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Grade 7 Reference Material that may helpful throughout the year is linked to the left.
Helpful Links & Resources are also posted in the CLASSWORK tab on Google Classroom. |
Grade 7
Unit 1: Theoretical & Experimental Probability
• Understand that the probability of a chance event is a number between 0 and 1.
• 0 indicates an impossible occurrence (0% probability) and 1 indicates a certainty (100% probability).
• 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.
• Approximate the probability of a chance event by collecting data.
• Develop a probability model and use it to find probabilities of events.
• Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation the observed frequencies?
• Understand that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
• Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. Identify the outcomes in the sample space that compose the event.
• Design and use a simulation to generate frequencies for compound events.
Unit 2: Integers
• Describe situations in which opposites combine to make zero
• Represent integer addition on a number line
• Evaluate integer sums
• Understand subtraction of a number as adding the additive inverse
• Show that the distance between two integers is the absolute value of their difference in real world contexts
• Evaluate integer products
• Understand quotients of integers with non-zero divisors
• Apply properties of operations to integers
• Solve real-world problems involving
Unit 3: Adding & Subtracting Rational Numbers
• Convert between different forms of rational numbers (decimals and fractions) • Understand that rational numbers in decimal form either terminate or repeat
• Show that a rational number and its opposite have a sum of zero (additive inverses)
• Evaluate rational sums
• Understand subtraction of rational numbers as adding the additive inverse
• Show that the distance between two rational numbers is the absolute value of their difference in real-world contexts
• Interpret sums and differences of rational numbers in real-world contexts
• Solve real-world problems involving addition and subtraction of rational numbers
Unit 4: Multiplying & Dividing Rational Numbers
• Evaluate rational products and quotients • Understand why the denominator cannot equal zero
• Apply properties (including distributive property) when performing operations with rational numbers
• Interpret products and quotients of rational numbers in real-world contexts
• Solve real-world problems using the four operations with rational numbers
Unit 5: Expressions
• Identify coefficients, variables, constants, and like terms.
• Add and subtract like terms including rational constants and rational coefficients
• Use properties of operations (including the distributive property) to expand linear expressions with rational numbers
• Use properties of operations (including the distributive property) to factor linear expressions with rational numbers
• Rewrite an expression in different forms in a problem context to recognize how the quantities are related
Unit 6: Equations & Inequalities
• Fluently solve equations in the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers
• Solve word problems by writing and solving equations
• Compare algebraic and arithmetic solutions by 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? (To solve algebraically: 2w + 2(6) = 54; To solve arithmetically: [54 – 2(6)] ÷ 2 is the width.)
• Solve inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. This includes ≤ and ≥
• Graph the solution set of the inequality
• Solve word problems by writing and solving inequalities. Interpret the solution set 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
Unit 7: Ratios, Proportions & Percents
• Use various strategies to determine whether two quantities are proportional (e.g., by constructing a rate table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin)
• Compute unit rates with ratios of fractions including ratios of lengths, areas, and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
• Identify the unit rate (constant of proportionality) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
• Write equations for proportional relationships using the unit rate. For example: d = 65t
• Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the origin and (1, r) where r is the unit rate.
•Solve multi-step ratio and percent problems involving:
• simple interest • tax • markups and markdowns
• gratuities and commissions • fees • percent increase and percent decrease
• percent error
• Solve multi-step real-world problems with positive and negative rational numbers in any form (whole numbers, fractions, decimals)
• Apply properties to numbers in any form
• convert between forms of numbers as appropriate
• assess reasonableness of answers using mental computation and estimation
Unit 8: Angle Relationships
• Recognize angle relationships, specifically supplementary, complementary, vertical, and adjacent angles.
• Apply knowledge of angle relationships in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
• Solve simple geometric problems using equations.
Unit 9: 2D & 3D Geometry
• Find the area of two-dimensional polygons (including composite figures).
• Solve real-world and mathematical problems involving area of polygons.
• Know and use the formulas to find the area and circumference of a circle.
• Solve real-world and mathematical problems involving area and circumference of circles.
• Informally derive the relationship between the circumference and area of a circle.
• Describe the two-dimensional figures that result from slicing right rectangular prisms
• Describe the two-dimensional figures that result from slicing right rectangular pyramids
• Solve real-world and mathematical problems involving volume of right prisms
• Solve real-world and mathematical problems involving surface area of figures composed of triangles, quadrilaterals, polygons, cubes, and right prisms
Unit 10: Sampling & Statistics
l• Examine a sample population
• Generalize about a population
• Determine validity of samples
• Understand random sampling, representative samples and making inferences
• Use random samples to draw inferences
• Generate multiple samples (or simulated) to gauge variation
• Assess degree of overlap of two data distributions with similar variability
• Use measures of center to draw inferences
• Use measures of variability to draw inferences
Unit 1: Theoretical & Experimental Probability
• Understand that the probability of a chance event is a number between 0 and 1.
