Math 6 Curriculum - oldsite.cambridgecsd.orgoldsite.cambridgecsd.org/Cambridge CCS Virtual Learning...

Cambridge Elementary Curriculum Guide

Math 6 Curriculum LESSON 1 (text 1-1): Place Value to the Trillions Place Standard 6.N.1 Objective read and write numbers to trillions in standard, expanded and word form and give the value of specified digits Vocabulary standard form, word form, short-word form, expanded form Materials place value chart to trillions Additional resources Examples 1. Write the place value for each underlined digit: 4,536,021,985. 2. Write 77,537,000,320 in short-word form and expanded form. 3. Write 20,000+5,000+60+2 in word form and in standard form. LESSON 2 (text 1-2): Exponents Standard 6.N.23-25 Objective Write powers as products and evaluate, write expressions in exponential form, and write numbers in expanded form using exponents. Vocabulary exponential form, base, exponent, power, standard form, squared, cubed, expanded form using exponents, algebra Materials Additional Resources Examples 1. Write 6 as a product and then evaluate.

2. Write 15 x 15 x 15 x 15 in exponential form.

3. Write 35, 402 in expanded form using exponents. LESSON 3 (text 1-3 & 1-4): Comparing, Ordering, and Rounding Whole Numbers


Standard 6.N.15 and 6.N.27 Objective Compare and order numbers with the same digits in different places or with the same digits in different places or with many of the same digits, and round whole numbers through ten-millions. Vocabulary Compare, order, round Materials number lines (blank) Additional Resources Examples 1. Use > or < to compare: 5,532 O 5,523

2. Order 35,002,010; 35,001,950; and 35,001,999 from least to greatest.

3. Round each number to the underlined place: 3,101,922 6,498,555 4. Write 2 numbers that would round to 5,600 when rounded to the

nearest hundred. LESSON 4 (text 1-5): Estimating Sums and Differences Standard 6.M.8 Objective Identify rounding, clustering, front-end estimation, and front-end estimation with adjusting as the method to be used, and apply it to estimate the sum or difference of whole numbers. Vocabulary round, front-end estimation, front-end estimation with adjusting, clustering Materials Additional Resources Examples Estimate each answer, and support (justify) the reasonableness of your estimate by explaining the method you used: 1). 668 + 4,329 2) 5,092 – 847 3). 774 + 802 + 815 + 785 + 798 LESSON 5 (text 1-6 & 1-7): Estimating Products and Quotients and Read and Understand Problems Standard 6.M.8 6.PS.3 & 17


Objective Estimate products and quotients with numbers up to ten thousands, and tell what is known and what needs to be determined in given word problems. Vocabulary product, quotient, compatible numbers, range Materials Additional Resources Examples Estimate and explain the method used: 1) 562 x 9,031 2) 638÷72 Read word problems (see p. 21) and tell a) what you know and b) what you are trying to find. LESSON 6 (text 1-8): Order of Operations Standard 6.N.22 Objective Evaluate expressions with three or more numbers, one with an exponent, and with two or more operations. Vocabulary numerical expression, order of operations Materials Chart (see lesson 53) Additional Resources Please Excuse My Dear Aunt Sally Examples Evaluate each expression: 1) 4 + 9 x 6 – 3 2) 62 – (5 x 4)÷ 2

3) Use parenthesis to make each sentence true: 9x3+4=63 200÷ 4x5=10 LESSON 7(text 1-9 & 1-10): Properties of Operations Standard 6.N.2-5


Objective Give missing numbers in equations and expressions and state which property is used. Vocabulary Commutative Properties, Associative Properties, Identity Properties, Multiplication Property of Zero, Distributive Property Materials Additional Resources Examples Find each missing number and tell what property (or properties) is (are) shown.

1. ____x (3x9) = (2x3) x 9 2. 1,588 + ___ = 72 + 1,5888

3. ____ x 85 + 0

4. 9 ( ___ + 7) = 9(80) + 9(7)

LESSON 8 (text 1-11 & 1-12): Mental Math Strategies and Problem Solving Standard 6.PS.3 Objective Mentally evaluate expressions with up to four numbers. Give appropriate strategies for solving word problems. Vocabulary break-apart, compatible numbers, compensation, equal additions, strategy Materials Additional Resources Examples Compute mentally: 1) 20 x 39 x 5 2) 973 – 645 3) 87 + 78 Analyze solutions to problems and name strategy used (see p.37). Choose a strategy to solve word problems and then solve. LESSON 9 (text 1-13): Variables and Expressions Standard 6.A.1-2


Objective Write numerical expressions with variables to represent relations expressed verbally or in written form. Vocabulary Variable, Algebraic Expression, Evaluate, Substitution Materials Additional Resources Examples Write each word or phrase as an algebraic expression: 1) 5 less than k 2) n increased by 7 3) twice b divided by 9 Evaluate each expression for x = 5 4) 45 5) 20x –1 6) x - 19 x LESSON 10 (text 1-14): Properties of Equality Standard 6.A.4 Objective Explain why expressions are or are not equivalent, and give values for variables that make equations true. Vocabulary equation, properties of equality, inverse operations Materials balance scale and centimeter cubes (gram) Additional Resources Examples 1) You know 35+22=57. Does 35+22+63=57+63? Why or Why not? 2) Explain how to get the variable alone in each equation: K-13=25 y =14 7 LESSON 11(text 1-15): Solving Equations with Whole Numbers Standard 6.A.4


