Unit

Unit Storyline

Full Objectives

Unit 1

Order of Operations

Timing

1 - 3 weeks

Objectives

7.N.2.2

7.N.2.4

7.A.4.1

7.A.4.2

     7.GM.2.2*

Students are using shapes comprised of squares and rectangles to explore and apply the order of operations and properties of numbers. Properties of squares allow students to interact with positive integer exponents.

7.N.2.2 - Illustrate multiplication and division of integers using a variety of representations.

7.N.2.4 - Raise integers to positive integer exponents.

7.A.4.1 - Use properties of operations (limited to associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents

7.A.4.2 - Apply understanding of order of operations and grouping symbols when using calculators and other technologies.

Unit 2

Rational Numbers

Timing

1 - 3 weeks

Objectives

  7.N.1.1*

7.N.1.2

7.N.2.3

7.N.2.6

 7.A.2.3*

Students will apply properties of operations to simplify expressions. Proportional reasoning allows students to work with rational numbers and explore scenarios to identify generalizable procedures and algorithms.

7.N.1.1 - Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal.

7.N.1.2 - Compare and order rational numbers expressed in various forms using the symbols <, >, and =.

7.N.2.3 - Solve real-world and mathematical problems involving addition, subtraction, multiplication and division of rational numbers; use efficient and generalizable procedures including but not limited to standard algorithms.

7.N.2.6 - Explain the relationship between the absolute value of a rational number and the distance of that number from zero on a number line. Use the symbol for absolute value.

Unit 3

Representing Probability

Timing

1 - 3 weeks

Objectives

7.N.1.3

7.D.2.1

7.D.2.2

Students will use reasoning to apply knowledge of probability to analyze situations.

7.N.1.3 - Recognize and generate equivalent representations of rational numbers, including equivalent fractions.

7.D.2.1 - Determine the theoretical probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1.

Unit 4

2D and 3D Shapes

Timing

4 - 6 weeks

Objectives

7.N.2.5

7.A.3.1

7.A.3.2

7.A.3.3

7.GM.1.1

7.GM.1.2

7.GM.2.1

7.GM.2.2*

Students will develop formulas in order to solve real-world problems involving 2D and 3D objects. Students will make connections between polygons and geometric solids.

7.N.2.5 - Solve real-world and mathematical problems involving calculations with rational numbers and positive integer exponents.

7.A.3.1 - Write and solve problems leading to linear equations with one variable in the form px + q = r and

p(x + q) = r, where p, q, and r are rational numbers.

7.A.3.2 - Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form x + p > q and x + p < q, where p and q are nonnegative rational numbers.

7.A.3.3 -  Represent real-world or mathematical situations using equations and inequalities involving variables and rational numbers

7.GM.1.1 - Using a variety of tools and strategies, develop the concept that surface area of a rectangular prism with rational-valued edge lengths can be found by wrapping the figure with same-sized square units without gaps or overlap. Use appropriate measurements such as cm².

7.GM.1.2 - Using a variety of tools and strategies, develop the concept that the volume of rectangular prisms with rational-valued edge lengths can be found by counting the total number of same-sized unit cubes that fill a shape without gaps or overlaps. Use appropriate measurements such as cm³ .

7.GM.2.1 - Develop and use the formula to determine the area of a trapezoid to solve problems.

Unit 5

Circles & Proportional Relationships

Timing

4 - 6 weeks

Objectives

7.N.1.1*

7.N.2.1

7.A.1.1

7.A.1.2

7.A.2.1

7.GM.3.1

7.GM.3.2

7.A.2.4

7.D.1.1

Students will identify the proportional relationships in circles and make connections by representing the relationships graphically and otherwise.

7.N.1.1 - Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal.

7.N.2.1 - Estimate solutions to multiplication and division of integers in order to assess the reasonableness of results.

7.A.1.1 -  Describe that the relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx; distinguish proportional relationships from other relationships, including inversely proportional relationships ( xy = k or y =k/x ).

7.A.1.2 - Recognize that the graph of a proportional relationship is a line through the origin and the coordinate (1, r), where both ! and the slope are the unit rate (constant of proportionality, k).

7.A.2.1 - Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations.

7.GM.3.1 - Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is π  and can be approximated by rational numbers such as 22/7 and 3.14.

7.GM.3.2 -  Calculate the circumference and area of circles to solve problems in various contexts, in terms of π and using approximations for π .

7.A.2.4 - Use proportional reasoning to assess the reasonableness of solutions.

Unit 6

Data & Proportional Reasoning

Timing

4 - 6 weeks

Objectives

7.A.2.1

7.A.2.2

7.A.2.3*

7.D.1.2

7.D.2.3

Students will represent proportional relationships in a variety of ways.

7.A.2.1 - Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations.

7.A.2.2 - Solve multi-step problems involving proportional relationships involving distance-time, percent increase or decrease, discounts, tips, unit pricing, similar figures, and other real-world and mathematical situations.

7.A.2.3 - Use proportional reasoning to solve real-world and mathematical problems involving ratios.

7.D.1.2 - Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.

Unit 7

Similarity & Transformations

Timing

5 - 7 weeks

Objectives

7.N.2.6*

7.GM.4.1

7.GM.4.2

7.GM.4.3

Students will look at transformations of 2D shapes and apply proportions to determine scale factors and new side lengths.

7.N.2.6 - Explain the relationship between the absolute value of a rational number and the distance of that number from zero on a number line. Use the symbol for absolute value.

7.GM.4.1 - Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors resulting from dilations.

7.GM.4.2 - Apply proportions, ratios, and scale factors to solve problems involving scale drawings and determine side lengths and areas of similar triangles and rectangles.

7.GM.4.3 - Graph and describe translations and reflections of figures on a coordinate plane and determine the coordinates of the vertices of the figure after the transformation.