SAUSD Curriculum Map 2015-2016: Math 6

(Last updated July 9, 2015) 1

Math 6

These curriculum maps are designed to address CCSS Mathematics and Literacy outcomes. The overarching focus for all curriculum maps is building student’s content knowledge and literacy skills as they develop knowledge about the world. Each unit provides several weeks of instruction. Each unit also includes various assessments. Taken as a whole, this curriculum map is designed to give teachers recommendations and some concrete strategies to address the shifts required by CCSS.

Instructional Shifts in Mathematics

Focus:

Focus strongly where the

Standards focus

Focus requires that we significantly narrow and deepen the scope of content in each grade so that students experience concepts at a deeper level.

• Instruction engages students through cross-curricular concepts and application. Each unit focuses on implementation of the Math Practices in conjunction with math content.

• Effective instruction is framed by performance tasks that engage students and promote inquiry. The tasks are sequenced around a topic leading to the big idea and essential questions in order to provide a clear and explicit purpose for instruction.

Coherence:

Think across grades, and link to major topics within grades

Coherence in our instruction supports students to make connections within and across grade levels.

• Problems and activities connect clusters and domains through the art of questioning. • A purposeful sequence of lessons build meaning by moving from concrete to abstract,

with new learning built upon prior knowledge and connections made to previous learning.

• Coherence promotes mathematical sense making. It is critical to think across grades and examine the progressions in the standards to ensure the development of major topics over time. The emphasis on problem solving, reasoning and proof, communication, representation, and connections require students to build comprehension of mathematical concepts, procedural fluency, and productive disposition.

Rigor:

In major topics, pursue

conceptual understanding,

procedural skills and fluency, and

application

Rigor helps students to read various depths of knowledge by balancing conceptual understanding, procedural skills and fluency, and real-world applications with equal intensity.

• Conceptual understanding underpins fluency; fluency is practiced in contextual applications; and applications build conceptual understanding.

• These elements may be explicitly addressed separately or at other times combined. Students demonstrate deep conceptual understanding of core math concepts by applying them in new situations, as well as writing and speaking about their understanding. Students will make meaning of content outside of math by applying math concepts to real-world situations.

• Each unit contains a balance of challenging, multiple-step problems to teach new mathematics, and exercises to practice mathematical skills

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8 Standards for Mathematical Practice

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. They describe how students should learn the content standards, helping them to build agency in math and become college and career ready. The Standards for Mathematical Practice are interwoven into every unit. Individual lessons may focus on one or more of the Math Practices, but every unit must include all eight: 1. Make sense of problems and persevere in solving them

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

2. Reason Abstractly and quantitatively

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

3. Construct viable arguments and critique the reasoning of others

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

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4. Model with mathematics

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

5. Use appropriate tools strategically

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

6. Attend to precision

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

7. Look for and make use of structure

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

8. Look for and express regularity in repeated reasoning

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x - 1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x2 + x + 1), and (x - 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

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English Language Development Standards

The California English Language Development Standards (CA ELD Standards) describe the key knowledge, skills, and abilities in core areas of English language development that students learning English as a new language need in order to access, engage with, and achieve in grade-level academic content, with particular alignment to the key knowledge, skills, and abilities for achieving college- and career-readiness. ELs must have full access to high quality English language arts, mathematics, science, and social studies content, as well as other subjects, at the same time as they are progressing through the ELD level continuum. The CA ELD Standards are intended to support this dual endeavor by providing fewer, clearer, and higher standards. The ELD Standards are interwoven into every unit.

Interacting in Meaningful Ways

A. Collaborative (engagement in dialogue with others) 1. Exchanging information/ideas via oral communication and conversations

B. Interpretive (comprehension and analysis of written and spoken texts)

5. Listening actively and asking/answering questions about what was heard 8. Analyzing how writers use vocabulary and other language resources

C. Productive (creation of oral presentations and written texts)

9. Expressing information and ideas in oral presentations 11. Supporting opinions or justifying arguments and evaluating others’ opinions or

arguments

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How to Read this Document

• The purpose of this document is to provide an overview of the progression of units of study within a

particular grade level and subject describing what students will achieve by the end of the year. The work of Big Ideas and Essential Questions is to provide an overarching understanding of the mathematics structure that builds a foundation to support the rigor of subsequent grade levels. The Performance Task will assess student learning via complex mathematical situations. Each unit incorporates components of the SAUSD Theoretical Framework and the philosophy of Quality Teaching for English Learners (QTEL). Each of the math units of study highlights the Common Core instructional shifts for mathematics of focus, coherence, and rigor.

• The 8 Standards for Mathematical Practice are the key shifts in the pedagogy of the classroom.

These 8 practices are to be interwoven throughout every lesson and taken into consideration during planning. These, along with the ELD Standards, are to be foundational to daily practice.

• First, read the Framework Description/Rationale paragraph, as well as the Common Core State

Standards. This describes the purpose for the unit and the connections with previous and subsequent units.

• The units show the progression of units drawn from various domains.

• The timeline tells the length of each unit and when each unit should begin and end.

