6 th Grade Mathematics Curriculum (Based on the 2010 Common Core Standards) Lambertville Public School (LPS) & West Amwell Township School (WATS)

Transcription

1 6 th Grade Mathematics Curriculum (Based on the 2010 Common Core Standards) Lambertville Public School (LPS) & West Amwell Township School (WATS) Written by Educator: Donna Blum (WATS) Curriculum Supervisors: Deborah Sarmir (WATS) Geoff Hewitt (LPS) Board of Education Approval Date: 1

2 Curriculum Guide Subject: Mathematics Grade Level: Sixth (6 th ) Ratios & Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes. Homeschoolmath.net (tutorials, examples) Mathgoodies.com (webquests) Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Ratio coloring activity: Express ratios and rates in fraction form o Write ratio in simplest form and explain meaning (i.e. compare number of red paper clips to number of blue paper clips) o Use ratios to compare parts to a whole (i.e. create chart to show survey results of favorite gum flavor) 2

3 g_game/ Glencoe McGraw-Hill Math Connects Course 1 Chapter 6 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (concepts in motion, extra examples, personal tutor, self-check quiz) Manipulatives: dice, counters, colored cubes, tangram template, vocabulary cards Ratios & Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. 1 1 Expectations for unit rates in this grade are limited to non-complex fractions. 3

4 Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Ratio coloring activity: g_game/ Express unit rates o Find a unit rate (i.e. write a rate that compares number of miles to number of hours, then divide to find unit rate) Determine if quantities are proportional o Use unit rates to determine if quantities in each pair of rates are proportional (i.e. write each rate as a fraction and find unit rate) o Use equivalent fractions to determine if quantities in each pair of ratios or rates are proportional Solve proportions using equivalent fractions (i.e. 4/7=m/35, find value for m so fractions are equivalent) Make predictions in proportional situations (i.e. write and solve proportion letting p represent number of people who can be expected to prefer eating at a restaurant) Solve proportions using unit rates (i.e. set up proportion, find unit rate, rewrite proportion using unit rate and solve using equivalent fractions) Glencoe McGraw-Hill Math Connects Course 1 Chapter 6 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (concepts in motion, extra examples, personal tutor, self-check quiz) Manipulatives: dice, counters, colored cubes, vocabulary cards, graph paper 4

5 Ratios & Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Explore relationship between ratio and area 5

6 Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Ratio coloring activity: g_game/ o Create a tangram using a sheet of paper, following specific steps o Use tangram pieces to determine fractional parts of original large square) Use ratio tables to represent and solve problems involving equivalent ratios o Create ratio tables where columns are filled with pairs of numbers that have the same ratio (i.e. 1 can of concentrate to 3 cans of water, etc.) o Find and extend patterns using ratio tables o Multiply or divide quantities by the same number (scaling) I(i.e. Cans of corn are on sale at 10 for $4. Use ratio table to find cost of 15 cans. Write an equation to describe a proportional situation o Write an equation to represent the function displayed in a table, examine how the value of each input and output changes in order to determine the equation that represents the function. Graph ordered pairs in ratio tables to solve problems o Graph orders pairs from a table and describe pattern in graph o Use order pairs and graphs to compare Solve percent problems involving find the whole or part o Write a proportion to find a part (i.e. What is 80% of 500??/500=80/100) o Write a proportion to find the whole (i.e. 15 is 30% of what number? 15/?=30/100) Express percents as fractions and fractions as 6

7 7 percents o Write a percent as a fraction in simplest form (i.e. 50% means 50 out of 100) o Write a percent as a mixed number in simplest form (i.e. 125% means 125 for every 100) o Write a fraction as a percent using a proportion (i.e. 9/20 = n/100) Estimate the percent of a number o Use a model to find a fractional part of a number o Review commonly used percents and their fraction equivalents o Use proportions or mental math to estimate the percent of a number Change units of length and measure length in the customary system o Review customary units of length o Draw line segments to an eighth of an inch o Use a ratio table and appropriate operation to change units (larger to smaller and smaller to larger Change units of capacity and weight in the customary system o Review customary units of capacity and weight o Use a ratio table and appropriate operation to change units (larger to smaller and smaller to larger Change units with the metric system o Review chart showing relationship between units in metric system and powers of 10 o Review methods for changing units (larger to smaller---multiply, smaller to larger---divide)

