Unit 1: Number Theory

Chico Unified School District 2014-2015: Grade 6 Everyday Mathematics Instructional Guide Draft: 7/14/10 Using the Mathematics Instructional Guide: 2007-CCSS Bridge

This year’s Math Instructional Guide (MIG) has been modified to assist teachers in making sound instructional decisions when using the Everyday Mathematics (2007 edition) to meet the changes brought about by CA CCSS-M. While much about the guide’s structure remains familiar, some substantial changes have been made. Every lesson has been correlated to CA CCSS-M Content Standards. This correlation is structured through the distinct parts of each lesson; Mental Math and Reflexes (MMR), Teaching the Lesson (Part 1), Ongoing Learning & Practice (Part 2) and Differentiation Options (Part 3). Additionally, all Comments have been rewritten. The Comments help to clarify the mathematical intent of each lesson and thus, allow you to focus instruction/assessment/ differentiation in terms of CA CCSS-M. It is recommended that you use this guide as you plan units and lessons and that you use it collaboratively within your grade-level team. This MIG is meant as a one year stop-gap. The new CCSS edition for grades 3- 6 will be ready for pilots in February. To reiterate, as the classroom teacher, you will need to make the necessary instructional decisions for your students (thus a guide). Use what your students know and can do (based on evidence) alongside the Comments to plan units and lessons. Change is difficult; it will take time.

Standards for Mathematical Practice (SMPs): The 8 SMPs are the vehicle through which the mathematics is performed. For this year, focus on the SMPs related to classroom discourse (1, 2, 3 and 6). As with the Big Ideas, make them explicit to students. Focus on one or two within each unit. Allow your students to do the thinking; you serve to orchestrate the discussion. Classroom posters for these are linked at www.cusdmathcoach.com, under CaCCSS. Focused Content & Making Connections

Big Ideas: The Big Ideas are based on the work and research of Randall Charles published in the NCSM Journal of Mathematics Educational Leadership. He defines a Big Idea as “a statement of an idea that is central to learning of mathematics; one that links numerous mathematical understandings into a coherent whole” (article is linked at www.cusdmathcoach.com, under Math Resources). Big ideas are a key to making connections across many concepts and, because they don’t change, across many grade levels. Phil Daro, one of the CCSS-M authors, deems the Unit (10-13 lessons) to be the proper grain size for mathematics instruction. Each Unit should be linked through 2-4 big mathematical ideas. These big ideas should be made explicit to students at the beginning of every unit of study and continually referenced during the unit’s lessons. Classroom posters of the Big Ideas by grade-level can be found at www.cusdmathcoach.com, under the CaCCSS tab; while these posters are by grade-level, the ideas throughout remain mostly the same; poster language is also grade-level appropriate. The Big Ideas listed for each unit are not necessarily the only ones that could have been used. Many units cover so many concepts that many more could have been listed. The ones shown are the most appropriate for the main concepts covered in the unit and thus, should be the ones you emphasize throughout each particular unit of study.

Here are some suggestions on how to use Big Ideas:  Post the Big Ideas in your classroom as they come up and keep them up the rest of the year.  Choose one of the unit’s Big Ideas that is most appropriate for the day’s lesson and start by discussing its connection to concepts previously learned.  Refer to this selected Big Idea often during the lesson.  When possible, connect content in the lesson to other Big Ideas and Learning Target.  At the end have students summarize the new concepts learned by discussing their connection to the Big Idea chosen.

Learning Targets: The Learning Targets are an attempt to draw a single area of focused content and depth from the activities in each lesson. The learning target tries to answer the question “what is the one thing that students should learn from this lesson?” The Learning Target can serve as your reference point but they will need to be modified into student friendly language, “I can” statements.

Flores, Canterbury, Fundanet, Grade 6 Key: TLG = Teacher’s Lesson Guide; MM = Math Masters; SRB = Student Reference Book; AH = Assessment Handbook; RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; and Preston Page 1 EP = Extra Practice; SMJ = Student Math Journal; TRM = Teacher Reference Manual; LIT= Literature Connection; P = Part Chico Unified School District 2014-2015: Grade 6 Everyday Mathematics Instructional Guide Draft: 7/14/10

Unit 1: Collection, Display, and Interpretation of Data Overview: To use Student Reference Manual to find information; to find data landmarks and compare median and mean; create, read, and interpret line plots, stem and leaf plots, broken line, bar, step, and circle graphs; analyze data and explain data misrepresentations. Data Collection and Representation: Some questions can be answered by collecting and analyzing data, and the question to be answered determines the data that’s needs to be collected and how to best collect it. Big Ideas Data can be collected visually using tables, charts and graphs. The type of data determines the best choice of visual representation. Data Distribution: There are special numerical measures that describe the center and spread (distribution) of numerical data sets. The most appropriate measure to use for a situation depends on the nature of the data and on how the measures will be used. Writing/Reaso Learning CA CCSS Comments Vocabulary Games Advanced Prep RSAs ning Prompt – Target Math Boxes MMR Part 1 Part 2 Part 3 Learn to use the Student The literature connections referenced in the unit G is for Googol by Multiply 2-digit 1

♦ Reference are not specific to a particular lesson. The titles David Schwartz is a whole 1 Book to find can be incorporated at any time during the unit. great fit in this chapter. numbers information. See TLG p 11 Students share data about themselves in line plots (6.SP.4). "Mystery Line Plots" are created, and students use what they know about the line plot, Prep the envelopes for shape of the data to determine which line plot Create and mystery plot, the mystery plot accompanies which scenario (6.SP.2). As they Demonstrate 6.SP.2 describe line landmark, activity in Part 1. Use 2 6.SP.4 discuss how they matched scenarios with data, High Number knowledge of

♦ 6.SP.4 plots using minimum, post-it notes as

1 6.SP.5c they must consider the source of the data and Toss landmark 6.SP.5b data maximum, mentioned on pg. 22 in justify their choices (6.SP.5c). In Part 3, students terms landmarks. median, mode, TLG. Copies of MM p. 7 review line plots (6.SP.4) from the Student range for all. Reference Book and/or discuss how outliers affect data (6.SP.5c).

Standard 6.SP.2 is partially met in this activity. Find min., Use stem-and- Students create stem and leaf plots and compare stem-and-leaf 6.SP.2* max., range, 3 leaf plot to them to other types of graphs. Students describe plot, stem,

♦ 6.SP.5b and mode in

1 organize and the center and spread, but not the shape of the leaf, double- stem-and-leaf analyze data. data in the traditional terms of a bell curve stem plot plot (6.SP.5b). Students participate in an activity in which they Calculate and An opportunity to use Know determine 6.SP.2 compare the excel to find the “data difference 4 median and mean in a data set. They discuss the

♦ 6.SP.3 6.SP.5c mean and landmarks” is an option between

1 impact of deviation. In Part 3, there is an option to 6.SP.5c median of a in the enrichment median and use computer software to help them determine data set. activity. mean deviations in a data set (6.SP.5c).

Students play the game Landmark Shark, wherein they determine the mean, median, range and mode of Prep the Landmark a data set (from a card deck). They can choose to Shark cards; MM p. 456 To find the Explain how to trade cards to alter the statistical landmarks in 1 set of three cards/ range, Make line plot convert 5 6.SP.5c 6.SP.5c attempt to get a higher score (6.SP.5c).They Landmark student

♦ median, mean, and compute between meters

1 6.SP.5d 6.SP.5d consider which landmark is best to use for the Shark & mode of a mean and situation to earn that score (6.SP.5d). Part 3 has a Additional 1 copy of data set. centimeters. readiness option that offers another activity that score card for each allows students to find range, median and mean group; MM p. 457 and to experiment with how different data will affect them. In this lesson students create 6.SP.4) and analyze broken line and double line graphs. As they discuss their data, students must be aware of the nature of the data and how it was measured to meet 6.SP.5b Students will meet 6.SP.2 if teachers are explicit about their discussion of line graph, Landmark Create, read, spread, shape and center. In Part 2, students play 6.SP.2 broken-line Shark Read data in 6 6.NS.6c 6.SP.5c 6.SP.4 & interpret Landmark Shark. They determine the mean,

♦ 6.SP.4 graph, broken-line

1 6.SP.5d broken-line median, range and mode of a data set (from a 6.SP.5b precipitation, Over & Up graph graphs. card deck). They can choose to trade cards to graph key Squares alter the statistical landmarks in attempt to get a higher score (6.SP.5c).They consider which landmark is best to use for the situation to earn that score (6.SP.5d). In Part 3, there is an option to create and analyze another broken line graph (6.SP.4). This lesson involves comparing side by side and stacked bar graphs. Students meet most of the requirement An additional for 6.SP.2. bar graph, opportunity to use Create, read, However, they do not examine shape in terms of side-by-side 7 6.SP.2 6.SP.4 6.SP.5b excel to create a bar Construct a

♦ & interpret bar interquartile range or deviation. *It is bar graph,

1 graph of data is found bar graph graphs. recommended that teachers incorporate this in stacked bar in the enrichment class discussions to fully meet the standard. In graph section. Part 2 students work more on broken line plots (6.SP.4). In Part 3, technology can be utilized to create bar graphs from data found in the SRB. Students create step graphs to depict data in Create, read, which change is not gradual. This graphing Make a 8 Name That

♦ & interpret representation is extremely rare and transfer of step graph broken-line

1 Number step graphs. learning would be minimal. It is recommended graph that teachers consider this an optional activity.

