• Big Ideas Syllabus

    7th Grade Math



    Chapter 1: The Number System

    Date

    Section

    Essential Questions

    Standards

    September - October

    Section 1.1 - Integers and Absolute Value


    Section 1.2 - Adding Integers


    Section 1.3 - Subtracting Integers


    Section 1.4 - Multiplying Integers


    Section 1.5 - Dividing 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 tell?


    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?

    7.NS.1a: Describe situations in which opposite quantities combine to make 0. 

    7.NS.1b: 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.

    7.NS.1c: 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.

    7.NS.1d: Apply properties of operations as strategies to add and subtract rational numbers.

    7.NS.2a: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.

    7.NS.2b: 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.

    7.NS.2c: Apply properties of operations as strategies to multiply and divide rational numbers.

    7.NS.2d: 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.











    Chapter 2: Rational Numbers

    Date

    Section

    Essential Questions

    Standards

    October - November

    Section 2.1 - Rational Numbers


    Section 2.2 - Adding Rational Numbers


    Section 2.3 - Subtracting Rational Numbers


    Section 2.4 - Multiplying and Dividing Rational Numbers

    How can you use a number line to order rational numbers?


    How can you use what you know about adding integers to add rational numbers?


    How can you use what you know about subtracting integers to subtract rational numbers?


    Why is the product of two negative rational numbers positive?

    7.NS.1a: Students will describe situations in which opposite quantities combine to make 0. 

    7.NS.1b: 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.

    7.NS.1c: 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.

    7.NS.1d: Apply properties of operations as strategies to add and subtract rational numbers.

    7.NS.2a: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.

    7.NS.2b: 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.

    7.NS.2c: Apply properties of operations as strategies to multiply and divide rational numbers.

    7.NS.2d: 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.














    Chapter 3: Expressions and Equations

    Date

    Section

    Essential Questions

    Standards

    Nov.-Dec.

    Section 3.1 - Algebraic Expressions


    Section 3.2 - Adding and Subtracting Linear Expressions


    Extension 3.2 - Factoring Expressions


    Section 3.3 - Solving Equations Using Addition or Subtraction


    Section 3.4 - Solving Equations Using Multiplication or Division


    Section 3.5 - Solving Two-Step Equations

    How can you simplify an algebraic expression?


    How can you use algebraic tiles to add or subtract algebraic expressions?







    How can you use algebraic tiles to solve addition or subtraction equations?



    How can you use multiplication or division to solve equations?



    How can you use algebraic tiles to solve a two-step equation?

    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.4a: 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.












    Chapter 4: Inequalities

    Date

    Section

    Essential Questions

    Standards

    December

    Section 4.1 - Writing and Graphing Inequalities


    Section 4.2 - Solving Inequalities Using Addition or Subtraction


    Section 4.3 - Solving Inequalities Using Multiplication or Division


    Section 4.4 - Solving Two-Step Inequalities

    How can you use a number line to represent solutions of an inequality?


    How can you use addition and subtraction to solve an inequality?



    How can you use multiplication and division to solve an inequality?



    How can you use an inequality to describe the dimensions of a figure?

    7.EE.4b: 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.

    Chapter 5: Ratios and Proportions

    Date

    Section

    Essential Questions

    Standards

    January

    Section 5.1 - Ratios and Rates


    Section 5.2 - Proportions


    Extension 5.2 - Graphing Proportional Relationships


    Section 5.3 - Writing Proportions


    Section 5.4 - Solving Proportions


    Section 5.5 - Slope


    Section 5.6 - Direct Variation

    How do rates help you describe real-life problems?


    How can proportions help you decide when things are fair?




    How can you write a proportion that solves a problem in real life?


    How can you use ratio tables and cross products to solve proportions?


    How can you compare two rates graphically?


    How can you use a graph to show the relationship between two quantities that vary directly? How can you use an equation?

    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.

    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. 

    7.RP.2d: 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 multistep ratio and percent problems.

