Courses of Study : Mathematics

Proportional Reasoning
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Mathematics (2019)
Grade(s): 7
All Resources: 2
Lesson Plans: 1
Classroom Resources: 1
1. Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Compute a unit rate for ratios that compare quantities with different units.
  • Determine the unit rate for a given ratio, including unit rates expressed as a complex fraction.

  • Example: if a runner runs 1/2 mile every 3/4 hour, a student should be able to write the ratio as a complex fraction.)
Teacher Vocabulary:
  • Unit rate
  • Ratio
  • Unit
  • Complex fractions
Knowledge:
Students know:
  • What a unit rate is and how to calculate it given a relationship between quantities.
  • Quantities compared in ratios are not always whole numbers but can be represented by fractions or decimals.
  • A fraction can be used to represent division.
Skills:
Students are able to:
Compute unit rates associated with ratios of fractional
  • lengths.
  • Areas.
  • quantities measured in like or different units.
Understanding:
Students understand that:
  • Two measurements that create a unit rate are always different (miles per gallon, dollars per hour)
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.1.1: Define unit rate, proportions, area, length, and ratio.
M.7.1.2: Recall how to find unit rates using ratios.
M.7.1.3: Recall the steps used to solve division of fraction problems.

Prior Knowledge Skills:
  • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
  • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
  • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
  • Generate equivalent fractions.
  • Define quantity, fraction, and ratio.
  • Reinterpret a fraction as a ratio.
    Example: Read 2/3 as 2 out of 3.
  • Write a ratio as a fraction.
  • Create a ratio or proportion from a given word problem, diagram, table, or equation.
  • Calculate unit rate or rate by using ratios or proportions.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.1 Calculate a unit rate (limited to whole numbers under 100).


Mathematics (2019)
Grade(s): 7
All Resources: 4
Learning Activities: 1
Lesson Plans: 1
Classroom Resources: 2
2. Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

a. Use equivalent ratios displayed in a table or in a graph of the relationship in the coordinate plane to determine whether a relationship between two quantities is proportional.

b. Identify the constant of proportionality (unit rate) and express the proportional relationship using multiple representations including tables, graphs, equations, diagrams, and verbal descriptions.

c. Explain in context the meaning of a point (x,y) on the graph of a proportional relationship, with special attention to the points (0,0) and (1, r) where r is the unit rate.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Decide whether a relationship between two quantities is proportional.
  • Recognize that not all relationships are proportional.
  • Use equivalent ratios in a table or a coordinate graph to verify a proportional relationship.
  • Identify the constant of proportionality when a proportional relationship exists between two quantities.
  • Use a variety of models (tables, graphs, equations, diagrams and verbal descriptions) to demonstrate the constant of proportionality.
  • Explain the meaning of a point (x, y) in the context of a real-world problem.
  • Example, if a boy charges $6 per hour to mow lawns, this relationship can be graphed on the coordinate plane. The point (1,6) means that after 1 hour of working the boy makes $6, which shows the unit rate of $6 per hour.
Teacher Vocabulary:
  • Equivalent ratios
  • proportional
  • Coordinate plane
  • Ratio table
  • Unit rate
  • Constant of proportionality
  • Equation
  • ordered pair
Knowledge:
Students know:
  • (2a) how to explain whether a relationship is proportional.
  • (2b) that the constant of proportionality is the same as a unit rate. Students know:
    • where the constant of proportionality can be found in a table, graph, equation or diagram.
    • (2c) that the constant of proportionality or unit rate can be found on a graph of a proportional relationship where the input value or x-coordinate is 1.
Skills:
Students are able to:
  • (2a) determine if a proportional relationship exists when given a table of equivalent ratios or a graph of the relationship in the coordinate plane.
  • (2b) identify the constant of proportionality and express the proportional relationship using a variety of representations including tables, graphs, equations, diagrams, and verbal descriptions.
  • (2c) model a proportional relationship using coordinate graphing.
  • Explain the meaning of the point (1, r), where r is the unit rate or constant of proportionality.
Understanding:
Students understand that:
  • (2a) A proportional relationship requires equivalent ratios between quantities. Students understand how to decide whether two quantities are proportional.
  • (2b) The constant of proportionality is the unit rate. Students are able to identify the constant of proportionality for a proportional relationship and explain its meaning in a real-world context. (2c) The context of a problem can help them interpret a point on a graph of a proportional relationship.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.2.1: Define proportions and proportional relationships.
M.7.2.2: Demonstrate how to write ratios as a fraction.
M.7.2.3: Define equivalent ratios and origin.
M.7.2.4: Locate the origin on a coordinate plane.
M.7.2.5 Show how to graph on Cartesian plane.
M.7.2.6: Determine if the graph is a straight line through the origin.
M.7.2.7: Use a table or graph to determine whether two quantities are proportional.
M.7.2.8: Define a constant and equations.
M.7.2.9: Create a table from a verbal description, diagram, or a graph.
M.7.2.10: Identify numeric patterns and finding the rule for that pattern.
M.7.2.11: Recall how to find unit rate.
M.7.2.12: Recall how to write equations to represent a proportional relationship.
M.7.2.13: Discuss the use of variables.
M.7.2.14: Define ordered pairs.
M.7.2.15: Show how to plot points on a Cartesian plane.
M.7.2.16: Locate the origin on the coordinate plane.

