Unit

Overarching Question

Essential Questions

Big Ideas

Full Objectives

Unit 0:
Growth Mindset

How does mindset affect learning mathematics? 

 Math is about learning not performing.
 Math is about making sense.
 Math is filled with conjectures, creativity, and uncertainty.
 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
34 weeks
Objectives
7.N.1.1
7.N.1.2
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?

 How do we mathematically represent rational numbers?
 How do multiplication and division apply to rational numbers?
 When is it appropriate to use estimation and/or approximation?
 How important are estimations in real life situations?
 How do I make a reasonable estimate?
 Where are rational numbers found in real life?

 Equivalent rational numbers can be represented in multiple ways.
 Multiplication and division of integers can be estimated and illustrated.
 Rational numbers are found in the realworld.

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
34 weeks
Objectives
7.A.3.1
7.A.3.2
7.A.4.1
7.A.4.2
7.GM.2.1
7.N.1.3

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


How does absolute value relate to distance?

How can situations be represented algebraically?

How can an equivalent expression be expressed?

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

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

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

 Rational numbers are used to represent and solve algebraic expressions.
 Equations are used to represent and solve mathematical and realworld problems.
 Inequalities are used to represent and solve mathematical and realworld 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.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
34 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?


When do I use proportional comparisons?

Why do I use proportional comparisons?

How does comparing quantities describe the relationship between them?

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

How do I know when to use which representation?

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

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 nonproportional 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:
Proportionality
Timing
45 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.3.3
7.GM.4.1
7.GM.4.2
7.GM.4.3

How can proportionality be applied to the real world?


In what situations are proportions most useful?

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

How can you use percents to solve a problem?

 Proportional relationships have real world applications.
 Proportionality can be applied to attributes of geometric figures.
 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 multistep problems with proportional relationships (e.g., distancetime, 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 yaxes, and rotations in 90^{o} 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
45 weeks
Objectives
7.GM.1.1
7.GM.1.2
7.GM.1.3
7.GM.2.1
7.GM.2.2
7.GM.4.3

How can we measure two and threedimensional shapes?


Why are geometric figures relevant and important?

How can you use different measurements to solve reallife problems?

How are two and threedimensional figures related to each other?

How are rational numbers used in two and threedimensional shapes?

 Threedimensional figures have surface area and volume.
 Twodimensional shapes have area and perimeter.

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 samesized square units without gaps or overlap. Use appropriate measurements (e.g., cm^{2} ).
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 samesized unit cubes that fill a shape without gaps or overlaps. Use appropriate measurements (e.g., cm^{3} ).
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 yaxes, and rotations in 90^{o} 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:
Probability
Timing
34 weeks
Objectives
7.D.1.1
7.D.1.2
7.D.1.3
7.D.2.1
7.D.2.2
7.D.2.3
7.N.1.2*

How does probability relate to rational numbers and proportionality?

 How do you predict future probability based on data?

How can we gather, organize and display data to communicate and justify results in the real world?

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

How is proportionality used in probability?

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

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.

Culminating Unit
Timing
12 Weeks
Objectives

How can students apply proportionality to realworld 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. 
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