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SAUSD Scope and Sequence for Math 6:

Unit 1 Unit 2 Unit 3 Unit 4 (begin) 9/1/15-

10/09/15 6 Weeks

10/12/15-11/13/15

5 Weeks

11/16/15-1/08/16 5 Weeks

1/11/16-1/22/16 2 Weeks

Ratios and Proportional

Reasoning

Arithmetic Operations (Dividing Fractions)

Rational Numbers (Integers,

Absolute Value, Coordinate

Plane)

Expressions (Start in 1st

Semester finish in 2nd Semester)

****SEMESTER****

Unit 4 (continued)

Unit 5 Unit 6 Unit 7 Unit 8

2/01/16-2/12/16 2 Weeks

2/15/16-3/18/16 5 Weeks

3/21/16-4/22/16 4 Weeks

4/25/16-5/27/16 5 Weeks

5/30/16-6/10/16 2 Weeks

Expressions (Start in 1st

Semester finish in 2nd

Semester)

Equations and Inequalities Statistics Geometry Enrichment

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Math 6 Overview:

In the years prior to grade six, students built a foundation in numbers and operations, geometry, and measurement and data. As they enter sixth grade, students are fluent in addition, subtraction, and multiplication with multi-digit whole numbers and have a solid conceptual understanding of all four operations with positive rational numbers, including fractions. Students’ understanding of measurement concepts (e.g., length, area, volume, and angles) has solidly begun, and how to represent and interpret data is emerging (Adapted from The Charles A. Dana Center Mathematics Common Core 9 Toolbox 2012). In grade six, instructional time should focus on four critical areas: (1) connecting ratio, rate, and percentage to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking (CCSSO 2010, Grade 6 Introduction). Students also work toward fluency with multi-digit division and multi-digit decimal operations.

(From the CA Mathematics Framework for Math 6)

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Unit 1: Ratios and Proportional Reasoning (6 Weeks 9/1-10/09)

Big Idea Numbers, expressions, and measures can be compared by their relative values.

Essential Questions Performance Task Problem of the Month

• What are different ways to represent a ratio?

• What are the differences/similarities between ratios, rates and unit rates?

• How can ratios and proportional reasoning be used to solve real-world mathematical problems?

• Rate Concentrate [6th grade 2012] • Table Decorations [5th Grade 2010] p.3 • Fig Pudding [5th Grade 2006] • Truffles [6th Grade 2009] p.3-4 • Plum Jelly [5th Grade 2011] • Candies [5th Grade 2007] p.2 • Linflower Seeds [6th Grade 2000] • Grandpa’s Knitting [6th Grade 2002] p.7-8 • 100 People [6th Grade 2011] (See the end of this document for Performance Task descriptions) *Please read SVMI’s document security information:

http://www.svmimac.org/memberresources.html

• Measuring Up POM and Teacher Notes

Unit Topics/Concepts Content Standards Resources

Ratios • Understand that a ratio is a pair of

non-negative, non-zero numbers A:B or A to B

• Know there are two types of ratios: Part-to-Whole and Part-to-Part

• Use ratio language to describe a relationship between two quantities, such as “For every___, there are ____.”

• Represent ratios in various ways to see the additive and multiplicative structure of ratios.

Rate/Unit Rate • Understand the concept of a

rate/unit rate • Understand unit rates are limited

to non-complex fractions (whole numbers) in this grade level

• Understand rates always have units associated with them

• Understand ratios and their associated rates by building on prior knowledge of division

Ratio and Rate Reasoning • Focus on “benchmark percents”

modeling ratio concepts with tables, tape diagrams and double number lines.

• Use ratio and rate reasoning to

Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.1 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.” 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. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” 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. 6.RP.3a Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs

Essential Resources: • CCSS 6th Grade Framework (pgs. 7

– 20) Instructional Resources: • SAUSD Resource Packet:

Ratios and Proportional Reasoning EngageNY (Module 1)

• Rates & Ratios Supplement (Lathrop)

Additional Resources: • SERP Problem: The Intensity of

Chocolate Milk • MAP Lessons:

Proportional Reasoning – 6th Grade Formative Assessment Lesson Solving Real Life Problems: Selling Soup – 6th Grade Formative Assessment Lesson

• Adopted Textbook CGP: Txt pp. 170-176. Wb pp. 91, 93, 95, 97-99, 101, 103

• Illustrative Mathematics • Dan Meyer 3-act videos (list and

interactive link to Dan Meyer's videos by standard); Nana's Paint Mix-up: Dan Meyer Video Series (good ratio video)

• New Tritional Info - Mathalicious • YouTube Video about Double

Number Lines and Tape Diagrams • Georgia Dept. of Education Unit 2

Framework

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solve unit price, constant speed, percent and use conversion of measurements

• Use ratio and reasoning to solve real-world and mathematical problems.

• Understand the difference between ratio, rate, and unit rate

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

• Percents Packet (Carr Resource Packet)

• Percent Resources (IMP) • Mercer Booklet (Percents)

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Unit 1: Ratios and Proportional Reasoning (Instructional Support & Strategies)

Framework Description/Rationale A critical area of instruction in grade six is to connect ratio, rate and percentage to whole number multiplication and division and use concepts of ratio and rate to solve problems. Students work with models to develop their understanding of ratios. Initially, students do not express ratios using fraction notation so that ratios can be differentiated from fractions and from rates. Also, although a ratio can have a 0, in Math 6, students will not see a ratio expressed with 0’s. Within the course of this unit students understand that ratios can be expressed in fraction notation, but ratios are also different from fractions in several ways. Percent is a rate out of 100 thus considered as part of rates. Percent, therefore it is not taught as an isolated topic (See CCSS 6th Grade Framework pgs. 7 – 20 for further information). Build on students’ knowledge of division concepts, for example:

Academic Language

Support Instructional Tool/Strategy Examples

Preparing the

Learner Key Terms for Word Bank: • Ratio • Unit Rate • Rate • Equivalent Ratios • Unit Price • Constant Speed • Percent • Tape Diagram • Double- Number Line

Academic Conversation Support ex: Conversation Placemat: Can you explain why you…? For every _____, there are ______

Visual Models: 1. Table 2. Tape Diagram—to use when the unit of measurement

is the same. 3. Double-sided Number Line—to use when the two units

of measurement are different 4. Coordinate Plane 5. Percent bar/Fraction bar (drawn or foldable) 6. Elastic ruler 7. Benchmark Percentages 8. Ratio tables—to generate equivalent ratios

Additional Strategy Examples: Have students design a tree map where they categorize different examples of ratios, rates, and unit rates. From there they can use their examples to create a double-bubble map comparing/contrasting two of the categories, then complete a sentence frame similar to the following: Ratios, rates, and unit rates are similar to each other because _____________ but they are also different because _______________________. Ratios: • Define ratio as a pair of non-negative numbers, A:B, which

are not both zero. • Use ratios to compare parts to whole. • Use ratios to compare parts to parts. • Identify and describe any ratio using language such as, “For

every ____, there are ____”. • When learning ratios we don’t want to introduce them as

fractions and don’t use the terms numerator or denominator so as to not confuse students.

Topics: • Multiplication Skills • Division Skills

including decimals • Fraction

understanding

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• In a ratio a:b, b can’t equal 0 due to division by 0 being undefined.

Percents: • Find the whole, given a part and the percent. • Connect percent to ratios • Arrange tables vertically to help students see the

multiplicative relationship and to help avoid confusing ratios with fractions.

• Students should notice the role of multi. and div. in how equivalent ratios are related.

• Use ratio and rate language to deepen their understanding of what a ratio describes.

• Properly use ratio notation, symbolism and label quantities. Teacher Notes:

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Unit 2: Arithmetic Operations (5 Weeks 10/12-11/13)

Big Idea Basic facts and algorithms for operations with rational numbers use notions of equivalence to transform calculations into simpler ones.

Essential Questions Performance Task Problem of the Month

• How can I use fractions in real life? • How can models be used to compute fractions

with like and unlike denominators? • How do I divide different sets of fractions? • What is the GCF and LCM of a given set of

numbers?

• Pet Food [5th Grade 1999] • Rabbit Costumes [6th Grade 2003] • How Much Money? [6th Grade 2005] p.16 • Smallest and Largest [6th Grade 2006] p.19-20 • Division [Grade 6 2007] p.35 • Fractions [6th Grade 2010] p.4 • Ribbons and Bows [6th Grade 2013] p.8-9

• Fractured Numbers POM and Teacher’s Notes

Unit Topics/Concepts Content Standards Resources

Quotients of Fractions • Divide whole numbers

by fractions. • Divide fractions by

fractions. Compute Fluently • Divide multi-digit

numbers • Add, subtract, multiply

and divide multi-digit decimals.

• Write decimals as fractions whose denominator is a power of 10.

GCF/LCM • Find the GCF of two

whole numbers less than or equal to 100.

• Find the LCM of two whole numbers less than or equal to 12.

Distributive Property • Express the 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. 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? Compute fluently with multi-digit numbers and find common factors and multiples. 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 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).

Essential Resources: • CCSS 6th Grade Framework

(pgs. 20 – 26) Instructional Resources: • EngageNY (Module 2) • Spurgeon Intermediate

Factors and Multiples Unit • Adopted Textbook CGP Additional Resources: • SERP Problem: No Matter

How You Slice It • MAP Lesson: • Interpreting Multiplication

and Division – 6th Grade Formative Assessment Lesson

• Illustrative Mathematics • NSA: Is Bigger Always Better-

comparing unit rates • FAL: Interpreting

Multiplication and Division

• Dan Meyer 3-act videos (list and interactive link to Dan Meyer's videos by standard)

Adopted Textbook CGP: • Txt pp.145-148, 151-162 • Wb pp. 61-64, 67-68, 79, 81,

83-87

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Unit 2: Arithmetic Operations (Instructional Support & Strategies) Framework Description/Rationale

Students expand their understanding of the number system and build their fluency in arithmetic operations in this unit. Students learned in Grade 5 to divide whole numbers by unit fractions and unit fractions by whole numbers. Now, they apply and extend their understanding of multiplication and division to divide fractions by fractions. The meaning of this operation is connected to real-world problems as students are asked to create and solve fraction division word problems. Students continue (from Fifth Grade) to build fluency with adding, subtracting, multiplying, and dividing multi-digit decimal numbers using the standard algorithms

(See CCSS 6th Grade Framework pgs. 20 – 31 for further information). Academic Language Support Instructional Tool/Strategy Examples

Preparing the

Learner

Key Terms for Word Bank: • Common Denominator • LCM • GCF • Numerator • Denominator • Multiplicative Inverse • Invert • Decimal • Quotients • Value vs. Place Value • Prime Numbers • Composite • Factors • Integers • Interpret • Ladder Method (GCF & LCM) • Scaffold Division

Academic Conversation Support ex: Conversation Placemat: Can you explain why you…?

Visual Models: • Area Model (i.e. graph paper models) to

divide fractions • Number Lines • Tape Diagrams • Ladder Method for GCF/LCM (pg. 31 of

framework)

Additional Strategy Examples: In partners, have one student create a circle map on LCM, and the second student create one on GCF. From there, have the two partners design a double-bubble map comparing and contrasting LCM and GCF based on the information on the two circle maps. As they do this task they will engage in conversation. • Represent a fraction with a picture and

divide the parts into smaller parts according to the denominator of the divisor.