Prior Knowledge Skills:
  • Recall basic addition, subtraction, multiplication, and division facts.
  • Define ordered pair of numbers.
  • Define x-axis, y-axis, and zero on a coordinate.
  • Specify locations on the coordinate system.
  • Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
  • Label the horizontal axis (x).
  • Label the vertical axis (y).
  • Identify the x- and y- values in ordered pairs.
  • Model writing ordered pairs.
  • Define quantity, fraction, and ratio.
  • Reinterpret a fraction as a ratio.
    Example: Read 2/3 as 2 out of 3.
  • Write a ratio as a fraction.
  • Create a ratio or proportion from a given word problem, diagram, table, or equation.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.2 Use a ratio to model or describe a real-world relationship.


Mathematics (2019)
Grade(s): 7
All Resources: 7
Learning Activities: 1
Classroom Resources: 6
3. Solve multi-step percent problems in context using proportional reasoning, including simple interest, tax, gratuities, commissions, fees, markups and markdowns, percent increase, and percent decrease.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use proportional reasoning strategies including setting up and solving proportions to solve problems involving simple interest, tax, gratuities, commissions, fees, markups, percent increase, markdowns or percent decrease.

  • Example: Students might be asked to "order" from a menu for lunch then calculate the tax and gratuities to determine the total cost.
Teacher Vocabulary:
  • Proportion
  • Simple interest
  • Tax
  • Gratuities
  • Commissions
  • Fees
  • Markups and markdowns
  • percent increase and percent decrease
Knowledge:
Students know:
  • how to interpret a real-world problem to determine what is being asked.
  • Techniques for calculating and using percents to solve problems in context.
  • how to interpret the solution in the context of the problem.
Skills:
Students are able to:
  • Write and solve proportions to help them solve real-world problems involving percent.
  • Solve problems that require them to calculate: simple interest, tax, gratuities, commission, fees, mark ups, markdowns, percent increase and percent decrease.
Understanding:
Students understand that:
  • percents relate to real-world contexts, and how to determine the reasonableness of their answers based on that context.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.3.1: Define interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.
M.7.3.2: Apply definitions to context in real world problems.
M.7.3.3: Solve proportional problems.
M.7.3.4: Recall how to find percent and ratios.
M.7.3.5: Recall steps for solving multi-step problems.

Prior Knowledge Skills:
  • Define percent.
  • Calculate a proportion for missing information.
  • Identify a proportion from given information.
  • Solve a proportion using part over whole equals percent over 100.
  • Define equation and variable.
  • Set up an equation to represent the given situation, using correct mathematical operations and variables.
  • Identify the unknown, in a given situation, as the variable.
  • Solve the equation represented by the real-world situation.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.3 Calculate 10%, 20%, 25%, and 50% of a number up to 100.


Number Systems and Operations
Apply and extend prior knowledge of addition, subtraction, multiplication, and division to operations with rational numbers.
Mathematics (2019)
Grade(s): 7
All Resources: 11
Learning Activities: 5
Classroom Resources: 6
4. Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.

a. Identify and explain situations where the sum of opposite quantities is 0 and opposite quantities are defined as additive inverses.

b. Interpret the sum of two or more rational numbers, by using a number line and in real-world contexts.

c. Explain subtraction of rational numbers as addition of additive inverses.

d. Use a number line to demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

e. Extend strategies of multiplication to rational numbers to develop rules for multiplying signed numbers, showing that the properties of the operations are preserved.

f. Divide integers and explain that division by zero is undefined. Interpret the quotient of integers (with a non-zero divisor) as a rational number.

