Mult/Div

Surface Area and Volume

8.1 Three Dimensional Figures

3 weeks 6.G.2, 6.G.4 8.2 Surface Area of Prisms

8.3 Surface Area of Pyramids

8.4 Volumes of Rectangular Prisms

Statistical Measures

9.1 Intro to Statistics

3 weeks 6.SP.1, 6.SP.2,6.SP.3, 6.SP.4 6.SP.5a-c

9.2 Mean

9.3 Measures of Center

9.4 Measures of Variation

9.5 Mean Absolute Deviation

Data Analysis

10.1 Stem-and-Leaf Plots

2 weeks 6.SP.2, 6.SP.4, 6.SP.5a-d 10.2 Histograms

10.3 Shapes of Distributions

10.4 Box-and-Whisker Plots

Course Title: Math 6 Grade Level:6th Overarching Essential Questions

How do we solve and simplify expressions? How do we multiply and divide fractions? How do we add, subtract, multiply and divide decimals? What do we do to convert between fractions, decimals, and percents? What is an equation? How do we solve a one-step and two-step equation? How do we find the area of polygons? Why would we need to figure out the area/perimeter of a composite figure in real

life? What is a ratio? Unit rate? How do we solve percent problems? Why would we use a unit rate in real-life situations? What is an inequality and how is it used in real-life situations? When is the appropriate time to use a certain measure of central tendency?

Overarching Enduring Understanding In Math 6, students will be working with ratio concepts and ration reasoning. Students will be performing fraction and decimal operations as well as understand rational numbers. They will write, interpret and use expressions, equations, and inequalities. Students will solve problems involving area, surface area, and volume. They will also summarize and describe distributions and understand variability.

Course Description In Math 6, students will be evaluating and writing algebraic expressions, learning properties of adding and multiplying, as well as the distributive property, when solving algebraic expressions. Students will multiply and divide fractions and decimals by fractions, whole numbers, and mixed numbers. Students will compare, convert, and order fractions, decimals, and percents. Students will write ratios, find unit rates, and analyze data and measures of central tendency. Students will write and solve one and two-step equations. They will also use equations to help identify dimensions of plane figures and prisms. Students will write, solve, and graph inequalities using multiplication and division. Students will create a variety of data displays and compute statistics abased on sets of data.

Technology Standards

8.1.12 A 3 - Construct a spreadsheet, enter data, use mathematical or logical functions to manipulate and process data, generate charts and graphs, and interpret the results.

8.1.12 B 9 - Create and manipulate information, independently and/or collaboratively, to solve problems and design and develop products.

Life Skills Standards

9.1.12.A.1 - Apply critical thinking and problem-solving strategies during structured learning experiences.

9.1.12.B.1 - Present resources and data in a format that effectively communicates the meaning of the data and its implications for solving problems, using multiple perspectives.

9.4.12.A.2 - Demonstrate mathematics knowledge and skills required to pursue the full range of postsecondary education and career opportunities.

9.4.12.O.(2).1 - Develop an understanding of how science and mathematics function to provide results, answers, and algorithms for engineering activities to solve problems and issues in the real world.

9.4.12.O.(2).2 - Apply science and mathematics when developing plans, processes, and projects to find solutions to real world problems.

Fractions and Decimals Essential Questions

What does it mean to multiply fractions? How can you divide by a fraction? How can you model division by a mixed number? How can you add and subtract decimals? How can you multiply decimals? How can you use base ten blocks to model decimal division?

Key Terms reciprocal Objectives Students will be able to:

Develop an understanding of how to multiply a fraction and whole number. Multiply fractions and whole numbers using a formal process. Develop an understanding of how to multiply a mixed number by a fraction. Develop an understanding of how to divide by a fraction. Use a formal rule to divide by a fraction. Develop an understanding of how to divide by a mixed number. Use a formal rule to divide with mixed numbers. Add and subtract decimal values Multiply a whole number by a decimal Multiply a decimal by a decimal.

Standards associate with objectives

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. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

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

Suggested Lesson Activities Have students choose a recipe and give them a number of people they have to make

the recipe for and from there, they must double, triple, quadruple, etc. and explain how much of each ingredient is needed.

Play jeopardy Differentiation /Customizing learning (strategies)

Allow students to verbally describe the process for adding, subtracting, multiplying, and dividing fractions.

Use fraction tiles to model multiplication and division

Algebraic Expressions and Properties Essential Questions

How can you write and evaluate an expression that represents a real life problem? How can you write an expression that represents an unknown quantity Does the order in which you perform and operation matter? How do you use mental math to multiply two numbers?

Key Terms Algebraic expression, terms, variable, coefficient, constant, equivalent expressions, like terms, factoring expressions Objectives Students will be able to:

Understand simple word problems, and then write and evaluate mathematical expressions that correspond to the given situations.