• Divide the numerators and the denominators. (If necessary, use an equivalent fraction for one or both of the fractions in the original expression.)

• Scaffold division method (aka The Hangman Method found in framework pg. 26)

Topics: • Multiplication

Skills • Division Skills

including decimals

• Fractions • Factors • Prime vs.

Composite

Fractions Resource Packet (Carr) IMP Dividing Fractions Packet

Teacher Notes:

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Unit 3: Rational Numbers (5 Weeks 11/16-1/08)

Big Idea The set of real numbers is infinite, and each real number can be associated with a unique point on the number line.

Essential Questions Performance Task Problem of the Month

• What are rational numbers? • How can you find the opposite of a rational

number? • How can you plot/locate a coordinate? • How can you determine the relative position of

two numbers on a number line? • How can you find the distance between two

coordinates?

• On the Line [5th Grade 2000] p.3 • Knowing Fractions [5thGrade 2012] p. 6-7 • Fractions [5th Grade 2005] p.18 • Make a Fraction [5th Grade 2013] p.10-11 • Pea Soup [5th Grade 2008] p.57 - 58 • Drip, Drip, Drip [5th Grade 2009] p.69-70 • Percent Cards [6th Grade 2008] p.55-56

• Part and Whole POM and Teacher Notes

Unit Topics/Concepts Content Standards Resources

Rational Numbers • Note: the standards do not

mention “integers” as a specific set of numbers; instead students understand the set of “rational numbers” in general. (Whole numbers, fractions and their opposites)

• Understand the meaning of 0 in various contexts

• Understand whole numbers and their opposite then move onto negative fractions and decimals. Understand all numbers have an “opposite”

• Plot points on the coordinate plane (note: previously, students only worked with positive numbers and quadrant I of the coordinate plane, in 6th grade this is expanded to all four quadrants)

• Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane.

• 6th graders do not explore operations with integers this learning now happens in 7th grade.

• Understand a rational number as a point on the number line, and find the position of rational numbers on a number line, both horizontal and vertical.

• Interpret statements of inequality to assist with relative position of

Apply and extend previous understandings of numbers to the system of rational numbers. 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.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. 6.NS.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. 6.NS.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. 6.NS.7 Understand ordering and absolute value of

Essential Resources: • CCSS 6th Grade

Framework (pgs. 27 – 31)

Instructional Resources: • EngageNY (Module

3) • Carr Resource

Packet • Spurgeon

Intermediate Fraction Units

• Adopted Textbook CGP

Additional Resources: • MAP Lesson:

Fractions, Decimals and Percents – 6th Grade Formative Assessment Lesson

• Illustrative Mathematics

• Extreme Weather by Yummy Math

• Which rides can you go on? Robert Kaplinsky (can also be used for inequalities)

• Share My Candy: NY • Dan Meyer 3-act

videos (list and

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two numbers. • Understand absolute value • Solve real-world and math

problems by graphing points in all quadrants including distance between 2 points with the same first coordinate.

rational numbers. 6.NS.7a 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.7b 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. 6.NS.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. 6.NS.7d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represent 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.

interactive link to Dan Meyer's videos by standard)

• Fraction Progression Videos (from Illustrative Math showing how students learn fractions from grade 3 to 5)

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Unit 3: Rational Numbers (Instructional Support & Strategies) Framework Description/Rationale

Major themes of Unit 3 are to understand rational numbers as points on the number line and to extend previous understandings of numbers to the system of rational numbers, which now include negative numbers. Students extend coordinate axes to represent points in the plane with negative number coordinates and, as part of doing so, see that negative numbers can represent quantities in real-world contexts. They use the number line to order numbers and to understand the absolute value of a number. They begin to solve real-world and mathematical problems by graphing points in all four quadrants, a concept that continues throughout to be used into high school and beyond (See CCSS 6th Grade Framework pgs. 31 – 36 for further detail).

Academic Language Support Instructional Tool/Strategy Examples

Preparing the Learner

Key Terms for Word Bank: • Positive • Negative • Above/below sea level • Temperature • Credits/debits • Positive/negative charge • Coordinate axes • Interpret • Absolute value • Rational numbers • Debt • Balance • Quadrant • Coordinate

Academic Conversation Support ex: Conversation Placemat: Can you explain why you…?

Visual Models: • Area Model • Number Lines (both vertical and

horizontal) • Tape Diagrams • Count models (positive and negative

signs); or using (+ or –) tiles

Additional Strategy Examples: • Using graph paper to draw the

coordinate plane, label the four quadrants, and plot various points

• Temperature above and below 0 degrees (thermometer)

• Elevation above and below sea level/ground

• Money (credit/deposit and debit/withdrawal)

• Positive and negative charges (protons and electrons)

Topics: • Number Lines • Review of Quadrant 1

of the coordinate grid

Teacher Notes:

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Unit 4: Expressions (4 Weeks 1/11-2/12) Big Idea Any number, measure, numerical expression, algebraic expression, or

equation can be represented in an infinite number of ways that have the same value. Mathematical situations and structures can be translated and represented abstractly using variables, expressions, and equations.

Essential Questions Performance Task Problem of the Month

• What is the difference between a numerical and algebraic expression?

• What is a term and how can it be used to simplify complex expressions?