g. Convert a rational number to a decimal using long division, explaining that the decimal form of a rational number terminates or eventually repeats.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Explain situations where opposite quantities combine to make zero, known as additive inverses.
  • Apply their knowledge of addition and subtraction of rational numbers to describe real-world contexts.
  • Add and subtract rational numbers using number lines to show connection to distance
  • Explain the connection between subtraction and addition of additive inverses.
  • Model multiplication and division of rational numbers (number horizontal and vertical number lines, integer chips, bar models).
  • Use properties of operations to multiply signed numbers.
  • Convert rational numbers to a decimal using long division and determine if the result is terminating or repeating.
Teacher Vocabulary:
  • Integers
  • Rational numbers
  • Additive inverses
  • opposite quantities
  • Absolute value
  • Terminating decimals
  • Repeating decimals
Knowledge:
Students know:
  • a number and its opposite have a sum of 0.
  • A number and its opposite are called additive inverses.
  • Strategies for adding and subtracting two or more numbers.
  • Absolute value represents distance on a number line, therefore it is always non-negative.
  • Strategies for multiplying signed numbers.
  • Every quotient of integers (with non-zero divisor) is a rational number.
  • If p and q are integers, then -(p/q) = (-p)/q = p/(-q).
  • The decimal form of a rational number terminates or eventually repeats.
Skills:
Students are able to:
  • add rational numbers.
  • Subtract rational numbers.
  • Represent addition and subtraction on a number line diagram.
  • Describe situations in which opposite quantities combine to make 0.
  • Find the opposite of a number.
  • Interpret sums of rational numbers by describing real-world contexts.
  • Show that the distance between two rational numbers on the number line is the absolute value of their difference.
  • Use absolute value in real-world contexts involving distances.
  • Multiply and divide rational numbers.
  • Convert a rational number to a decimal using long division.
Understanding:
Students understand that:
  • finding sums and differences of rational numbers (negative and positive) involves determining direction and distance on the number line.
  • Subtraction of rational numbers is the same as adding the additive inverse, p - q = p + (-q).
  • If a factor is multiplied by a number greater than one, the answer is larger than that factor.
  • If a factor is multiplied by a number between 0 and 1, the answer is smaller than that factor.
  • Multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers.
  • Integers can be divided, provided that the divisor is not zero.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.4.1: Define rational numbers, horizontal, and vertical.
M.7.4.2: Recall how to extend a horizontal number line.
M.7.4.3: Recall how to extend a vertical number line.
M.7.4.4: Demonstrate addition and subtraction of whole numbers using a horizontal or vertical number line.
M.7.4.5: Give examples of rational numbers.
M.7.4.6: Define absolute value and additive inverse.
M.7.4.7: Explain that the sum of a number and its opposite is zero.
M.7.4.8: Locate positive, negative, and zero numbers on a number line.
M.7.4.9: Recall properties of addition and subtraction.
M.7.4.10: Model addition and subtraction using manipulatives.
M.7.4.11: Show addition and subtraction of 2 or more rational numbers using a number line within real world context.
M.7.4.12: Define absolute value and additive inverse.
M.7.4.13: Show subtraction as the additive inverse.
M.7.4.14: Give examples of the opposite of a given number.
M.7.4.15: Show addition and subtraction using a number line.
M.7.4.16: Discuss various strategies for solving real-world and mathematical problems.
M.7.4.17: Identify properties of operations for addition and subtraction.
M.7.4.18: Recall the steps for solving addition and subtraction of rational numbers.
M.7.4.19: Identify the difference between two rational numbers on a number line.
M.7.4.20: Recall the steps of solving multiplication of rational numbers.
M.7.4.21: Identify the pattern for multiplying signed numbers.
M.7.4.22: Recall the steps of solving division of rational numbers.
M.7.4.23: Explain that dividing a rational number zero is undefined.
M.7.4.24: Recall that a fraction can be written as a division problem.
M.7.4.25: Recall the steps to divide two rational numbers.
M.7.4.26: Identify whether a decimal is terminating or repeating.

Prior Knowledge Skills:
  • Define parentheses, braces, and brackets.
  • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
  • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
  • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
  • Generate equivalent fractions.
  • Show on a number line that numbers that are equal distance from 0 and on opposite sides of 0 have opposite signs.
  • Define rational number.
  • Arrange integers and /or rational numbers on a horizontal or vertical number line.
  • Locate the position of integers and/or rational numbers on a horizontal or vertical number line.
  • Identify a rational number as a point on the number line.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.4 Add and subtract integers up to 15.


Mathematics (2019)
Grade(s): 7
All Resources: 0
5. Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Apply their knowledge of addition, subtraction, multiplication and division of rational numbers to describe real-world contexts.
  • Solve multi-step problems using numerical expressions that involve addition, subtraction, multiplication, and/or division of rational numbers, including problems that involve complex fractions
Teacher Vocabulary:
  • Rational numbers
  • Complex fractions
  • properties of operations
Knowledge:
Students know:
  • how to model real-world problems to include situations involving elevation, temperature changes, debits and credits, and proportional relationships with negative rates of change.
  • how to evaluate numerical expressions with greater fluency, using the properties of operations when necessary.
Skills:
Students are able to:
  • Solve real-world and mathematical problems involving the four operations with rational numbers.
Understanding:
Students understand that:
  • rational numbers can represent values in real-world situations.
  • properties of operations learned with whole numbers in elementary apply to rational numbers.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.5.1: Discuss various strategies for solving real-world and mathematical problems.
M.7.5.2: Recall steps for solving fractional problems.
M.7.5.3: Identify properties of operations for addition and multiplication.
M.7.5.4: Recall the rules for multiplication and division of rational numbers.
M.7.5.5: Recall the rules for addition and subtraction of rational numbers.