8 Glencoe McGraw-Hill Math Connects Course 1 Chapter 6, 7, 8 Glencoe.com (CCSS Lesson 1 Graph Ratio Tables, Lesson 2 Solve Percent Problems) Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (concepts in motion, extra examples, personal tutor, self-check quiz) Manipulatives: dice, counters, colored cubes, vocabulary cards, tangram puzzles, graph paper, rulers The Number System Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Compute fluently with multi-digit numbers and find common factors and multiples. 8

9 Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Find the Greatest Common Factor of two or more numbers o List factors of sets of numbers in order to identify common factors o List common factors of numbers in order to identify GCF o Find the GCF using prime factorization Find the Least Common Multiple of two or more numbers o List multiples of sets of numbers in order to identify common multiples o List common multiples of numbers in order to identify LCM Divide Fractions and Mixed Numbers o Find reciprocals of whole numbers and fractions o Review how to divide fractions by multiplying by its reciprocal o Write mixed numbers as improper fractions in order to divide/multiply by reciprocal Glencoe McGraw-Hill Math Connects Course 1 Chapter 4, 5 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (concepts in motion, extra examples, personal tutor, self-check quiz) Manipulatives: dice, counters, colored cubes, vocabulary cards, fraction cards 9

10 The Number System Compute fluently with multi-digit numbers and find common factors and multiples. 6.NS.2. Fluently divide multi-digit numbers using the standard algorithm. Hands-On Activity (Hand students play money and separate it so each has same amount. Have students write equations to show what they did. Multiply and divide whole numbers o Show all steps in order to multiply 2 and 3 digit numbers (76x8, 535x24) o Use long division to divide each place-value position from left to right, showing quotient and remainder 10

11 Scaffolding (Write a long division problem on board. Ask: What is quotient? What is estimate? What method did you use? Glencoe McGraw-Hill Math Connects Course 1 Concepts and Skills Bank 6 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: play money, vocabulary cards The Number System Compute fluently with multi-digit numbers and find common factors and multiples. 6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 11

12 Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Add and subtract decimals o Find estimates, sums, or differences by lining up decimals points o Evaluate expressions using given decimals (a=2.56, b= 28.96) o Use addition and subtraction to solve word problems involving decimals Estimate and find products of decimals and whole numbers o Round decimals to whole numbers to estimate products o Multiply and count decimal places from the right to show products o Annex (add) zeros to make needed decimals places o Evaluate expressions using given decimals o Use multiplication to solve word problems involving decimals Divide decimals by whole numbers and by decimals o Divide a decimal by a 1-digit number by placing the decimal point directly above the decimal in the dividend o Divide a decimal by a 2-digit number by placing the decimal point and annexing a zero (i.e become ) and rounding the quotient to a specified place-value position if necessary o Divide decimals by decimals by multiplying the divisor and dividend by the same power of 10 to make the divisor a whole number (i.e becomes

13 Glencoe McGraw-Hill Math Connects Course 1 Chapter 3 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: dice, counters, colored cubes, Base-10 blocks, vocabulary cards The Number System Compute fluently with multi-digit numbers and find common factors and multiples. 6.NS.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4 (9 + 2). Model the distributive property 13

14 Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) o Find areas of given rectangles by adding lengths and multiplying (i.e. a 5x8 rectangle and a 5x4 rectangle becomes 5(8+4)=5(12)=60 o Find areas of given rectangles by adding each separately then adding (5x8 + 5x4)=40+20=60 o Draw models to match equations Use the distributive property to compute multiplication problems mentally and to rewrite algebraic expressions o Find products mentally using the Distributive Property (i.e. 7x62 = 7(60+2) = 7(60) + 7(2) o Rewrite algebraic expressions (i.e. 2(x+3) =2(x) + 2(3)= 2x+6 Apply the Distributive Property to solve word problems o Use the multiply then add strategy or the add then multiply strategy Use the Commutative and Associative Properties to simplify expressions o Review Commutative and Associative Properties with words and examples o Simplify expressions using properties or models Solve word problems using appropriate properties and/or models Use the distributive property to find factors of numeric and algebraic expressions o Find prime factorization of sets of numbers o Use distributive property to factor out the GCF (12+18 = 6(2) + 6(3) = 6(2+3) Use algebra tiles to factor expressions 14

