Unit Overview. Content Area: Math. Unit Title Operations and Properties Target Course/Grade Level 6th

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1 Content Area: Math Garfield Middle School Unit Title Operations and Properties Target Course/Grade Level 6th Duration: 16 Blocks Unit Overview Description Standards Addressed: CC.6.NS.2, CC.6.NS4,CC.6.EE.1, CC.6.EE.2c, CC.6.EE.3 In this chapter, students will be able to use the order of operations including exponents. Students will also be able to use the standard algorithm to divide multi-digit numbers. Students will use the mathematical properties to compute whole number operations mentally. Students will be able to represent whole numbers by using exponents. Students will increase their mathematical vocabulary and language when describing mathematical solutions. This unit will serve as a building block for future lessons in Algebra. Assessment for this unit will include : chapter tests, performance tasks, informal teacher observation, homework, and daily participation Concepts CPI Codes Estimation Dividing Multi-Digit Numbers Exponents Order of Operations Properties and Mental Math Concepts & Understandings CC.6.NS.2, CC.6.NS.4,CC.6.EE.1, CC.6.EE.2c, CC.6.EE.3 Understandings Estimation can be used to find approximate answers. Using the standard algorithm to divide multi-digit numbers. Representing whole numbers by using exponents. Using the order of operations, including exponents Apply the properties of mathematics to compute whole number operations mentally. Equations Learning Targets 21 st Century Themes and Skills See Addendum Guiding Questions Suppose you are buying items for a party and you have $50. Would it be better to overestimate or underestimate the cost of the items? Suppose your car can travel between 20 and 25 miles on a gallon of gas. You want to go on a 100-mile trip. Would it be better to overestimate or underestimate the number of miles per gallon your car can travel? What are the steps needed to solve long division? How can you decide where to write the first digit of your quotient? How do you know when you need to write a zero in the quotient? What is an exponent? What are the special names for the exponents 2 and 3? What is a base? What is a power? What operation is used for exponents? What order would you perform the operations in the expression ? Does it matter which operation you perform first in ? Explain.

2 What is an expression? What is the order of operations? Can you explain why 6+7x10 = 76 but (6+7)x10 = 130? How you can add parentheses to the numerical expression x3 so that 27 is the Correct answer? Can you give examples of the Commutative Property and the Associative Property? Can you name some situations in which you might use mental math? Unit Results Students will... Estimating with Whole Numbers: The student will be able to estimate whole numbers. Divide Multi-Digit Whole Numbers: The student will be able to use the algorithm for division and interpret the quotient and remainder in a real-world setting. Exponents: The student will be able to use exponents and to simplify expressions with exponents. Exploring the Order of Operations: The student will be able to use a calculator to evaluate two-step equations. Order of Operations: The student will be able to find the value of expressions using PEMDAS. Properties and Mental Math: The student will be able to use number properties to compute mentally. Suggested Activities The following activities can be incorporated into the daily lessons: Estimating with Whole Numbers: Have students plan a party for 12 people. They ll need to estimate the number of plates and napkins and the amount of food and drink to buy. Tell them that sometimes you do not need to use exact numbers. Planning a party is one situation where an estimate is sufficient. Divide Multi-Digit Whole Numbers: Have students solve a long division problem in groups. Students must show the steps used to complete the problem, and write out the steps in word form. Exponents: If Dana s school closes, a phone tree is used to contact each student s family. The secretary calls 3 families. Then each family calls 3 other families, and so on. How many families will be notified during the 6 th round of calls? How many families were called all together? Have students work in groups and demonstrate the answer using a diagram, repeated multiplication, and exponential form. Order of Operations: Have students work in groups to try to stump their classmates. Each group writes five numerical expressions, with no more than three operations, for which the order of operations must be used. Groups switch papers and find the correct value for each expression. Properties and Mental Math: Students will roll number cubes and generate numbers to be used in mentally applying the Distributive Property. Ex. Three rolls of the number cube yield 6, 4, and 3. Use the numbers to write the expression 6 x 43 and apply the Distributive Property to the expression. Content Area: Math Unit Title: Introduction to Algebra Target Course/Grade Level 6th Duration: 15 Blocks Unit Overview Description: In this chapter, students use algebraic concepts and properties of numbers to investigate patterns, to write and use expressions, and to write and solve one-step equations involving addition, subtraction, multiplication, or division. Students will increase their mathematical vocabulary when describing mathematical solutions. Assessments for this unit will include: chapter tests, performance tasks, daily participation, and informal assessments. Concepts & Understandings