Objective Solve one-step equations with one variable. Vocabulary equations, inverse operations, properties of equality, substitute Materials Additional Resources Examples Solve each equation and check your answer: 1) 43 + X = 72 2) y – 17 = 45 3) 3n = 72 LESSON 12 (text 1-16) Evaluate Answers in Problem-Solving Standard 6.PS.22-23 Objective Tell whether and why the work shown for given problems is correct or not. Vocabulary support, reasonableness or a solution Materials Additional Resources Examples For any given problem:

1) Has the question been answered? 2) Does the work match the information in the problem? 3) Are operations correctly used, and are calculations correct? 4) Is the answer reasonable?

LESSON 13 – 14 Review and Assess LESSON 15 (text 2-1 & 2-2) Understanding, Comparing, and Ordering Decimals Standard 6.N.21


Objective Read and write decimals through hundred thousandths, and compare two decimals using >, <, or =; order three or more decimals. Vocabulary decimal, standard form, word form, short-word form, expanded form Materials Place-value chart (decimals) Additional Resources Examples Give the place and value of the 7 in each number: 1) 34.789 2) 0.079 3) 45.62173 Use >, < or = to compare: 4) 1.45 ___ 1.3942 5) 0.001 ___ 0.0019 Order from least to greatest: 1.58, 0.99, 1.4 LESSON 16 (text 2-3 & 2-4) Rounding and Estimating with Decimals Standard 6.M.8 Objective Round decimals to a given place, and estimate sums, differences, products, and quotients of decimals, using rounding or compatible numbers. Vocabulary compatible Materials Additional Resources Examples Estimate each answer: 1) $95.89 + $12.02 2) 70.508 ÷ 8.4 3) 48.52 x 3.9 4) Is 6 or 7 a better estimate for the quotient 35.8 ÷ 5.6? Explain. LESSON 17 (text 2-5): Adding and Subtracting Whole Numbers and Decimals


Standard Objective Add and subtract whole numbers and decimals of varying place values. Vocabulary Annex Materials Additional Resources Examples 1) 16.4 – 3.85 2) 5.83+6.025+13.7 LESSON 18 (text 2-6 & 2-7): Multiplying and Dividing Whole Numbers and Decimals Standard Objective Multiply whole numbers and decimals and divide whole numbers and decimals by a whole number Vocabulary Materials Calculator Additional Resources Examples 1) 6.8 x 2.3 2) 5.68÷8 3) Explain why 0.8 x 0.6≠4.8 LESSON 19 (text 2-8): Interpreting Remainders Standard 6.PS.23 Objective Interpret remainders when solving division problems Vocabulary interpret Materials Additional Resources


LESSON 19 Examples Mrs. Aimi plans to serve 100 hamburgers at the company picnic. How many packages of buns will she need if the buns come in packages of 8? In packages of 12? LESSON 20 (text 2-12 & 2-13): Writing and Solving Equations with Decimals Standard 6.A.3 Objective Solve one-step linear equations involving decimals, and solve word problems by writing and solving equations. Vocabulary inverse operations, properties of equality, equation Materials Additional Resources Examples 1) c + 0.17 = 3 2) 0.03n = 21

3) The number of tomato plants at the nursery is twice the number of broccoli plants. If there are 106 tomato plants, how many broccoli plants are there? Write an equation and solve.

LESSON 21 Review and Assess LESSON 22 (text 3-1 & 3-2): Factors, Multiples, Divisibility; Prime and Composite Numbers Standard Objective Use divisibility rules to determine if one number is divisible by another. Identify numbers as prime or composite, and give the prime factorization for numbers. Vocabulary divisible, multiple, factor, divisor, prime number, composite number, prime factorization Materials Additional Resources


LESSON 22 Examples 1) Tell whether each numbers is divisible by 2, 3, 4, 5, 6, 9, or 10: a) 75 b) 162 2) Tell whether the first number is a multiple of the second: a) 6,005; 5 b) 734; 6 3) Tell whether each number is a prime or composite: a) 87 b) 41 c) 51

4) Write the prime factorization of 63. LESSON 23 (text 3-3 & 3-4): Greatest Common Factor and Least Common Multiple Standard Objective Find common factors and the greatest common factor of numbers, and find common multiples and the least common multiple of numbers. Vocabulary common factor, greatest common factor, prime factorization, common multiple, least common multiple Materials Additional Resources Examples Find the GCF for 1) 12, 21 and 20 18, 72. 3) The GCF of 6 and 24 is 6. Find another pair of numbers in which the lower number of the pair is also the GCF. Find the LCM of 4) 4, 6 5) 3, 13 LESSON 24 (text 3-6 & 3-7): Understanding Fractions and Equivalent Fractions Standard Objective Use fractions to describe fractional parts of regions and sets, and to represent division; and write equivalent fractions and express fractions in lowest terms. Vocabulary fraction, denominator, numerator, equivalent fractions, common factor, least common denominator, greatest common factor, simplest form Materials fraction strips


