10/26/2015. Grade 7 Math Connects Course 2

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1 Grade 7 Math Connects Course 2 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2 / / 4 = 8 / / 12 = 23 / 12. (In general, a /b + c /d = (ad + bc) /bd.) 3.MD.8 Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. 3 days Start Smart Review (eliminate Venn Diagrams) 1. What are the important steps to use in problems solving? A four-step plan for problem-solving suggests steps to: Understand, Plan, Solve and Check. 2. What is the standard algorithm for multiplying decimals? To multiply by decimal numbers, multiply as if they were whole numbers. Then, the answer will have the same number of decimal places as the sum of the decimal places in the original factors. 3. What is the standard algorithm for dividing decimals? The divisor must be a whole number, so if it is not, multiply the divisor and the dividend by the same power of 10 that makes the divisor a whole number. Then divide. 4. How is the greatest common factor, GCF, used to find equivalent ratios? Dividing the numerator and denominator by the GCF will give an equivalent ratio which is in simplest form. Multiplying the numerator and the denominator by any non-zero number will also give an equivalent ratio. 5. What is the perimeter, and how is it found? The distance around a geometric figure is called the perimeter. The sum of all sides is the perimeter. 1. Students will use the Understand, Plan, Solve and Check steps when trying to solve problems. 2. Students will multiply decimals correctly. 3. Students will divide decimals correctly. 4. Students will be able to generate equivalent ratios, as well as determine if given ratios are equaivalent. 1

2 Writing: 5. Students will be able to find the perimeter of a figure, or find the missing side of a figure given the perimeter. Expressions and Patterns 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. a. 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. b. 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. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s 3 and A = 6s 2 to find the volume and surface area of a cube with sides of length s = ½. 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. 6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. 7.EE.4 Use variables to represent quantities in real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 2

3 7.EE.4 MA. 4.c Extend analysis of patterns to include analyzing, extending, and determining an expression for simple arithmetic and geometric sequences (e.g. compounding, increasing area), using tables, graphs, words, and expressions. 10 days 2 weeks Chapter 1 Expressions and Patterns (eliminate lesson 3 A, B, C) 1. How can exponents be used to express numbers? The exponent tells how many times the base is used as a factor 2. What is the Order of Operations? The rules that state the required order of computation steps are called the Order of Operations. 3. What is an algebraic expression and how do you evaluate it? An algebraic expression contains numbers, variables and at least one operation. You evaluate one by replacing any variable with its value and using the order of operations to simplify. 4. What are the steps to make an algebraic expression from a verbal phrase? Start by defining the variable, then write an algebraic expression to describe the verbal description 5. What properties can be used to generate equivalent expressions? The Associative and Commutative Properties of Addition and Multiplication and the Distributive Property and the Identity Property will generate equivalent expressions. 6. How can a sequence be used to solve a problem? Students will solve problems by looking for a pattern and extending it to find an answer. 7. What mathematical activities can be done with sequences? Students can use manipulatives, tables, lists and expressions to describe relationships and extend terms in arithmetic and geometric sequences. Vocabulary: factors, exponent, base, powers, squared, cubed, evaluate, standard form, exponential form, variable, algebra, algebraic expression, coefficient, define a variable, equivalent expressions, properties, sequence, term, arithmetic sequence, geometric sequence, monomial 1. Students will evaluate exponential expressions with whole numbers 1. Students will convert between exponential and standard form with whole numbers 2. Students will use the Order of Operations correctly to simplify numerical expressions with whole numbers 3. Students will evaluate algebraic expressions including those with coefficients and exponents showing 3

4 Writing: substitution and simplifying steps 4. Students will define variables and write algebraic expressions to describe verbal phrases 5. Students will use the Associative, Commutative, Distributive and Identity Properties to evaluate expressions. 6. Students will find a pattern in given information and extend the pattern to solve a problem 7. Students will use arithmetic and geometric sequences to model situations 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 1 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as ( 1)( 1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then (p/q) = ( p)/q = p/( q). Interpret quotients of rational numbers by describing real-world contexts. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 12 days 3 weeks 1 Computations with rational numbers extend the rules for manipulating fractions to complex fractions. 4