Explain how to evaluate and algebraic expression containing a variable. Write algebraic expressions to represent phrases that include words corresponding

to the operations of addition, subtraction, multiplication, and division. Write an algebraic expression that represents a verbal phrase. Gain an understanding of what is meant by order and grouping as they apply to

number operations. Use the commutative and associative properties, and two other properties, to show

that expressions are equivalent. Learn how to use graphic organizers as a study tool. Gain an understanding of how the distributive property can be used to perform

multiplication problems using mental math. Use the distributive property to show that two expressions are equivalent.

Standards associate with objectives

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

c. 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 whole number exponents, in the conventional order when there are no parentheses to specify a particular order.

6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, 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.

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). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

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.

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. For example, express 36 + 8 as 4 (9 + 2).

Suggested Lesson Activities Use graphic organizers to help with properties of numbers Students create their own expression with operations and then trade with a

partner/in the class/or with other classes to have them solve (extension: trade with another class from another teacher during the same period and have a race or competition to see who can solve the most)

Differentiation /Customizing learning (strategies) Allow students to create their own table of phrases that indicate which operation

goes with which phrase Allow students to use index cards for assistance with operations/phrases

Areas of Polygons Essential Questions

How can you derive the formula for the area of a parallelogram How can you derive the formula for the area of a triangle How can you derive the formula for the area of a trapezoid? How can you find the lengths of line segments in the coordinate plane?

Key Terms Polygon, composite figure Objectives Students will be able to:

Derive and use the formula for the area of a parallelogram Derive and use the formula for the area of a triangle Derive and use the formula for the area of a trapezoid Find the lengths of line segments in a coordinate plane

Standards associate with objectives

6.G.1 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.

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.

Suggested Lesson Activities Students create their own composite figure and swap with a classmate and find the

area

Differentiation /Customizing learning (strategies)

Use calculator Use reference sheet Use word wall Create glossary

Ratios and Rates Essential Questions

How can you represent a relationship between two quantities? How can you find two ratios that describe the same relationship? How can you use rates to describe changes in real life problems? How can you compare two ratios? What is the relationship between ratios, fractions and percents? How can you use mental math to find the percent of a number? How can you compare lengths between the customary and metric systems?

Key Terms Ratio, equivalent ratios, ratio table, rate, unit rate, equivalent rates, percent, US Customary system, metric system, conversation factor, unit analysis Objectives Students will be able to:

Represent relationships between quantities in different ways Write and simplify ratios. Explore how to calculate rates and convert a rate to a unit rate. Write rates to describe real life situations. Recognize how ones perspective might change when rates are rewritten using

different time units.

Standards associate with objectives 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio

relationship between two quantities. 6.RP.2 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 6.RP.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.

6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.

6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Suggested Lesson Activities Have students collect data (such as age, height, weight, etc) within the classroom or

school setting and have them calculate the measures of central tendency. Find the unit price of an item sold in two different sizes and find the price per oz, lb,

etc.

Differentiation /Customizing learning (strategies) Create a chart to reinforce the relationship between distance, rate, time. Create your own glossary and use illustrations.

Integers and the Coordinate Plane Essential Questions

How can you represent numbers that are less than 0? How can you use the number line to order real-life events? How can you use the number line to compare positive and negative fractions and

decimals? How can you describe how far an object is from sea level? How can you graph and locate the points that contain negative numbers on a

coordinate plane? Key Terms Positive numbers, negative numbers, opposites, integers, absolute values, coordinate plan, origin, quadrants Objectives Students will be able to:

Use positive and negative numbers to represent situations Graph integers and their opposites Order integers from least to greatest Plot decimals and fractions on a number line Compare fractions and decimals Evaluate absolute values Compare absolute value expressions

Standards 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, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

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.

6.NS.6.a 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.

6.NS.6.b 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.

6.NS.6.c 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.

6.NS.7.a 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. 6.NS.7.b 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.

6.NS.7.c 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.

6.NS.7.d 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.

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.

Suggested Lesson Activities Have students create tutorial videos using iMovie/Keynote/Doceri/EduCreations. Research tides – use this to show relevance of absolute value – change in tides etc

Differentiation /Customizing learning (strategies) Look for fun activities on the web to differentiate lesson. Summary Triangles

Equations and Inequalities Essential Questions

How does rewriting a word problem help you solve the word problem? How can you use addition or subtraction to solve an equation? How can you use multiplication or division to solve an equation? How can you write an equation in two variables? How can you use a number line to represent solutions of an inequality? How can you use addition or subtraction to solve an inequality? How can you use multiplication or division to solve an inequality?