    Chapter 6: Percents

    Date

    Section

    Essential Questions

    Standards

    February

    Section 6.1 - Percents and Decimals



    Section 6.2 - Comparing and Ordering Fractions, Decimals, and Percents


    Section 6.3 - The Percent Proportion


    Section 6.4 - The Percent Equation


    Section 6.5 - Percents of Increase and Decrease


    Section 6.6 - Discounts and Markups


    Section 6.7 - Simple Interest

    How does the decimal point move when you rewrite a percent as a decimal and when you rewrite a decimal as a percent?


    How can you order numbers that are written as fractions, decimals, and percents?



    How can you use models to estimate percent questions?


    How can you use an equivalent form of the percent proportion to solve a percent problem?


    What is a percent of decrease? What is a percent of increase?


    How can you find discounts and selling prices?



    How can you find the amount of simple interest earned on a savings account? How can you find the amount of interest owed on a loan?

    7.RP.3:  Use proportional relationships to solve multistep ratio and percent problems.

    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.

    Chapter 7: Constructions and Scale Drawings

    Date

    Section

    Essential Questions

    Standards

    March

    Section 7.1 - Adjacent and Vertical Angles


    Section 7.2 - Complementary and Supplementary Angles


    Section 7.3 - Triangles


    Extension 7.3 - Angle Measures of Triangles


    Section 7.4 - Quadrilaterals


    Section 7.5 - Scale Drawings

    What can you conclude about the angles formed by two intersecting lines?


    How can you classify two angles as complementary or supplementary?


    How can you construct triangles?





    How can you classify quadrilaterals?


    How can you enlarge or reduce a drawing proportionally?

    7.G.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

    7.G.2: Draw (freehand, with a 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 solve simple equations for an unknown angle in a figure.








    Chapter 8:  Circles and Area

    Date

    Section

    Essential Questions

    Standards

    April- May

    Section 8.1 - Circles and Circumference


    Section 8.2 - Perimeters of Composite Figures


    Section 8.3 - Areas of Circles


    Section 8.4 Areas of Composite Figures

    How can you find the circumference of a circle?



    How can you find the perimeter of a composite figure?


    How can you find the area of a circle?


    How can you find the area of a composite figure?

    7.G.4: Know the formulas for the area and circumference of a circle and use them to 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.

    Chapter 9: Surface Area and Volume

    Date

    Section

    Essential Questions

    Standards

    May

    Section 9.1 - Surface Areas of Prisms


    Section 9.2 - Surface Areas of Pyramids


    Section 9.3 - Surface Areas of Cylinders


    Section 9.4 - Volumes of Prisms


    Section 9.5 - Volumes of Pyramids

    How can you find the surface area of a prism?



    How can you find the surface area of a pyramid?


    How can you find the surface area of a cylinder?


    How can you find the volume of a prism?



    How can you find the volume of a pyramid?

    7.G.4: Know the formulas for the area and circumference of a circle and use them to 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.


    Chapter 10: Probability and Statistics

    Date

    Section

    Essential Questions

    Standards

    June

    Section 10.1 - Outcomes and Events


    Section 10.2 - Probability



    Section 10.3 - Experimental and Theoretical Probability


    Section 10.4 - Compound Events


    Section 10.5 - Independent and Dependent Events


    Extension 10.5 - Simulations


    Section 10.6 - Samples and Populations


    Extension 10.6 - Generating Multiple Samples


    Section 10.7 - Comparing Populations 

    In an experiment, how can you determine the number of possible results?


    How can you describe the likelihood of an event?


    How can you use relative frequencies to find probabilities?


    How can you find the number of possible outcomes of one or more events?


    What is the difference between dependent and independent events?




    How can you determine whether a sample accurately represents a population?





    How can you compare data sets that represent 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.

    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. 

    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.

    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 1/2 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.

    7.SP.7a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

    7.SP.7b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. 

    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.8c: Design and use a simulation to generate frequencies for compound events.