The lesson entails collection of data from students regarding whether girls should be able to play on boys' athletic teams and vice versa. While students do meet the requirements of standard 6.SP.5b, they create circle graphs. Sixth grade interior of a Estimate and Create, read, standards for Statistics and Probability refer only circle, arc, Copies of MM p. 26 (1 9 6.SP.2 Percent-Sector measure

♦ & interpret to box plots, dot plots and histograms. This lesson sector, radius, copy/ 3 students; cut

1 6.SP.5b Match sectors in circle graphs. could be modified to more fully meet 6th grade percent circle, them into strips) circle graph standards by gathering data that could be circle graph represented in a histogram, box plot or dot plot. In addition, teachers should be explicit about how data describes spread, center and shape to meet 6.S Students calculate areas and try to determine the largest possible area for a given perimeter (6.G.1). They complete Describe the equations involving the formula for area (6.EE.2c). Calculate relationship In Part 2, students play Landmark Shark. They landmarks and

0 6.SP.5b

1 6.G.1 between the determine mean, median, range and mode of a perimeter, Landmark explain how 6.SP.5c 6.G.1 ♦ 6.EE.2c perimeter and data set (from a card deck). They can choose to area Shark they change 1 6.SP.5d area of trade cards to alter the statistical landmarks in with changes rectangles. attempt to get a higher score (6.SP.5c).They in data set consider which landmark is best to use for the situation to earn that score (6.SP.5d). In Part 3, given a painting scenario, students determine which area will require more paint (6.G.1). Students learn about how graphs can be used to When might Explain ways communicate specific ideas (persuasive graphs) Read and someone what

1 that data can by considering the source of the data, the way in

1 High Number interpret to talk about 6.SP.5d 6.SP.5d be presented which it was collected, and the choice in ♦ Toss broken-line the median 1 to mislead or measures of center (6.SP.5d). In Part 3, students graph instead of the misrepresent. have an opportunity to create persuasive graphs mode or mean? of their own (6.SP.5d). Students learn about sample techniques and sample sets when gathering data (6.SP.5b). In sample, Determine Part 3, students can collect data about drink random Read and

2 whether a

1 6.SP.5b preferences and create their own graph to sample, interpret side- 6.SP.5b sample is ♦ 6.SP.5d compare to the graph used earlier in the lesson biased by-side bar 1 random or (6.SP.5b). Their discussion should include choices sample, recall graph biased. of measure and shape of data distribution survey (6.SP.5d).

Unit 2: Operations with Whole Numbers and Decimals Overview: To read, write, and interpret numbers in standard, word, expanded, and scientific form; to review adding and subtracting decimals; to develop power-often strategies; to develop strategies for multiplying and dividing decimals. The Base 10 Numeration System: The base-ten numeration system is a scheme for recording numbers using digits 0-9, groups of ten, and place value. Operation Meanings and Relationships: There are many Big Ideas ways to show addition, subtraction, multiplication and division, and each operation is related. Writing/Reaso Learning CA CCSS Comments Vocabulary Games Advanced Prep RSAs ning Prompt – Target Math Boxes There are no 6th grade CCSS tied to this lesson. MMR Part 1 Part 2 Part 3 However, Read and students will continue to use expanded notation standard write large in their math. Therefore it is recommended that Explain how notation, numbers in teachers keep this lesson in 6th grade math. Write whole you solved 1 expanded Copy MM p409 & 410,

♦ std., Number Top-It numbers to problem 5a?

2 notation, one per student expanded, & The literature connections referenced in the unit billions. (Marta’s number-and- number-and- are not specific to a particular lesson. The titles mother) word notation word notation. can be incorporated at any time during the unit. See TLG p 95

Read and write small There are no sixth grade CCSS tied to this lesson. Compare standard numbers in However, High-Number decimals 2 notation,

♦ 6.NS.3 std., students will continue to use expanded notation Toss numbers

2 expanded expanded, & in their math. Therefore it is recommended that (decimals) through notation number-and- teachers keep this lesson in 6th grade math. thousandths. word notation. Align digits of Students add and subtract decimals (6.NS.3). Add, subtract, whole 3 They also round decimals. In Part 3, the children

♦ 6.NS.3 6.NS.3 and round precise numbers and

2 have the opportunity to continue subtracting decimals. decimals by decimals (6.NS.3) with models. place value. The lesson centers on multiplying by powers of ten, which meets 6.EE.1 - evaluate numerical expressions involving whole number exponents. Develop and In Part 2, the class plays Doggone Decimal to practice powers of 10, Write decimals 4 6.EE.1 reinforce multiplication of decimals (6.NS.3). In Doggone

♦ 6.EE.1 6.NS.3 strategies for exponential to the

2 6.NS.3 Part 3, there is an option to complete "What's My Decimals multiplying by notation thousandths. Rule?" problems involving multiplication and powers of 10. division decimals by 10 (6.NS.3). There are also two options in which children can multiply by powers of 10 (6.EE.1).

In this lesson, students estimate and multiply decimals (6.NS.3). In Part 2, the class practices multiplying multi-digit numbers (6.NS.2). *It is Develop Explain why the recommended that teachers have students use Estimate 5 6.NS.2 decimal Multiplication product of 77 X

♦ 6.EE.1 6.NS.3 6.NS.2* the standard algorithm for some of the problems products of

2 6.NS.3 multiplication Bull’s-Eye 0.1 is less than to meet the standard, but allow choice of decimals. strategies. 77. algorithm for some problems as well. In Part 3, there is an option to multiply whole numbers (6.NS.2*) and/or calculate costs (6.NS.3). Students multiply decimal numbers (6.NS.3) in Estimate both Parts 1 and 3. In Part 2, students practice Develop products and dividing (6.NS.2*). *It is 6 decimal Divisibility Copy of MM p 414 & use reliable

♦ 6.NS.3 6.NS.2* recommended that teachers have students use

2 multiplication Dash 415 of each student algorithm to the standard algorithm for some of the problems strategies. multiply to meet the standard, but allow choice of decimals. algorithm for some problems as well. Estimate partial- partial The class practices division (6.NS.2*) in all parts quotients quotients and Estimate of the lesson. *It is recommended that teachers division Have copies of choose 7 quotients and have students use the standard algorithm for algorithm, Division Top-It

♦ 6.NS.2* 6.NS.2* 6.NS.2* computation grids reliable

2 solve division some of the problems to meet the standard, but dividend, (adv. version) available for students. algorithm to problems. allow choice of algorithm for some problems as divisor, divide with well. quotient, multidigit remainder divisor. Long Division U.S.