• What are the parts of an expression? • How can you use the distributive property to combine

like terms?

• Cecilio’s Tiles [5th Grade 2014] p.6-7 • Modeling Expressions [6th Grade

2013] p.2-3

• Perfect Pair POM and Teacher’s Notes

Unit Topics/Concepts Content Standards Resources

Numerical Expressions • Write and evaluate numerical

expressions with whole number exponents, the base can be a whole number, positive decimal or fractions, starting with simple expressions and move to more complex expressions.

• Strengthen/build their conceptual understanding of terms to simplify expressions with order of operations (note: students at this grade level have some basic order of operations skills)

Algebraic Expressions • Read, Write and evaluate

expressions with variables. • Identify the parts of an algebraic

expression. • Apply conventions of algebraic

notation (traditional x and ÷ symbols are replaced by this)

• Evaluate various expressions at multiple values of a variable to help develop the concept of a function.

• Use modeling to interpret 3(2+x) as 3 groups of (2 + x).

• Understand the Distributive property is the basis for combining “like” terms in an expression. 4a +7a = (4 + 7)a = 11a

• Use the ability to use the distributive property forwards and backwards.

• Identify when two expressions are equivalent

• Work with expressions to represent real-world contexts

Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. 6.EE.2a 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. 6.EE.2b 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. 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.

Essential Resources: • CCSS 6th Grade

Framework (pgs. 31 – 35)

Instructional Resources: • SAUSD Unit of Study:

Expressions and Equations (part will be used for this unit, and the other part will be used for Unit 5)

• Carr Resource Packet • EngageNY (Module 4) • Adopted Textbook CGP Additional Resources: • SERP Problem: Rating

Rate Plans • MAP Lesson:

Laws of Arithmetic – 6th Grade Formative Assessment Lesson

• Mercer--Order of Operations Packet

• Illustrative Mathematics • Fantasy Football- Yummy

Math • Introducing Exponents:

square numbers • The Djinni’s Offer:

Exponents Illustrative Mathematics

• Dan Meyer 3-act videos (list and interactive link to Dan Meyer's videos by standard)

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Unit 4: Expressions (Instructional Support & Strategies) Framework Description/Rationale

With their sense of number expanded to include negative numbers, in Unit 4 students begin a formal study of algebraic expressions. Students learn equivalent expressions by continuously relating algebraic expressions back to arithmetic and the properties of arithmetic (commutative, associative, and distributive) (See CCSS 6th Grade Framework pgs. 37 – 41 for more details).

Academic Language Support Instructional Tool/Strategy Examples

Preparing the Learner

Key Terms for Word Bank: • Numerical expressions • Exponents • Base • Power • Sum • Term • Like terms • Unlike terms • Combine like terms • Order of operations • Product • Factor • Quotient • Coefficient • Evaluate • Variable • Greater than • Less than

Academic Conversation Support ex: Conversation Placemat: Can you explain why you…?

Visual Models: • Area Model • Algebra Tiles • Counters • Cubes

Strategy Examples: • Conceptual Idea of Terms taught for

Order of Operations (Keep in mind the focus is no longer using PEMDAS, which is more procedural. Rather the focus is on developing the conceptual understanding of why expressions are simplified in an order)

• Multiple representations using T-tables, graphs, contextual situation, and expression

Topics: • Number Lines • Basic arithmetic skills with

whole numbers, decimals and fractions.

• Exponents

Teacher Notes:

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Unit 5: Equations and Inequalities (5 Weeks 2/15-3/18)

Big Idea Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found.

Essential Questions Performance Task Problem of the Month

• When given a set of values, how can you determine which value makes an equation or inequality true.

• What is a variable and what can it represent? • How can you use inequalities to show constraint? • How can you show the relationship between a

dependent and independent variable?

• Unknowns [5th Grade 2014] p.6 • Boxes [6th Grade 2009] p.4

• On Balance POM and Teacher’s Notes

Unit Topics/Concepts Content Standards Resources

Solving one-Variable Equations and Inequalities • Solve an equation or

inequality based on selecting values from a specified set to determine if the equation or inequality is true.

• Understand that a solution is a value of the variable that makes the equation or inequality true.

• Identify solutions to variable using mental math or tape diagrams—focusing on conceptual understanding (note: they are not solving equations using the formal method—solving using one-step and multi-step occurs in Math 7).

• Use variables to represent numbers and expressions in a real world context as independent variables

Inequalities • Use simple inequalities

using < or > to represent real world or mathematical situations.

• Represent inequalities on a number line with an open circle and a solid line arrow.

Dependent vs. Independent • Use variables to represent

two quantities that change in relationship to one

Reason about and solve one-variable equations and inequalities 6.EE.2c 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 (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 = ½. 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. Represent and analyze quantitative

Essential Resources: • CCSS 6th Grade

Framework (pgs. 35 – 38) Instructional Resources: • SAUSD Unit of Study:

Expressions and Equations (part will be used for this unit, and the other part was used for Unit 4).

• EngageNY (Module 4) • Adopted Textbook CGP Additional Resources: • YouTube Video on Bar

Models • SERP Problem:

Toothpick Patterns • MAP Lessons:

Interpreting Equations – 6th Grade Formative Assessment Lesson Modeling: Car Skid Marks – 6th Grade Formative Assessment Lesson

• Illustrative Mathematics • Formative Assessment

Lesson(FAL): Evaluating Statements About Number Operations

• NY Task: Dance and Task • Dan Meyer 3-act videos

(list and interactive link to Dan Meyer's videos by standard)

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another in a real-world problem.