LESSON 24 Additional Resources Examples 1) Write a fraction for the shaded portion of each picture (see p. 161) 2) Write a division expression for 5 12 3) Write 2 fractions equivalent to 3 4

4)Write 15 and 10 in simplest form 24 35

LESSON 25 (text 3-8): Improper Fractions and Mixed Numbers Standard Objective Write improper fractions as mixed numbers and mixed numbers as improper fractions. Vocabulary proper fraction, improper fraction, mixed number Materials Additional Resources Examples 1) Write 19 as a whole number or mixed number in simplest form. 4 3 2) Write 2 5 as an improper fraction. 3) Write 3 as an improper fraction with a denominator of 5. LESSON 26 (text 3-9): Estimation Fractional Amounts Standard 6.M.8 Objective Estimate fractions using fraction benchmarks. Vocabulary benchmark fraction


LESSON 26 Materials Additional Resources Examples 1) Estimate the shaded part of each picture (see p. 171) 2) Which benchmark fraction is close to 304 ? 416 LESSON 27 (text 3-10): Connecting Fractions and Decimals Standard 6.N.20-21 Objective Identify and write equivalent fractions and decimals. Vocabulary terminating decimal, repeating decimal Materials place value blocks and/or decimal models (teaching tool 8) Additional Resources Examples 1) Write a decimal and a fraction in simplest form for each model (see p. 174) 2) Write 0.08 as a fraction in simplest form. 3) Write 9.15 as a mixed number in simplest form.

4)Write 4 1 as a decimal. 6 LESSON 28 (text 3-5 & 3-12): Problem Solving Strategies Standard 6.PS.14 & 21 Objective Make tables and use them to solve word problems; and solve multiple-step word problem. Vocabulary table, multiple-step


LESSON 28 Materials Additional Resources Examples 1) Make a table to solve the problem: The Skinner family has a savings account for their vacation. They will deposit $175 the first week and continue to deposit money on a weekly basis. Each week they will deposit $15 more than the previous week. How much money will be deposited on the fifth week? What will be the total amount after 5 weeks?

2) A radio station broadcasts a jazz show for 1.25 hours each weekday. On Saturday and Sunday, the jazz show is twice as long. How many hours of jazz does the station broadcast during a 4-week period?

LESSONS 29 – 30 Review and Assess LESSON 31 (text 41 & 42): Adding and Subtracting Fractions with Like and Unlike Denominators Standard 6.N.16 Objective Add and subtract fractions with like denominators; find common denominators for fractions with unlike denominators and find their sums and differences in simplest form. Vocabulary like denominators, common denominator, unlike denominators, least common multiple, least common denominator Materials fraction strips Additional Resources Examples Find each sum or difference and simplify your answer: 1) 6 + 3 2) 11 - 3 3) 5 - 1 4) 7 + 1 15 15 20 20 6 2 8 6 LESSON 32 (text 4-4): Estimation Sums and Differences of Fractions and Mixed Numbers Standard 6.M.8


LESSON 32 Objective Estimate sums and differences of fractions and mixed numbers using a number line, benchmark fractions, and rounding to the nearest whole number. Vocabulary round, benchmark fraction Materials number line Additional Resources Examples Estimate each sum or difference: 1) 5 2 + 6 8 2) 7 – 5 2 3) 8 2 - 1 4 7 15 3 3 9 LESSON 33 (text 4-5): Adding Mixed Numbers Standard 6.N.18 Objective Find sums of mixed numbers with and without renaming. Vocabulary Mixed number Materials Additional Resources Examples Find each sum and simplify your answer: 1) 4 3 + 5 5 2) 3 5 + 7 8 8 12 6 9 LESSON 34 (text 4-6): Subtracting Mixed Numbers Standard 6.N.18 Objective Find differences of mixed numbers with and without renaming. Vocabulary mixed number, renaming, borrowing Materials


LESSON 34 Additional Resources Examples Find each difference and simplify if possible: 1) 8 5 - 3 8 2) 11 1 - 3 6 9 2 4 LESSON 35 (text 4-3 & 4-8): Problem Solving using Patterns, or Choosing an Exact Answer or Estimate Standard 6.PS.13, 6.PS.14 Objective Give missing numbers or figures in a pattern, and obtain exact or estimated results to solve problems in real-world contexts. Vocabulary Materials Additional Resources Examples Name the missing numbers and describe the patterns:

0, 1, 3, 6, 10, ___, ___, ___ Tell whether an exact answer or estimate is needed, then solve. (see p. 227) LESSONS 36 – 37 Review and Assess LESSON 38 (text 5-1 & 5-2) Multiplying Fractions Standard 6.N.17 Objective Multiply a fraction times a whole number, and give the product of two fractions. Vocabulary greatest common factor, simplify Materials fractions bars