3 Part A

1 Traditional

t Use the U.S. c long division e j traditional method, TLG p 441 Z o r long division divisor, P algorithm with dividend, short A

C whole division numbers and decimals. Make a In this lesson, students divide decimals with the Estimate reasonable partial quotients algorithm. It would be necessary 8 quotients and Scientific estimate for a

♦ 6.NS.3* 6.NS.3* 6.NS.3* to also teach the standard division algorithm to truncated

2 solve division Notation Toss quotient and meet the requirements of 6.NS.3. They divide in problems. solve division all parts of the lesson. problems. U.S. Long Traditional Division TLG p 441 Z long division Part B method,

Use the U.S. 3

1 traditional

c long division divisor, e j algorithm with dividend, short o r whole division P

A numbers and

C decimals. Explain how positive power Determine the Convert In this lesson, the children evaluate numerical you decided of 10, power of 10 between expressions with whole number exponents If doing E, you will need where to put 9 6.EE.1 6.EE.1 6.EE.1 negative needed to

♦ standard and (6.EE.1). The same is true for Part 3. In Part 2, the the square footage of the decimal

2 power of 10, move the scientific class plays Scientific Notation Toss where they your school. point in scientific decimal left or notation. practice the same skill. problems 1c notation right. and 1d. Students work on the concepts in standard 6.EE.1 Make sure you know (computation with exponents), but they do not Interpret Extend power key, how to use the power evaluate expressions. Rather, they complete a exponential

0 exponential exponential key on the calculators

1 6.EE.1* 6.EE.1 6.NS.3 6.EE.1 chart and play Exponent Ball to meet this notation on notation notation, Exponent Ball the students are using. ♦ standard. Part 3 offers an option to convert calculator and 2 through use of factor, base, Copy or project the between base-ten numbers and binary numbers use power the calculator. exponent second journal page on to continue practice with 6.EE.1. In Part 2, key. the board. students multiply and divide decimals (6.NS.3). Calculator Students use a calculator to evaluate expressions conversions with whole number expressions (6.EE.1). In Part 2, Doggone Translate from

1 6.NS.3 Calculator use again;

1 6.EE.1 6.EE.1 between the class can play Doggone Decimal (6.NS.3) or Decimals scientific to 6.EE.1 make sure you know ♦ standard and Exponent Ball (6.EE.1). In Part 3, students standard 2 how to use them. scientific continue to evaluate expressions with exponents Exponent Ball notation. notation. (6.EE.1).

Unit 3: Variables, Formulas, and Graphs

Overview: To use variables to describe number patterns; to write and evaluate algebraic expressions; to use tables, formulas, and graphs for predicting and analyzing; to estimate products and quotients of decimals while developing strategies for solving these types of problems. Variable: Mathematical situations and structures can be translated and represented abstractly using variables, expressions and equations. Patterns, Relations and Functions: We can learn about the Big Ideas relationships between numbers and objects by noticing patterns that repeat in ways we can predict. We also see how one set of numbers is related to another set. Writing/Reaso Learning CA CCSS Comments Vocabulary Games Advanced Prep RSAs ning Prompt – Target Math Boxes In Part 1, the class uses variables to describe situations MMR Part 1 Part 2 Part 3 (6.EE.2, 6.EE.2a).This lesson meets the second part of 6.EE.6, understand that variables represent an unknown number or any number in Describe a specified set. *In order to fully meet the How do you 6.EE.2 general math requirements of the standard, it is recommended general Write a special know where to 6.EE.2a 1 patterns in that students write their own expressions to pattern, case for a place the

♦ 6.EE.5

3 words, accompany a given situation. They learn that variable, general decimal in the 6.EE.6 including solving equations involves determining whether special case pattern. quotient in special cases. any values make the equation untrue (6.EE.5). problem 4.

The literature connections referenced in the unit are not specific to a particular lesson. The titles can be incorporated at any time during the unit. See TLG p 175 The students write expressions and use variables Write a Describe to describe general patterns (6.EE.2a) in both Part Commutative For P2, make copies for general case general case 2 6.EE.2a 6.EE.2a 1 and part 3. Property Grid 1 or 2 MM p437 & w/ two

♦ for 2 variables, Factor Captor

3 (addition and 438 for each pair of variables to including LIT Math Talk: Mathematical Ideas in Poems For multiplication) students. represent a special cases. Two Voices by Theoni Pappas special case. Students evaluate expressions and write Find decimal Write and algebraic 6.EE.2a 6.EE.2 expressions to match a given situation (6.EE.2, solutions to 3 6.NS.3 evaluate expression,

♦ 6.EE.2a 6.EE.2a 6.EE.2a). Part 3 has an option to continue work on whole number

3 algebraic evaluate an these two standards. In Part 2, the class divides division expressions. expression numbers with decimal quotients (6.NS.3). problems Students evaluate formulas for area (6.EE.7) They Use algebraic continue Examine and formula, notation to 4 6.EE.7 6.EE.7 this practice in Part 3 when they study special

♦ evaluate evaluate, describe

3 cases for formulas and contemplate a formula for formulas. substitute general the area of a brick wall (figuring in space for patterns. mortar). Represent In this lesson, the class represents rate on a line rates with graph and compare rates (6.RP.3; 6.NS.8). In Part Division Top-It Review rules for Over Complete a 6.NS.6c 6.NS.6c tables and 2, students divide in an advanced version of rate, speed, How can you 5 6.SP.4c* 6.NS.2 and Up for R activity table from 4

♦ 6.NS.8 6.RP.3 express rules Division Top-It (6.NS.2). In Part 3, students can unit rate, line use 2 to figure

3 Up and Over MM 465 formula and 6.RP.3 in words, practice working with ordered pairs in Over and graph 28 ? Squares Gameboards MM p 466 graph result. formulas, and Up Squares (6.NS.6c) and/or solve rate problems graphs. (6.RP.3).

Students graph points on a grid to correspond Predict and with rates of Complete a conclude from free-falling objects (6.NS.8) and learn a formula to table from 6 6.EE.2

♦ 6.NS.8 6.RP.3b formulas, go with the activity. In Part 2, the students formula and

3 6.EE.2c graphs, and compare prices using unit rates (6.RP.3b). In Part graph result. diagrams. 3, students evaluate expressions (6.EE.2, 6.EE.2c) and make predictions using graphs. Students learn about positive and negative Spreadsheet Use formulas numbers in a spreadsheet, Scramble 7 6.NS.5 6.NS.5 and operations

♦ spreadsheet (6.NS.5) as they explore formulas. update, cell, Add integers.

3 in They play column, row Credits/ Debits spreadsheets. Spreadsheet Scramble (6.NS.5). Game Students play Spreadsheet Scramble (6.NS.5) in Solve open Computation 6.EE.2 the beginning of this lesson. In Part 2, they number 8 6.EE.2 6.NS.5 6.NS.5 and functions horizon, Spreadsheet

♦ 6.EE.2c evaluate a formula for distance (6.EE.2, 6.EE.2c) a sentences

3 in square root Scramble person can see. In Part 3, students solve a involving spreadsheets. problem with Spreadsheet Scramble (6.NS.5). integers. There are no CCSS associated with this lesson. It Analyze the Interpret and is an shape of a

9 6.NS.7 draw graphs interesting lesson in applying knowledge about a Scientific graph and

♦ time graph

3 that model situation to the shape of a graph, so teachers Notation Toss make situations. should consider leaving it in their 6th grade conclusions curriculum if time permits. about trends. In this lesson, students complete tables in which Name a variables need to be applied. This meets part of spreadsheet Analyze real

0 standard 6.EE.2c, however students do not write cell and

1 6.RP.3 situations by MM p99 for container the expressions before solving the problems Getting to One identify a ♦ 6.RP.3a making tables ideas. 3 within the table. In order to better meet the formula for and graphs. standards, teachers could have students write the computing a expressions total.