5 Chapter 2 Integers 1. What are the set of integers? Integers are the set of whole numbers and their opposites. 2. What is the absolute value of a number? The absolute value of a number is its distance from 0 on the number line. 3. What is a coordinate plane? The x-axis and the y-axis intersect to make the coordinate plane which is used for graphing. 4. What are the rules for computation with integers? When adding integers with the same signs, you add the absolute values of the numbers and keep the sign. When adding with different signs, you subtract the absolute values and use the sign of the larger absolute value. Subtraction is the same as addition of the opposite integer, so change the number being subtracted to its opposite, and add. Multiplication and division of integers is the same as whole number multiplication and division, but the sign of the answer is found by counting the number of negative signs (an odd number of negative signs results in a negative number) or by using the chart: or using opposite of method Writing: Vocabulary: absolute value, origin, additive inverse, positive integer, coordinate plane, quadrant, graph, x-axis, y-axis, x-coordinate, y-coordinate, integer, negative integer, opposites, ordered pair 1. Students will read and write integers. 2. Students will find the absolute value of an integer. 3. Students will graph points in all four quadrants of the coordinate plane. 4. Students will be able to add, subtract, multiply and divide integers. 5

6 7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. b. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. c. Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. d. Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as ( 1)( 1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then (p/q) = ( p)/q = p/( q). Interpret quotients of rational numbers by describing real-world contexts. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 2 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 14 days 3 weeks 2 Computations with rational numbers extend the rules for manipulating fractions to complex fractions. 6

7 Chapter 3 Rational Numbers (Eliminate Lesson 4 A, B, C mult/divide monomials, negative exponents, scientific notation) 1. What is the difference between a terminating and a repeating decimal? The digits end in a terminating decimal and there is a pattern of repeating digits that go on forever in a repeating decimal. 2. How do you convert a fraction into a decimal? Dividing the numerator by the denominator creates an equivalent decimal. 3. How do you convert a decimal into a fraction? Decimals named according to the digits and their place value can be written as a fraction and then simplified (ex.6 = = ). 4. How do you add and subtract fractions? Fractions are added and subtracted once they have common denominators (the least common denominator LCD may be more efficient but is not necessary). The denominators stay the same and the numerators are added or subtracted. Usually final answers must be in simplest form (reduced to lowest terms). 5. How do you multiply fractions? Fractions are multiplied by multiplying the numerators and then multiplying the denominators. All final answers must be simplified (reduced to lowest terms). The problem can also be simplified first by dividing out a common factor between any numerator and denominator, and then multiplying the remaining numerators and denominators. Mixed numbers can also be changed to improper fractions before multiplying. 6. How do you divide fractions? Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. Mixed numbers should be changed to improper fractions before dividing. All final answers must be simplified (reduced to lowest terms). Vocabulary: bar notation, common denominator, least common denominator (LCD), like fractions (same denominator), rational numbers, repeating decimals, standard form, terminating decimal, unlike fractions, reciprocal, multiplicative inverse 1. Students will write fractions as terminating or repeating decimals. 2. Students will write decimals as fractions. 3. Students will add and subtract fractions with like and unlike denominators. 4. Students will multiply fractions and mixed numbers. 5. Students will divide fractions and mixed numbers. 7

8 Writing: 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. MA.4.c. Extend analysis of patterns to include analyzing, extending, and determining an expression for simple arithmetic and geometric sequences (e.g., compounding, increasing area), using tables, graphs, words, and expressions. 18 days 4 weeks Chapter 4 Equations and Inequalities 1. How do you solve addition and subtraction equations? Solve addition equations by subtracting the same number from both sides of the equation and solve subtraction equations by adding the same number to both sides of the equation. Performing the same operation to both sides of an equation maintains the equality. 2. How do you solve multiplication and division equations? Solve multiplication equations by dividing both sides of the equation by a non-zero number, and solve division equations by multiplying both sides of the equation by the same number. Performing the same operation to both sides of an equation maintains the equality. 3. How do you solve multiple step equations? The Properties of Equality can be used to undo the operations on the variable. These processes are done in reverse order of the order of operations. If there are variables on both sides of the equation, the Properties of Equality are used to isolate the variables on one side of the equation. 4. How do you solve inequalities? 8