3 Concepts Create and extend patterns Create algebraic expressions Solve one-step expressions Addition, subtraction, multiplication and division equations Area and perimeter of rectangles Understandings Making predictions about what may happen can be an effective way to extend patterns Algebraic expressions can be used to write word problems in number form Estimating solutions to equations can be done using mental math Understanding of inverse operations can help to solve equations CPI Codes CC.6.EE.2, CC.6.EE.3, CC.6.EE.5, CC.6.EE6, CC.6.EE.7 Learning Targets 21 st Century Themes and Skills See addendum Guiding Questions What is a numerical expression? What is a variable? Does the letter you choose for a variable make any difference? Why is the order of operations important for evaluating expressions? How can algebraic expressions be helpful in real life? How can you take a word phrase and write it as an algebraic expression? How do you describe an algebraic expression in words? What is an equation? What word is close to equation? What is an open sentence? How can you use mental math to solve algebraic equations? How do area and perimeter differ? What label is used with area? Unit Results Students will... Variables and Expressions: The student will be able to identify and evaluate algebraic expressions. Translating Between Words and Math: The student will be able to translate between words and math. Translating Between Tables and Expressions: The student will be able to write expressions tables and sequences. Explore Area and Perimeter of Rectangles: The student will be able to use grid paper to model the perimeter and area of rectangles. Equations and Their Solutions: The student will be able to determine whether a number is a solution of an equation. Addition Equations: The student will be able to solve whole number addition equations. Subtraction Equations: The student will be able to solve whole number subtraction equations. Multiplication Equations: The student will be able to solve whole number multiplication equations. Division Equations: The student will be able to solve whole number division equations. Suggested Activities The following activities can be incorporated into the daily lessons:

4 Variables and Expressions: Students can create a table to demonstrate the possible lengths and widths for a given area. Translating Between Words and Math: Students create an algebraic and numerical expression for each operation. Then write two phrases to match each expression. Translating Between Tables and Expressions: If 1 car has four wheels, 2 cars have 8 wheels, and 3 cars have 12 wheels, how many wheels will n cars have? Have students work in groups to create a table and expression to solve the problem. Equations and Their Solutions: Students will be given several scales showing equations and solutions. They will be asked to determine whether the given value of the variable is a solution to keep the scales balanced. Equations: Project: Students will demonstrate knowledge of solving equations using inverse operations. Students create 2 equations for each operation along with the steps for solving the equation. They will choose an artistic format to display their work. Examples: Show each equation on the petals of a flower, or create a tree showing the equations on the leaves. Content Area: Math Applications Unit Title Decimals Target Course/Grade Level Duration: 17 Blocks 6th Unit Overview Description In this chapter, students will read, write, compare, order, add, subtract, multiply, and divide decimals. Students will be able to round to estimate answers to problems that involve decimals. Students will be able to solve decimal equations. Students will increase their mathematical vocabulary and language when describing mathematical solutions. Assessments for this unit will include: chapter tests, performance tasks, daily participation, informal teacher observation, homework. Concepts CPI Codes Representing, Comparing, and Ordering Decimals Estimating Decimals Decimal Equations Solving Problems using Four Operations CC.6.NS.3, CC.6.EE.7, CC.6.EE.6 See Addendum Concepts & Understandings Learning Targets Understandings 21 st Century Themes and Skills Guiding Questions Reading, writing, comparing, and ordering decimals. Using rounding to estimate answers to problems that involve decimals Solving decimal equations. Add and Subtract Decimals. Multiply Decimals by Decimals and whole numbers, and Divide Decimals by whole numbers and decimals

