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Grade 6 Go Math! Quarterly Planner 12-13 Days Chapter 1 Whole Numbers and Decimals Big Idea: In 6th grade, students use basic facts and algorithms for operations with rational numbers and notions of equivalence to transform calculations into simpler ones. Fluency and accuracy with multidigit addition, subtraction, and division is the big idea along with a spotlight on greatest common factors and least common multiples. Students build on previous learning of the multiplicative structure as well as prime and composite numbers. Essential Question: How do you solve real-world problems involving whole numbers and decimals? Standards: 6.NS 2, 6.NS 4, 6.NS 3 Emphasized Math Practice standard: MP 5 - Use appropriate tools strategically ELD Standards: ELD.PI.6.1-Exchanging information/ideas via oral communication and conversations. ELD.PI.6.9- Expressing information and ideas in oral presentations. ELD.PI.6.3-Offering opinions and negotiating with/persuading others. ELD.PI.6.11- Supporting opinions or justifying arguments and evaluating others’ opinions or arguments. ELD.P1.6.5-Listening actively and asking/answering questions about what was heard. ELD.PI.6.12-Selecting and applying varied and precise vocabulary. Lesson Standards & Math Practices 1.1 Divide MultiDigit Numbers 6.NS.2 MP.1, MP.2, MP.3, MP.4 1.2 Prime Factorization 6.NS.4 MP.1, MP.7, MP.8 1.3 1.4 Least Common Multiple Greatest Common Factor 6.NS.4 MP.4, MP.6 6.NS.4 MP.2, MP.4 Essential Question Math Content/Strategies Models/Tools Go Math! Teacher Resources G6 Connections Vocabulary How do you divide multi-digit numbers? Apply estimation to long division to begin long division algorithm, to determine numbers to use after each regrouping and to check reasonableness. Apply to 1-digit, 2-digit divisors first. Base-Ten Blocks Base-Ten Grid Paper Base Ten 15x20 Base Ten 50x70 Review division (area models, partial quotients) estimation, long division, compatible numbers, remainder, Review prime factors/trees; factor 40, 150 prime factorization, prime factors, ladder diagram See Problem of the Day 1.3 and Vocabulary Builder least common multiple, prime factorization How do you write the prime factorization of a number? How can you find the least common multiple of two whole numbers? How can you find the greatest common factor of two whole numbers? Understand prime factorization as the breaking apart of a number into all its prime factors Find LCM by prime factorization or listing multiples. Students will use LCM to find a least common denominator and write equivalent fractions. Find GCF by prime factorization or listing factors. Students will use GCF to simplify fractional factors before multiplying, simplify fractional products, and write equivalent algebraic expressions Factor Trees Ladder Diagram Prime Factorization Listing Multiples Academic Language Support ELD Standards ELD Standards ELA/ELD Framework ELPD Framework Access Strategies Organizing Learning for Student Access to Challenging Content Student Engagement Strategies Problem Solving Steps and Approaches Use a diagram to show groups of objects; Prime Factorization, Listing multiples; Distributive Property; Estimation; Multiplication Strategies; Base-Ten Blocks; Long Division Strategies; Base Ten 15x20; DRAFT Journal Find 56,794 ÷338. Write the quotient twice, once with the remainder as a fraction and once with an r. Describe 2 methods for finding the prime factorization of a number. Explain when you would use each method (finding multiples or prime factorization) for finding the LCM and why. Equitable Talk Simplify fractions: 3/6, 72/100. Write an equivalent expression: 5n + 45 Greatest Common Factor, prime factorization, prime factors, Distributive Property, sum as a product Accountable Talk Simply Stated Equitable Talk Conversation Prompts Accountable Talk Posters Five Talk Moves Bookmark Write a short paragraph to explain how to use prime factorization and the Distributive Property to express the sum of 2 whole numbers as a product. Base Ten 50x70; Ladder Diagram 1.5 1.6 Problem Solving: Apply the Greatest Common Factor Add and Subtract Decimals 6.NS.4 MP.1, MP.4, MP.5, MP.6 6.NS.3 MP.2, MP.6, MP.7 Cooperative Learning Role Cards How can you use the strategy draw a diagram to help you solve problems involving the CGF and the Distributive property? Apply GCF and the Distributive Property to solve problems. How do you add and subtract multi-digit decimals? Review addition and subtraction of decimals (NBT 5.4). Use estimation and the inverse operation to check reasonableness of answers. 6.NS.3 MP.1, MP.2, MP.3, MP.6, MP.7, MP.8 How do you multiply multidigit decimals? Extend understanding of multiplication of whole numbers to decimals. Model decimal division using base-ten blocks. Extend understanding of division of whole numbers to decimals. 