9 Inequalities are solved like equations except when multiplying or dividing by negative numbers. When multiplying or dividing by a negative number, the direction of the inequality symbol must be reversed for the inequality to be true. Vocabulary: coefficient, equation, equivalent equations, formula, inequality, multiplicative inverse, reciprocal, two-step equation 1. Students will solve one-step addition and subtraction equations. 2. Students will solve one-step multiplication and division equations. 3. Students will solve equations with rational coefficients. 3. Students will solve two-step equations. 3. Students will use the properties of equality to simplify and solve equations with variables on both sides. 4. Students will solve inequalities by using Addition, Subtraction, Multiplication and Division Properties of Inequality. Writing: 7. RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For example, if a person walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles per hour. 7. RP.2 Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table, or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r ) where r is the unit rate. 7. RP.3 Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple 9

10 Writing: interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 7. G. 1 Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 16 days 4 weeks Chapter 5 Proportions and Similarity 1. What is a unit rate? A rate is a comparison of two quantities with different units. A unit rate has a denominator of What is a proportion and how is one solved? A proportion is an equation that shows two ratios are equal. Proportions can be solved using cross products or horizontal multiplication or division by a common factor. 3. How are problems solved using scale drawings? Use the scale factor, which is a ratio, to create a proportion with the unknown value. Solve the proportion to determine quantities. 4. How can similar figures be used to solve problems? If figure B is similar to figure A by a scale factor, then: The perimeter of figure B = perimeter of figure A times the scale factor The area of figure B = area of figure A times (the scale factor) 2 Vocabulary: corresponding angles, corresponding sides, cross products, equivalent ratios, indirect measurement, nonproportional, proportion, proportional, rate, scale, scale drawing, scale factor, scale model, similar figures, unit rate 1. Students will determine unit rates. 2. Students will identify proportional and non-proportional relationships using part / whole. 2. Students will use proportions to solve problems concerning cost, measurement, units, etc. 3. Students will solve problems involving scale drawings of maps, dimensions of rooms, size of objects, models, etc. 4. Students will solve problems involving similar figures to find missing measurements. 4. Students will find the relationship between perimeters and areas of similar figures. 10

11 7.RP.3 Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1 / 10 of her salary an hour, or $2.50, for a new salary of $ If you want to place a towel bar 9¾ inches long in the center of a door that is 27½ inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. 17 days 4 weeks Chapter 6 Percent 1. What are percent diagrams and how are they used to solve problems? Bar diagrams divided into ten sections of 10% each, or circle graphs divided into sectors of various percentages can be used to model problems where 100% of a whole is included the problem. 2. What are the steps to finding the percent of a number? Find the percent of a number by changing the percent to either a fraction or decimal and multiplying. 3. How can an estimate of a percent be found? When an estimate of a percent is acceptable, use a friendly percent and multiply or divide that result to get an approximate answer. (For example: Find 10% and half of that is 5% or 25% is 11

12 10% twice plus 5%) 4. What is the setup for percent proportion and how can a problem be solved with one? A percent proportion has one side of the proportion as a ratio of part to whole, and the other side as the percent written as a fraction. Solving the proportion gives the final answer. Percent proportion: 5. What is the percent equation? Percent equation: 6. What is the percent of change ratio and how is it used to solve problems of increase or decrease Percent of change A positive result is a percent of increase, and a negative amount is a percent of decrease. If the final amount is less than the original, then it is a decrease. 7. What are some applications of percents? Finding Discounts (amount off) Finding tax, tips, etc. (amount added on) Simple Interest ( Vocabulary: discount, gratuity, percent of decrease, percent of increase, principal, sales tax, percent equation, percent proportion, percent of change, simple interest, tip 1. Students will be able to create or interpret models of percents using bar diagrams and circle diagrams. 2. Students will find the percent of a number, including percents greater than 100%. 3. Students will estimate percents using fractions and/or decimals Students will solve problems using percent proportion and/or the percent equation. 6. Students will find the percent of change for both increases and decreases. 7. Students will calculate taxes, tips, discounts and simple interest. Writing: DDM created for this chapter 12