5 Why 0.5 is greater than 0.29 even though 29 is greater than 5? What is the decimal with the least value: 0.29, 2.09, 2.009, and 0.029? Can you name three numbers between 1.5 and 1.6? Can you explain the following types of estimation: clustering, rounding, compatible numbers, and front-end estimation? What is the number that follows the decimals cluster around: 34.5, 36.78, and ? Can you determine whether a front-end estimation without adjustment is always an overestimation or an underestimation? How you would write to find the sum? Why it is a good idea to estimate the answer before you add and subtract? Can you explain why you must align the decimals when adding or subtracting decimals? Can you show how you would write to find the sum? Why it is a good idea to estimate the answer before you add and subtract? Why you must align the decimals when adding or subtracting decimals? How many decimal places are in the product of and 0.24? How can you use the Distributive Property to find 1.7 x 2? Describe how the products of 0.3 x 0.5 and 3 x 5 are similar. How are they different? How you know where to place the decimal point in the quotient? Why you can use multiplication to check your answer to a division problem? How the quotient of is similar to the quotient of How is it different? How you would interpret the quotient. A group of 27 students will ride in vans that carry 12 students each. How many vans are needed? Can you explain whether the value of m will be less than or greater than 1 when you solve 5m = 4.5? How you can check the answer to a variable equation? Unit Results Students will... Representing, Comparing, and Ordering Decimals: The student will be able to write, compare, and order decimals using place value and number lines. Estimating Decimals: The student will be able to estimate decimal sums, differences, products, and quotients. Explore Decimal Addition and Subtraction: The student will be able to use decimal grids to model addition and subtraction of decimals. Add and Subtract Decimals: The student will be able to add and subtract decimals. Explore Decimal Multiplication and Division: The student will be able to use decimal grids to model multiplication and division of decimals. Multiplying Decimals: The student will be able to multiply decimals by whole numbers and decimals. Dividing Decimals by Whole Numbers: The student will be able to divide decimals by whole numbers. Dividing by Decimals: The student will be able to divide whole numbers and decimals by decimals. Interpreting the Quotient: The student will be able to solve equations by interpreting the quotient. Solving Decimal Equations: The student will be able to solve equations involving decimals. Suggested Activities The following activities can be incorporated into the daily lessons: Representing, Comparing, and Ordering Decimals: Give students a list of 5 decimals. Students will make a chart in which they write each decimal in standard form, expanded form, and words. Students must draw or model each decimal using base ten blocks. Finally, the students will put all 5 decimals in order from least to greatest. Estimating Decimals: Students will choose a meal to make and search for the items needed in a food store flyer. Students will work in groups and choose an estimation strategy to come up with the estimated total for the

6 groceries needed. Adding and Subtracting Decimals: Students will be going on a shopping spree. They will be looking through sale ads for items to purchase. Each student will be given $100 to spend and must purchase a minimum of 5 items. Students must come as close to $100 as possible. They will also be responsible for calculating the change they will receive. Multiplying Decimals: Emphasize the fact that the algorithm for multiplying decimals is the same as that for multiplying whole numbers except that the placement of the decimal in the product is determined by the total number of digits behind the decimal points in both factors. To help demonstrate this, have students multiply a three digit number by a two digit number. Then use the same two numbers but add a decimal in each. Have students change the placement of the decimals 3 times. Example: 345 x 74; 3.45 x 7.4; 34.5 x 0.74; x 7.4 Dividing Decimals: Have students work in groups of three or four. Give each group a set of index cards labeled 0-9. Have the groups mix the cards face down in a pile. Students should then draw three cards to make a dividend and two cards to make a divisor. Have students take turns determining where to place the decimal point in the dividend and then do the division problem. When students are confident with decimals in the dividend, use the same procedure with a decimal in the divisor as well. Interpreting the Quotient: Have students make up and write a numerical division problem that would have a remainder. Use these problems in various word problems to create a game for students. Present each word problem and have students answer the questions on communicators to see how many correct answers each student can get. Example: There are 64 students going on a trip. Each bus can hold 30 students. How many busses do you need? Content Area: Math Unit Title: Number Theory and Fractions Target Course/Grade Level 6TH Duration: 20 Blocks `Unit Overview Description In this chapter on fractions, students focus on several fraction concepts and properties in preparation for computing with fractions. They use divisibility and mental math skills to investigate prime numbers and prime factorization of a number. They work with concepts of finding the greatest common factor of a set of numbers. Students will generate equivalent forms of numbers, including whole numbers, fractions, and decimals. They will be able to compare and order fractions, decimals, and whole numbers. Students will increase their mathematical vocabulary when describing mathematical solutions. Assessments for this unit will include: chapter tests, performance tasks, daily participation, informal teacher observation, homework. Concepts Factors and Prime Factorization Greatest common factor Equivalent expressions Decimals and Fractions Equivalent Fractions Mixed numbers and improper fractions Comparing and ordering fractions Concepts & Understandings Understandings When we find one whole number that divides a second, we know that all factors of that whole number also divide the second number. Exponents are a faster way to represent repeated multiplication. Every integer greater than one can be expressed as a product of prime factors in one way. Two or more whole numbers may have several common factors, but they have only one greatest common factor.