1.7 Multiply Decimals 1.8 Divide Decimals by Whole Numbers 6.NS.3 MP.1, MP.2, MP.6 How do you divide decimals by whole numbers? 1.9 Divide with Decimals 6.NS.3 MP.1, MP.2, MP.8 How do you divide whole numbers and decimals by decimals? Cooperative Learning Extend the pattern of division by powers of ten. Base Ten 15x20; Base Ten 50x70; Ladder Diagram Decimal Models Decimal Place Value Chart Digit Tiles Base-Ten Blocks Decimal Models Decimal Place Value Chart Decimal Place Value Chart Base Ten 15x20; Base Ten 50x70; Decimal Place Value Chart Digit Tiles DRAFT Review the Distributive Property by writing (4 x 5) + (4 x 7) = 4 (5 + ___) Associative Property of Addition, Greatest Common Factor Collaborative Learning Table Mats Seating Chart Suggestions Vocabulary Strategy: Have students work in pairs to complete a word map for key terms. Write a problem in which you need to put as many of 2 different types of objects as possible into equal groups. Then use the GCF, Distributive property, and a diagram to solve your problem. Project a menu and have students buy 2-3 side dishes with $20. tenths, hundredths, thousandths, difference, sum, order of operations Write a word problem that involves adding or subtracting decimals. Include the solution. 6 x 5, 6 x 0.5, 0.6 x 5, .06 x 5, 0.6 x 0.5 tenths, hundredths, thousandths regroup, ones, tens, hundreds, product, order of operations 54 ÷ 6, 5.4 ÷ 6, 0.54 ÷ 6 tenths, hundredths, thousandths difference, subtract, quotient, average Have students work in pairs. One student holds up a vocabulary card; the other draws or writes an example for that term. Explain the importance of correctly placing the decimal point in the quotient of a division problem. Present problem on bottom left pg. 39A compatible numbers, divisor, quotient, order of operations Model: Have students model decimals using decimal place value mats, base ten blocks and/or decimal models. Explain how dividing by a decimal is different from dividing by a whole number and how it is similar. Explain how to mentally multiply a decimal number by 100. Literacy Connection: Have students create real world problems for which you could use compatible numbers to estimate 23,881 ÷ 54. Literature Connection Grab & Go: A Drive Through History Read about how the Alvarez family uses multiplication and division to plan their vacation. Have students color code parts of a division problem (quotient, remainder, dividend, and divisor). Give it a context and have students discuss what each part means in context. DRAFT Literature Grab & Go: Fabulous Fibonacci Numbers; Halfpipe Have students read about adding and subtracting decimals to rank snowboarders in a competition. Modeling: Use a decimal place value chart and/or base ten blocks to add and subtract decimals. Modeling: Use Base Ten Blocks to model Decimal Division. Literature Connection Grab & Go: A Peek into a Tiny World Students using a stage micrometer to make measurements of tiny creatures. DRAFT Math Talk Frames: Restate/Repeat • I just heard you say _________. • Did you mean __________? • Let me see if I heard you correctly, you said _______. • If I understand you correctly, you believe ______. • It sounds like you think that____. Agree/Disagree • I agree with (name), when he/she said that ______. • I agree with (name), and the reason is because ____. • If ____, then ____ must also be true. • I disagree with (name) because _______. Elaboration • Since ______ then_____. • An example might be _________. • I previously learned ______, and it supports _________. • If _____, then_____. • Another example of this is ______. Add-on • In addition to what has been stated, I think ________. DRAFT • I would add that ________ based On _____ (evidence). • What I just heard makes me think of __________. • Building on what I heard, I think _____. Connections • Similarly to ______, I think ____. • Both examples show_____. • This is similar to ______. • The first example shows ____, this is different than _____. • In the same way, __________. • ______ is like _________. • I think that _____ is like ______. Call to Action • Based on what we just learned, I think we should _________. • What can we do about _______? • I believe it is important for us to _______. • Considering the evidence, we should ______. Assessments: Go Math Prerequisite Skills Inventory Go Math Chapter 1 Test Go Math Chapter 1 Performance Task: Orchestra Outing Portfolio Assessment DRAFT Grade 6 Go Math! Quarterly Planner 15 Days Chapter 2 Fractions Big idea: Students use visual fraction models and equations to divide whole umber by fractions and fractions by fractions. 