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# 7th Grade Learning Progression (v2)

last edited by 2 years, 9 months ago

Welcome to the new progression for 7th Grade. This progression builds upon Math Framework Project Phase 1 work (see Progression v1 here), taking many of the best features and building in an Overarching Question, Essential Questions, and Big Ideas for each unit. This new model takes the work of bundling standards to the next level by grouping together grade level concepts under Big Ideas. The Big Ideas are designed to represent the critical mathematics of this grade level in a manner we believe to be more coherent and productive as a guide for planning instruction, assessment, and intervention. Big Ideas are not a replacement for the objectives.

### Full Objectives

Unit 0:

How does mindset affect learning mathematics?
1. Math is about learning not performing.
2. Math is about making sense.
3. Math is filled with conjectures, creativity, and uncertainty.
4. Mistakes are a beautiful thing.
• Develop a deep and flexible conceptual understanding
• Develop accurate and appropriate procedural fluency
• Develop strategies for problem solving
• Develop mathematical reasoning
• Develop a productive mathematical disposition
• Develop the ability to make conjectures, model and generalize
• Develop the ability to communicate mathematically

Unit 1:

Rationals

Timing

3-4 weeks

Objectives

7.N.1.1

7.N.1.2

7.N.1.3

7.N.2.1

7.N.2.2

7.N.2.3

7.N.2.4

7.N.2.5

What are rational numbers and why are they useful?

1. How do we mathematically represent rational numbers?
2. How do multiplication and division apply to rational numbers?
3. When is it appropriate to use estimation and/or approximation?
4. How important are estimations in real life situations?
5. How do I make a reasonable estimate?
6. Where are rational numbers found in real life?
1. Equivalent rational numbers can be represented in multiple ways.
2. Multiplication and division of integers can be estimated and illustrated.
3. Rational numbers are found in the real-world.

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.1.3  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  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 algorithm.

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

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

Unit 2:

Expressions, Equations and Inequalities

Timing

3-4 weeks

Objectives

7.A.3.1

7.A.3.2

7.A.4.1

7.A.4.2

7.GM.2.1

7.N.2.6

How are rational numbers used in expressions, equations and inequalities?

1. How does absolute value relate to distance?

2. How can situations be represented algebraically?

3. How can an equivalent expression be expressed?

4. How do the number properties apply to expressions, equations, and inequalities?

5. Does the order in which operations are worked in expressions, equations and inequalities impact the answer?

6. How does the use of technology, such as calculators, impact my answer?

1. Rational numbers are used to represent and solve algebraic expressions.
2. Equations are used to represent and solve mathematical and real-world problems.
3. Inequalities are used to represent and solve mathematical and real-world problems.

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.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.

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

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:

Introduction to Proportional Relationships

Timing

3-4 weeks

Objectives

7.A.1.1

7.A.1.2

7.A.2.1

7.A.2.3

7.A.2.4

What are proportional relationships?

1. When do I use proportional comparisons?

2. Why do I use proportional comparisons?

3. How does comparing quantities describe the relationship between them?

4. How do I determine which way best represents a  proportional relationship?

5. How do I know when to use which representation?

1. A proportional relationship is when two quantities vary directly.
2. Proportionality is used in the real world.
3. Proportional relationships can be represented in a variety of ways. Different representations are useful in different situations.

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

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

Unit 4:

Proportionality

Timing

4-5 weeks

Objectives

7.A.2.2

7.A.2.3

7.A.2.4

7.D.1.2

7.GM.3.1

7.GM.3.2

7.GM.4.1

7.GM.4.2

7.GM.4.3

How can proportionality be applied to the real world?

1. In what situations are proportions most useful?

2. How can measurements and information about similar figures be used to solve problems?

3. How can you use percents to solve a problem?

1. Proportional relationships have real world applications.
2. Proportionality can be applied to attributes of geometric figures.
3. There is a proportional relationship between diameter and the circumference which is applied to the circumference and area of a circle.

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.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. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.

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.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.

Unit 5:

Two Dimensional and Three Dimensional Shapes

Timing

4-5 weeks

Objectives

7.GM.1.1

7.GM.1.2

7.GM.2.1

7.GM.2.2

7.GM.4.3

How can we measure two and three-dimensional shapes?

1. Why are geometric figures relevant and important?

2. How can you use different measurements to solve real-life problems?

3. How are two and three-dimensional figures related to each other?

4. How are rational numbers used in two and three-dimensional shapes?

1. Three-dimensional figures have surface area and volume.
2. Two-dimensional shapes have area and perimeter.

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.

7.GM.2.2 Find the area and perimeter of composite figures to solve real-world and mathematical problems.

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.

Unit 6:

Probability

Timing

3-4 weeks

Objectives

7.D.1.1

7.D.1.2

7.D.2.1

7.D.2.2

7.D.2.3

7.N.1.3*

How does probability relate to rational numbers and proportionality?

1.  How do you predict future probability based on data?
2. How can we gather, organize and display data to communicate and justify results in the real world?

3. What is the best way to display data for given real world situation?

4. How is proportionality used in probability?

1. Data can be displayed, analyzed and applied in a variety of ways.
2. Proportional reasoning can be used to determine probability.
3. Probability can be expressed as a rational number.

7.D.1.1 Design simple experiments, collect data and calculate measures of central tendency (mean, median, and mode) and spread (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. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.

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 probabilities.

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

Culminating Unit

Timing

1-2 Weeks

Objectives

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