15 o 2x+8 (arrange tiles of X, X, 1, 1, 1, 1, 1, 1, 1, 1 into a rectangle of equal rows and columns, total area of rectangle represents the product Glencoe McGraw-Hill Math Connects Course 1 Chapter 12 Glencoe.com (CCSS Lesson 3 Extend: Factoring) Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: dice, counters, colored cubes, algebra tiles, vocabulary cards The Number System Apply and extend previous understandings of numbers to the system of rational numbers. 6.NS.5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 15

16 Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Use integers to represent real-world data o Review positive and negative integers o Graph integers on a number line o Create line plots of data involving positive and negative integers Glencoe McGraw-Hill Math Connects Course 1 Chapter 2 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: integer tiles, vocabulary cards 16

17 The Number System Apply and extend previous understandings of numbers to the system of rational numbers. 6.NS.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., ( 3) = 3, and that 0 is its own opposite. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane Homeschoolmath.net (tutorials, examples) Mathgoodies.com Compare and order integers o Graph integers on a number line o Order sets of integers (least to greatest, greatest to least) Locate and graph ordered pairs on a coordinate plane Model, compare, and order negative fractions and decimals o Use models (fraction strips) to graph rational 17

18 Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) numbers on a number line o Use number lines to compare and order negative rational numbers Determine the absolute value of rational numbers o Evaluate expressions with absolute value (distance number is from zero on number line) Glencoe McGraw-Hill Math Connects Course 1 Chapter 11, Look Ahead 1 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: integer tiles, graph paper, fraction strips, vocabulary cards The Number System Apply and extend previous understandings of numbers to the system of rational numbers. 6.NS.7. Understand ordering and absolute value of rational numbers. Interpret statements of inequality as statements about the relative position of two numbers on a number line 18

19 diagram. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write 3 o C > 7 o C to express the fact that 3 o C is warmer than 7 o C. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars. Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Compare and order decimals o Use greater than and less than symbols to write an equality (mathematical sentence indicating that two quantities are not equal) o Order decimals (least to greatest and greatest to least) Compare and order fractions o Compare fractions and mixed numbers using models (fraction strips) or the least common denominator o Order fractions (least to greatest and greatest to least) Glencoe McGraw-Hill Math Connects Course 1 Chapter 3,4 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: Base-10 blocks, decimal place-value charts, vocabulary cards 19

20 The Number System Apply and extend previous understandings of numbers to the system of rational numbers. 6.NS.8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Homeschoolmath.net (tutorials, examples) Use ordered pairs to locate points and organize data o Review that the coordinate plane is formed when two number lines (x-axis an y-axis) interest at an origin (zero) o Name points using ordered pairs o Graph ordered pairs and label points Find the distance between two points with the same 20

21 Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) first or second coordinate o Find distances between pairs of points ***If X-coordinates are the same, subtract y- coordinates. ***If y-coordinates are the same, subtract x- coordinates. Glencoe McGraw-Hill Math Connects Course 1 and Chapter 4 Glencoe.com (CCSS Lesson 4 Extend: Distance on the Coordinate Plane) Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: graph paper, coordinate grids, rulers, vocabulary cards Expressions & Equations Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.1. Write and evaluate numerical expressions involving whole-number exponents. 21

22 Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Use powers and exponents in expressions o Write a product of identical factors using an exponent (how many times base is used as a factor) and a base ((number used as a factor) o Write powers (numbers expressed using exponents) and products o Write powers as a product of the same factor and find the value (i.e. 2 3 = 2x2x2 = 8 Write prime factorization of numbers using exponents (72=2x2x2x3x3 = 2 3 x 3 2 ) Find the value of expressions using the order of operations o Review order of operations (parentheses, exponents, multiply, divide, add, subtract) Write numerical expressions for verbal expressions and find values (i.e. the product of 7 and 6, minus 2 becomes 7x6-2=40) Glencoe McGraw-Hill Math Connects Course 1 Chapter 1 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: Order of Operations chart, vocabulary cards 22