Unit 4: Rational Number Uses and Operations Overview: To review rational number notation-fractions, decimals, percents, & mixed numbers; to review and order these numbers by value; to review the operations (+, x, --) with fractions and extend this to mixed numbers; to build connections between whole & decimal number divisors in the division of fractions; to review the meaning of percent and solve problems involving percents and discounts. Equivalence: Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value. Numbers and the Number Line: The set of real numbers is infinite and ordered. Whole numbers, integers, and fractions are real numbers. Each real number can be associated with a unique point on the number line. Basic Facts and Algorithms: There is Big Ideas more than one algorithm for each of the operations with rational numbers. Some strategies for basic facts and most algorithms for operations with rational number (both mental math and paper and pencil) use equivalence to transform calculations into simpler ones. Writing/Reaso Learning CA CCSS Comments Vocabulary Games Advanced Prep RSAs ning Prompt – Target Math Boxes Students learn how to create equivalent fractions MMR Part 1 Part 2 Part 3 by determining what fraction for 1 whole needs to equivalent be multiplied by the existing fraction to solve the fractions, Find and equation (6.NS.4) They complete a journal page in simplest form, 6.NS.4 1 rename which they find common denominators by finding common Fraction Rename

♦ 6.NS.4* 6.EE.5 6.NS.4

4 equivalent the value of a variable (6.EE.5). In Part 2, factor, Capture fractions in fractions. students play Fraction Capture where they greatest simplest form. strategically create equivalent fractions to claim common fractional pieces of squares (divided into various factor fractional pieces). This game meets 6.NS.4. Students find common denominators using number sense, QCD (quick common denominators) and LCD (least common common Compare denominators). The skill of finding LCD is 6.NS.4. denominator Name the LCM 6.NS.4 Explain how 2 6.NS.4* 6.NS.7 6.NS.7 fractions with This lesson involves comparison of fractions (least (LCD), for a given

♦ 6.NS.7 Build It you solved

4 unlike (ordering rational numbers - 6.NS.7). Part 2 quick), least pair of problem 2b. denominators. teaches students Build It, a game in which they common numbers. compare fractions (6.NS.7). In Part 3, students multiple (LCM) compare fractions by using benchmark fractions and/or by cross multiplying (6.NS.7). This standard requires that students add and subtract fractions with unlike denominators. Since this skill will be utilized in future mathematics, it is recommended that teachers keep this lesson in Add and Add and grade 6 as a brief review. It does require that subtract 3 6.NS.4 6.NS.3 6.NS.7 Divisibility

♦ subtract students find LCD, which meets 6.NS.4). In Part 2 fractions w/

4 Dash fractions. of the lesson, the class plays Divisibility Dash. *If unlike students use the standard algorithm for all or denominators. some of the problems, they will meet 6.NS.3. In Part 3, there is a 5-Minute Math option to compare and order fractions (6.NS.7). There are no 6th grade CCSS associated with this mixed Add and lesson that involves adding and subtracting number, subtract fractions and mixed numbers with like Fraction P1 Math Message Add mixed proper 4 mixed denominators (4.NF.3c). However, this lesson Action, needs copies numbers w/

♦ fraction,

4 numbers with could be treated as a quick review for students. Fraction MM p 117, 1 copy for like improper like Friction every 2 students. denominators. fraction, denominators. LIT Math Talk: Mathematical Ideas in Poems For simplest form Two Voices by Theoni Pappas

Students determine common denominators in order to add Add and and subtract fractions and mixed numbers with 6.EE.2 subtract unlike denominators (6.NS.4). In Part 2, they class Subtract 5 6.NS.4 6.EE.2a mixed P1, copy of MM p120, 1

♦ complete journal page 138. This activity practices mixed

4 6.EE.2c numbers with for every 2 students. several standards (6.EE.2 - evaluate expressions numbers. unlike with variables, 6.EE.2a - write expressions with denominators. variables, 6.EE.2c – evaluate expressions at specific values for variables). In Part 2, the class adds and subtracts mixed Add and How did you Use algorithm numbers with subtract compare the 6 6.NS.4 6.NS.4 for the unlike denominators (GCF - 6.NS.4). Part 3 offers

♦ fractions w/ fractions in

4 multiplication a 5-Minute unlike problem 1a and of fractions. Math option to add, subtract and multiply denominators. 1b? fractions with unlike denominators (6.NS.4).

Students multiply mixed numbers as they use Multiply and 7 6.EE.2c Multiply mixed Mixed- P1, copy of MM p126, 1

♦ formulas to simplify

4 numbers. Number Spin for every 2 students. determine area of various figures (6.EE.2c). fractions.

Students solve expressions as they convert from fractions to percents (and vice versa). This meets Conversions 6.RP.3c. *The expressions use empty boxes in 2-4-8 Frac- Convert between place of variables. Frac-Tac- Toe in Part 2 Tac-Toe 3-6-9 between 8 6.EE.4 6.RP.3c

♦ fractions, reinforces the same skill. percent Frac-Tac-Toe fractions, 4 decimals, and (decimal decimals, and percentages. LIT Twizzlers Percentages Book by Jerry Pallotta version) percents.

Articulate the Find the Students find percents based on fractions, and patterns for 2-4-8 Frac- fractional part convert between fractions, decimals and percents 9 6.RP.3c 6.RP.3c conversions Tac-Toe 3-6-9 of a whole

♦ (6.RP.3c) They continue to work on this standard

4 between Frac-Tac-Toe number; whole in Part 2 when they play decimals and (% version) times a Frac-Tac-Toe. percents. fraction. Rename Use circle P1, MM p136, 1 for

0 fractions as

1 6.RP.3c graphs to Students construct circle graphs by converting every 2 students (cut decimals and ♦ represent from fractions to percents (6.RP.3c). apart) and distribute 4 percents. data. for the Math Message.

Convert

1 Find the regular price, between

1 6.RP.3c Students find the percent of a number in percent of a discount, sale fractions, ♦ contextual problems (6.RP.3c). 4 number. price, interest decimals, and percents.

Unit 5: Geometry: Congruence, Construction, and Parallel Lines Overview: To classify, draw, and estimate (with and without tools) angles and their measures; to apply properties of angle orientation in drawings and within shapes(sum of triangles and quadrangles); identify and describe congruence; study geometric transformations (reflection, translation, and rotation) about a plane. Geometric Figures: 2- and 3-dimensional objects with or without curved surfaces can be described, classified, and analyzed by their attributes. An object’s location in space can be described quantitatively. Big Ideas Comparison and Relationships: Numbers, expressions, measures, and objects can be compared and related to other numbers, expressions, measures, and objects in different ways. Writing/Reaso Learning CA CCSS Comments Vocabulary Games Advanced Prep RSAs ning Prompt – Target Math Boxes Students measure angles and draw them as well. This is a CCSS for a later grade level (7.G.2). If MMR Part 1 Part 2 Part 3 time permits, it is recommended that teachers model this lesson and guide practice to provide a solid foundation for future mastery. In Part 2, right, acute, P3R: full, 3/4, & 1/2 Use half-circle Classify, students practice 6.RP3c when they find the straight, 1 6.RP.3c length straws and protractor to

♦ measure, and percent of a given number. Part three revisits obtuse, and Angle Tangle

5 copies of MM p146, 1 measure draw angles. angle measurement skills. reflex angles, for every 2 students. angles. vertex The literature connections referenced in the unit are not specific to a particular lesson. The titles can be incorporated at any time during the unit. See TLG p 331 Infer angle measure of supplementary How might you unknown This lesson continues with the concept of angle , find the sum of angles P3R; cut out the measurement. As with the previous lesson, it is complementar Name, label, the interior 2 through the triangles and

♦ recommended that teachers guide practice to y, vertical Angle Tangle and measure angles of the

5 use of quadrangles on MM p provide solid foundation for future learning. (opposite), angles. hexagon definition of 149 and adjacent without using a triangle & angles protractor? quadrangle sum totals. Apply Students make circle graphs after computing definitions of Calculate the percents of a whole (6.RP.3c). In Part 2, students supplementary 3 6.RP.3c 6.RP.3c 6.RP.3c degree calculate prices of sale

♦ sector and vertical

5 measure of items (6.RP.3c). In Part 3, the children work with angles to find sectors. angle measures and sums of angles, which is a corresponding skill for future grade levels (7.G.5). angles.