• Write an equation to express one quantity as dependent and the other as independent

• Analyze the relationship between the variables using graphs and tables and relate these to the equation.

relationships between dependent and independent variables. 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.

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Unit 5: Equations and Inequalities (Instructional Support & Strategies) Framework Description/Rationale

With their sense of number expanded to include negative numbers, in Unit 5 students begin a formal study of algebraic equations and inequalities. They write, interpret, and use expressions and equations as they reason about and solve one-variable equations and inequalities and analyze quantitative relationships between two variables (See CCSS 6th Grade Framework pgs. 42 – 46 for more information).

Academic Language Support Instructional Tool/Strategy Examples Preparing the Learner

Key Terms for Word Bank: • Variable • Distribute • Distibutive property • Variable expressions • Equivalent expressions • Solution • Substitution • Constraint • Rational Numbers • Equations • Inequalities • Solution Set • Infinitely many solutions • Independent Variable • Dependent Variable • Graph • Table • Formula • Volume • Surface area

Academic Conversation Support ex: Conversation Placemat: Can you explain why you…?

Visual Models: • Number Line Diagrams • Pictures • Tape Diagram • Tables • Coordinate Plane • Algebra tiles • Counters and cubes • CLOZE Activity; Ex: t - 7;The number _______

minus ______. ______ less ______. • Word bank to decontextualize problems into

math • Manipulatives and pictures representing

variables • Coloring squares on a graph • 1 and 2 double number

Additional Strategy Examples: Multiple representations using T-tables, graphs, contextual situation, and equation

Topics: • Number Lines • Basic arithmetic

skills with whole numbers, decimals and fractions.

• Exponents • Coordinate Plane

Teacher Notes:

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Unit 6: Statistics (4 Weeks 3/21-4/22)

Big Idea There are special numerical measures that describe the center and spread of numerical data sets.

Essential Questions Performance Task Problem of the Month

• How can you collect, organize and represent data?

• How can you summarize data sets? • How can you display data graphically? • How can graphical data be interpreted? • How can you determine which type of

graphical display is appropriate to a particular data set?

• T-Shirts [5th Grade 2002] p.5-6 • Wintry Showers [5th Grade 2005] p.10-11 • Life of an Umbrella [5th Grade 2009] p.64 • Pencils [6th Grade 2000] p.1 • Baseball Players [6th Grade 2003] p.4 • Speech Speeds [6th Grade 2011] p.3 • World Sports Leagues [6th Grade 2013] p.4-5 • Supermarket [7th Grade 2000] p.4-5 • Ducklings [7th Grade 2005] p.14-15

• Through the Grapevine POM and Teacher’s Notes

Unit Topics/Concepts Content Standards Resources

Statistical Variability • Recognize that to be a

statistical question the data must vary and apply appropriate responses and can result in a narrow or wide range of numerical values and variability.

• Design survey questions that anticipate variability.

• Recognize that data sets contain many numerical values that can be summarized by one number such as a measure of center (mean and median), spread, and overall shape and range.

• Measure variability using the interquartile range (IQR) or the mean absolute deviation (MAD).

• Understand both the IQR and MAD are represented by a single numerical value. Higher values represent a greater variability in the data.

Distributions • Understand that data can be

displayed graphically and interpreted using number lines, dot plots, histograms or box plots.

• Determine the appropriate graph to display data and how

Develop understanding of statistical variability. 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. Summarize and describe distributions. 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.5 Summarize numerical data sets in relation to their context, such as by: 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

Essential Resources: • CCSS 6th Grade

Framework (pgs. 41 – 46)

Instructional Resources: • EngageNY (Module

6) • CPM Statistics Unit

Student Version Teacher Version

• Adopted Textbook CGP

Additional Resources: • SERP Problem:

Roving Ranges • MAP Lessons:

Mean, Median, Mode and Range – 6th Grade Formative Assessment Lesson

• Representing Data Using Grouped Frequency Graphs and Box Plots – 6th Grade Formative Assessment Lesson

• NCTM Illuminations Using NBA Statistics for Box and Whiskers Plots

• Illustrative Mathematics

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to read data from graphs generated by others (using dot plots, histograms, and box plot number lines)

• Interpret data displays and determine measures of center and variability from them.

• Summarize numerical data sets in relation to context.

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.

• Who makes the best Animated Movies? Yummy Math

• FAL: Representing Data...Box Plots

• Dan Meyer 3-act videos (list and interactive link to Dan Meyer's videos by standard)

Adopted Textbook CGP • Course 1 (6th grade)

Chapter 5 • Txt pp.311-332, 336-

348 • Wb pp. 167-180, 189 • Course 2 (7th Grade)

Chapter 6

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Unit 6: Statistics (Instructional Support & Strategies) Framework Description/Rationale

In Unit 7, students develop an understanding of statistical variability and apply that understanding as they summarize, describe, and display distributions. In particular, careful attention is given to measures of center and variability (See CCSS 6th Grade Framework pgs. 50 – 55 for more details).

Academic Language Support Instructional Tool/Strategy Examples

Preparing the Learner

Key Terms for Word Bank: • Statistics • Variability • Data • Distribution • Center • Spread • Shape • Measures of Center • Mean • Median • Range • Dot Plot • Histogram • Box Plot • IQR (interquartile range) • Quartile • MAD (mean absolute deviation) • Quantitative • Qualitative

Academic Conversation Support ex: Conversation Placemat: Can you explain why you…?