13 Writing: 7.RP.2 Recognize and represent proportional relationships between quantities. 7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table, or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7.RP.2c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. 8 days 1 week (end of year, after state testing) Chapter 7 Linear Functions section 7-3 (pages in text) 1. Why would a graph be used to solve problems? A graph will show any trends from multiple pieces of data, especially when a line of best fit is put on the graph. 2. What makes a relationship proportional? When is constant for all values of x and y, then the relationship is proportional. 3. What are the characteristics of direct variation? In direct variation (also called direct proportion) the constant rate of change and the constant ratio (called the constant of variation) are the same. When graphed, the line goes through the origin. Vocabulary: direct variation, direct proportion, constant of variation, slope-intercept form, y-intercept 1. Given data, students will graph it and sketch a line of best fit. 1. Students will use a line of best fit to make predictions. 2. Students will determine if a relationship is proportional and if so, write it in form. 3. Given a verbal description, graph or a table of values, students will determine whether it is an example of direct variation. 13

14 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? 7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. 7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. 7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. 7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. 7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? 7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. 15 days 3 weeks Chapter 8 Probability and Predictions 14

15 1. If all outcomes are equally likely, what is the probability of a simple event? ( 2. How can the sample space (total number of possible outcomes) be found? Sample space is found by either a tree diagram or by using the Fundamental Counting Principle. 3. How do you find the number of permutations of a set of objects and find their probabilities? The Fundamental Counting Principle will give the total number of possibilities. 4. What is the difference in finding the probability of dependent vs. independent events? Independent events do not influence each other, ie., pick a card, replace the card and pick again; whereas dependent events do influence each other, ie., pick a card, do not replace it, and pick a second card from the same deck. 5. What is the difference between making predictions based on theoretical probability and experimental probability? When conducting an experiment, theoretical probability is what should happen, and experimental probability is what actually happens. Predictions are more accurate when they are based on theoretical probability. Vocabulary: complementary event, compound event, experimental probability, Fundamental Counting Principle, independent event, outcome, population, probability, random, sample, sample space, permutation, simple event, survey, theoretical probability, tree diagram 1. Student will be able to find the probability of a simple event. 2. Students will be able to determine the sample space using a tree diagram and the Fundamental Counting Principal. 3. Students will use the fundamental counting principle to find permutations and probabilities. 4. Students will calculate the probabilities of dependent events P(A and B)= P(A) P(B following A) and independent events P(A and B) = P(A) P(B) 5. Students will calculate theoretical and experimental probabilities. 5. Students will identify a game as fair or unfair based on experimental and theoretical probabilities. 5. Students will predict the actions of a larger group by using data and biased vs. unbiased samples. Writing: 15

16 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. 6-7 days 1 week Chapter 9 Statistical Displays (Additional lessons 15 and 16) 1. What can be determined from the comparison of two data sets? By using the same scale on two dot plots, students can see how the centers differ, and the spread of the data differs. By using the same scale on a double box-and-whisker plot, students can compare medians, ranges, interquartile ranges and overall spread of the data. Vocabulary: visual overlap, double box-and-whisker, variation 1. Given two dot plots or a double box-and-whisker plot, students will be able to compare the centers of the data sets, the spread of the data, and make inferences about the two populations. Writing: 16

17 7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. 7.G.4 Know the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and use them to solve simple equations for an unknown angle in a figure. 7.G.6 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 7.G.MA.7 Solve real-world and mathematical problems involving the surface area of spheres. 18 days 4 weeks Chapter 10 Volume and Surface Area 1. What are the parts of 3 dimensional figures? 3-dimensional figures have edges, vertices, faces, bases, and diagonals. 2. What shapes result from cross sections of 3-dimensional shapes? 3. What are the formulas for calculating volume of 3-dimensional shapes? Rectangular prism l w h or B h (where B is the area of the base) Triangular prism B h Cylinder B h or π r 2 h Pyramid ⅓ B h Cone ⅓ B h or ⅓ B π r 2 h 4. What are the formulas for the circumference and area of a circle? Circumference πd or 2 π r Area π r 2 h 5. What is the formula for the surface area of a sphere? Surface Area of a sphere SA= 4 π r 2 6. What is the area, surface area or volume of a given figure? Substitute into the given formula, use the order of operations and correctly label with units the surface area, area or volume. 1. Students will identify the edges, vertices, faces, bases, and diagonals of a 3 dimensional figure. 2. Students will name or draw the result of cross sections of 3-dimensional figures. 17

