Content Area: Mathematics Course Title: Math 7 Grade Level: 7 Integers Rational Numbers and Equations Expressions and Equations Marking Period 1 Inequalities Ratio and Proportion Marking Period 2 Percents Constructions and Scaled Drawings Circles and Area Marking Period 3 Surface Area and Volume Probability and Statistics Marking Period 4 Date Created: July 2013 Board Approved on:
Unit Title Lessons to include Time Common Core Standards Math Integers Rational Numbers Expressions and Equations Inequalities Ratios and Proportions Percents 1.1 Integers and Absolute Value 1.2 Adding Integers 1.3 Subtracting Integers 1.4 Multiplying Integers 1.5 Dividing Integers 2.1 Rational Numbers 2.2 Adding Rational Numbers 2.3 Subtracting Rational Numbers 2.4 Multiplying and Dividing Rational Numbers 3.1 Algebraic Expressions 3.2 Adding and Subtracting Linear Expressions 3.3 Solving Equations using Addition and Subtraction 3.4 Solving Equations using Multiplication and Division 3.5 Solving Two-Step Equations 4.1 Writing and Graphing Inequalities 4.2 Solving Inequalities using Addition and Subtraction 4.3 Solving Inequalities using Multiplication and Division 4.4 Solving Two-Step Inequalities 5.1 Ratios and Rates 5.2 Proportions 5.3 Writing Proportions 5.4 Solving Proportions 5.5 Slope 5.6 Direct Variation 6.1 Percents 6.2 Comparing and Ordering Fractions, Decimals and Percents 6.3 The Percent Proportion 6.4 The Percent Equation 6.5 Percents of Increase and Decrease 6.6 Discounts and Markups 6.7 Simple Interest 14 days 7.NS.1a d, 7.NS.2a d, 7.NS.3 12 days 7.NS.1a d, 7.NS.2a d, 7.NS.3 15 days 7.EE.1, 7.EE.2, 7.EE.4a 12 days 7.EE.4b 17 days 7.RP.1, 7.RP.2a d, 7.RP.3 18 days 7.RP.3, 7.EE.3
Constructions and Scale Drawings Circles and Area Surface Area and Volume Probabilities and Statistics 7.1 Adjacent and Vertical Angles 7.2 Complimentary and Supplementary Angles 7.3 Triangles 7.4 Quadrilaterals 7.5 Scaled Drawings 8.1 Circles and Circumference 8.2 Perimeters and Composite Figures 8.3 Areas of Circles 8.4 Areas of Composite Figures 9.1 Surface Areas of Prisms 9.2 Surface Areas of Pyramids 9.3 Surface Areas of Cylinders 9.4 Volumes of Prisms 9.5 Volume of Pyramids 10.1 Outcomes and Events 10.2 Probability 10.3 Experimental and Theoretical Probability 10.4 Compound Events 10.5 Independent and Dependent Events 10.6 Samples and Populations 10.7 Comparing Populations 17 days 7.G.1, 7.G.2, 7.G.5 12 days 7.G.4, 7.G.6 16 days 7.G.4, 7.G.6 20 days 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4, 7.SP.5, 7.SP.6, 7.SP.7a b, 7.SP.8a c
Course Title: Math 7 Grade Level:7 th Overarching What is an Integer? What is a Rational Number and Equation? How can you use a proportion to solve a problem? When are percents useful? What makes shapes similar? When and how would you use surface area equations to solve problems? When and how would you use volume equations to solve problems? What is Data Analysis? What is Probability? What are linear equations and functions? How are angles classified? What is the Pythagorean Theorem? What is Scientific Notation? Overarching Enduring Understanding Course Description Math 7students will learn about operations with integers, rational numbers and equations, proportions and variation, percents, similarity and transformations, surface areas and volumes of solids, analyze data and samples, and probability. Math 7 Advanced students will also explore linear equations and functions, angles and similarity, radicals and the Pythagorean Theorem, exponents and scientific notation. Technology Standards 8.1.12 A 3 - Construct a spreadsheet, enter data, use mathematical or logical functions to manipulate and process data, generate charts and graphs, and interpret the results. 8.1.12 B 9 - Create and manipulate information, independently and/or collaboratively, to solve problems and design and develop products. Life Skills Standards 9.1.12.A.1 - Apply critical thinking and problem-solving strategies during structured learning experiences. 9.1.12.B.1 - Present resources and data in a format that effectively communicates the meaning of the data and its implications for solving problems, using multiple perspectives. 9.4.12.A.2 - Demonstrate mathematics knowledge and skills required to pursue the full range of postsecondary education and career opportunities.