In this lesson, students review the coordinate grid system and ordered pairs in all 4 quadrants Plot ordered (6.NS.6b). They also create polygons on the grid. pairs & locate origin, ordered They find (6.NS.6c) and plot (6.G.3) the Spoon Use a strategy 6.NS.6b 6.NS.6b midpoints and number pair, 6.NS.3 corresponding ordered pairs. In Part 2, the class Scramble for solving 4 6.NS.6b 6.NS.6c 6.NS.6c endpoints of axis,

♦ 6.RP.3c plays Spoon Scramble to practice computing with problems

5 6.G.3 6.G.3 segments coordinate decimals (6.NS.3) and finding "percent-of" a X and O—Tic- involving %s created by (and coor. number (6.RP.3c). In Part 3, there are more Tac-Toe and discounts. those ordered grid), midpoint opportunities to identify and plot ordered pairs on pairs. a coordinate grid (6.NS.6b). One of the options involves geometric shapes on a grid (6.G.3). Use transformation transformation Name ordered Students perform isometric transformations on a s (translation, s to create Set aside red number pairs 6.NS.6b coordinate grid (6.NS.6b) as they learn about the reflection, rd 5 6.NS.6a another figure trapezoids for the in the 3

♦ 6.NS.6c relationship between ordered pairs in one figure rotation),

5 on coordinate optional readiness quadrant of and ordered pairs of a figure that has been slid, preimage, line plane while activity. coordinate rotated or reflected (6.NS.6c). of reflection, maintaining plane. isometry congruence. P1, draw and cut out Explore The class learns about congruent figures, which is congruent, congruent polygons Rotate a figure congruence an 8th grade CCSS (8.G.2). If time permits, corresponding, similar to those on p and name 6 6.RP.3c and use tools

♦ teachers could model the lesson and guide rough sketch, 178 in SRB; size so that points on

5 to create practice. If there is no time, this lesson could be accurate both fit under doc. coordinate congruent omitted. drawing camera or on overhead plane. figures. AT THE SAME TIME. This lesson is not associated with any 6th grade compass & 2-4-8 Frac- Construct CCSS as students use straight edges to construct straightedge Convert Tac-Toe 3-6-9 7 6.RP.3c figures with triangles (7.G.2; 8.G.2). Teachers could use this construction, between

♦ Frac-Tac-Toe

5 straightedge as an exploratory lesson if time permits. In Part 2, anchor, fractions and (decimal and compass. students play Frac-Tac-Toe to practice finding concentric decimals. version) percent of a number (6.RP.3c). circles perpendicular Students continue as they construct figures using Add, subtract, Copy angles & How did you a straight edge and a compass. This is associated and multiply 8 (and th perpendicular Polygon find the angle

♦ with 8.G.2, an 8 grade CCSS. Teachers might fractions and

5 perpendicular bisector, Capture measure in consider treating this lesson as an exploratory mixed bisectors). inscribed, problem 1? lesson. numbers. bisect The intent of this lesson is for students to explore Determine angle relationships. This is a skill associated with parallel, skew, angle 7.G.2 and 8.G.2. Teachers are encouraged to & transversal; measures by Explore and 9 6.RP.3c 6.EE.2 keep this lesson as an exploration, not expecting adjacent applying

♦ apply angle

5 mastery. In Part 2, Students calculate percents of supplementary knowledge relationships. numbers as they determine sales tax , & vertical instead of and/or tips (6.RP.3c). In Part 3, the class can angles using a practice 6.EE.2 (evaluate expressions). protractor.

Calculate the Introduce In this lesson, explore angle relationships which is degree relationship of not related to 6th grade CCSS. To determine measure of 0

1 6.EE.2a* angles in a missing angle measures, students need to create consecutive 3-D Shape sectors of a

♦ parallelogram and solve expressions (6.EE.2a). *To fully meet angles Sort circle graph 5 and do a this standard, students must use letters as and use a construction. variables. protractor to draw sectors.

Unit 6: Number Systems and Algebra Concepts Overview: To review multiplication of fractions and mixed numbers; to introduce an algorithm for the division of fractions; to perform operations on integers and to review equation-solving techniques. Big Operation Meanings and Relationships: There are many ways to show addition, subtraction, multiplication and division, and each operation is related. Solving Equations and Inequalities: Rules of arithmetic and Ideas algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found. Writing/Reaso Learning CA CCSS Comments Vocabulary Games Advanced Prep RSAs ning Prompt – Target Math Boxes Students multiply fractions and mixed numbers. MMR Part 1 Part 2 Part 3 Review These are 5th grade standards so should serve as

multiplication a nice review. Name and of fractions Fraction/ 1 6.NS.4 identify the

♦ and mixed reciprocal Whole

6 reciprocal of a numbers; The literature connections referenced in the unit Number Top-It number. learn to find are not specific to a particular lesson. The titles reciprocals. can be incorporated at any time during the unit.

See TLG p 523

Introduce a Students meet 6.NS.1 when they divide fractions Use an How did you Division of 2 fraction and mixed numbers. They begin with visual algorithm to determine the

♦ 6.NS.4 6.NS.1 6.NS.1 Fractions

6 division models and move towards use of an algorithm. divide number in Property algorithm. Practice on this standard continues in Part 3. fractions. problem 4c?

Students begin by using a calculator to explore "opposite" or negative numbers (6.NS.5). They Review how to input locate numbers on a number line (6.NS.6, negative numbers on 6.NS.6a) and use the number line to perform calculator. Have real Understand 6.NS.5 computations with integers (6.NS.7c). In Part 2, number poster posted the inverse 6.NS.6 6.NS.6 Add and students play Credit/Debits game (6.NS.7c). In 3 opposite of a Credits/Debts and visible to all relationship

♦ 6.NS.7 6.NS.6a 6.NS.7c 6.NS.6a subtract Part 3, students may use + and tiles to model

6 number (advanced ver.) students. between 6.NS.7c 6.NS.7 integers. computation with signed numbers. They can also For P3R, copy of MM addition and 6.NS.7 complete an activity where they use absolute p188 for each student; subtraction. value to add and subtract signed numbers and/or have kids cut the tiles use 5-Minute Math to use a number line model for apart. adding and subtracting signed numbers (6.NS.6 and 6.NS.6a). Part 1 of this lesson practices 7th grade standards Develop and Calculate and (7.NS.2a apply rules for compare the 4 and 7.NS.2c) when students multiply and divide Multiplication Top-It

♦ 6.NS.7 multiplying sums and

6 signed numbers. In Part 2, students compare Property of -1 (integers) and dividing differences of positive and negative numbers (6.NS.7d) when integers. integers. they play a Top-It game.

number sets, Students complete much of the work necessary (counting, for standard 6.NS.6c (find and position integers whole, Summarize 6.NS.6 and other rational numbers on a number line), integers, Divide the properties Explain why ¾ 5 6.NS.6a however, they do not plot points on a coordinate rational, fractions and

♦ of number of 80 in less

6 6.NS.6c* plane. They do find the opposite of numbers on irrational, mixed systems and than 80? 6.NS.7c the number line (6.NS.6a) to think about how the real), numbers. operations. absolute value of a number determines its repeating & distance from 0 on a number line (6.NS.7c). terminating decimals Take a look at p269 & Review and There are no 6th grade CCSS associated with this 270 in SRB. Apply the Explain how order of evaluate lesson. Order of operations is a skill that students Additionally, be sure order of you know that 6 operations, Name That 行 ♦ expressions will need to employ as they continue in their math that the calculators in operations to L and O in

6 nested Number using order of classes, so it is recommended that teachers keep your room are “smart” evaluate parentheses problem 3 are operations. this lesson in the curriculum. (they follow order of expressions. congruent. operations). Students solve expressions without variables to equation, Apply the Translate word practice using parentheses. In Part 2, the class inequality, order of 7 6.G.1 sentences into

♦ solves area problems (6.G.1) for real life relation & operations to

6 6.EE.2c number situations. Evaluating expressions with specific operation evaluate sentences. values arising from formulas is 6.EE.2c. symbols expressions. Some of the problems that students complete in variable, Use the trial- Use trial-and- this lesson involve evaluating expressions on If using the P3R solution, open and-error and error & cover- either side of the equality symbol. *When activity, ask a 4th or 5th 8 6.EE.5 sentence, trial- Name That cover-up

♦ up methods to students are focused on these tasks, it is grade colleague about

6 6.EE.7 and-error & Number method to solve recommended that teachers reinforce the the game, Broken cover-up solve equations. vocabulary found in 6.EE.2b (sum, term, product, Calculator. methods equations. factor, quotient, coefficient). Work through the Students solve pan balance problems, first with “suggested” problems Solve Model objects, and later with letters and numbers in P3R activity before equations and 9 equation- substituted in (6.EE.5). They solve more trying them with your

♦ 6.EE.5 6.EE.5 pan balance check

6 solving expressions when they complete more pan students; they may solutions using techniques. balance problems in pan balance problems in Part need to be adjusted substitution. 3. depending on available materials. Again, the P3R activity Explore assists those students Use a pan-

0 another The class solves and generates equivalent in making the transition

1 equivalent balance model 6.EE.5 6.EE.5 method for equations with pan balances (6.EE.5). They to solving problems ♦ equations to solve 6 solving continue to practice this skill in Part 3. algebraically (without equations. equations. using the pan balance) and is recommended.