• 0 indicates an impossible occurrence (0% probability) and 1 indicates a certainty (100% probability).
• 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.
• Approximate the probability of a chance event by collecting data.
• Develop a probability model and use it to find probabilities of events.
• Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation the observed frequencies?
• Understand that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
• Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. Identify the outcomes in the sample space that compose the event.
• Design and use a simulation to generate frequencies for compound events.
Unit 2: Integers
• Describe situations in which opposites combine to make zero
• Represent integer addition on a number line
• Evaluate integer sums
• Understand subtraction of a number as adding the additive inverse
• Show that the distance between two integers is the absolute value of their difference in real world contexts
• Evaluate integer products
• Understand quotients of integers with non-zero divisors
• Apply properties of operations to integers
• Solve real-world problems involving
Unit 3: Adding & Subtracting Rational Numbers
• Convert between different forms of rational numbers (decimals and fractions) • Understand that rational numbers in decimal form either terminate or repeat
• Show that a rational number and its opposite have a sum of zero (additive inverses)
• Evaluate rational sums
• Understand subtraction of rational numbers as adding the additive inverse
• Show that the distance between two rational numbers is the absolute value of their difference in real-world contexts
• Interpret sums and differences of rational numbers in real-world contexts
• Solve real-world problems involving addition and subtraction of rational numbers
Unit 4: Multiplying & Dividing Rational Numbers
• Evaluate rational products and quotients • Understand why the denominator cannot equal zero
• Apply properties (including distributive property) when performing operations with rational numbers
• Interpret products and quotients of rational numbers in real-world contexts
• Solve real-world problems using the four operations with rational numbers
Unit 5: Expressions
• Identify coefficients, variables, constants, and like terms.
• Add and subtract like terms including rational constants and rational coefficients
• Use properties of operations (including the distributive property) to expand linear expressions with rational numbers
• Use properties of operations (including the distributive property) to factor linear expressions with rational numbers
• Rewrite an expression in different forms in a problem context to recognize how the quantities are related
Unit 6: Equations & Inequalities
• Fluently solve equations in the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers
• Solve word problems by writing and solving equations
• Compare algebraic and arithmetic solutions by 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? (To solve algebraically: 2w + 2(6) = 54; To solve arithmetically: [54 – 2(6)] ÷ 2 is the width.)
• Solve inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. This includes ≤ and ≥
• Graph the solution set of the inequality
• Solve word problems by writing and solving inequalities. Interpret the solution set 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
Unit 7: Ratios, Proportions & Percents
• Use various strategies to determine whether two quantities are proportional (e.g., by constructing a rate table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin)
• Compute unit rates with ratios of fractions including ratios of lengths, areas, and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
• Identify the unit rate (constant of proportionality) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
• Write equations for proportional relationships using the unit rate. For example: d = 65t
• Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the origin and (1, r) where r is the unit rate.
•Solve multi-step ratio and percent problems involving:
• simple interest • tax • markups and markdowns
• gratuities and commissions • fees • percent increase and percent decrease
• percent error
• Solve multi-step real-world problems with positive and negative rational numbers in any form (whole numbers, fractions, decimals)
• Apply properties to numbers in any form
• convert between forms of numbers as appropriate
• assess reasonableness of answers using mental computation and estimation
Unit 8: Angle Relationships
• Recognize angle relationships, specifically supplementary, complementary, vertical, and adjacent angles.
• Apply knowledge of angle relationships in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
• Solve simple geometric problems using equations.
Unit 9: 2D & 3D Geometry
• Find the area of two-dimensional polygons (including composite figures).
• Solve real-world and mathematical problems involving area of polygons.
• Know and use the formulas to find the area and circumference of a circle.
• Solve real-world and mathematical problems involving area and circumference of circles.
• Informally derive the relationship between the circumference and area of a circle.
• Describe the two-dimensional figures that result from slicing right rectangular prisms
• Describe the two-dimensional figures that result from slicing right rectangular pyramids
• Solve real-world and mathematical problems involving volume of right prisms
• Solve real-world and mathematical problems involving surface area of figures composed of triangles, quadrilaterals, polygons, cubes, and right prisms
Unit 10: Sampling & Statistics
l• Examine a sample population
• Generalize about a population
• Determine validity of samples
• Understand random sampling, representative samples and making inferences
• Use random samples to draw inferences
• Generate multiple samples (or simulated) to gauge variation
• Assess degree of overlap of two data distributions with similar variability
• Use measures of center to draw inferences
• Use measures of variability to draw inferences