6th graders interpret the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Essential Question: How can you use the relationship between multiplication and division to divide fractions? Standards: 6.NS.6c, 6.NS.4, 6.NS.1 Math Practice Standards Emphasized: MP 7 - Look for and make use of structure ELD Standards: ELD.PI.6.1-Exchanging information/ideas via oral communication and conversations. ELD.PI.6.9- Expressing information and ideas in oral presentations. ELD.PI.6.3-Offering opinions and negotiating with/persuading others. ELD.PI.6.11- Supporting opinions or justifying arguments and evaluating others’ opinions or arguments. ELD.P1.6.5-Listening actively and asking/answering questions about what was heard. ELD.PI.6.12-Selecting and applying varied and precise vocabulary. Lesson Standards & Math Practices Essential Question Math Content/Strategies Models/Tools Go Math! Teacher Resources G6 Connections Vocabulary Academic Language Support Cognates: 6.NS.6c MP.2, MP.4 How can you convert between fractions and decimals? Convert fractions to decimals using long division. Decimal Models Relating Fractions Create list of words that describe 0.5, 0.75. 0.43, 1.60 terminating, repeating decimals, simplest form 2.2 Compare and Order Fractions and Decimals 6.NS.6c MP.4, MP.5 How can you compare and order fractions and decimals? Use number lines to understand benchmark fractions, convert fractions to decimals to compare on a decimal number line. Decimal Models Fraction Tiles Fraction Number Lines Fraction # Line Templates See pg. 55A, Using a Number Line to Compare numerator, denominator, equivalent fractions 2.3 Multiply Fractions 6.NS.4 MP.2, MP.6 How do you multiply fractions? Review multiplication of fractions (NBT 5.45.6). Use GCF to simplify. Fraction Area Squares 2.4 Simplify Factors 6.NS.4 MP.3, MP.6 How do you simplify fractions by using the GCF? Extend understanding of simplifying fractions to simplify prior to multiplication. 6.NS.1 MP.1, MP.4, MP.5 How can you use a model to show division of fractions? Use fraction strips to represent 1 whole, as well as, the divisor and the quotient 6.NS.1 MP.1 How can you use compatible numbers to estimate quotients of fractions and mixed numbers? 2.1 Fractions and Decimals 2.5 2.6 Investigate Model Fraction Division Estimate Quotients Understand using compatible numbers as a strategy to check the reasonableness of answers when dividing fractions. Fraction Tiles Color Multiplication Table Ladder Diagram Fraction Strips, Legos, Fraction Tiles Color, Fractions Seeing Division Fraction # Line Templates Fraction Strips, Legos, Pattern Blocks, Number Lines, Fraction Tiles Color DRAFT See POD 2.3, pg. 59B and Fluency Builder See pg. 63A, Teaching for Depth Use fraction strips or pattern blocks to show 2÷1/3, 5/6÷1/6, 2/3÷1/6 See pg. 73A, Teaching for Depth, estimating using benchmarks and the number line. simplest form, order of operations, simplify, product, GCF, numerators, factors fraction models compatible numbers, quotient, possible estimates Modeling: Have student use fraction strips or pattern blacks to model operations with fractions. Language Objective: Have students write a note to an absent classmate to answer the essential question. Literacy Connection: Have students write a story in which the main character needs to plant trees by order of height. Modeling: Use number lines to order and compare fractions and decimals. EL Strategy: Have students write 20 Journal Write an example of a fraction that is a terminating decimal and a fraction that is a repeating decimal. Explain how you know your examples are terminating or repeating. Explain how you would compare the numbers 0.4 and 3/8. Write and solve a word problem that involves multiplying by a fraction. Show 2 ways to multiply 2/15 x 3/20. Then tell which way is easier and justify your choice. Explain how to use a model to show 2/6 ÷ 1/12 and 2/6 ÷ 4. How is estimating quotients different from estimating products? 2.7 Divide Fractions 2.8 Investigate Model Mixed Number Division 2.9 Divide Mixed Numbers 2.10 Problem Solving - Fraction Operations Extend strategies for dividing fractions to include using a number line or reciprocals and inverse operations. 6.NS.1 MP.1, MP.7, MP.8 How do you divide fractions? 6.NS.1 MP.2, MP.4, MP.5 How can you use a model to show division of mixed numbers? Use pattern blocks and bar models/tape diagrams to model division of mixed numbers. 6.NS.1 MP.1, MP.6 How do you divide mixed numbers? Review strategies of converting mixed numbers and division of fractions to extend to division of mixed numbers. 