LESSON 38 Additional Resources Examples Find each product: 1) 5 x 24 2) 7 of 80 3) 6 x 4 6 8 11 9 4) 10 x 3 5) 18 x 3 12 5 4 LESSON 39 (text 5-4): Multiplying Mixed Numbers Standard 6.N.18 Objective Multiply mixed numbers and simplify answers when possible. Vocabulary distributive property, simplify Materials Additional Resources Examples Find each product and simplify if possible: 1) 2 3 x 4 2 2) 5 x 7 1 3) 12 x 11 4 3 8 3 2 LESSON 40 (text 5-6): Dividing Fractions Standard 6.N.17, 6.N.19 Objective Divide fractions by multiplying by the reciprocal Vocabulary reciprocal, multiplicative, inverse Materials Additional Resources


LESSON 40 Examples Write the reciprocal of: 1) 8 2) 12 3) 4

9 3 Find each quotient and simplify if possible: 4) 8 ÷ 2 5) 2 ÷ 3 6) 5 ÷ 3 3 3 4 12 LESSON 41 (text 5-7): Dividing Mixed Numbers Standard 6.N.18 Objective Find the quotient of divisions with mixed numbers. Vocabulary reciprocal Materials Additional Resources Examples Find each quotient and simplify if possible: 1) 2 3 ÷ 4 2 2) 2 2 ÷ 1 1 3) 3 ÷ 6 1 8 5 3 2 4 LESSON 42 (text 5-5): Organized List in Problem Solving (and Review of 5-6, 5-7) Standard 6.N.17-19 Objective Solve word problems by making organized lists, and review division of fractions and mixed numbers. Vocabulary strategy Materials Additional Resources Diagnostic Checkpoint p. 273 Examples Solve by making an organized list: How many different arrangements of 3 letters can be made from the letters in the word MATH if no repetition of letters is allowed?


LESSON 43 (text 5-8): Expressions with Fractions Standard 6.A.1-3 Objective Write word phrases as algebraic expressions with fractions and evaluate. Vocabulary expression, equation Materials Additional Resources Examples Write each word phrase as an algebraic expression: 1) two thirds Josh’s age 2) 4 more than 1 x 8 Evaluate each expression for n = 3 and n = 2 1

4 2 3) 8n 4) 1 n 5) 2 1 n + 8

2 2 LESSON 44 (text 5-9): Solving Equations with Fractions Standard Objective Solve one-step equations in one variable with fractions. Vocabulary inverse operation Materials Additional Resources Examples Solve each equation and check your answer: 1) C + 4 = 7 1 2) 5 b = 7 1 3) m – 5 = 4 2 4) w ÷ 3= 4 1 2 6 2 6 3 4 2 LESSONS 45-46 Review and Assess


LESSON 47 (text 6-1, 6-2): Understanding Ratios and Equal Ratios Standard 6.N.7-8 Objective Express comparisons as ratios in three ways and create equal ratios. Vocabulary ratio, terms Materials Additional Resources Examples Based on the students in your math class, write the ratio for each in three different ways: 1) boys to girls 2) girls to all students 4)Give three ratios that are equal to 6:10 5)Tell whether the ratios 3 to 5 and 12 to 15 are equal. LESSON 48 (text 6-3): Rates and Unit Rates Standard 6.N.6 & 8 Objective Find the unit rate for a given rate, and use rates to identify the better buy or the lower rate. Vocabulary rate, unit rate Materials Additional Resources Examples Write each as a unit rate: 1) 300 miles in 5 hours 2) 250 calories in 10 crackers 3)Which is a better buy? 6 T-shirts for $31.50 or 5 T-shirts for $27.50 LESSON 49 (text 6-4): Problem Solving Using Objects Standard 6.PS.4&13 Objective Find, and write in sentences, solutions to word problems involving rates.


LESSON 49 Vocabulary Materials 2-color counters, centimeter cubes, misc. objects Additional Resources Examples Use objects to solve each problem and give the answer in sentence form: There are 24 baseball players on a team. Two out of every three players were on the team last year. How many players were on the team last year? LESSON 50 (text 6-5): Understanding Proportions Standard 6.N.7 Objective Understand what a proportion is and identify ratios that form proportions. Vocabulary proportion, cross products Materials Additional Resources Examples Decide if the ratios form a proportion: 1) 2 tbs. ; 4 oz. 2) 100 mi.; 125mi. 3) 5 ft.; 10s. 1oz. 8 tbs. 4 h. 5 h. 8 s. 6ft. LESSON 51 (text 6-7): Solving Proportions using Cross Products Standard 6.N.9 & 6.A.5 Objective Use cross products to solve proportions Vocabulary cross products Materials calculator Additional Resources


LESSON 51 Examples Solve each proportion using cross products. Round to the nearest hundredth. 1) b = 8 2) 2.4 = d 3 4 4.5 1.8 3)How can you tell without solving 45 = h that h is greater than 100?

