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Seventh Grade Mathematics Curriculum Objectives

2016-2017

Seventh Grade Mathematics Curriculum

Ratios and Proportional Relationships

1a. Finds and uses unit rates

1. Compute unit rates in like and different units (7.RP.1)

2. Identifies the unit rate in tables, graphs, equations, diagrams, and verbal descriptions (7.RP.2)

1b. Uses proportional reasoning to solve problems

1. Determine if two quantities are in proportion by testing for equivalent ratios in tables and graphs (7.RP.2)

2. Represents proportional relationships by equations (7.RP.2)

3. Explains what point (x,y) on the graph of a proportional relationship means in terms of the situation, particularly points (0,0) and (1,r) where r is the unit rate (7.RP.2)

4. Solves multi-step ratio and percent problems by using proportional relationships (7.RP.3)

5. Solves problems involving scale drawings of geometric figures; computes length and area from a scale drawing and reproduces a scale drawing at a different scale (7.G.1)

 

The Number System

2a. Operations with integers

1. Represents addition and subtraction on a horizontal and vertical number line (7.NS.1)

2. Understands addition as the number located a distance (absolute value) from the other addend in the positive or negative direction. Shows that a number and its opposite have a sum of zero (7.NS.1)

3. Understands subtraction of rational numbers as adding the additive inverse and shows the distance (difference) between two rational numbers as the absolute value of their difference (7.NS.1)

4. Adds and subtracts rational numbers (7.NS.1)

5. Applies and extends previous understandings of multiplication and division and of fractions to multiply and divide rational numbers (7NS.2)

6. Interprets computation of rational numbers by describing real-world contexts and solves these problems (7.NS.1; NS.2)

 

 

 

2b. Knows and approximates irrational numbers

1. Knows there are irrational numbers and uses rational approximations of irrational numbers to compare the size of irrational numbers and locates them on a number line (8.NS.1; 8.NS.2)

2. Estimate the value of expressions containing irrational numbers (8.NS.2)

3. Evaluates square roots of small perfect squares and cube roots of small perfect cubes (8.EE.2)

2c. Write numbers in scientific notation

1. Uses scientific notation to estimate very large quantities and expresses comparisons between two quantities in this form (8.EE.3)

2. Converts numbers between scientific notation to standard notation

 

Expressions and Equations

3a. Uses distributive property

1. Uses properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients - distributive property (7.EE.1)

2. Utilizes different forms of an expression to make sense of the problem (7.EE.2)

3. Solves linear equations with rational number coefficients that require expanding expressions with the distributive property and collecting like terms (8.EE.7)

3b. Models and solves equations and inequalities

1. Solves real world and mathematical problems using numerical and algebraic expressions and equations. (7.EE.3)

2. Uses variables to represent quantities and construct simple equations and inequalities to solve problems (7.EE.4)

3c. Understands linear equations through tables, graphs, and equations

1. Interprets unit rate as slope of the graph and compares relationships of different proportions and in different ways (8.EE.5)

3d. Solves linear equations

  1. 1.Solves linear equations with rational number coefficients that require expanding expressions with the distributive property and collecting like terms (8.EE.7)

 

 

 

 

 

Statistics and Probability

4a. Sampling and inferencing about populations

1. Understands random sampling to uses it to draw inferences about a population (7.SP1; SP.2)

2. Draws informal comparative inferences about two populations by measuring the difference between the centers and measures of variability (7.SP.3; SP.4)

          4b. Understands and models simple and compound events

1.Understands probability as a number between 0 and 1 and relates the probability to "impossible", "less likely than not", "neither likely or not", "more likely than not", "certain" (7.SP.5)

2. Approximates the probability of a chance event by collecting data and understands that the long-term relative frequency migrates toward theoretical probability (7.SP.6)

3. Develops a probability model and uses it to find probabilities and explains why discrepancy exists if the agreement is not close to the observed frequencies (7.SP.7)

4. Finds probabilities of compound events by using lists, tables, tree diagrams and simulations (7.SP.8)

 

Geometry

5a. Solves area and volume of two and three dimensional figures

1. Knows formulas for the area and circumference of a circles and uses them to solve problems (7.G.4)

2. Solves real-world problems involving area, surface area and volume of two and three-dimensional figures composed of other known figures. (7.G.6)

3. Knows and uses the formulas for the volume of cones, cylinders, and spheres to solve problems - pyramids (8.G.9)

5b. Applies and draws geometric transformations

1. Verifies the properties of rotation, reflections, and translations and describes the effect these have on 2-dimensional figures (8.G.1; 8.G.3)

2.Understands that a two-dimension figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections or translations (8.G.2)

3. Understands that a two-dimension figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations (8.G.4)

 

5c. Solves and reasons about angles

1. Uses facts about types of angles in a problem to write and solve equations for an unknown angle in a figure (7.G.5)

2. Makes informal arguments to establish facts about the angle sum and exterior angle of triangles and uses these in exploring parallel lines cut by transversal (8.G.5)

5d. Describes and draws geometric figures with given conditions.

1. Draws geometric shapes (triangles) with given conditions (7.G.2)

2. Describes the two-dimensional figures that result from slicing three-dimensional figures (7.G.3)

 

Mathematical Problem Solving

6a. Accurately solves grade appropriate problems

6b. Effectively communicates problem solving steps, strategies, and solutions

6c. Accurately solves and communicates solutions for each of the foundational 24 skills

 

Mathematical Practices

7a. Applies mathematical practices to solving problems

1. Makes sense of problems and perseveres in solving them

2. Reasons abstractly and quantitatively

3. Constructs viable arguments and critiques the reasoning of others

4. Models with mathematics

5. Uses appropriate tools strategically

6. Attends to precision

7. Looks for and makes use of structure

8. Looks for and expresses regularity in repeated reasoning

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