Prior Knowledge Skills:
  • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
  • Define rational number.
  • Arrange integers and /or rational numbers on a horizontal or vertical number line.
  • Locate the position of integers and/or rational numbers on a horizontal or vertical number line.
  • Identify a rational number as a point on the number line.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.5 Solve multiplication problems up to fifteen with whole number factors.


Algebra and Functions
Create equivalent expressions using the properties of operations.
Mathematics (2019)
Grade(s): 7
All Resources: 1
Classroom Resources: 1
6. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use properties of operations to produce combined and re-written forms of the expressions that are useful in resolving mathematical and contextual problems.
Teacher Vocabulary:
Term
  • like terms
  • Constant
  • Factor
  • Expression
  • Rational coefficient
  • Knowledge:
    Students know:
    • how to add, subtract, multiply, and divide rational numbers.
    • A(b + c) = ab + ac.
    • how to find the greatest common factor of two or more terms.
    Skills:
    Students are able to:
    • apply properties of operations as strategies to add and subtract linear expressions with rational coefficients.
    • Apply properties of operations as strategies to factor linear expressions with rational coefficients.
    • Apply properties of operations as strategies to expand linear expressions with rational coefficients.
    Understanding:
    Students understand that:
    • only like terms can be combined, e.g., x + y = x + y but x + x = 2x.
    • To factor an expression, one must factor out the greatest common factor.
    • There are many different ways to write the same expression.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.6.1: Define linear expression, rational, coefficient, and rational coefficient.
    M.7.6.2: Simplify an expression by dividing by the greatest common factor (Ex. 18x + 6y= 6(3x + y).
    M.7.6.3: Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
    M.7.6.4: Recognize the property demonstrated in a given expression.
    M.7.6.5: Combine like terms of a given expression.
    M.7.6.6: Recall how to find the greatest common factor.
    M.7.6.7: Give examples of the properties of operations including distributive, commutative, and associative.

    Prior Knowledge Skills:
    • Apply properties of operations for addition and subtraction.
    • Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.
    • Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
    • Combine terms that are alike of a given expression.
    • Recognize the property demonstrated in a given expression.
    • Simplify an expression by dividing by the greatest common factor.
      Example: 18x + 6y = 6(3x + y).
    • Determine the greatest common factor.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.5 Solve multiplication problems up to fifteen with whole number factors.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 3
    Learning Activities: 1
    Classroom Resources: 2
    7. Generate expressions in equivalent forms based on context and explain how the quantities are related.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Write an expression for a situation and determine equivalent expressions for the same situation.
    Teacher Vocabulary:
    • like terms
    • Equivalent expressions
    • Distributive property
    • Factor
    Knowledge:
    Students know:
    • properties of operations can be used to identify or create equivalent linear expressions.
    • Equivalent expressions can reveal real-world and mathematical relationships, and some forms of equivalent expressions can provide more insight than others.
    Skills:
    Students are able to:
    • determine whether two expressions are equivalent.
    • Rewrite expressions into equivalent forms by combining like terms, using the distributive property, and factoring.
    Understanding:
    Students understand that:
    • rewriting expressions in multiple equivalent forms allows for thinking about problems in different ways and highlights different aspects/relationships of quantities in problems.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.7.1: Define expression, equivalent, and equivalent expressions.
    M.7.7.2: Recall mathematical terms such as sum, difference, etc.
    M.7.7.3: Recognize that a variable without a written coefficient is understood to have a coefficient of one.
    M.7.7.4: Recall how to convert mathematical terms to mathematical symbols and numbers and vice versa.
    M.7.7.5: Restate numerical expressions with words.

    Prior Knowledge Skills:
    • Define equivalent expressions.
    • Recognize equivalent expressions.
    • Recognize that a variable without a written coefficient is understood to be one.
    • Convert mathematical terms to mathematical symbols and numbers (Ex. sum: +, difference: -; product: ·, quotient: ÷).

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.7 Match equivalent expressions using the properties of operations.
    M.AAS.7.7a Identify a pattern in a sequence of whole numbers with a whole number common difference (e.g. when skip counting by 5, the whole number common difference is 5).


    Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 1
    Classroom Resources: 1
    8. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form.
    • Interpret solutions of problems with rational numbers in the context of the problem.
    • Assess the reasonableness of answers using mental computation and estimation strategies.
    • Use variables to represent quantities in a real-world or mathematical problem.
    Teacher Vocabulary:
    • Rational numbers
    • Integers
    • Estimation
    Knowledge:
    Students know:
    • techniques for converting between fractions, decimals, and percents.
    • Techniques for estimation, mental computations, and how to assess the reasonableness of their answers.
    Skills:
    Students are able to:
    • convert between different forms of a rational number.
    • Add, subtract, multiply and divide rational numbers. -translate verbal forms of problems into algebraic symbols, expressions, and equations.
    • Use estimation and mental computation techniques to assess the reasonableness of their answers.
    Understanding:
    Students understand that:
    • One form of a number may be more advantageous than another form, based on the problem context.
    • Using estimation strategies helps to determine the reasonableness of answers.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.8.1: Define estimation, rational numbers, and reasonable.
    M.7.8.2: Recall mental calculation strategies.
    M.7.8.3: Recall estimation strategies.
    M.7.8.4: Analyze the given word problem to set up a mathematical problem.
    M.7.8.5: Recognize the mathematical operations of rational numbers in any form, including converting between forms. (Ex. 0.25=1/4 =25%).
    M.7.8.6: Recognize the rules of operations of positive and negative numbers.
    M.7.8.7: Recognize properties of numbers (Distributive, Associative, Commutative).
    M.7.8.8: Recall problem solving methods.

    Prior Knowledge Skills:
    • Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.
    • Define integers, positive and negative numbers.
    • Define rational number.
    • Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.8 Add and subtract integers in a real-world situation.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 2
    Classroom Resources: 2
    9. Use variables to represent quantities in real-world or mathematical problems and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.

    a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

    b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality, and interpret it in the context of the problem.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Write and solve mathematical equations (or inequalities) to model real world problems.
    • Interpret the solution to an equation in the context of a problem
    • Interpret the solution set of an inequality in the context of a problem.
    • Graph the solution to an inequality on a number line.
    Teacher Vocabulary:
    • Algebraic expressions
    • Equations
    • Inequalities
    • Greater than
    • Greater than or equal to
    • less than
    • less than or equal to
    Knowledge:
    Students know:
    • p(x + q) = px + pq, where p and q are specific rational numbers.
    • When multiplying or dividing both sides of an inequality by a negative number, every term must change signs and the inequality symbol reversed.
    • In the graph of an inequality, the endpoint will be a closed circle indicating the number is included in the solution set (≤ or ≥) or an open circle indicating the number is not included in the solution set ( < or >).
    Skills:
    Students are able to:
    • use variables to represent quantities in a real-world or mathematical problem.
    • Construct equations (px + q = r and p(x + q) = r) to solve problems by reasoning about the quantities.
    • Construct simple inequalities (px + q > r or px + q < r) to solve problems by reasoning about the quantities.
    • Graph the solution set of an inequality.
    Understanding:
    Students understand that:
    • Real-world problems can be represented through algebraic expressions, equations, and inequalities.
    • Why the inequality symbol reverses when multiplying or dividing both sides of an inequality by a negative number.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.9.1: Define equation, inequality, and variable.
    M.7.9.2: Set up equations and inequalities to represent the given situation, using correct mathematical operations and variables.
    M.7.9.3: Calculate a solution or solution set by combining like terms, isolating the variable, and/or using inverse operations.
    M.7.9.4: Test the found number or number set for accuracy by substitution.
    M.7.9.5: Recall solving one step equations and inequalities.
    M.7.9.6: Recognize properties of numbers (Distributive, Associative, Commutative).
    M.7.9.7: Define equation and variable.
    M.7.9.8: Set up an equation to represent the given situation, using correct mathematical operations and variables.
    M.7.9.9: Calculate a solution to an equation by combining like terms, isolating the variable, and/or using inverse operations.
    M.7.9.10: Test the found number for accuracy by substitution.
    Example: Is 5 an accurate solution of 2(x + 5)=12?.
    M.7.9.11: Identify the unknown, in a given situation, as the variable.
    M.7.9.12: List given information from the problem.
    M.7.9.13: Recalling one-step equations.
    M.7.9.14: Explain the distributive property.
    M.7.9.15: Define inequality and variable.
    M.7.9.16: Set up an inequality to represent the given situation, using correct mathematical operations and variables.
    M.7.9.17: Calculate a solution set to an inequality by combining like terms, isolating the variable, and/or using inverse operations.
    M.7.9.18: Test the solution set for accuracy.
    M.7.9.19: Identify the unknown, of a given situation, as the variable.
    M.7.9.20: List information from the problem.
    M.7.9.21: Recall how to graph inequalities on a number line.
    M.7.9.22: Recall how to solve one step inequalities.

    Prior Knowledge Skills:
    • Define inequality.
    • Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.
    • Define equation, solution of an equation, solution of an inequality, and inequality.
    • Compare and contrast equations and inequalities.
    • Determine if an inequality is by replacing the variable with a given number.
    • Determine if an equation is true by replacing the variable with a given number.
    • Simplify a numerical sentence to determine equivalence.
    • Recognize the symbols for =, >, <, ?, and ?.
    • Define equation and variable.
    • Set up an equation to represent the given situation, using correct mathematical operations and variables.
    • Identify the unknown, in a given situation, as the variable.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.9 Use the properties of operations to solve one-step equations and inequalities from real-world and mathematical problems.