20 50 LESSON 52 (text 6-8): Problem Solving with Explanation Standard 6.PS.21 Objective Solve word problems and explain how the solution was obtained. Vocabulary Materials Additional Resources Examples For every 6 girls on a bus, there are 5 boys. If there are 18 girls on the bus, how many boys are on the bus? Write to explain how to find the answer. LESSON 53 (text 6-9): Using Formulas Standard 6.A.6 Objective Use formulas to solve problems involving rates. Vocabulary formula Materials given formulas i.e. d=r x t Additional Resources Examples At a furniture design center, all dimensions for custom orders must be given in centimeters. Use the formula C = 2.54i to find the dimensions of a 9 ft. by 5 ft. dining room table in centimeters. LESSON 54 – 55 Review and Assess


LESSON 56 (text 7-1): Understanding Percent Standard 6.N.11 Objective Understand that a percent is a ratio in which the first term is compared to 100, and write percents. Vocabulary percent Materials ruler, hundred square Additional Resources Examples 1) Write the percent of the shaded portion: 2) Line segment AB represents 50%. How long would the line segment be that represents 100%? A/-----------------------/B LESSON 57 (text 7-2): Fractions, Decimals, and Percents Standard 6.N.11 & 21 Objective Change among fractions, decimals, and percents. Vocabulary Materials grid paper, colored pencils Additional Resources Examples Write each in two other ways: 1) 78% 2) 0.85 3) 3 4) 0.333 5 LESSON 58 (text 7-3): Problem Solving Standard 6.PS.22 Objective Write to explain why a solution is or is not reasonable. Vocabulary


LESSON 58 Materials Additional Resources Diagnostic Checkpoint p. 365 Examples 1) Daren says he spends 25% of the day in school. Does this statement make sense? Explain. 2) Does the circle graph make sense? Explain. LESSON 59 (text 7-4): Use Fraction Equivalents to find a Percent of a Number Standard 6.N.12 Objective Use fraction equivalents and mental math to find the percent of a number. Vocabulary fraction equivalents Materials chart to show common fraction equivalents Additional Resources Examples Use fraction equivalents to find the percent of each number: 1) 20% of 15 2) 80% of 25 3) 33 1 % of 36 3 LESSON 60 (text 7-5): Estimating with Percents Standard 6.N.12 Objective Estimate percents of numbers using compatible numbers. Vocabulary compatible numbers Materials Additional Resources Examples Estimate: 1) 43% of 28 2) 78% of 123 3) 58% of 93 4)Explain how to estimate 54% of 214. How can you use your estimate to find 154% of 214?


LESSON 61 (text 7-6): Finding a Percent of a Number Standard 6.N.26 Objective Find a percent of a number using multiplication or proportions. Vocabulary decimal equivalent, proportion Materials Additional Resources Examples Find the percent of each number: 1) 43% of 120 2) 30% of 63 Find the missing amount: 3) 30% of ___ is 75 4) 3% of ___ is 0.63 LESSON 62 (text 7-7): Problem Solving/Review Standard 6.PS.18-19 Objective Solve complex problems by breaking them apart or changing them into smaller parts. Vocabulary Materials Additional Resources Diagnostic Checkpoint p. 379 Examples 1) To help raise money for new library books, Max decided to give 1⊄ the first day, and each day thereafter give double the previous days’ amount. How much money will Max give in 10 days? LESSON 63 (text 7-8): Sales Tax and Discount Standard 6.A.6 Objective Calculate sales tax for given values and find the sale price after a discount. Vocabulary sales tax, discount Materials calculator Additional Resources


LESSON 63 Examples Find the sale price or total cost: 1)regular price $250 2) regular price $145 3) subtotal $64.89 4)subtotal $ 120.63 discount: 10% discount: 15% sales tax: 6% sales tax 4% sales price: ______ sales price: _____ total cost: ____ total cost: _____ LESSON 64 (text 7-9): Percent of Increase and Decrease Standard 6.A.6 Objective Determine the percent of increase or decrease in an amount. Vocabulary Materials Calculator Additional Resources Examples Find the percent of increase or decrease: 1)a $20 item is increased to $25 2)a $72 item is on sale for $54 3)a price decreased from $120 to $114 LESSON 65 (text 7-10) Simple Interest Standard 6.A.6 Objective Use the simple interest formula (1=p x r x t) to determine the amount of interest and the total amount of money. Vocabulary principal, interest, simple interest, interest rate Materials Additional Resources Find the amount of interest and the total amount: 1)$1,000 for 4 years at a simple interest rate of 10% per year. 2)$250 for 2 years at a simple interest rate of 7.5% per year. 3)Mr. Masters used his credit card to purchase a living room set for $2,547.00. Find the total price of the furniture if the simple interest is 8% per year and he takes 3 years to pay it.