7 CPI Codes Garfield Middle School Learning Targets CC.6.NS.4, CC.6.EE.2b, CC.6.EE.3, CC.6.NS.7, CC.6.EE.4 Fractions are a way of representing amounts that are less than 1. A fraction has a unique simplest form, which may be an improper fraction or mixed number. Two positive integers have an infinite number of common multiples but only one LCM. GCF can be used to help compare and order fractions 21 st Century Themes and Skills See addendum Guiding Questions What is a factor? What is a common factor? How can you find the greatest common factors of two or more numbers? How can factor trees be used to find the GCF? How can divisibility rules help you find factors? What is a prime number? What is a composite number? What is the difference between prime and composite numbers? What is prime factorization? What are equivalent fractions? How many ways are there to write a fraction? When you make equivalent fractions, what operations are you actually performing? How can the GCF help to write a fraction in simplest form? What is a proper fraction? What is an improper fraction? What is a mixed number? What is the process for turning an improper fraction to mixed number and vice versa? What is a fraction How do the benchmarks of 0, 1/2, and 1 help to determine the value of fractions? How can LCDs help to compare and order fractions? Can you compare mixed number with fractions or should you turn them into improper fractions first? Unit Results Students will... Factors and Prime Factorization: The student will be able to write prime factorizations of composite numbers. Greatest Common Factor: The student will be able to find the greatest common factor of a set of numbers. Equivalent Expressions: The student will be able to factor numerical and algebraic expressions and write equivalent numeric and algebraic expressions. Decimals and Fractions: The student will be able to convert between decimals and fractions. Equivalent Fractions: The student will be able to find equivalent forms of fractions. Mixed Numbers and Improper Fractions: The student will be able to use mixed numbers and improper fractions. Comparing and Ordering Fractions: The student will be able to compare and order fractions.

8 Suggested Activities The following activities can be incorporated into the daily lessons: Factors and Prime Factorization: Have students choose 5 numbers consisting of two or more digits. Students must find all factors of each number and create a factor tree to show prime factorization in exponential form when possible. Greatest Common Factor: Have students work in groups of three to find the GCF. Each member of the group will use a different method for finding the GCF on the same problem. Each member should explain their method as they compare their answers. For the next problem, the group members will switch methods within the group and proceed as before the find the GCF. Allow group members to assist other group members when necessary. Use a factor tree to find prime factorizations of numbers. Find the GCF using various strategies such as, factor tree, division ladder, or factor list. Model fractions using fraction bars and other graphics. Compare fractions by converting to decimals, using number sense, or cross multiplication of fractional parts. Find the LCM using multiple lists and prime factorizations. What s the Error? Use this strategy to help students recognize their own errors. Use word problems to model situations: -A teacher ordered 6 pizzas for her class. Each pizza had 8 slices, 20 slices were left after the party. How many pizzas were left? -In a parade, there are 15 riders on bicycles and tricycles. In all there are 34 wheels. How many bicycles and tricycles are in the parade? -There are 36 sixth graders and 40 seventh graders. What is the greatest number of teams that the students can form if each team has the same number of sixth graders and seventh graders, and every student must be on a team? Project: Glacier National Park: This National Park has 700 miles of hiking trails. Research the names and lengths of 7 trails (in miles). Create a chart showing the trails and their lengths in fractions and in decimals. Put them in order from least to greatest. Write 5 questions that can be answered using the chart you have produced (show answers to the questions, show work to justify your answer). Content Area: Math Honors Unit Title: Fraction Operations Target Course/Grade Level: 6 th Duration: 20 Blocks Unit Overview Description In this chapter, students continue their study of fractions as they add, subtract, multiply and divide fractions and mixed numbers with unlike denominators. Students will also solve equations involving fractions. In addition, students will model division situations involving fractions. Students will increase their mathematical vocabulary and language when describing mathematical solutions. Assessments for this unit include: chapter tests, performance tasks, homework, informal teacher observation, daily participation, and class projects. Concepts Least Common Multiple (LCM) Concepts & Understandings Understandings Finding Least Common Multiple to find common