    Data Analysis, Statistics, and Probability
    Make inferences about a population using random sampling.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 5
    Learning Activities: 1
    Classroom Resources: 4
    10. Examine a sample of a population to generalize information about the population.

    a. Differentiate between a sample and a population.

    b. Compare sampling techniques to determine whether a sample is random and thus representative of a population, explaining that random sampling tends to produce representative samples and support valid inferences.

    c. Determine whether conclusions and generalizations can be made about a population based on a sample.

    d. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples to gauge variation and making predictions or conclusions about the population.

    e. Informally explain situations in which statistical bias may exist.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • distinguish between a population and a sample population, and identify both for statistical questions.
    • Understand that a population characteristic is determined using data from the entire population, whereas a sample statistic is determined using data from a sample of the population.
    • Describe different ways that data can be collected to answer a statistical question.
    • Understand why a sample of a population may be useful or necessary to answer a statistical question.
    Teacher Vocabulary:
    • Population
    • Sample
    • biased
    • Unbiased
    • Sampling techniques
    • Random sampling
    • Representative samples
    • Inferences
    Knowledge:
    Students know:
    • a random sample can be found by various methods, including simulations or a random number generator.
    • Samples should be the same size in order to compare the variation in estimates or predictions.
    Skills:
    Students are able to:
    • determine whether a sample is random or not and justify their reasoning.
    • Use the center and variability of data collected from multiple same-size samples to estimate parameters of a population.
    • Make inferences about a population from random sampling of that population.
    • Informally assess the difference between two data sets by examining the overlap and separation between the graphical representations of two data sets.
    Understanding:
    Students understand that:
    • statistics can be used to gain information about a population by examining a sample of the populations.
    • Generalizations about a population from a sample are valid only if the sample is representative of that population.
    • Random sampling tends to produce representative samples and support valid inferences
    • The way that data is collected, organized and displayed influences interpretation.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.10.1: Recall how to calculate range, outlier, ratio, and proportion.
    M.7.10.2: Define sample, data, variation, prediction, estimation, validity, population, inference, random sampling, statistic, and generalization.
    M.7.10.3: Explain the validity of random sampling.
    M.7.10.4: Differentiate the appropriate sampling method.
    M.7.10.5: Analyze attributes of sample size.
    M.7.10.6: Compare and contrast the random sampling data to the population.
    M.7.10.7: Compare sample size with population to check for validity.
    M.7.10.8: Analyze conclusions of the sample to determine its appropriateness for the population.
    M.7.10.9: Predict an outcome of the entire population based on random samplings.
    M.7.10.10: Discuss real world examples of valid sampling and generalizations.
    M.7.10.11: Recall the nature of the attribute, how it was measured, and its unit of measure.
    M.7.10.12: Collect data from population randomly, choosing same size samples. (Ex. If population is your school, different random samplings should be same number of students).
    M.7.10.13: Define and discuss bias.
    M.7.10.14: Compare and contrast statistical situations to determine if statistical bias exists.

    Prior Knowledge Skills:
    • Define statistical question.
    • Calculate the range, mean, median, and mode of a numerical data set.
    • Recognize the difference between population and sample.
    • Identify bias from real world context.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.10 Find the range and median (when given an odd number of data points), and mean (involving one or two-digit numbers) in real-world situations.


    Make inferences from an informal comparison of two populations.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 1
    Classroom Resources: 1
    11. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Determine which measure of center best represents the typical value in the data set.
    • Calculate measures of variability (range, interquartile range, and mean absolute deviation), noting how larger values indicate that values are more spread out from the center of the distribution.
    Teacher Vocabulary:
    • Visual overlap
    • Measure of variability
    • Data distribution
    • range
    • interquartile range
    • mean absolute deviation
    Knowledge:
    Students know:
    • populations can be compared using measures of center and measures of variability
    Skills:
    Students are able to:
    • informally assess the degree of visual overlap of two numerical data distributions with similar variabilities.
    • Measure the difference between the centers by expressing it as a multiple of a measure of variability.
    Understanding:
    Students understand that:
    • outliers skew data, which in turn affects the display.
    • Measures of center give information about the location of mean, median, and mode, whereas measures of variability give information about how spread out the data is.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.11.1: Define measure of variability, distribution, and measure of center.
    M.7.11.2: Analyze the skew of the distributions and recognize the difference in measure of center and variability.
    M.7.11.3: Compare the measure of center and measure of variability of two distributions.
    M.7.11.4: Relate the measure of variation with the concept of range.
    M.7.11.5: Relate the measure of the center with the concept of mean.
    M.7.11.6: Recall how to calculate measure of center and measure of variability.
    M.7.11.7: Discuss how to read and interpret a graph.

    Prior Knowledge Skills:
    • Describe the center of a set of data in a given distribution.
    • Compare and contrast the center and variation.
    • Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.11 Make inferences from graphical representations of a data set (e.g. line plot, dot plots, histograms, bar graphs, stem and leaf plots, or line graphs).