LESSON 66 (text 7-8 to 7-10) Review Tax, Percent of Increase of Decrease, Interest Standard 6.A.6, 6.PS.5 Objective Review content learned in lessons 63 – 65 Materials calculators Additional Resources Examples See examples for Lessons 63 – 65. LESSON 67 – 68 Review and Assess LESSON 69 (text 9-1): Geometric Ideas Standard Geometry prerequisite Objective Identify important geometric terms relating to lines, parts of lines, angles, and planes. Vocabulary point, line, ray, line segment, midpoint, congruent line segments, plane, intersecting lines, parallel lines, perpendicular lines, skew lines Materials ruler or straight edge Additional Resources Examples Given visual representation of the geometric terms/figures above (see vocabulary), students will match it to its correct term. Refer to the diagram: 1)Name 3 rays. 2)Name 3 line segments. 3)Name 2 lines that intersect CM. LESSON 70 (text 9-2 & 9-3): Measuring, Drawing, and Classifying Angles and Angle Pairs Standard prerequisite


LESSON 70 Objective Measure and draw angles, and classify angles according to their measure; Identify and find measures of congruent, vertical, adjacent, complementary, and supplementary angles. Vocabulary angle, sides, vertex, degrees, acute angle, right angle, obtuse angle, straight angle, congruent angles, vertical angles, adjacent angles, complementary angles, supplementary angles Materials ruler, protractor, tracing paper Additional Resources Examples Classify each angle, then measure: 1) 2) 3) 4)Draw an angle whose measure is 112°. 5)Find x. 6)Find the measure of an angle complementary and supplementary to 68°. LESSON 71 (text 9-6 & 9-7): Polygons and Triangles Standard prerequisite Objective Identify and classify polygons and triangles, and find missing angle measures in triangles. Vocabulary polygon, triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, diagonal, regular polygon, acute triangle, right triangle, obtuse triangle, equilateral triangle, isosceles triangle, scalene triangle Materials ruler, protractor Additional Resources


LESSON 71 Examples From pictures (see p.495), name each polygon and tell if it appears to be a regular polygon. Find the missing angle measure, then classify the triangle by its angles and by its sides. 1) 2) LESSON 72 (text 9-8): Quadrilaterals Standard Objective Identify, Classify, and find missing angle measures in quadrilaterals Vocabulary quadrilateral, trapezoid, parallelogram, rhombus, rectangle, square Materials compass, ruler, protractor Additional Resources Examples Classify each polygon in as many ways as possible: 1) 2) 3) The measures of 3 angles of a quadrilateral are given. Find the measure of the fourth. 4)80° 120° 66° 5)90° 90° 90° LESSON 73 (text 9-9): Circles Standard 6.G.5-6 Objective Identify relationships between parts of a circle, such as center, radius, diameter, chord, sector, semicircle, and central angle, and construct circles. Vocabulary circle, center, radius, diameter, chord, sector, semicircle, central angle, arc Materials compass, ruler, protractor


LESSON 73 Additional Resources Examples From diagrams showing a part of a circle, identify the part (see p. 503) 1)Two congruent central angles in circle P are indicated in the diagram. Find the value of X LESSON 74 (text 9-6 to 9-9): Review of Polygons and Circles Standard see lessons 71 – 73 Objective Review content of lessons 71 – 73 Additional Resources Diagnostic Checkpoint p. 505 LESSON 75 (text 9-10): Congruent and Similar Figures Standard 6.G.1 Objective Identify congruent figures and similar figures, and find missing measures in similar and congruent figures. Vocabulary congruent figures, similar figures Materials grid paper of varying sizes Additional Resources Examples 1) These triangles are congruent. Find m< V and ON. 2)These parallelograms are similar. Find m<R, M<H, and SR.


LESSON 76 (text 9-11): Transformations Standard Objective Determine whether a pair of congruent figures are related by a slide, flip, a glide reflection, or turn, and determine the direction and number of degrees in a rotation. Vocabulary slide(translation), flip (reflection), turn (rotation), glide reflection Materials tracing paper, grid paper Additional Resources Examples Based on diagrams of congruent pairs (see 511), tell whether the figures in each pair are related by a slide, a flip, a glide reflection, or a turn. If a turn, tell the direction and degree. 1)What happens if you turn a figure 180° and then turn the resulting figure 180° about the same point? LESSON 77 (text 9-13 & 9-14) Symmetry and Tessellations Standard Objective Identify and make symmetrical figures and draw a line or lines of symmetry. Create tessellations and recognize figures that tessellate. Vocabulary reflection symmetry, line of symmetry, rotational symmetry, tessellation Material paper, scissors, ruler, tape Additional Resources Examples Tell whether figures have symmetry and tell which type, and draw lines of symmetry on given figures (see 515). Tell whether a given figure will tessellate and draw a simple tessellation (see 517). LESSON 78 Review (lesson 71 – 77) LESSON 79 (text 10-1): Customary Measurement Standard 6.M.2 –3&9


LESSON 79 Objective Change between customary units of length, weight, and capacity. Vocabulary capacity Materials examples of actual items to demonstrate units of customary measurement; equivalent charts Additional Resources Examples 1)96in. = ___ft. 2)2.5lb. = ___oz. 3)2gal. = ___pt. 4)During a marathon, volunteers passed out 21 quarts of water at one stating. How many one-cut servings did this provide? LESSON 80 (text 10-2): Metric Measurement Standard 6.M.4-6 & 9 Objective Change between metric units of length, mass, and capacity Vocabulary metric system, meter, liter, mass, gram, kilo-, centi, milli- Materials examples of actual items to show units of metric measurement, metric conversion chart Additional Resources Examples Name the appropriate metric unit for measure: 1)capacity of a teacup 2)mass of a coin 3)height of a desk 4)98g. = ___kg. 5)9cm = ___mm 6)3.25km = ___m LESSON 81 (text 10-3): Units of Measure and Precision Standard Objective Measure length to the nearest inch, half inch, quarter inch, eight inch, sixteenth inch, centimeter and millimeter. Identify the more precise unit of measure. Vocabulary precision, precise Materials customary ruler, metric ruler Additional Resources