6.NS.1 MP.1, MP.2 How can you use the strategy use a model to help you solve a division problem? Use a model (bar model/tape diagram) to divide fractions to solve a problem. Fraction Strips, Legos, Pattern Blocks, Number Lines, Fraction Tiles Color Pattern Blocks, Bar Models/Tape Diagrams, Number Lines, Fraction Tiles Color Fraction Strips, Pattern Blocks, Number Lines, Fraction Tiles Color Bar Models/Tape Diagrams Use pattern blocks or Legos to solve 1÷6, 1/2÷6,1/3÷6 reciprocal, multiplicative inverse Use patterns blocks to model 2 1/2÷1/6. Then do it with a number line, bar model Mixed number, quotient, whole numbers Use fraction strips to show 3 1/4÷1/2 Mixed numbers, quotient, simplest form See About the Math, pg. 89A and POD 2.10, p. 89B model, equivalent different fractions on index cards and the symbols < and >. Have students create inequalities using the cards in pairs and read them to each other. Modeling: Use fraction strips or pattern blocks to model division of fractions. Write a word problem that involves dividing a mixed number by a whole number. Solve the problem and describe how you found the answer. Explain how you would find how many 1 ½ cup servings there are in a pot that contains 22 ½ cups of soup. Vocabulary Builder: Graphic Organizer Literature Connection Grab & Go: Fair Share DRAFT Write a word problem that involves 2 fractions. Include the solution. Explain how to draw a model that represents (1 ¼ - ½)÷1/8 Modeling: Use number lines to model division of fractions. 2/5 ÷ 4 = Vocabulary Builder: Word Definition Map Assessments: Go Math Chapter 2 Go Math Chapter 2 Performance Task: Clock Fractions DRAFT Grade 6 Go Math! Quarterly Planner 13-14 Days Chapter 3 Rational Numbers Big idea: At this level, students use fractions, decimals, and integers to represent real-world situations. They extend the number line to represent all rational numbers and recognize that number lines may be either horizontal or vertical which helps 6th graders move from number lines to coordinate grids. The focus is to learn about negative numbers, their relationship to positive numbers, and the meaning and uses of absolute value. This is the foundation for working with rational numbers, algebraic expressions and equations, functions, and the coordinate plane in 7th and 8th grades. Essential Question: How do you write, interpret, and use rational numbers? Standards: 6.NS.5, 6.NS.7a, 6.NS.6a, 6.NS.7a, 6.NS.7c, 6.NS.7d, 6.NS.6c, 6.NS.6b Emphasized Math Practice Standard: MP 5 - Use appropriate tools strategically ELD Standards: ELD.PI.6.1-Exchanging information/ideas via oral communication and conversations. ELD.PI.6.9- Expressing information and ideas in oral presentations. ELD.PI.6.3-Offering opinions and negotiating with/persuading others. ELD.PI.6.11- Supporting opinions or justifying arguments and evaluating others’ opinions or arguments. ELD.P1.6.5-Listening actively and asking/answering questions about what was heard. ELD.PI.6.12-Selecting and applying varied and precise vocabulary. Lesson How can you use positive and negative numbers to represent real world quantities? How can you compare and order integers? Understand the meaning of 0 in real world situations. Understand positive and negative numbers as quantities from 0.. Models/Tools Go Math! Teacher Resources G6 Integer # Line Integer # Line 2 Integer Mat Compare and order fractions by using their relative position on a number line. Understand that numbers become greater as you move right on a horizontal number line or up on a vertical number line. How can you plot rational numbers on a number line? Understand a rational number as a point on a number line. Recognize that numbers with opposite signs have locations on opposite sides of 0. 6.NS.7a, 6.NS.7b MP1, MP.5 How can you compare and order rational numbers? Understand how to change fractions and decimals to the same form and plot on a number line to use to order from least to greatest. Number Line Present stats from football game…yards lost, gained, or $$ debit/credit 6.NS.7c MP.2, MP.3, MP.4, MP.8 How can you find and interpret the absolute value Understand absolute value as the distance from 0. Number Line Present real-world scenarios: Cecily has -30 dollars in her account. Explain what that means. Standards & Math Practices 3.1 Understand Positive and Negative Numbers 6.NS.5, 6.NS.6a MP.5, MP.6, MP.7 3.2 How can you compare and order integers? 6.NS.7a, 6.NS.7b MP.5, MP.8 3.3 Rational Numbers and the Number Line 6.NS.6a, 6.NS.6c MP.2, MP.4, MP.7 3.4 Compare and Order Rational Numbers 3.5 Absolute Value Essential Question Math Content/Strategies Connections Vocabulary Explore real-world situations: bank accounts, temperature, sea level, football yardage integers, opposites, situation, number line, distance Integer # Line Integer # Line 2 Thermometer, checkbooks, sports page Use number lines, thermometers, and checkbooks to focus on ordering and inequalities. absolute value, temperatures, from least to greatest, vertical number line, integers Integer # Line Integer # Line 2 Thermometer Locate integers on horizontal and vertical number lines depending on context rational number, absolute value, temperatures, from least to greatest, vertical number line, integers, magnitude Common denominators, elevations, absolute value, vertical number line, integers magnitude, absolute value, number line DRAFT Academic Language Support Math