Visual Models: • Tables • Graphs • Number Lines • Dot Plots • Histograms • Box Plots (formerly known as box and

whisker plots)

Strategy Examples: Put the data in numerical order Use data sets that are meaningful to the students such as movies, sports, technology, etc.

Topics: • Basic arithmetic

skills with whole numbers, decimals and fractions.

• Coordinate Plane • Graphing Data

Teacher Notes:

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Unit 7: Geometry (5 Weeks 4/25-5/27)

Big Idea Two- and three-dimensional objects with or without curved surfaces can be described, classified, and analyzed by their attributes.

Essential Questions Performance Task Problem of the Month

• How does the area of a triangle relate to the area of a rectangle?

• How can you find the area of a polygon by decomposing (deconstructing) it into other shapes?

• How can you find the side lengths of a polygon on a coordinate plane?

• Shapes [5th Grade 2002] p.7-8 • How Many Cubes? [5th Grade 2004] p.17-18 • Halves [5th Grade 2009] p.66-67 • Floors 4U [5th Grade 2010] p.8-9 • A Box of Cubes [5th Grade 2012] p.4-5 • Sugar Cube Construction [5th Grade 2014] p.4-5

• Between the Lines POM and Teacher’s Notes

Unit Topics/Concepts Content Standards Resources

Polygon Area • Derive the area of a triangle

(students use their previous knowledge of decomposing a rectangular area to derive it); including right triangles and other triangles

• Use their knowledge of rectangular and triangular area to decompose and compose other shapes: (special quadrilaterals, and polygons)

Volume • Find the volume of right

rectangular prisms with fractional edge lengths.

• Apply the idea of “packing shapes” to determine the number of unit cubes that could make up a prism and how this relates to the formulas for volume (V=lwh and V=bh)

• Solve real-world problems using volume

Coordinate Plane Area • Draw polygons on a coordinate

plane and find side lengths given coordinates for the vertices

• Find the length of a side • Solve real-world problems using

Area Surface Area • Apply knowledge of rectangular

and triangular area in

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

Essential Resource: • CCSS 6th Grade Framework

(pgs. 38-41) Instructional Resources: • EngageNY (Module 5) and

T.E. • Spurgeon Intermediate

Geometry Units: Geometry Packet Part I Geometry Packet Part II Geometry Packet Part III Geometry Packet Part IV Geometry Packet Part II with notes Geometry Packet Part III with notes Geometry Packet Part IV with notes

• UCI Materials: Volume and Surface Area Common Core Tasks (Amy’s Tank-1, Cari’s Aquarium, Banana Break, Christo’s building, Building Bath Tubs, Scaling and Building; Good, Better, Best Container; Geo-Nets

Additional Resources: • SERP Problem: Knowing

Nets • MAP Lessons:

Optimizing: Packing it In – 6th Grade Formative Assessment Lesson Using Co-Ordinates to

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conjunction with nets that form 3-D figures.

• Solve real-world problems using surface area

Represent and Interpret Data – 6th Grade Formative Assessment Lesson

• Adopted Textbook CGP Course 1: Lessons 7.3.3, 7.4.1, and 7.4.2

• Georgia Dept. of Education Frameworks: Unit 5: Area and Volume

• NCTM Illuminations: Areas in Geometry

• Illustrative Mathematics: Polygons in the Coordinate Plane

• Sample lessons: Teaching Channel: Lessons on surface area Real world geometry lesson

• Inside Mathematics: Lesson or

• California Department of Education: Resources for Teachers or http://www.cde.ca.gov/re/cc/

• Worksheets: CommonCoreSheetswebpage:Area, Volume

• CCSS Progressions: • Illustrative Mathematics • How many Legos to build

the Fireman- Yummy Math • Irregular Shape Area math

hunt • Dan Meyer 3-act videos (list

and interactive link to Dan Meyer's videos by standard); Bubble Wrap: Dan Meyer Video Series

• GeoGebra (free downloadable graphing calculator)

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Unit 7: Geometry (Instructional Support & Strategies) Framework Description/Rationale

Unit 6 is an opportunity to practice the material learned in Unit 4 & 5 in the context of geometry; students apply their newly acquired capabilities with expressions and equations to solve for unknowns in area, surface area, and volume problems. They find the area of triangles and other two- dimensional figures and use the formulas to find the volumes of right rectangular prisms with fractional edge lengths. Students use negative numbers in coordinates as they draw lines and polygons in the coordinate plane. They also find the lengths of sides of figures, joining points with the same first coordinate or the same second coordinate and apply these techniques to solve real-world and mathematical problems (See CCSS 6th Grade Framework pgs. 46 – 50).

Academic Language Support Instructional Tool/Strategy Examples

Preparing the Learner

Key Terms for Word Bank: • Area • Surface Area • Volume • Polygon • Rectangular Prism • Base • Edge • Vertices • Face • Net • Coordinate • Coordinate Plane • Side length • Packing • Constructing • Deconstructing • Composing • Decomposing

Academic Conversation Support ex: Conversation Placemat: Can you explain why you…?

Visual Models: • Number Line Diagrams • Manipulatives • Pictures • Tape Diagram • Tables • Coordinate Plane • Stacking bread into a loaf to understand

volume of a rectangular prism • Graph paper for drawing nets

Additional Strategy Examples: Compose and decompose shapes to determine area as opposed to formula memorization (using the composition and decomposition of shapes to derive the formulas) Building boxes (e.g. cereal boxes) Find the volume of a rectangular prism by packing it with unit cubes and counting fractional cubic units

Topics: • Number Lines • Basic arithmetic

skills with whole numbers, decimals and fractions.