LESSON 81 Examples Measure actual items (or representations) to the nearest eighth inch and centimeter: 1)Which is more precise, liters or cups? Explain. LESSON 82 (text 10-7) Perimeter Standard 6.A.6 Objective Select and use appropriate units, tools, and/or formula to measure and solve problems involving perimeter of regular and irregular polygons Vocabulary perimeter, regular polygon Materials grid paper Additional Resources Examples Find the perimeter of 1)a square with sides 13.5 cm. 2) 3) LESSON 83 (text 10-8): Areas of Squares and Rectangles Standard 6.G.2-3 & 11 Objective Find the area of a rectangle or a square by counting square units or by using a formula. Vocabulary area Materials samples of square units: foot, centimeter, inch Additional Resources


LESSON 83 Examples Find the area: 1) 2) 3)If the area of a rectangle is 480ft and its length is 24 ft., what is its width? LESSON 84 (text 10-10): Area of Parallelograms and Triangles Standard 6.A.6, 6.G.3 Objective Develop and use the formulas for the areas of parallelograms and triangles. Vocabulary base, height Materials rectangular paper, scissors Additional Resources Examples Find the area: 1) 2) 3)triangle 4)parallelogram b = 5m b = 16 ft h = 8.4 m h = 7 ft LESSON 85 (text 10-11): Circumference Standard 6.A.6 and 6.G.7, 9 Objective Measure the circumference of circles, find a pattern for circumference divided by diameter, and use a formula to find the circumference or diameter, given the other dimension. Vocabulary circumference, diameter, pi, radius Materials circular objects, tape measure or string and metric stick Additional Resources


LESSON 85 Examples Find the circumference: 1) 2)d=10.3m c=___ 3)c = 10.6cm d= ___ LESSON 86 (text 10-12): Area of a Circle Standard 6.A.6 and 6.G.7 – 8 Objective Use the formula A=πr to find the area of a circle and calculate the area of a section of a circle, given the measure of a central angle and the radius of the circle. Vocabulary area, pi, sector, central angle Materials Additional Resources Examples Find the area:1 ) 2) 3)Find the area of the shaded portion. LESSON 87 (text 10-13): Problem Solving and Review of Perimeter, Circumference, Area Standard 6.PS.1 Objective Solve problems involving too much information by using only the information needed, and decide when there is not enough information to solve a problem. Review steps to find perimeter, circumference, and area. Vocabulary See lessons 82 – 86. Materials


LESSON 87 Additional Resources Diagnostic Checkpoint p. 585 Example Decide if there is extra or missing information in a variety of problems and solve when possible (see p. 583). LESSON 88 (text 10-14 & 10-16): Solid Figures and Volume of a Rectangular Prism Standard 6.G.4 & 6.M.1 & 7 Objective Classify polyhedral and identify the vertices, edges, and faces. Find the volume of a rectangular prism. Vocabulary polyhedron, face, edge, vertex, prism, pyramid, cylinder, cone, sphere, volume, cubic units Materials Additional Resources Examples Classify representations of polyhedral. Find the volume of 1)cube s=6m 2)rectangular prism l = 5cm w = 4cm h = 3cm LESSON 89 – 90 Review and Assess LESSON 91 (text 11-1 & 11-2): Samples and Surveys, and Mean, Median, Mode Standard 6.S.1 & 5-6 Objective Identify the population studied in a survey, and tell whether the data are from a sample or the entire population. Find the mean, median, mode, and range of a set of data, and choose the measure that best represents a given set of data. Vocabulary data, population, sample, survey, representative sample, biased sample, statistics, random sampling, range, mean, median, mode, minimum, maximum Materials Additional Resources


LESSON 91 Examples Identify the population studied, then tell whether you think the statistics are drawn from a sample or from the entire population: 1)The average life of a grasshopper is about 50 days. 2)The average height of the boys’ basketball team is 5ft.11in. Find the mean, median, mode, and range of each data set: 3)10,4,7,4,5,6,4,7,7,8,9,3 4)85,78,65,77,91,88,80,93,90 LESSON 92 (text 11-3 & 11-4) Frequency Tables and Line Plots, and Stem-and-Leaf Plots Standard 6.S.2 & 7 Objective Make a frequency table and a line plot to display a set of data. Make a stem-and-leaf plot, and analyze the data in both data sets. Vocabulary frequency table, interval, line plot, outlier, stem-and-leaf plot, stem, leaf Materials data sets relevant to students Additional Resources Examples Represent the data below with a frequency table and line plot. Identify any clusters, gaps, and outliers. Noon Temperatures 75° 72° 73° 71° 71° 84° 74° 73° 74° 73° Represent the data below in a stem-and-leaf plot. Find the mean, median, mode, and range of the data. Price Paid for Backpack $35 $21 $19 $38 $24 $20 $39 $17 $15 $38 $20 $16 $42 $26 LESSON 93 Review of Lessons 91 – 92 on Interpreting Data Additional Resources Diagnostic Checkpoint p. 635