Talk: Generate examples of positive and negative numbers as a class and record them on a two column sheet. Examples: a loss of 3 yards, climbing 5 feet, taking three steps back, receiving 4 dollars. Have students take turns generating a real world context where the partner identifies the integer being referenced. Journal Give 3 examples of when negative numbers are used in daily life. Explain how to use a number line to compare 2 negative integers. Give an example. Modeling: Use a number line to discuss negative and positive numbers as opposites. Describe how to plot -3 ¾ on a number line. Math Talk: Have each student 4 cards and have them write a positive integer on one card with a matching situation and a negative integer on the third card with a matching situation. Have students take turns flipping the cards to match the integers with the situations. Describe 2 situations in which it would be helpful to compare or order positive and negative rational numbers. Write 2 different real-world examples. One should involve the absolute value of a positive number, and the other should 3.6 3.7 Compare Absolute Value 6.NS.7d MP.1, MP.2 Rational Numbers and the Coordinate Plane 6.NS.6c MP.6, MP.8 3.8 Ordered Pair Relationships 6.NS.6b MP.4, MP.7 3.9 Distance on the Coordinate Plane 6.NS.8 MP.1, MP.5, MP.8 3.10 Problem Solving • The Coordinate Plane 6.NS.8 MP.1, MP.5, MP.6 of rational numbers? How can you interpret comparisons involving absolute value? How do you plot ordered pairs of rational numbers on a coordinate plane? How can you identify the relationship between points on a coordinate plane? How can you find the distance between two points that lie on a horizontal or vertical line on a coordinate plane? How can you use the strategy draw a diagram to help you solve a problem on a coordinate plane? Understand absolute value as the distance from 0. Determine absolute values in real life situations and use absolute values to compare which is greater. Understand the order of (x, y) coordinates in an ordered pair. Use the ordered pair to move the given distance and plot on a coordinate plane. Coordinate Plane Coordinate Plane See About the Math, pg. 123A quadrants, line symmetry, line of symmetry See if students can explain the difference between the locations of (3,2), and (2,3); (-3,2) and (-2,3). coordinate plane, xaxis, y-axis, origin, ordered pair, xcoordinate, ycoordinate Recognize the quadrants of a coordinate plane and identify if values will have + or signs in each quadrant. Understand how reflections across and axis affect the signs of the coordinates. Coordinate Plane, Desmos, Graphing Website Plot (3,1), (-3,1), (-3,-1), (3,-1) and discuss how the coordinates change. reflection, quadrants, line symmetry, line of symmetry reflection Use the absolute value to find the distance between two points on a coordinate plane. Use graphing to help understand the position of points in the four quadrants. Coordinate Plane, Desmos Graphing Website See About the Math, p. 135A distance, coordinate plane, coordinates, vertical line, y-axis EL Strategy: Have students draw number lines to illustrate the following: positive, negative, zero, less than <, and greater than >. Modeling: Use number lines to model positive and negative numbers and compare integers. involve the absolute value of a negative number. Give 2 numbers that fit this description: a number is less than another number but has a greater absolute value. Describe how you determined the numbers. Describe how to graph the ordered pair (-1, 4.5). Literature Connection Grab & Go: How much should it Cost? Students read the book and learn about negative integers as Rosa repays a loan from her father. Explain to a new student how a reflection across the y-axis changes the coordinates of the original point. Literature Connection Grab & Go: Searching for a Shipwreck Students read the book and learn how integers can describe the sinking of the Titanic and the discovery of its ruins. Graph the points (-3,3), (-3,7), and (4,3) on a coordinate plane. Explain how to find their distance from (-3,3) to (-3,7) and from (-3,3) and (4,3). Vocabulary Builder: Semantic Mapping Understand a word problem may have multiple pieces of information, including starting point, movements and distances. Use information in the problem to graph positions on a coordinate plane and find the solution to the problem. Maps, Coordinate Plane Assessments: Go Math Chapter 3 Test Go Math Chapter 3 Performance Task: Negative Numbers Through History **Common Assignment Critical Area 1 Performance Assessment The Number System: Math Carnival Critical Area Project 1 The Number System: Sweet Success (See Chapter 1 TE) DRAFT Use a map and create a problem which students can solve. coordinate plane, graph the location, located at Write a problem that can be solved by drawing a diagram on a coordinate plane.