9 Adding and Subtracting with unlike denominators Multiplying Mixed Numbers Dividing Fractions and Mixed Numbers Solving Fraction Equations CPI Codes EE.6.06 NS.6.04 EE.6.07 NS.6.01 denominators. Adding, subtracting, multiplying, and dividing fractions and mixed numbers with unlike denominators. Solving equations with fractions Learning Targets Reason about and solve one-variable equations and inequalities: Use variables to represent numbe understand that a variable can represent an unknown number, or, depending on the purpose at han Reason about and solve one-variable equations and inequalities: Solve real-world and mathematica which p, q and x are all nonnegative rational numbers. Apply and extend previous understandings of multiplication and division to divide fractions by frac division of fractions by fractions, e.g., by using visual fraction models and equations to represent the model to show the quotient; use the relationship between multiplication and division to explain that much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cu length 3/4 mi and area 1/2 square mi? Compute fluently with multi-digit numbers and find common factors and multiples: Find the greatest common fact numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Us property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole n common factor. For example, express as 4 (9 + 2). 21 st Century Themes and Skills See Addendum. Guiding Questions How is multiplying mixed numbers different from multiplying fractions? Can you explain why you cannot find a greatest common multiple for a group of numbers? Can you tell whether the LCM of a set of numbers can ever be smaller than any of the numbers in the set? Can you explain an advantage of using the least common denominator (LCD) when adding unlike fractions? Can you tell when the least common denominator (LCD) of two fractions is the product of their denominators? Can you explain how to use mental math to subtract 1/12 from ¾? Can you explain why you regroup 2 as 1 8/8 instead of 1 3/3 when you find 2-1 3/8? Can you give an example of a subtraction expression in which you would need to regroup the first mixed number to subtract? Can you explain whether you would need to regroup to simplify the expression 7 7/8-2 5/8-1 3/8? Can you explain how regrouping a mixed number when subtracting is similar to regrouping when subtracting whole numbers? Can you give an example of an addition equation with a solution that is a fraction between 3 and 4? Can you explain how you know the number of groups into which you must divide the squares in the following problem when using fraction bars: 4 1/2 3 = 1 ½? What is a reciprocal? How are reciprocals used to divide fractions? Can GCF be used to help you divide fractions? Can you explain how to use mental math to find the value of n in the equation 5/8 n = 1? Can you explain how to find the reciprocal of 3 6/11?

10 Can you explain whether 2/3x = 4 is the same as 2/3 = 4x? How do you know which numbers to divide by in the following equations: 2/3x = 4 and 4/5 = 8x? How do you multiply a mixed number by a mixed number? Can you explain two ways you would multiply a mixed number by a whole number? Can you explain whether the product of a proper fraction and a mixed number is less than, between, or greater than the two factors? Unit Results Students will... Least Common Multiple: The students will be able to find the least common multiples (LCM) of a group of numbers. Adding and Subtracting with Unlike Denominators: The student will be able to add and subtract fractions with unlike denominators. Regrouping to Subtract Mixed Numbers: The student will be able to regroup mixed numbers to subtract Solving Fraction Equations: Addition and Subtraction: The student will be able to solve equations by adding and subtracting fractions. Model Fraction Division in Context: The student will be able to use fraction bars to model the division of fractions in word problems. Dividing Fractions and Mixed Numbers: The student will be able to divide fractions and mixed numbers. Solving Fraction Equations: Multiplication and Division: The student will be able to solve equations by multiplying and dividing. Multiplying Mixed Numbers: The student will be able to multiply mixed numbers. Suggested Activities The following activities can be incorporated into the daily lessons: Real-World Connections: Students will research different recipes for barbecue sauce. They will write problems based on quantities in the recipes they find. They will also multiply the recipe by 3 ½ times the amount. Least Common Multiple: Students will spin their spinners to generate three or four 1- and 2- digit numbers. Students will use each of the three given methods to find the LCM for each set of numbers. Breakfast Project: Students will create a breakfast Students will work on the Problem Solving Section of the book. They will first attempt the problems without multiple choice options. If the students struggle, provide the multiple choice options to alleviate some of the difficulty. Students will also work from additional sources to improve their test taking skills. Sources will include additional workbooks (i.e. Math Coach) and sample questions. Students will work on the Standardized Test Prep Section. They will work on and discuss the short response and extended response sections. Content Area: Math Unit Title: Data Collection and Analysis Target Course/Grade Level: 6th Duration: 12 Blocks Unit Overview Description : In this chapter, students will use mean, median, mode, and range to describe data. Students will also solve problems by collecting, organizing, and displaying data. Students will be able to draw and compare different