9.4.12.O.(2).1 - Develop an understanding of how science and mathematics function to provide results, answers, and algorithms for engineering activities to solve problems and issues in the real world. 9.4.12.O.(2).2 - Apply science and mathematics when developing plans, processes, and projects to find solutions to real world problems.
Integers How can you use integers to represent the velocity and the speed of an object? Is the sum of two integers positive, negative, or zero? How can you know? How are adding integers and subtracting integers related? Is the product of two integers positive, negative, or zero? How can you tell? Is the quotient of two integers positive, negative, or zero? How can you tell? Integer, absolute value, opposites, additive inverse Find absolute values Add integers Subtract integers Multiply integers Divide integers
Percents How can you use models to estimate percent questions What is a percent of decrease? What is a percent of increase? How can you use the percent equation to find discounts and markups of items? How can you use the simple interest formula? Percent, percent of change, percent of increase, percent of decrease, markup, discount, interest, principle, simple interest Use the percent equation to solve three types of percent problems Use a percent change formula to solve problems Use the percent equation to find discounts and markups on items Use the simple interest formula to solve problems 7.RP.3Analyze proportional relationships and use them to solve real-world and mathematical problems. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 7.EE.2 Use properties of operations to generate equivalent expressions. 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. For example, a + 0.05a = 1.05a means that increase by 5% is the same as multiply by 1.05. 7.EE.3 Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 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 operationsto 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 $27.50. If you want to place a towel bar 9 3 /4 inches long in the center of a door that is 27 1 /2 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. Shopping with coupons, Performance Task Part-Time Job, Performance Task Lesson Tutorial
Similarity and Transformations How can you use proportions to determine if two figures are similar? How can you find ratios of perimeters and areas of similar figures? How can you find unknown measures in similar figures? How can you use scale drawings to find missing measurements? How can you find actual areas using a scale drawing? How can you identify translations? How can you identify and draw reflections How can you identify and draw rotations Similar figures, corresponding angles, corresponding sides, indirect measurement, scale drawing, scale model, scale, scale factor, transformation, image, translation, reflection, line of reflection, rotation, center of rotation, angle of rotation Use the formal definition of similar figures Use the stated relationships to solve problems Find unknown measures in similar figures by setting up a proportion Use a scale drawing to find a missing measure Find areas using scale drawings and recreate scale drawings at different scales Use their visual skills to draw translations in the coordinate plane Use their visual skills to draw reflections in the coordinate plane Use their visual skills to draw rotations in the coordinate plane 7.G.2Draw, construct, and describe geometrical figures and describe the relationships between them. 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. Popcorn Containers Performance Containers Lesson Tutorial
Surface Areas of Solids How can you sketch three-dimensional solids accurately? How can you use a formula to find the surface area of a prism? How can you find the circumference and area of a circle? How can you find the surface area of a cylinder using a formula? How can you find the surface area of a pyramid using a formula? How can you find the surface area of a cone using a formula? How can you use previously learned formulas to find the surface area of a composite solid? Three-dimensional figure, polyhedron, lateral face, surface area, net, circle, center, radius, diameter, circumference, pi, regular pyramid, slant height, composite solid Learn the vocabulary of common solids and sketch the solids Develop an intuition about how to find the surface area of a prism Work with a formula for the surface area of a prism Find the circumferences and areas of circles Work with a formula for the surface area of a cylinder Work with a formula for the surface area of a pyramid Work with a formula for the surface area of a cone Use formulas for the surface area of prisms, cylinders, pyramids, and cones to find the surface area of composite figures 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.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. Trough, Performance Task Lesson Tutorial
Volumes of Solids How can you find the volume of prisms? How can you find the volumes of cylinders? How can you find the volume of a pyramid? How can you find the volume of a cone? How can you find the volume of composite solids? How can you find the surface areas and volumes of similar solids? Volume, similar solids Use the formula for the volume of a prism to solve problems Work with a formula for the volume of a cylinder Work with a formula for the volume of a pyramid Work with the formula for the volume of a cone Work with the formula to find the volume of a composite solid Use properties of similar solids to solve problems 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.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. Hiking Performance Task Lesson Tutorial