23 Expressions & Equations Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.2. Write, read, and evaluate expressions in which letters stand for numbers. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s 3 and A = 6 s 2 to find the volume and surface area of a cube with sides of length s = 1/2. Complete function tables and find function rules (relationship between each input and output) Write verbal phrases as simple algebraic expressions o Describe situation, define variables, write expression (i.e. total cost of shirt and $8 pair of 23

24 Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) socks becomes s + 8) Write 2-step expressions (i.e. 2 bottles of nail polish and a $5 magazine becomes 2d + 5) Find the prime factorization of a composite number o Identify numbers as prime, composite, or neither Use powers and exponents in expressions Evaluate algebraic expressions (combinations of variables, numbers, at least one operation) Use the Commutative and Associative properties to simplify expressions o Review commutative and associative properties o Use properties to simplify expressions (i.e. (14+x) + 22=(x+14) + 22 commutative = x + (14+22) associative = x + 36 add 14 and 22 o Use models to simplify expressions (i.e. 2x+4+3x use 2 x-tiles to model 2x, 4 1-tiles to model 4, and 3 x-tiles to model 3x so it becomes 5x + 4 Find the areas of rectangles and squares Extend and describe arithmetic sequences (term found by adding the same number to the previous term) using algebraic expressions o Describe sequences by using words and symbols and find values of given terms (i.e. position n Value of term Notice the value of each term is 3 times its number position, so the value of the term in position n is 3n 24

25 Find the areas of parallelograms(a=bh) Find the areas of triangles (A=1/2bh) Find the volume (amount of space inside a threedimensional figure) of rectangular prisms (V=lwh) Glencoe McGraw-Hill Math Connects Course 1 Chapter 1, 6, 10, 12 Glencoe.com (CCSS Lesson 5 Algebra: Write Expressions) Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: algebra tiles, polygons, centimeter cubes, three-dimensional shapes (cubes and rectangular prisms), graph paper, rulers, index cards, vocabulary cards Expressions & Equations Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.3. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the 25

26 expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Review how to use the Commutative and Associative Properties to simplify expressions Use understanding of multiplication to interpret 3(2 + x) o Use a model to represent x and make an array using algebra tiles to show meaning of 3(2+x) so it becomes 6 + 3x Glencoe McGraw-Hill Math Connects Course 1 Chapter 12 Glencoe.com (CCSS Lesson 3 Extend Factoring) Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: algebra tiles, vocabulary cards 26

27 Expressions & Equations Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Find and identify equivalent forms of whole numbers and write expressions in various forms o Form equivalent expressions using the associative, commutative, and distributive properties o Simply expressions into the same form (i.e. 3m+8+m becomes 4m+8) 27

28 Glencoe McGraw-Hill Math Connects Course 1 Chapter 12 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: algebra tiles, vocabulary cards Expressions & Equations Reason about and solve one-variable equations and inequalities. 6.EE.5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Solve equations (sentences containing equal signs) by using mental math and the guess and check 28

29 Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) strategy o Use centimeter cubes and a paper bag on a balance to model equations (let x represent the bag, find the number of cubes needed to balance the scale) Find solutions of inequalities by using mental math or the guess, check, revise strategy (i.e. write inequality, replace, simplify x+ 3 > 9, x=4 7 is not greater than 9 Glencoe McGraw-Hill Math Connects Course 1 Chapter 1, 12 Glencoe.com (CCSS Lessons 6 Inequalities) Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: algebra tiles, centimeter cubes, paper bags, vocabulary cards 29

30 Expressions & Equations Reason about and solve one-variable equations and inequalities. 6.EE.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Write expressions with word problems or drawings showing that variables represent numbers (i.e. Maria has 3 more than twice as many crayons as Elizabeth. Write an algebraic expression to represent the number of crayons Maria has. Solution: 2c+3, where c represents Elizabeth s crayons) Glencoe McGraw-Hill Math Connects Course 1 Chapter 1, 6 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: algebra tiles, centimeter cubes, paper bags, vocabulary cards 30