LESSON 94 (text 11-5 & 11-6): Bar Graphs and Line Graphs Standard 6.S.7 Objective Read and create bar graphs and line graphs, and identify trends in the data displayed. Vocabulary double-bar graph, axis, line graph, trend, double-line graph Materials quarter-inch grid paper, sample data sets Additional Resources Examples Read bar and line graphs and answer questions related to the data (see p.637 & 639). LESSON 95 (text 11-7): Circle Graphs Standard 6.S.7 Objective Read and make circle graphs, and use information in circle graphs to solve problems. Vocabulary circle graph, central angle, sector Materials compass, protractor, prepared circles, colored pencils Additional Resources Enrichment Activity E 11-7 Examples Read and analyze data in a variety of circle graphs (see p. 643) and create a simple circle graph based on given statistics. LESSON 96 (text 11-8 & 11-9): Making Graphs and Misleading Graphs Standard 6.S.4 & 8 Objective Make the most appropriate graph to represent a set of data, and explain why a graph is misleading. Vocabulary misleading Materials quarter-inch grid paper, a variety of data sets Additional Resources Diagnostic Checkpoint p. 653


LESSON 96 Examples 1)Make the most appropriate graph to show the data: Summer Tours England 37% Italy 26% France 17% Japan 5% Germany 7% Spain 8% 2)Explain why a given graph is misleading (see p.653). LESSON 97 (text 11-10): Counting Methods Standard 6.S.9 & 11 Objective Find all possibilities of an event by drawing a tree diagram, making a list, or multiplying. Vocabulary tree diagram, Counting Principle, event, outcome, sample space, compound event Materials Additional Resources Example 1)For a vacation, Carl packed a white and gray shirt. He also packed blue, black, and tan pants. Make a tree diagram to show all of Carl’s possible outfits. 2)For breakfast, students have a choice of 2 beverages, 3 muffins, and 3 fruits. If they may have only one of each, what are the numbers of possible combinations? LESSON 98 (text 11-11): Permutations and Combinations Standard 6.S.10 Objective Find the number of arrangements of a set of objects when order matters and when order does not matter. Vocabulary permutations, combinations Materials


LESSON 98 Additional Resources Examples 1)Inez is choosing 2 pizza toppings from a choice of 5 toppings. 2)8 children line up at the water fountain. How many possible arrangements are there for the children? LESSON 99 (text 11-12 & 11-13): Probability, and Predictions and Probability Standard 6.S.11 Objective Express the probability of an event as a fraction, decimal, or percent, and use probability to predict results. Vocabulary probability, impossible event, certain event, complement, theoretical probability, experimental probability, trial Materials number cubes, cards, basket and ball, etc. Additional Materials Examples Cards numbered from 1 to 50 are placed in a box. Sue picks one without looking. Find each probability as a fraction, decimal, and percent: 1)P (number less than 25) 2)P (two-digit number) 3)P (not a multiple of 10) 4)If you spin a spinner 400 times, how many times might you expect to land on red when 3 or the 8 equal spaces are red? 5)Sean dropped his bread 200 times. It landed burred-side-up 62 times. What is the probability, given as a percent, that Sean will have the bread land buttered-side-up on the next drop? LESSON 100 – 101 Review & Assess LESSON 102 (text 8-1 & 8-2): Understanding, Comparing, and Ordering Integers Standard 6.N.13 & 15 Objective Read, write, and compare positive and negative integers.


LESSON 102 Vocabulary opposites, integers, absolute, value Materials number line Additional Resources Examples Given a number line with points marked by a letter, give the integer for the point; then give its opposite and its absolute value. Use >, < or = to compare: 1)-18 ___ 3 2)-5 ___ -10 3)4 ___/4/ Order from least to greatest: 4)10, -8, -9 5) –1, 1, -5, -2 LESSON 103 (text 8-3): Understanding Rational Numbers Standard 6.N.13 – 15 Objective Identify, write, compare, and order rational numbers. Vocabulary rational number Materials number line Additional Resources Examples Graph these rational numbers on the same line: 1) –1 3 2)0.75 3) – 7

8 8 Use >,< to compare: 4)-3.7 ___ -41 5)-21 ___ -23 Order: 6)0.5,-51 ,-12, 0 2 2 4 3 LESSON 104 (text 8-11): Graphing Ordered Pairs Standard 6.G.10 Objective Identify and graph points on a coordinate plane in 4 quadrants. Vocabulary coordinate plane, quadrant, ordered pair, origin, x-coordinate, y-coordinate, x-axis, y-axis Materials grid paper


LESSON 104 Additional Resources Examples Draw a coordinate plane. Graph and label the points given: 1) Y (0, -3) 2) W (-3, 3) 3) V (-4, -1)

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