Students solve equations that have the same variable on both sides of the equation. They use substitution to determine if the equation is true For P1, get Algebra (6.EE.5). Standard 6.EE.2b requires that teachers term of the Solve Write and Election sheets(3&4)

1 are explicit about using the correct vocabulary equation, equations and

1 6.EE.5 6.EE.5 solve Algebra from SMJ. Have kids while working with equations (sum, term, product, variable & check ♦ 6.EE.2b equivalent Election tape US map together 6 factor, quotient, coefficient). Teachers who constant term, solutions using equations. (1 map/group) MM provide (or have students provide) real-world coefficient substitution. p434 & 435 context for the equations will meet the requirements of 6.EE.7. This is true for Part 1 of the lesson and for Part 3 of the lesson as well. Students are asked to provide alternate solutions for inequalities, which is closely tied to 6.EE.6. Find and Teachers could represent all P1: copy MM p473(1 for Determine extend this lesson by adding context for each

2 values that every 3 student) whether

1 inequality to meet the requirements of this inequality, Solution 6.EE.5 6.NS.3 make an If doing 2nd P3E activity, inequalities ♦ standard. In addition, the concepts of 6.EE.8 solution set Search 6 inequality in cut 50ish 3x5 cards in are true or (recognize that there is an infinite number of one variable half (widthwise) false. solutions for an inequality) are reinforced without true. real world context. If context is added, this standard would be met.

Unit 7: Probability and Discrete Mathematics Overview: Review basics concepts and vocabulary of probability; to calculate probabilities and express them as fractions, decimals, and percentages; to investigate and generate random numbers; to compare experimental and expected outcomes; to use tree diagrams to calculated expected probabilities; to use Venn diagrams to analyze situations.

Big Ideas Equivalence: Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.

Writing/Reaso Learning CA CCSS Comments Vocabulary Games Advanced Prep RSAs ning Prompt – Target Math Boxes Standards for probability skills learned in this MMR Part 1 Part 2 Part 3 lesson are found in 7th grade CCSS (7.SP.7, 7.SP.7c and 7.SP.8). Students do use fractions to talk about how likely an event is to occur (6.RP.1). It is recommended that teachers use this lesson Use to practice with ratios and to lay foundation for experiences to outcomes 6.NS.4 6.RP.1 6.EE.2c 6.RP.1 future learning. In Part 2, the class plays Solution Identify find (possible, Solution Search, in which they must evaluate expressions outcomes and 1 probabilities favorable), Search Have Probability Meter

♦ with specific values for variables (6.EE.2c). calculate the

7 for events event, Poster up. probability of where all probability, Grab Bag The literature connections referenced in the unit an event. events are equally likely are not specific to a particular lesson. The titles equally likely. can be incorporated at any time during the unit. See TLG p 615

LIT G is for Googol: A Math Alphabet Book by David M Schwartz Understand how sample size affects Investigate outcomes and Students continue work with ratios in probability and generate explain how 2 6.RP.1 6.RP.1 problems (6.RP.1). Much of the content of this random P1, set aside number

♦ random th the larger the

7 lesson is tied to 7 grade CCSS (7.SP.7b and numbers cards 1-5 numbers with sample size, 7.SP.8b). a given range. the more likely the actual will match the predicted. Solve equations Use random using trial- numbers to and-error or If doing P3E, practice simulate equivalent 2-4-8 & 3-6-9 generating random 3 results to Students use random numbers to simulate simulate, equation

♦ Frac-Tac-Toe numbers with the

7 estimate the winners brackets in a tournament. simulation methods and (% versions) calculators the chance of check the students would use. each possible solution outcome. through substitution of the variable.

Students simulate results of a random walk through a maze in this lesson. They meet most of Use tree the requirements of 7.SP.8c (use a simulation to diagrams to generate frequencies for compound events). Calculate tree diagram, find expected However, they do not design their own simulation. probabilities 4 expected Name That

♦ outcome and and express

7 outcomes, Number compare these LIT Anno’s Hat Tricks by Akihiro Nozaki and as fractions actual results with results of Mitsumasa Anno and percents. a simulation. LIT Do You Wanna Bet? by Jean Cushman LIT Socrates and the Three Little Pigs by Tuyosi Mori Students make tree diagrams to solve problems. Determine The skills in this lesson are associated with expected Why does the 6.RP.3c when they find how likely an event is to outcomes and graph in Use tree occur (percent of a number). The use of tree Multiplication use a tree problem 2 does 5 6.RP.3c 6.RP.3c 6.NS.4 diagrams to

♦ diagrams could prove useful to students as a Counting diagram to not represent

7 calculate strategy for problem solving and/or organization Principle calculate the set of probabilities. of information. In Part 3, there is an option to add probabilities counting fractions with unlike denominators. This requires for chance numbers? that they determine the GCF (6.NS.4). events.

Probability 2 1

Calculate t

c probabilities,

e TLG p 957 U j

o including with r

P independent, dependent, and disjointed events. Find probabilities of Students use Venn diagrams to organize given events Solve See TLG p 651 if you information. There are no 6th grade CCSS in this and apply tree 6 problems Venn Diagram plan on doing the

♦ lesson. Teachers could choose to use integrate Venn diagram diagrams to

7 using Venn Challenge second optional activity the use of Venn diagrams into other subjects or find the diagrams. in P3E teach this lesson if time permits. probabilities of compound events. P1, each student will Find the need a small paper bag probability of Determine the and 5 counters; 3 black selecting each fairness or Students continue to be exposed to concepts of and 2 white (2 different branch of a 7 games (fair &

♦ unfairness of probability, which is associated with 7th grade Greedy color rainbow cubes tree diagram

7 unfair) games of CCSS (7.SP.8a, 7.SP.8b). would also work); make and determine chance. adjustments to the number of “directions in their possible journals accordingly. outcomes.

P1 Make a Calculate transparency of the Activities in this lesson involve more practice with probabilities Investigate tables from problem 6 6.EE.2 probability. In Part 2, the class reviews algebraic and determine 8 guessing on on SJ

♦ 6.EE.2b* expressions. *Teachers must be explicit about the expected

7 multiple- p 273 and problem 12 vocabulary (sum, term, product, factor, quotient, outcomes for choice tests. on p 275 to record coefficient) when working towards 6.EE.2b. chance tallies during the events. discussion.

Unit 8: Rates and Ratios Overview: To review rates and solve rate problems; to use proportions to model and solve rate problems; to introduce and use cross multiplication to solve open proportion and percent problems; to review ratios and solve problems involving part-to-part and part-to-whole ratios; to find the length of unknown sides of similar figures. Ratio and Proportionality: When mathematical or real-world quantities have a relationship that can be stated as “for every x units of the first quantity there are y units of the second quantity,” this relationship remains Big Ideas constant as the corresponding values of the quantities change. In a proportional relationship there are an infinite number of ratios equal to the lowest terms or constant ratio. Comparison and Relationships: Numbers, expressions, measures, and objects can be compared and related to other numbers, expressions, measures, and objects in different ways. Writing/Reaso Learning CA CCSS Comments Vocabulary Games Advanced Prep RSAs ning Prompt – Target Math Boxes

Students learn rate about using rate tables and MMR Part 1 Part 2 Part 3 proportions to find "per-unit" rates (6.RP.2). They use fractions to show the relationship between two numbers, however they do not transfer that to two numbers separated by a colon. Teachers must be explicit about writing rates in this manner. They use real world problems (6.RP.3), 6.RP.2 6.RP.1 Apply the per- Review rates including constant speed (6.RP.3b). In Part 2, 6.RP.3 6.NS.2 6.RP.3 rate (per-unit unit rate and and solve rate students revisit whole number division with Have a nutrition label 1 6.RP.3b 6.RP.3c & equivalent), rate-table

♦ problems using quotients involving decimal remainders (6.NS.2). ready to share with

8 rate table, methods to various In Part 3, the first option explicitly notes that rate students. proportion solve methods. is a comparison of two items with different units problems. (6.RP.1) in connection with constant speed (6.RP.3b) (which is a real world example – 6.RP.3).