11 graphical representations of the same data. They will also be able to understand statistical variability. Students will summarize and describe various distributions. Students will increase mathematical vocabulary when describing mathematical solutions. Assessments for this unit will include: performance tasks, daily participation, informal teacher observation, homework, chapter tests. Concepts CPI Codes NS.6.07 SP.6.01 SP.6.02 Mean, Median, Mode and Range Additional Data and Outliers Line Plots, Frequency Tables, and Histograms Measures of Variations Describing Distributions Concepts & Understandings Learning Targets Understandings Using mean, median, mode, and range to describe data Solving problems by collecting, organizing, and displaying data Drawing and comparing different graphical representations of the same data Understanding statistical variability Summarizing and describing distributions Apply and extend previous understandings of numbers to the system of rational numbers: Understand ordering and absolute value of rational numbers. 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. 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. Develop understanding of statistical variability: 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. Develop understanding of statistical variability: 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. SP.6.03 SP.6.04 SP.6.05 Develop understanding of statistical variability: 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. Summarize and describe distributions: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Summarize and describe distributions: Summarize numerical data sets in relation to their context, such as by: a.reporting the number of observations. b.describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

12 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 were gathered. d.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. 21 st Century Themes and Skills See addendum Guiding Questions What other word can we use for mean? Approximately where in the data could the mean lie? What is an outlier? What would happen to the mean if the outlier is dropped? What you can say about the values in a data set if the set has a small range? How many modes are in the following set of data? 15,12,13,15,11,11 Explain your answer. What word is the word median close to? What would happen if two numbers were in the middle? Why is it necessary to put the data in order before finding the median? Can you have more than one mode? Will there always be a mode? Explain how an outlier with a large value will affect the mean of a data set. What is the effect of a small outlier value? Can you explain why the mean would not be a good description of the following high temperatures that occurred over 5 days: 72 F, 68 F, 70 F, 71 F, and 39 F. What is shown in a box-and-whisker plot? What does the mean absolute deviation shows about a set of data? Can you describe a data set that can be displayed using a histogram? How a frequency table can be used to gather data? How a line plot can be used to visualize data? How can a box-and-whisker plot give information that is hard to see by just looking at the numbers? Can you describe the benefits of displaying data using a dot plot as opposed to a box-and-whisker plot? Unit Results Students will : Find and analyze the median and mode of a data set, and learn the effect of additional data and outliers. Find the range of a set of data. Calculate, interpret, and compare measures of variation in a data set. Record and organize data in line plots, frequency tables and histograms. Describe and compare data distributions by their center, spread, and shape using box-and-whisker plots or dot plots. Suggested Activities The following activities can be incorporated into the daily lessons: Students will find the mode and median for a set of data. They will determine the value of this data in various situations. Students will calculate the mean by using math test grades. They will analyze their results and discuss effects of

13 outliers. Students will use frequency tables and line plots to record data, and then find the range. Students will compare information presented in various formats such as line graphs, bar graphs and organized lists. Provide multiple opportunities to collect and represent data relating to topics chosen by the students. Students will show examples where outliers affect the range, median and mean. Use word problems and real-world data to describe situations where range, median, mode and mean are applicable. Content Area: Math Unit Title: Proportional Relationships Target Course/Grade Level: 6th Duration: 22 Blocks Unit Overview Description : In this chapter, students will use ratios to describe proportional situations. They will also represent ratios and percents with concrete models, fractions, and decimals. Next, they will be able to use multiplication and division to solve problems involving equivalent ratios and rates. Finally, using ratios to make predictions in proportional situations. Students will increase their mathematical vocabulary when describing mathematical solutions. Assessments for this unit will include: chapter tests, performance tasks, daily participation, informal teacher observation, and homework Concepts Concepts & Understandings Understandings Ratios and Rates Proportions Using ratios to make predictions and describe Using Tables to Explore Equivalent Ratios and proportional situations. Rates. Using multiplication and division to solve problems Ordered Pairs. involving equivalent ratios and rates. Percents, Decimals, and Fractions Percent of a Finding rational numbers on a vertical and Number. horizontal line. Representing ratios and percents with concrete models, fractions, and decimals. Learning Targets CPI Codes NS.6.06 RP.6.02 Apply and extend previous understandings of numbers to the system of rational numbers: 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. 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. Understand ratio concepts and use ratio reasoning to solve problems: 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