Key Terms Equation, solution, inverse operations, equation in two variables, solution of an equation in two variables, independent variable, dependent variable, inequality, solution of an inequality, solution set, graph of an inequality Objectives Students will be able to:

Rewrite word problems using fewer words, focusing on the mathematics that must be done.

Translate words into mathematical equations. Use the properties of equality to solve equations. Use familiar contexts including area formulas to develop an intuitive understanding

about what happens when multiplying or dividing by the same amount on both sides of the equation.

Tell whether an ordered pair is a solution to an equation Explore the concept of inequality and develop an understanding of the difference

between <, >, ≤,≥.

Translate words into mathematical inequalities and determine what numbers are solutions to an inequality.

Use real-life contexts to explore inequalities that can be solved by addition or subtraction.

Use the properties of inequality to solve inequalities. Standards associate with objectives

6.RP.3.a 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.

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.

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.

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 nonnegative rational numbers.

6.EE.8 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.

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. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Suggested Lesson Activities

Use a balance activity demonstrating the importance of keeping equations balance when solving.

Inequality Race – students will solve inequalities, while a classmate for each team moves “player” along number line

Tic-Tac-Toe Equations and Inequalities (see internet)

Differentiation /Customizing learning (strategies) Create a visual glossary of terms Create a classroom word wall Allow use of blocks Allow use of algebra tiles to solve equations

Surface Area and Volume Essential Questions

How can you draw three dimensional figures? How can you find the area of the entire surface of a prism?

How can you use a net to find the surface area of a pyramid? How can you find the volume of a rectangular prism with fractional edge lengths? How can you order numbers that are written as fractions, decimals, and percents? How can you compare fractions, decimals, and percents? How can you use mental math to find the percent of a number? How can you find the percent of a number? How can you use mental math and estimation to help solve real life problems?

Key Terms Percent Objectives Students will be able to

Use the percent bar model to help solve three types of percent problems. Convert between percents and fractions. Use a visual model to represent a percent. Convert between percents and decimals. Develop greater fluency with common benchmark fractions, decimals, and percents. Compare and order fractions, decimals, and percents. Develop an understanding of how to find 10% and 1% of a number using mental

math. Use multiplication to find the percent of a number. Use rounding skills to estimate the answer to a real life problem. Estimate percents using common fractional equivalence.

Standards associate with objectives

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 = 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.

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 real-world and mathematical problems.

Suggested Lesson Activities Students bring in cereal boxes and other containers and find the surface area and

volumes Minecraft activity (Students use creative mode to create a building – must give

dimensions of length, width, and height and find the volume and surface area) Create own cereal box and use a ruler to find the dimensions of length, width, and

height and find the volume and surface area Differentiation /Customizing learning (strategies)

Nets

Statistical Measures Essential Questions

How can you tell whether a question is a statistical question? How can you find an average value of a data set? In what other ways can you describe an average of a data set? How can you describe the spread of a data set? How can you use the distance between each data value and the mean of a data set to

measure the spread of a data set? Key Terms Statistics, statistical question, mean, outlier, measure of center, median, mode, measures of variation, range, quartiles, first quartile, third quartile, interquartile range, mean absolute deviation Objectives Students will be able to:

Display data in dot plots. Identify peaks, clusters and gaps in a dot plot Find the mean, median, mode and range of a set of data Find the mean absolute deviation of a set of data

Standards associate with objectives

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. 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.

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.

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.

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

6.SP.5a Reporting the number of observations. 6.SP.5b Describing the nature of the attribute under investigation, including how it

was measured and its units of measurement. 6.SP.5c 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.

Suggested Lesson Activities Two jars with object, allow student sto guess, calculate the MADs

Differentiation /Customizing learning (strategies) Concept Circles

Data Displays Essential Questions

How can you use place values to represent data graphically? How can you use intervals, tables, and graphs to organize data? How can you describe the shape of the distribution of a data set?

How can you use quartiles to represent data graphically?

Key Terms Stem and leaf plot, stem, leaf, frequency table, frequency, histogram, box-and-whisker plot, five-number summary Objectives Students will be able to:

Make a stem and leaf plot Answer questions using a stem and leaf plot Display data in a histogram Describe the shapes of distributions Make a box-and-whisker plot

Standards associate with objectives 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. 6.SP.4 Display numerical data in plots on a number line, including dot plots,

histograms, and box plots. 6.SP.5a Reporting the number of observations. 6.SP.5b Describing the nature of the attribute under investigation, including how it

was measured and its units of measurement. 6.SP.5c 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.

6.SP.5d 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.

Suggested Lesson Activities Use the graphing calculator to create box-and-whisker plots

Differentiation /Customizing learning (strategies) Group (pairs, threes, or fours) students by varying ability.