The literature connections referenced in the unit are not specific to a particular lesson. The titles can be incorporated at any time during the unit. See TLG p 685

In this lesson, the class uses proportions to solve rate problems. They need to make the direct connection between the fraction that expresses the rate and the rate expressed with a colon (6.RP.2) They work with real world examples and equivalent ratios (6.RP.3), including constant speed (6.RP.3c) Students use tables and find 6.RP.2 missing values in tables (6.RP.3a), *but they do Assign Part A of the Use a How did you Use 6.RP.3 not plot the numbers on a coordinate plane. In open table in the Study Links proportion to use the info. 6.RP.3 proportions to 2 6.RP.3c 6.RP.3a* 6.NS.3 Part 2 the class focuses on decimal division proportion, p189 early, as this will model, given in

♦ 6.RP.3b model and

8 6.RP.3b (6.NS.3). In Part 3, there is an option to write rate solution of the give students time to summarize, problem 3 to solve rate problems and share them with a partner (6.RP.3). proportion plan a visit to the and solve rate complete the problems. grocery store. problems. Venn diagram? LIT Math Curse by Jon Scieszka

LIT Sir Cumference and the Dragon of Pi by Cindy Neuschwander

LIT The Librarian Who Measured the Earth by Kathryn Lasky

LIT Counting On Frank by Rod Clement

Long Division C

U.S. Part C 3 Traditional 1

t long division

c Use the U.S. e j traditional long method, TLG p 957 Z o r division divisor, P dividend, short

A algorithm with

C whole numbers division and decimals.

In this lesson, students learn about cross products Introduce to determine equivalence between two Use cross cross- proportions. They create equations to show their cross product, Fraction/ products to 3 6.EE.5

♦ multiplication work (6.EE.5). The real world context of the rate cross Whole write an open

8 6.RP.3 to solve problems, and the relationship to equations is multiplication Number Top-It number proportions. 6.RP.3. In Part 3, there is an option to solve sentence. equations without exponents (part of 6.EE.1).

Students learn about rate as "percent of" a whole Solve rate and (6.RP.3c). They continue this focus in Part 2 as Use percent Explain how they complete a journal page, and in Part 3 when protein, fat, proportions to 5 6.RP.3c problems you found the

♦ 6.RP.3c 6.RP.3c they plan meals based on percents of calories carbohydrate, model and

8 6.RP.3b involving area of DAPE in from fat, cars, and protein. In Part 3, they also balanced diet solve rate caloric content problem 5. solve rate problems involving constant speed problems. of food. (6.RP.3b).

Review In this lesson, the class makes the direct meaning and connection between rate and ratio (6.RP.1) They Use notation of solve real-world problems (6.RP.3). In Part 2, the ratio proportions to 6 6.RP.1 6.RP.1 ratios and class plays Build It to compare fractions. Part 3 (equivalent,

♦ 6.EE.2a <4.NF.2> Build It model and

8 6.RP.3 6.RP.3 solve problems revisits the concepts from Part 1 when students part-to-whole, solve ratio involving part- write their own ratio number stories and model part-to-part) problems. to-part & part- ratio problems with counters. to-whole. Students solve percent-of problems (6.RP.3c) as Solve percent they find Use open problems by 7 6.RP.3c relationships between two quantities (6.RP.1) In proportions to

♦ 6.NS.2 6.RP.3c writing and Division Top-It

8 6.RP.1 Part 2, the students practice division in Division solve percent solving Top-It (6.NS.2) Part 3 offers practice with problems. proportions. "percent-of" problems (6.RP.3c). Consider providing Estimate students with the Express ratios percents materials listed below as fractions Students think about sale pricing in terms of equivalents for to solve problem 5 MM and percents 8 6.RP.1 proportions (6.RP.1) and percent off (6.RP.3c).

♦ 6.NS.1d 6.RP.3c fractions and Top-It p261: and correctly

8 6.RP.3c Part 3 offers a 5- Minute Math activity to practice convert postcard, index card, round to the "percent-of" problems (6.RP.3c). fractions to regular envelope, nearest whole percents. business envelope, percent. notebook paper size-change Measure line Students express ratios as they compare Explain the Explore and factor, scale, segments to 6.RP.1 quantities (6.RP.1) including the use of colons For Math Message, method you 9 use ratios to reduction, 1 ♦ 6.RP.2 6.RP.3 (6.RP.2). They focus on change factor in real copies of MM p264 (1 used to find the

8 describe scale factor, n- the nearest 6.RP.3 world problems (6.RP.3). They continue to focus for every 2 students) difference in change. to-1 ratio, 16 on size change (6.RP.3). problem 3b. enlargement inch. similar & Use ratios to Describe the Students use proportions to see the relationship Explore the congruent solve steps you used

0 between similar polygons (6.RP.1). In Part 2,

1 6.NS.3 properties of figures Spoon problems to rename the 6.RP.1 students practice decimal multiplication (6.NS.3) ♦ 6.RP.3c similar (polygons), Scramble involving fraction in 8 and find "percent-of" numbers (6.RP.3c) in Spoon polygons. corresponding similar problem 3 as a Scramble. sides & angles polygons. decimal. Students compare ratios for real world problems Compare ratios Use fraction (6.RP.3), and they complete one problem which

1 in For Math Message, equivalents or

1 6.RP.3 involves plotting the information on a coordinate Golden 6.RP.3c 6.RP.3a n-to-1 format; copies of MM p272 (1 proportions to ♦ 6.RP.3a grid (6.RP.3a). Part 3 offers two practice pages Rectangle 8 introduce for every 8 students) solve percent- that involve plotting ordered pairs when students Golden Ratio. of problems. learn about slope (6.RP.3a). Find corresponding side length of Students learn about the Golden Ratio (6.RP.3). In For P2, have students

2 Explore Golden similar

1 Part 2, cut apart the 32 cards 6.RP.3 6.EE.5 Rectangle and Golden Ratio First to 100 polygons; use ♦ they play First to 100 to practice making variable on SMJ 2, activity 8 Golden Ratio. n-to-1 or substitutions (6.EE.55). sheets 5 & 6. proportion to find length of unknown side.

Unit 9: More about Variables, Formulas, and Graphs Overview: To explore the distributive property; to apply the order of operations and the distributive strategies to simplify algebraic expressions, evaluate formulas, and solve equations; to apply the Pythagorean theorem and find the missing lengths in similar figures using a size-change factor. Properties: For a given set of numbers, there are relationships that are always true called properties, and these are the rules that govern arithmetic and algebra. Ratio and Proportionality: When mathematical or real-world quantities have a relationship that can be stated as “for every x units of the first quantity there are y units of the second quantity,” this relationship remains constant as the corresponding values of the quantities Big Ideas change. In a proportional relationship there are an infinite number of ratios equal to the lowest terms or constant ratio. Variable: Mathematical situations and structures can be translated and represented abstractly using variables, expressions and equations. Writing/Reaso Learning CA CCSS Comments Vocabulary Games Advanced Prep RSAs ning Prompt – Target Math Boxes Students determine which expression (or in some MMR Part 1 Part 2 Part 3 cases, which equation) matches an area model involving distributive property (6.EE.3). In Part 2, the class finds quotients involving decimal Explore the remainders (6.NS.2), and in Part 3 there are Use a trial- Explain how distributive opportunities to practice using the distributive and-error you identified 1 6.EE.3 6.NS.2 6.EE.3 property using property when playing Multiplication Wrestling Multiplication strategy to

♦ Area Model the regular

9 the area model and finding areas of rectangles (6.EE.3). Wrestling solve for an polygons in of unknown problem 4. multiplication. The literature connections referenced in the unit value. are not specific to a particular lesson. The titles can be incorporated at any time during the unit. See TLG p 779

Students focus on the distributive property in this lesson as they consider solving expressions (6.E.3). Teachers must be explicit about the Find the total vocabulary (sum, term, product, factor, quotient, number of Recognize, 6.EE.3 coefficient) when working towards 6.EE.2b objects in a

2 6.EE.3 write, and use distributive ♦ 6.EE.2b (identifying parts of an expression). In Part 3, Getting to 1 set when a

9 the distributive property students have multiple opportunities to continue fractional part property. work on 6.EE.3 as they write number stories to of the set is match expressions and/or complete an extra given. practice sheet regarding us of the distributive property when solving expressions. Students combine like terms in expressions to prepare them for 6.EE.2c. * This lesson is a good Use a strategy opportunity to be explicit about vocabulary for to find a Explain how the Simplify For P3, students will 6.EE.2c* 6.EE.5 6.EE.2b (sum, term, factor, product, quotient, like terms solution and ratio in problem algebraic need Algebra Elections

3 6.EE.2 6.EE.2 6.EE.2 coefficient). In Part 3, the children can play (combine like), Algebra then check it 3c is related to ♦ expressions by cards and the Electoral

9 6.EE.2b* 6.EE.2b Algebra Election to practice substituting for simplify an Election by substituting the ratio of combining like Vote Map from Lesson variables in equations (6.EE.5). The Enrichment expression the solution corresponding terms. 6♦11. opportunity is a good opportunity to reinforce for the sides. vocabulary terms in expressions (6.EE.2b) variable. .

