Welcome to the learning progression for 7th grade. This progression incorporates the overall topics of this grade-level's mathematics and is formatted with Overarching Questions, Essential Questions, and Big Ideas for each unit. This progression model takes the work of bundling standards to the next level by grouping together grade-level concepts in the Big Ideas sections. The Big Ideas are designed to represent the critical mathematics of this grade level in a manner that is more coherent and productive as a guide for planning instruction, assessment, and intervention. Big Ideas are for progression and planning and are not a replacement for the OAS-M objectives.
The use of an asterisk (*) indicates an objective is repeated in another unit or an objective that is partially taught in a unit and will be taught in its entirety in a later unit.
Unit |
Overarching Question |
Essential Questions |
Big Ideas |
Full Objectives |
How does mindset affect learning mathematics? |
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Unit 1: Timing 3-4 weeks Objectives
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What are rational numbers and why are they useful? |
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7.N.1.1 Compare and order rational numbers expressed in various forms using the symbols "<", ">", and "=". 7.N.1.2 Recognize and generate equivalent representations of rational numbers, including equivalent fractions. 7.N.2.1 Estimate solutions to multiplication and division of integers in order to assess the reasonableness of results. 7.N.2.2 Illustrate multiplication and division of integers using a variety of representations. 7.N.2.3 Multiply and divide integers in a variety of situations; use efficient and generalizable procedures, including standard algorithms. 7.N.2.4 Raise rational numbers (integers, fractions, and decimals) to positive integer exponents. 7.N.2.5 Model and solve problems using rational numbers involving addition, subtraction, multiplication, division, and positive integer exponents. |
Unit 2: Expressions, Equations and Inequalities Timing 3-4 weeks Objectives
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How are rational numbers used in expressions, equations and inequalities? |
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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.4.1 Use properties of operations (associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. 7.A.4.2 Evaluate numerical expressions using calculators and other technologies and justify solutions using order of operations and grouping symbols. 7.GM.2.1 Develop and use the formula to determine the area of a trapezoid. 7.N.1.3 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. Apply the concept of absolute value to model and solve problems. |
Unit 3: Introduction to Proportional Relationships
Timing 3-4 weeks Objectives |
What are proportional relationships? |
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7.A.1.1 Identify a relationship between two varying quantities, x and y, as proportional if it can be expressed in the form y/x = k or y=kx; distinguish proportional relationships from non-proportional relationships. 7.A.1.2 Recognize that the graph of a proportional relationship is a line through the origin and the coordinate (1, r), where r is the slope and 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.A.2.3 Use proportional reasoning to solve problems involving ratios. 7.A.2.4 Use proportional reasoning to assess the reasonableness of solutions. |
Unit 4:
Timing 4-5 weeks Objectives |
How can proportionality be applied to the real world? |
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7.A.2.2 Solve multi-step problems with proportional relationships (e.g., distance-time, percent increase or decrease, discounts, tips, unit pricing, mixtures and concentrations, similar figures, other mathematical situations). 7.A.2.3 Use proportional reasoning to solve problems involving ratios. 7.A.2.4 Use proportional reasoning to assess the reasonableness of solutions. 7.D.1.2 Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. 7.GM.3.1 Solve problems that require the conversion of weights and capacities within the same measurement systems using appropriate units. 7.GM.3.2 Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is pi (𝜋) and can be approximated by rational numbers such as 22/7 and 3.14. 7.GM.3.3 Calculate the circumference and area of circles to solve problems in various contexts, in terms of pi (𝜋) and using approximations for pi (𝜋). 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 to determine side lengths and areas of similar triangles and rectangles. 7.GM.4.3 Graph and describe translations (with directional and algebraic instructions), reflections across the x- and y-axes, and rotations in 90o increments about the origin of figures on a coordinate plane, and determine the coordinates of the vertices of a figure after a transformation. |
Unit 5: Two Dimensional and Three Dimensional Shapes Timing 4-5 weeks Objectives |
How can we measure two and three-dimensional shapes? |
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7.GM.1.1 Recognize that the surface area of a rectangular prism can be found by finding the area of each component of the net of that figure. Know that rectangular prisms of different dimensions can have the same surface area. 7.GM.1.2 Using a variety of tools and strategies, develop the concept that surface area of a rectangular prism can be found by wrapping the figure with same-sized square units without gaps or overlap. Use appropriate measurements (e.g., cm2 ). 7.GM.1.3 Using a variety of tools and strategies, develop the concept that the volume of rectangular prisms can be found by counting the total number of same-sized unit cubes that fill a shape without gaps or overlaps. Use appropriate measurements (e.g., cm3 ). 7.GM.2.1 Develop and use the formula to determine the area of a trapezoid. 7.GM.2.2 Find the area and perimeter of composite figures. 7.GM.4.3 Graph and describe translations (with directional and algebraic instructions), reflections across the x- and y-axes, and rotations in 90o increments about the origin of figures on a coordinate plane, and determine the coordinates of the vertices of a figure after a transformation. |
Unit 6: Timing 3-4 weeks Objectives |
How does probability relate to rational numbers and proportionality?
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7.D.1.1 Design simple experiments, collect data, and calculate measures of center (mean, median, and mode) and spread (range and interquartile range). Use these quantities to draw conclusions about the data collected and make predictions. 7.D.1.2 Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. 7.D.1.3 Use technology to create and analyze box plots. 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. 7.D.2.2 Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions. 7.D.2.3 Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on theoretical probabilities. 7.N.1.2 Recognize and generate equivalent representations of rational numbers, including equivalent fractions.
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Timing 1-2 Weeks Objectives
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How can students apply proportionality to real-world contexts? | |||
Distance Learning Resources/ Supplemental Activities |
How can students develop and show evidence of understanding? | Multiple objectives are covered in this material. These math tasks are designed to enhance current curriculum and support distance learning. |
Introduction to the OKMath Framework