Data Analysis and Samples How can you construct and interpret stem-and-leaf plots? How can you construct and interpret a histogram? How can you accurately construct and interpret a circle graph? How can you identify a reasonable sample for a population? How can you compare two populations? Stem-and-leaf plot, stem, leaf, histogram, circle graph, population, sample Construct and interpret stem-and-leaf plots Construct and interpret a histogram Construct and interpret a circle graph Identify a reasonable sample for a population Use samples to make predictions and draw conclusions about two populations 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. 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. Survey, Using the Internet Performance Task Lesson Tutorials
Probability How can you identify the favorable outcomes of an experiment? How can you find the theoretical probability of an event? How can you find the experimental probability of an event? How can you identify and find the probability of dependent and independent events? Experiment, outcomes, event, probability, theoretical probability, fair experiment, experimental probability, independent events, dependent events, Describe the outcomes of an experiment Compute the theoretical probability of an event Compute the experimental probability of an event Use a formal definition to compute theoretical probabilities of dependent and independent events 7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. 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.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Using Spinners performance task Choosing a Block performance task Lesson Tutorials
Linear Equations and Functions How can you convert temperatures between the Fahrenheit and Celsius scales? How can you solve equations with variables on both sides? How can you solve equations in one variable with no solution, on solution, or infinitely many solutions? How can you use tables and graphs to solve equations with variables on both sides? How can you find the slope of a line? How can you find the slope intercept form of a linear equation? Equation, solution of an equation, inverse operations, equivalent equations, coordinate plane, origin, quadrants, x-axis, y-axis, ordered pair Solve multi-step equations by using inverse operations Learn how to solve equations with variables on both sides Learn how to solve equations in one variable with no solution, one solution, or infinitely many solutions Use tables and graphs to solve equations with variables on both sides Use rise over run to find the slope of lines Use the slope intercept form of a linear equation Currency Exchange Rates Performance Task Lesson Tutorials
Angles and Similarity How can you classify angles? How can you find angles of a triangle and classify the triangle? How can you find angle measures of a polygon? How can you use similar triangles to solve problems? How can you find measures of angles formed by parallel lines and a transversal? Similar figures, proportion, ratio, cross products property, corresponding parts, polygon, regular polygon, convex polygon, concave polygon, isosceles triangle, congruent sides, equilateral triangle, perpendicular lines, transversal, Several pairs of angles Find the missing angle of the triangle and classify the triangle Use a formula to find the missing angle measure of a polygon Use similar triangles to solve real-life problems Find the measures of many types of angles, all formed when parallel lines are cut by a transversal Geometry Scavenger Hunt Lesson Tutorials Radicals and the Pythagorean Theorem How can you find the side length of a square when you are given the area of a square? How can you use the Pythagorean Theorem to solve for the lengths of a right triangle? How can you find decimal approximations of square roots that are irrational? How can you simplify expressions involving square roots? How can you use the Pythagorean Theorem to find distances? Greater than, less than, order of operations, square root, perfect square, radical sign, radicand, theorem, hypotenuse, legs, Pythagorean Theorem, irrational number, real numbers, cube root, perfect cube, Pythagorean triple Find the square root of a perfect square Use the Pythagorean Theorem to find the missing lengths of a right triangle
Approximate non perfect square roots as being between two integers Use properties of square roots to simplify expressions Find cube roots and simplify expressions involving cube roots Solve right triangle problems and determine if three lengths are the sides of a right triangle Wheel of Theodorus Lesson Tutorials Exponents and Scientific Notation How can you write and evaluate powers? How can you use the Product of Powers Property to simplify expressions? How can you use the Quotient of Powers Property to simplify expressions? How can you simplify and evaluate expressions with negative and zero exponents? How can you read numbers in scientific notation and write them in standard form? How can you write numbers in scientific notation? How can you add, subtract, or divide numbers in scientific notation? Divisor, dividend, power, base, exponent, scientific notation Write expressions involving exponents and evaluate powers Use the product of powers property to simplify expressions Use the quotient of powers property to simplify expressions Use the definition of zero and negative exponents to evaluate and simplify expressions Read numbers in scientific notation and write them in standard form Convert numbers in standard form to scientific notation Perform operations with numbers written in scientific notation Make a tutorial on Scientific Notation Lesson Tutorials