14 RP.6.03 RP.6.01 hamburger. (Expectations for unit rates in this grade are limited to non-complex fractions.) Understand ratio concepts and use ratio reasoning to solve problems: 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. 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. b.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? c.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. Understand ratio concepts and use ratio reasoning to solve problems: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes. 21 st Century Themes and Skills See Addendum Guiding Questions What is a ratio? What are the three ways to write ratios? How can you find equivalent ratios? Why the ratio 2:5 is different from the ratio 5:2? Can you tell whether the ratios 4:5 and 16:25 are equivalent? If they are not, give a ratio that is equivalent to 4:5. How many wheels are on a skateboard? How many wheels are needed for 85 boards and how many wheels are needed for 124 boards? How you can be sure that all ratios you have written are correct when you have multiplied or divided a ratio to find equivalent ratios? How you can be sure that you have written the numerator and denominator in the correct order when rewriting ratios that have colons as fractions? What you define the terms coordinate grid and ordered pair? How are the terms related? What point is the starting location when you are graphing on a coordinate grid? Describe how to graph (2½, 8) on a coordinate grid. How do you express ratios as fractions? How do you find equivalent ratios? How do you find a missing value in a proportion by using cross products? Tell whether 7/8 = 4/14 is a proportion. How do you know? Can you give an example of a proportion? Tell how you know that it is a proportion. What are some examples of different ways that you saw percents being used? How much sales tax would you have to pay on $1, $10, and $100 if your state had a 5% sales tax rate? How can you write a percent as a fraction?

15 Can you write 100% as a decimal and as a fraction? How can you convert from a percent to a fraction and from percent to a decimal? Tell which method you prefer for converting decimals to percents-using equivalent fractions or multiplying by 100. Why? What are two different ways to write three-tenths? How can you write fractions as percents using two different methods? Can you compare the two methods of finding a percent of a number: using a proportion and multiplying by a decimal? Can you explain how to set up a proportion to find 150% of a number? Can you describe a situation in which you might need to find a percent of a number? Can you describe two methods for solving percent problems? Which would you prefer to use the proportion method or the equation method when solving percent problems? What is the first step is in solving a sales tax problem? Unit Results Students will... Ratios and Rates The student will be able to write ratios and rates and find unit rates Using Tables to Explore Equivalent Ratios and Rates The student will be able to use a table to find equivalent ratios and rates. Ordered Pairs: The student will be able to graph ordered pairs on a coordinate grid. Proportions The student will be able to write and solve proportions using number sense and cross products. Percents: The student will be able to write percents as decimals and as fractions. Percent of a Number: The student will be able to find the percent of a number. Solving Percent Problems: The student will be able to solve problems using percents Suggested Activities The following activities can be incorporated into the daily lessons: Social Studies Link: Students will use proportions to use foreign currency conversions. Ratios and Rates: Provide students quantity pricing (e.g. 3 for $1.46) for several different items from two different grocery stores. Have students work to find the unit rates for the items and compare their findings with those of their classmates. Which store had the best unit rates for each item? Students will work on the Problem Solving Section of the book. They will first attempt the problems without multiple choice options. If the students struggle, provide the multiple choice options to alleviate some of the difficulty. Students will also work from additional sources to improve their test taking skills. Sources will include additional workbooks (i.e. Math Coach) and sample questions. Students will work on the Standardized Test Prep Section. They will work on and discuss the short response and extended response sections. Unit Overview Content Area: Math Unit Title: Measurement and Geometry Target Course/Grade Level: 6th Duration: 30 Blocks Description : In this chapter, students begin by converting measures within the same measurement system. They will

16 apply their knowledge solving problems involving perimeter and area. They will be able to identify, draw and build three-dimensional figures. Next, they will find the surface area or prisms, pyramids, and cylinders. Finally, they will find the volume of prisms. Students will increase their mathematical vocabulary when describing mathematical solutions. Assessments for this unit will include: performance tasks, daily participation, informal teacher observations, homework, and chapter tests. Concepts CPI Codes EE.6.02 G.6.01 G.6.02 G.6.04 Converting Customary Units Converting Metric Units Area of Rectangles and Parallelograms Area of Triangles and Trapezoids Area of Composite Figures Volume of Prisms Surface Areas Concepts & Understandings Learning Targets Understandings Converting measures within the same measurement system Convert metric units of measure Estimate the area of irregular figures and find the area of rectangles and parallelograms Find the area of triangles and trapezoids. Break a polygon into simpler parts to find its area. Estimate and find the volumes of rectangular prisms and triangular prisms. Find the surface area of prisms, pyramids, and cylinders. Apply and extend previous understandings of arithmetic to algebraic expressions: Write, read, and evaluate expressions in which letters stand for numbers. 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 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 = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2. Solve real-world and mathematical problems involving area, surface area, and volume: 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. Solve real-world and mathematical problems involving area, surface area, and volume: 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. Solve real-world and mathematical problems involving area, surface area, and volume: 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. Understand ratio concepts and use ratio reasoning to solve problems: Use ratio and rate reasoning