    Mathematics (2019)
    Grade(s): 7
    All Resources: 2
    Classroom Resources: 2
    12. Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use measures of center for numerical data from random samples to draw informal comparative inferences about two populations.
    • Use measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
    Teacher Vocabulary:
    • Mean
    • median
    • mode
    • Mean absolute deviation
    • Range
    • Interquartile range
    Knowledge:
    Students know:
    • measures of center are insufficient to compare populations. measures of variability are necessary to assess if data sets are significantly different or not.
    • Mean is the sum of the numerical values divided by the number of values.
    • Median is the number that is the midpoint of an ordered set of numerical data.
    • Mode is the data value or category occurring with the greatest frequency (there can be no mode, one mode, or several modes).
    • Mean absolute deviation of a data set is found by the following steps: 1) calculate the mean 2) determine the deviation of each variable from the mean 3) divide the sum of the absolute value of each deviation by the number of data points.
    • Range is a number found by subtracting the minimum value from the maximum. value.
    Skills:
    Students are able to:
    • find the measures of center of a data set.
    • Find the interquartile range of a data set and use to compare variability between data sets.
    Understanding:
    Students understand that:
    • outliers skew data, which in turn affects the display.
    • Measures of center give information about the location of mean, median and mode, whereas measures of variability give information about how spread out the data is.
    • The mean absolute deviation of a data set describes the average distance that points within a data set are from the mean of the data set.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.12.1: Define measure of variability, measure of center, inference and mean absolute deviation.
    M.7.12.2: Recall how to calculate measure of center and measure of variability.
    M.7.12.3: Recall that center is related to measure of center and measure of variability is related to variation.
    M.7.12.4: Compare and contrast the measure of center and measure of variability of two numerical data sets.
    M.7.12.5: Calculate the mean absolute deviation of a data set in context.

    Prior Knowledge Skills:
    • Describe the center of a set of data in a given distribution.
    • Compare and contrast the center and variation.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.12 Compare two sets of data within a single data display such as a picture graph, line plot, or bar graph.


    Investigate probability models.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 3
    Classroom Resources: 3
    13. Use a number from 0 to 1 to represent the probability of a chance event occurring, explaining that larger numbers indicate greater likelihood of the event occurring, while a number near zero indicates an unlikely event.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Accurately describe the likelihood of an event occurring.
    • Describe the probability of an event occurring on a scale of 0 to 1 and using appropriate vocabulary based on the scale.
    • Categorize and order the probabilities of events by their likelihood.
    • Use words like impossible, very unlikely, unlikely, equally likely/unlikely, likely, very likely, and certain to describe the probabilities of events.
    Teacher Vocabulary:
    • probability
    • Event
    • Chance
    • likely
    • Unlikely
    • very unlikely
    • very likely
    • Equally likely
    • Impossible
    • Certain
    Knowledge:
    Students know:
    • probability is equal to the ratio of favorable number of outcomes to total possible number of outcomes.
    • As a number for probability increases, so does the likelihood of the event occurring.
    • A probability near 0 indicates an unlikely event.
    • A probability around 1/2 indicates an event that is neither unlikely nor likely.
    • A probability near 1 indicates a likely event.
    Skills:
    Students are able to:
    • approximate the probability of a chance event.
    • Use words like impossible, very unlikely, unlikely, equally likely/unlikely, likely, very likely, and certain to describe the probabilities of events.
    Understanding:
    Students understand that:
    • the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.
    • An event that is equally likely or equally unlikely has a probability of about 0.5 or .
    • The sum of the probabilities of an event and its complement must be 1.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.13.1: Define probability and event.
    M.7.13.2: Recall the order of fractions on a number line.
    M.7.13.3: Recall how to compare fractions with like denominators.
    M.7.13.4: Demonstrate how to compare fractions with different denominators.
    M.7.13.5: Determine the likelihood of an event occurring.

    Prior Knowledge Skills:
    • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
    • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
    • Generate equivalent fractions.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 5
    Learning Activities: 2
    Classroom Resources: 3
    14. Define and develop a probability model, including models that may or may not be uniform, where uniform models assign equal probability to all outcomes and non-uniform models involve events that are not equally likely.

    a. Collect and use data to predict probabilities of events.