31 Expressions & Equations Reason about and solve one-variable equations and inequalities. 6.EE.7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Homeschoolmath.net (tutorials, examples) Mathgoodies.com Write equations to describe proportional situations o Write equations to represent functions displayed in tables (i.e. Examine how value of each input and output changes. Each output y is equal to 9 times the input x, so the equation that represents the function is y=9x. Input x, Output y, Solve addition equations 31

32 Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) o Solve equations by subtracting using models (counters) or symbols o Solve equations using zero pairs using models (counters) or symbols (i.e. b+5 = 2-5 = 5 b = 3 Check: b+5=2-3+5=2 2=2 Solve subtraction equations o Solve equations by adding using models (counters) or symbols o Review addition property of equality (if you add same number to each side, two sides remain equal) x-2 = 3 +2=+2 x = 5 Glencoe McGraw-Hill Math Connects Course 1 Chapter 1, 6, 12 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: counters, vocabulary cards 32

33 Expressions & Equations Reason about and solve one-variable equations and inequalities. 6.EE.8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Glencoe.com (CCSS Lesson 7 Write and Graph Inequalities) Write and graph inequalities o Write inequalities for sentences using < or > signs (i.e. words to variable to inequality Your age is at least 16 years Let a = your age a < 16 o Graph inequalities on a number line by using a dot an arrow 33

34 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: graph paper, rulers, vocabulary cards Expressions & Equations Represent and analyze quantitative relationships between dependent and independent variables. 6.EE.9.Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Use many forms to represent relationships between 34

35 Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) quantities (Each form represents the same relationship and provides a different perspective on the function.) o Describe a relationship using words, tables, equations, or graphs (i.e. What is the relationship between the two variables? Write an expression. X Y Use a coordinate grid to describe the change in y as the x increases by 1. Glencoe McGraw-Hill Math Connects Course 1 Chapter 1, 6 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: graph paper, coordinate grid, rulers, vocabulary cards 35

36 Geometry Solve real-world and mathematical problems involving area, surface area, and volume. 6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Find areas of parallelograms Find areas of triangles Find perimeters and areas of composite (made of triangles, squares, rectangles, etc) and irregular figures o Find sum of side lengths around composite figure to find perimeter o To find area of composite figure, separate figure into figures with areas known how to find. Then add areas. o Use graph paper to find area and perimeter of irregular figures (each square on grid represents 1 square foot), count squares to estimate perimeter and area Glencoe McGraw-Hill Math Connects Course 1 Chapter 10, Concept and Skills Bank 13 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: polygons, graph paper, rulers, vocabulary cards 36

37 Geometry Solve real-world and mathematical problems involving area, surface area, and volume. 6.G.2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Find volume of rectangular prisms Measure volume by filling rectangular prisms with blocks o Look at relationship between total volume and area of base (see Cubes Tool on NCTM s Iluminations: 37

38 Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) =6 Glencoe McGraw-Hill Math Connects Course 1 Chapter 10 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: three-dimensional shapes (cubes and rectangular prisms), centimeter cubes, graph paper, rulers, vocabulary cards Geometry Solve real-world and mathematical problems involving area, surface area, and volume. 38

39 6.G.3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Homeschoolmath.net (tutorials, examples) Mathgoodies.com Fun With Dimensional Analysis (alysion.org/dimensional/fun.htm) Draw polygons in the coordinate plane and use coordinates to find length o Use geo boards and coordinate planes to plot points and describe locations o Graph and classify figures on a geo board or on a coordinate plane o Use coordinates to find lengths in order to find perimeter and area Glencoe.com (CCSS Lesson 8 Polygons on the Coordinate Plane) Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: graph paper, coordinate grid, polygons, geo boards, rulers, vocabulary cards 39

40 Geometry Solve real-world and mathematical problems involving area, surface area, and volume. 6.G.4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Math-play.com (games) Find the surface areas of rectangular prisms Review the formula using a model (S=2lw+2lh+2wh) Construct models and nets of three-dimensional figures describing edges, vertices, and faces (rectangular and triangular prisms) o (see dynamic Paper Tool on NCTM s Iluminations: Create nets for prisms and pyramids and use net to calculate surface area Glencoe McGraw-Hill Math Connects Course 1 Chapter 10 Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check 40