18 Writing: 3. Students will calculate the volume of 3-dimensional figures given standard formulas. 4. Students will calculate the circumference and area of a circle using given formulas. 5. Given the formula, students will calculate the surface area of a sphere. 7.G.6 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 5 days 1 week Chapter 11 Measurement and Proportional Reasoning (sections 11-2A, B, C) 1. When is it important to build a model? Models are used to visualize information provided in a problem, especially those involving volume and surface area. 2. What is scale? Scale is the ratio of the measurements of the drawing or model to the measurements of the real object. 3. How do changes in dimensions affect area and volume? If the original and the changed figures are similar, then the perimeters are related by the scale factor between them, and the areas are related by the square of the scale factor. 4. What is the relationship between the surface areas of similar solids? If Solid X is similar to Solid Y by a scale factor, then the surface area of X is equal to the surface area of Y times the square of the scale factor. 5. What is the relationship between the volumes of similar solids? If Solid X is similar to Solid Y by a scale factor, then the volume of X is equal to the volume of Y times the cube of the scale factor. Vocabulary: scale, scale factor, similar solids 18

19 1. Students can make a model from a verbal problem. 2. Given changes to the side length of a figure, students will be able to determine the changes in the perimeter, surface area or volume. 3. Given the scale factor between two figures, students will be able to determine the relative changes in the perimeter, surface area or volume. Writing: 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and use them to solve simple equations for an unknown angle in a figure. 10 days 2 weeks Chapter 12 Polygons and Transformations (sections 12-1A-12-1E) 1. What are the ways to identify and classify angles. Angles are identified and classified based on the location of the angles and/or their measures. 2. What steps can be taken to find missing angle measures in a figure? Parallel lines cut by a transversal reveal alternate interior angles, alternate exterior angles, corresponding angles, vertical angles, and supplementary angles. Using definitions and given angle measures, remaining angle measures can be found. 3. What are the ways to identify and classify triangles? Acute triangle, right triangle, obtuse triangle, scalene triangle, isosceles triangle, equilateral triangle can be identified by the measure of the angles in the triangle. Scalene triangle, isosceles triangle, equilateral 19

20 triangle can also be identified by their side lengths. 4. What steps can be taken to find missing angle measures in a triangle? Use the sum of the angles in a triangle formula and substitute given information to solve for the missing information. 5. What are the ways to classify quadrilaterals? A quadrilateral can be classified as a rectangle, square, parallelogram, rhombus, or trapezoid based on angle measures and side lengths. 6. How can missing angles be found in a quadrilateral? Use the sum of the angles in a quadrilateral formula and substitute given information to solve for the missing information. 7. What are the names of 3-10 sided figures? Three to ten sided figures are called triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, nonagons, and decagons. 8. What is the sum of the angles in a polygon? The formula for the sum of the angles in an n-sided polygon is ( 9. What is the measure of the interior angle in a regular polygon? The measure of the interior angle in a regular n-sided polygon is ( Vocabulary: angle, straight angle, vertical angles, adjacent angles, complementary angles, supplementary angles, parallel lines, transversal, alternate interior angles, alternate exterior angles, corresponding angles, triangle, congruent segments, acute triangle, right triangle, obtuse triangle, scalene triangle, isosceles triangle, equilateral triangle, quadrilateral, rectangle, square, parallelogram, rhombus, trapezoid, polygon, pentagon, hexagon, heptagon, octagon, nonagon, decagon, equilateral, equiangular, regular polygon 1,2. Given a drawing, students will identify angles by name and find their measures. 3,4. Given a triangle and measurements of the sides or angles, students will identify the triangle by name and find measures of missing angles or sides using the definitions or standard formulas. 5,6. Given a quadrilateral and measurements of the sides or angles, students will identify the quadrilateral by name and find measures of missing angles or sides using the definitions or standard formulas. 7. Students will identify 3-10 sided figures by name. 8. Students will calculate the sum of the angles in any polygon. 9. Students will calculate the measure of the interior angles in a regular n-sided figure (n-gon). Writing: 20