• Exponents • Coordinate Plane

Teacher Notes:

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Performance Task Descriptions by Unit Unit 1: Ratios and

Proportional Reasoning Unit 2: Arithmetic

Operations Unit 3: Rational Numbers

• Rate Concentrate [6th grade 2012] (Use rates or find equivalent ratios to compare and explain the relative size of two rates]

• Table Decorations [5th Grade 2010] (Given a ratio, determine the value of a missing part or the whole)

• Fig Pudding [5th Grade 2006] (Interpret and make comparisons of a bar graph; use ratio to convert a recipe)

• Truffles [6th Grade 2009] (Use proportional reasoning to determine relationships between cups of chocolate and cups of cream)

• Plum Jelly [5th Grade 2011] (Use proportional reasoning in a real life context)

• Candies [5th Grade 2007] (Work with part/whole concept in a practical context]

• Linflower Seeds [6th Grade 2000] (Use proportional reasoning to answer questions0

• Grandpa’s Knitting [6th Grade 2002] (Use conversions and proportional reasoning)

• 100 People [6th Grade 2011] (Using proportional reasoning to solve questions about real data]

• Pet Food [5th Grade 1999] (Use operations with fractions and/or understanding of ratios to solve a real world problem)

• Rabbit Costumes [6th Grade 2003] (Use division of fractions in a real world context)

• How Much Money? [6th Grade 2005] (Use fractions to work out a money problem)

• Smallest and Largest [6th Grade 2006] (Choose numbers and operations to give the largest and smallest results using integers and the fraction 1/2)

• Division [Grade 6 2007] (Relate a given division calculation to the appropriate situation)

• Fractions [6th Grade 2010] (Given 6 operational statements, students are to determine if each is correct or not; if correct they are to give another example; if incorrect, they must correct the original statement)

• Ribbons and Bows [6th Grade 2013] (division and multiplication of fractions by fractions; understanding of a unit rate and ratio reasoning)

• On the Line [5ht Grade 2000] (represent simple fractions/decimals on a number line; explain the meaning of a decimal digit)

• Knowing Fractions [5thGrade 2012] (Use a number line to critique the reasoning of others on the sum and difference of fractions; justify and explain if a given statement about addition and multiplication of fractions is always true, sometimes true, or never true)

• Fractions [5th Grade 2005] (Use a number line to order and compare the two fractions 2/3 and 2/5)

• Make a Fraction [5th Grade 2013] (Select digits to make fractions that will make inequality and equality statements true; given a number line with the given points 0, ½, and 1 on it, place 3 more fractions on the number line)

• Pea Soup [5th Grade 2008] (Use proportional reasoning to extend a table, analyze two linear patterns/lines on a graph, graph a set of ordered pairs within a table and describe why information from one ingredient will produce the same linear representation as another ingredient)

• Drip, Drip, Drip [5th Grade 2009] (Represent, analyze and interpret patterns using tables and graphs; use proportional reasoning to determine the relationship between the rate waters fills a bucket)

• Percent Cards [6th Grade 2008] (Use equivalencies and make comparisons on a number line of fractions, decimals, and percents)

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Performance Task Descriptions by Unit Unit 4: Expressions Unit 5: Equations

and Inequalities Unit 6: Geometry Unit 7: Statistics

• Cecilio’s Tiles [5th Grade 2014] (Use order of operations)

• Modeling Expressions [6th Grade 2013] (Use and understand different representations for the distributive property and the different expressions that represent them)

• Unknowns [5th Grade 2014] (Write an equation to match each of four given math stories)

• Boxes [6th Grade 2009] (Understand the equality and inequality of balance scales)

• Shapes [5th Grade 2002] (Decompose and compose triangles and quadrilaterals)

• How Many Cubes? [5th Grade 2004] (Find volume and dimensions)

• Halves [5th Grade 2009] (Given a shape that is cut into two on a grid explain why the two shapes are equal; compare two shapes on three different grids and determine if one specified shape is more than equal to or less than the other)

• Floors 4U [5th Grade 2010] (Work with the definition of a square; determine the area of triangular segments of a square area given length and width dimensions; given a specified area, construct three different sized rectangles of varying perimeters)

• A Box of Cubes [5th Grade 2012] (Determine the volume of a rectangular prism)

• Sugar Cube Construction [5th Grade 2014] (Determine the volume of two rectangular constructions)

• T-Shirts [5th Grade 2002] (Interpret a frequency chart and apply information to questions)

• Wintry Showers [5th Grade 2005] (Use a table to interpret and analyze data; find the mean and median)

• Life of an Umbrella [5th Grade 2009] Use measures of center and understand what each indicates about a data set)

• Pencils [6th Grade 2000] (Critical thinking with mean/median/mode)

• Baseball Players [6th Grade 2003] (Working with the mean)

• Speech Speeds [6th Grade 2011] (Find measures of center for a data set)

• World Sports Leagues [6th Grade 2013] (Interpret a table; calculate the mean number of teams; compare and explain whether the median or the mode best represents the typical number of games played; find the best average total attendance)

• Supermarket [7th Grade 2000] (Use a measures of center to make comparisons)

• Ducklings [7th Grade 2005] (Use a frequency table to determine the median and mean of a data set)