41 quiz) Manipulatives: three-dimensional shapes (cubes, pyramids, prisms), centimeter cubes, graph paper, coordinate grid, rulers, vocabulary cards Statistics & Probability Develop understanding of statistical variability. 6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, How old am I? is not a statistical question, but How old are the students in my school? is a statistical question because one anticipates variability in students ages. Recognize statistical questions as anticipating and accounting for a variety of answers o Differentiate between statistical and not statistical questions 41

42 Math-play.com (games) o Survey classmates and record results in a table in order to analyze results Glencoe.com (CCSS Lesson 9 Explore: Statistical Questions) Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: vocabulary cards Statistics & Probability Develop understanding of statistical variability. 6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described 42

43 by its center, spread, and overall shape. Math-play.com (games) Display, analyze, and interpret data using line plots o Make line plots of data o Analyze line plots Display and interpret data in box-and-whisker plots (diagram that is constructed using median, quartiles, and extreme values) o Order data and draw a number line to show range o Mark median, extremes, and upper and lower quartiles o Draw box so it includes quartile values, draw vertical line through box at median, extend whiskers from quartiles to extreme data points Display and interpret data in double box-and-whisker plots (2 diagrams that are constructed using median, quartiles, and extreme values) in order to compare and contrast range and variance Glencoe McGraw-Hill Math Connects Course 1 Chapter 2 Glencoe.com (CCSS Lesson 11 Box and Whisker Plots) Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: graph paper, rulers, vocabulary cards 43

44 Statistics & Probability Develop understanding of statistical variability. 6.SP.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Math-play.com (games) Glencoe McGraw-Hill Math Connects Course 1 Chapter 2 Find the mean in a set of data o Determine how outliers affect the mean Find and interpret median, mode, and range of a set of data Find the measures of variation in a set of data o Describe measures of variation (upper and lower quartiles, interquartile range, range o Find outliers in a set of data o Analyze data in a table in order to compare and contrast measures of variation 44

45 Glencoe.com (CCSS Lesson 10 Measures of Variation) Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: graph paper, centimeter cubes, counters, rulers, vocabulary cards Statistics & Probability Summarize and describe distributions. 6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Display and interpret data in box-and-whisker plots (diagram that is constructed using median, quartiles, and extreme values) o Order data and draw a number line to show range o Mark median, extremes, and upper and lower 45

46 Math-play.com (games) quartiles o Draw box so it includes quartile values, draw vertical line through box at median, extend whiskers from quartiles to extreme data points Display and interpret data in double box-and-whisker plots (2 diagrams that are constructed using median, quartiles, and extreme values) in order to compare and contrast range and variance Collect, organize, analyze, and display data to solve problems with histograms, and use data displays to show frequency distribution o Draw histograms to represent sets of data o Analyze histograms to compare and contrast data Glencoe McGraw-Hill Math Connects Course 1 Looking Ahead 6 Histograms Glencoe.com (CCSS Lesson 11 Box and Whisker Plots) Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: graph paper, rulers, vocabulary cards 46

47 Statistics & Probability Summarize and describe distributions. 6.SP.5. Summarize numerical data sets in relation to their context, such as by: Reporting the number of observations. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Math-play.com (games) Select an appropriate display for a set of data o Choose displays based on type of data and what you want to show Select appropriate units and tools to measure objects or activities o Discuss attributes (characteristics of an object) in order to measure attributes of objects or activities o Select objects and activities and list measurable attributes o Measure and record attributes in a table Find and interpret the mean absolute deviation (average distance between each data value and the 47

48 mean) for a set of data o Find mean o Find distance between each data value and mean o Find average of distances o Compare variation In sets of data Describe a data distribution by its center, spread (variation), and overall shape o Use clusters, gaps, peaks, outliers, and symmetry to describe shape of data o Choose appropriate measures to describe shape of distribution Glencoe McGraw-Hill Math Connects Course 1 Chapter 2, 8 Glencoe.com (CCSS Lesson 12 Mean Absolute Deviation, Lesson 13 Shape of Data Distribution) Technology Supplies: Calculators, SMART Board, ipad, glencoe.com (extra examples, personal tutor, self-check quiz) Manipulatives: graph paper, rulers, tape measures, yardsticks, balance scales, measuring cups, thermometers, vocabulary cards 48

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