17 RP.6.03 to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. d.use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. 21 st Century Themes and Skills See addendum Guiding Questions When would you use the common customary measurement units for length, capacity, and weight? How can you convert measurements by canceling units? How can you set up a proportion to convert between units of measurement? Can you explain how to break apart an irregular figure to calculate its area? When would you need to use area in your real life? What is the process to convert from a larger unit to a smaller unit and from a smaller unit to a larger unit? What are the similarities between the formulas for area of a rectangle and area of a parallelogram? Explain how the area of a parallelogram and the area of a rectangle that have the same base and the same height are related. How can you describe the formula for the area of a square? Can you identify the base and height on each triangle? Can you explain why any side can be a base? How are the areas of a triangle and a parallelogram with the same base and height are related? How can you find the area of a regular octagon by breaking it apart into congruent triangles, if you know the area of one triangle? Can you explain another way that you can divide the irregular shape above? What is volume? How is volume different from area? How do use the formulas for finding the volume of a rectangular prism (V=lwh) and the volume of a triangular prism (V=Bh). Can you draw an illustration of a triangular prism and a rectangular prism? How can you find the height of a rectangular prism if you know its length, width, and volume? Can you describe the difference between the units used to measure perimeter, area and volume? How can you use a net to find the surface area of a 3 dimensional figure? Why can a net be helpful when finding the surface area of a three-dimensional figure? What is the procedure for finding the surface area of a pentagonal prism? How can you find the surface area of a cube if you know the area of one face? Unit Results Students will... Convert between customary units of measure. Convert between metric measurements. Estimate the areas of irregular figures and find the area of rectangles and parallelograms. Find the area of trapezoids and triangles. Break a polygon into simpler parts to find its area. Estimate and find the volumes of rectangular prisms and triangular prisms.

18 Find the surface area of prisms, pyramids, and cylinders. Suggested Activities The following activities can be incorporated into the daily lessons: Show visual representations of each unit of measurement so students can refer back to these concrete examples when necessary. Have students find the distance between several US cities in miles and then convert these miles to kilometers. Students can measure the classroom in inches, and convert the inches into feet, centimeters and meters. Use gallon man to introduce customary units of liquid measurement, have students copy picture into their notebooks. Students will convert between kilometers, meters, and centimeters using a visual representation such as a map of the classroom, or the City of Garfield. Find the areas of parallelograms and triangles using graph paper to convey understanding. Create geometry people using various geometric figures, identify the figures and calculate the area and perimeter for each one. Students will draw various irregular polygons on graph paper and find the area of each one by breaking the figure into smaller parts. Project: Students will create a rectangular prism and a triangular prism, and use formulas to show surface area and volume of their prisms. Students will create a cylinder and use formulas to calculate surface area and volume. All work must be shown. Content Area: Math Unit Title: Integers and the Coordinate Plane Target Course/Grade Level: 6th Duration: 15 Blocks Unit Overview Description : In this chapter, students will use integers to represent real-life situations. They will graph and locate ordered pairs on four quadrants of a coordinate plane. Finally, they will be able to understand absolute value. Students will increase their mathematical vocabulary when describing mathematical solutions. Assessments for this unit will include: Performance tasks, daily participation, informal teacher observations, homework, and chapter tests. Concepts Integers and Absolute Value Comparing and Ordering Integers. Coordinate Plane Polygons in the Coordinate Plane. Transformations in the Coordinate plane Concepts & Understandings Learning Targets Understandings Understanding absolute value Using integers to represent real-life situations. Graphing and locating ordered pairs on four quadrants of a coordinate plane.

19 CPI Codes G.6.03 NS.6.05 NS.6.06 NS.6.07 Solve real-world and mathematical problems involving area, surface area, and volume: 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. Apply and extend previous understandings of numbers to the system of rational numbers: 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. Apply and extend previous understandings of numbers to the system of rational numbers: 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. 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. 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. 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. Apply and extend previous understandings of numbers to the system of rational numbers: Understand ordering and absolute value of rational numbers. 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. b.write, interpret, and explain 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. 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. 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. Apply and extend previous understandings of numbers to the system of rational numbers: Solve NS.6.08 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. 21 st Century Themes and Skills See Addendum Guiding Questions Review the vocabulary: positive, negative, opposites, integer and absolute value. How do the terms relate to each other?