Students simplify expressions and equations in this lesson. This is a good opportunity to reinforce the mathematical terms associated with expressions (6.EE.2b). On journal page 334, they use the Simplify Copies of MM p290 (1 Write an distributive property (6.EE.3) and identify algebraic for every 2 students) expression for 6.EE.2b equivalent expressions (6.EE.4). In Part 2, the 6.EE.2 expressions by for the Math Message; an area model

4 6.EE.3 6.EE.5 class plays First to 100, which involves ♦ 6.EE.2a eliminating First To 100 cut them apart. For P2, and then

9 6.EE.4 determining if a given value makes an expression parentheses students will need the evaluate that true or false (6.EE.5). Part 3 offers three options and combining First to 100 cards they expression for for evaluating expressions (6.EE.2, 6.EE.2a), like terms. cut out in lesson 8♦12. a given value. including using pan-balance problems and writing equations and solving them.

LIT G is for Googol by David M. Schwartz

For R, fill in problems on MM p296 before Simplify Simplify and making copies (see TLG equations and

5 6.EE.2 6.EE.2 Students simplify and solve expressions (6.EE.2). equivalent ♦ solve p815 for these recognize

9 They continue to practice this in Part 3. equations equations. problems); you can equivalent create your own if you equations. desire. Use a Students solve equations to test whether a given Write and solve distributive 6.EE.5 value is true (6.EE.5; 6.EE.7). In Part 2, students Prep a geometry

6 6.EE.2c 6.EE.7 equations mobile, Solution strategy to ♦ 6.EE.7 play Solution Search (6.EE.2c). They write and template for this lesson

9 based on given fulcrum Search mentally solve equations to combine weight values to (TLG p820). formulas. calculate make a mobile balance (6.EE.7). quotients. spreadsheet, Evaluate Describe the Enter and Students learn about formulas in spreadsheets cell, labels, algebraic steps you

7 6.EE.2c 6.EE.2c display data in Spreadsheet P1; copies of MM p301 ♦ (6.EE.2c) in address(box), expressions followed to

9 a spreadsheet Scramble (1 for every 4 students) Parts 1 and 3. display bar, using order of draw the circle program. formulas operations. in problem 5. Students apply knowledge of how to solve expressions in real life to solving for variables in equations as they apply area formulas (6.EE.2c*). *This standard calls for solving for variables in formulas, specifically with expressions. Students meet 6.EE.7 when they solve simple equations. Apply area Review and use Part 3 continues with these skills as students formulas and 6.EE.2c 6.EE.7 formulas for solve perimeter problems and/or area problems.

8 3-D Shape measure line ♦ 6.EE.7 6.EE.2c area,

9 Sort segments to perimeter, and LIT Sir Cumference and the First Round Table by the nearest circumference. Cindy Neschwander millimeter. LIT Spaghetti and Meatballs for All! by Marilyn Burns

LIT What’s Your Angle, Pythagoras? by Julie Ellis

Students apply knowledge of how to solve expressions in real life to solving for variables in equations as Use an they apply Review volume Gather base-10 blocks equivalent- volume formulas (6.EE.2c*). *This standard calls 6.EE.7 formulas for for the R activity. Use equation

9 6.EE.2 for ♦ 6.EE.2c prisms, heavy paper or method to

9 solving for variables in formulas, specifically with cylinders and tagboard (TLG p839) to simplify and expressions. Students meet 6.EE.7 when they spheres. make cylinders. solve solve simple equations. equations. Part 3 continues with these skills as students solve volume and capacity problems.

Journal page 354 asks students to evaluate expressions with specific values of variables (6.EE.2c) as they think about solving a particular If doing E activity (P3), Use a trial- Approximate equation by trial and error. This helps them to Describe each cut out an 8-inch and-error 6.NS.8 the solutions of determine whether a given variable makes the step you used 0 6.NS.3 6.EE.5 test number, Spoon square of paper. Draw method to 1

♦ 6.EE.5 equations by equation true (6.EE.5). The test numbers are to find the trial-and-error Scramble smaller squares inside approximate 9 trial-and-error graphed on a coordinate grid (6.NS.8). Students solution to (2 inches inward for solutions of method. play Spoon Scramble in Part 2 to meet 6.NS.3 problem 2d. each edge) equations. (computation with decimals). In Part 3, students check to see if values for variables make an equation true (6.EE.5).

Substitute Evaluate Students use formulas to solve problems known values formulas (6.EE.2c). Teachers must be explicit about the Explain how 6.EE.2b in appropriate 1 6.EE.2a through vocabulary (sum, term, product, factor, quotient, you calculated 1

♦ 6.EE.2c 6.G.4 formulas and substitution of coefficient) when working towards 6.EE.2b. In Part the height in 9 then solve values for 2, students represent 3-D figures using nets to problem 2. resulting variables. determine area of specified faces (6.G.4). expression. square (root & Students practice evaluating expressions that of a number), Use the Apply the involve formulas (6.EE.2c) as they learn about the hypotenuse, appropriate 2 6.EE.2c 6.EE.2c 1

♦ Pythagorean Pythagorean Theorem. They continue to work right triangle, formula to

9 Theorem. with the Pythagorean Theorem in Part 3 of the theorem, solve an area lesson. Pythagorean problem. Theorem, legs For extra practice, draw a black circle target about 1 Find the Apply a size- inch in missing length change factor Students consider indirect measurement by using diameter. Tape 3 in similar indirect to find the 1

♦ 6.RP.1 6.RP.1 ratio Getting to 1 it to the figures with a measurement missing length 9 (6.RP1) in Parts 1 and 3. classroom wall, size-change of a similar near the ceiling. factor. figure. Measure the height of the target from the floor in cm.

Unit 10: Geometry Topics

Overview: To review and explore both regular and semi-regular tessellations; to explore both point and rotational symmetry; to introduce topology and perform topological transformations; experiment with MÖbius strip.

Big Ideas

Writing/Reaso CA CCSS Learning Target Comments Vocabulary Games Advanced Prep RSAs ning Prompt – Math Boxes For P1, copies of MM p329 on cardstock. Cut out the templates or Apply the How did you pass copies of the 1

♦ Introduce tessellation, definitions of decide whether

0 master around and <7.G.5> semiregular LIT G is for Googol; An Math Alphabet Book vertex, regular Angle Tangle supplementary problems 6a 1 have each student cut tessellations. by David M. Schwartz polygon and vertical and 6b are true out one (each student angles. or false? will need one, so 2 copies covers 30 students). In Part 2 of this lesson, students use ordered pairs to perform translations, reflections and rotations (6.NS.6b). *To fully meet the requirements of For P1, cut 3 by 3 inch Create non- 6.NS.8, students must discuss absolute value squares from index Compare 2

♦ 6.NS.6b polygonal translation

0 when they look for patterns in figures on the cards. Review SRB rational 6.NS.8* translation tessellation 1 coordinate grid. page p360 prior to numbers. tessellations. teaching the lesson. LIT Eight Hands Round: A Patchwork Alphabet by Ann Whitford Apply For P1, copies of MM symmetry properties of Explore point p336 & 337 on 3

♦ (rotation, angle

0 <8.G.2> and rotational cardstock (1 copy of point, & order orientations. 1 symmetry. each). Cut out square of rotation) ABCD from MM p337

Introduce Apply order of topology topology and operations to (equivalent, 4

♦ perform Name That write numeric

0 . property, topological Number expressions 1 transformation transformations for rational ), genus . numbers.

Flores, Canterbury, Fundanet, Grade 6 Key: TLG = Teacher’s Lesson Guide; MM = Math Masters; SRB = Student Reference Book; AH = Assessment Handbook; RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; and Preston Page 28 EP = Extra Practice; SMJ = Student Math Journal; TRM = Teacher Reference Manual; LIT= Literature Connection; P = Part