    b. Compare probabilities from a model to observed frequencies, explaining possible sources of discrepancy.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Develop uniform (all outcomes have the same probability) and non-uniform (outcomes with different probabilities) probability models and use them to find probabilities of simple events.
    • Explain possible sources of discrepancy if the agreement between the probability model and observed frequencies is not good.
    • Estimate the probability of an event happening in an experiment.
    • Compare the accuracy of estimated probabilities from different experiments to the actual probability.
    Teacher Vocabulary:
    • Probability model
    • Uniform model
    • non-uniform model
    • observed frequencies
    Knowledge:
    Students know:
    • the probability of any single event can be expressed using terminology like impossible, unlikely, likely, or certain or as a number between 0 and 1, inclusive, with numbers closer to 1 indicating greater likelihood.
    • A probability model is a visual display of the sample space and each corresponding probability
    • probability models can be used to find the probability of events.
    • A uniform probability model has equally likely probabilities.
    • Sample space and related probabilities should be used to determine an appropriate probability model for a random circumstance.
    Skills:
    Students are able to:
    • make predictions before conducting probability experiments, run trials of the experiment, and refine their conjectures as they run additional trials.
    • Collect data on the chance process that produces an event.
    • Use a developed probability model to find probabilities of events.
    • Compare probabilities from a model to observed frequencies
    • Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
    Understanding:
    Students understand that:
    • long-run frequencies tend to approximate theoretical probability.
    • predictions are reasonable estimates and not exact measures.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.14.1: Define probability of chance, probability of events, outcome, and probability of observed frequency.
    M.7.14.2: Compare and contrast probability of chance and probability of observed frequency.
    M.7.14.3: Display all outcomes in a graphic representation (probability model-tree diagram, organized list, table, etc.).
    M.7.14.4: Demonstrate how to write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.
    M.7.14.5: Recall how to simplify fractions to lowest terms.
    M.7.14.6: Recognize equivalent fractions.
    M.7.14.7: Recall how to create a table or graphic display of data.
    M.7.14.8: Define probability of chance, outcome, and event.
    M.7.14.9: List all possible outcomes using a graphic representation (probability model-tree diagram, organized list, table, etc.).
    M.7.14.10: Using the model, count the frequency of the desired outcome.
    M.7.14.11: Demonstrate how to write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.
    M.7.14.12: Recall how to simplify fractions to lowest terms.
    M.7.14.13: Recognize equivalent fractions.
    M.7.14.14: Recall how to create a table or graphic display of data.
    M.7.14.15: Analyze collected data to predict probability of events.
    M.7.14.16: Define probability of observed frequency, outcome, discrepancy and event.
    M.7.14.17: List all actual outcomes using a graphic representation (probability model-tree diagram, organized list, table, etc.).
    M.7.14.18: Using the model, count the frequency of the actual outcome.
    M.7.14.19: Demonstrate how to write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.
    M.7.14.20: Recall how to simplify fractions in lowest terms.
    M.7.14.21: Recognize equivalent fractions.
    M.7.14.22: Recall how to create a table or graphic display of data.

    Prior Knowledge Skills:
    • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
    • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
    • Generate equivalent fractions.
    • Recall how to read a graph or table.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.14 Describe the probability of events occurring as possible or impossible.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 2
    Classroom Resources: 2
    15. Approximate the probability of an event using data generated by a simulation (experimental probability) and compare it to the theoretical probability.

    a. Observe the relative frequency of an event over the long run, using simulation or technology, and use those results to predict approximate relative frequency.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Predict the approximate relative frequency of an event given the probability.
    • Compare the accuracy of estimated probabilities from different experiments to the actual probability.
    • Describe how a single event can be simulated using an experiment.
    Teacher Vocabulary:
    • Experimental probability
    • Simulation
    • Theoretical probability
    • Relative frequency
    Knowledge:
    Students know:
    • relative frequencies for experimental probabilities become closer to the theoretical probabilities over a large number of trials.
    • Theoretical probability is the likelihood of an event happening based on all possible outcomes.
    • long-run relative frequencies allow one to approximate the probability of a chance event and vice versa.
    Skills:
    Students are able to:
    • approximate the probability of a chance event.
    • observe an event's long-run relative frequency.
    Understanding:
    Students understand that:
    • real-world outcomes can be simulated using probability models and tools.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.15.1: Define probability of chance, outcome, theoretical probability, experimental probability and event.
    M.7.15.2: Recognize the difference between possible outcomes and likely outcomes.
    M.7.15.3: Write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.
    M.7.15.4: Recall how to simplify fraction to lowest terms.
    M.7.15.5: Recognize equivalent fractions.
    M.7.15.6: Define relative frequency.

    Prior Knowledge Skills:
    • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
    • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
    • Generate equivalent fractions.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.15 Given a data set that represents a series of events, identify the event most likely to occur.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 5
    Classroom Resources: 5
    16. Find probabilities of simple and compound events through experimentation or simulation and by analyzing the sample space, representing the probabilities as percents, decimals, or fractions.

    a. Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams, and determine the probability of an event by finding the fraction of outcomes in the sample space for which the compound event occurred.

    b. Design and use a simulation to generate frequencies for compound events.

    c. Represent events described in everyday language in terms of outcomes in the sample space which composed the event.

    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Conduct probability experiments to quantify and interpret likeliness of an event occurring.
    • Design and use a simulation to generate frequencies for compound events
    • Analyze the results from a simulation of a compound event to estimate the probability of the compound event.
    • Represent probabilities as percents, decimals, and fractions.
    Teacher Vocabulary:
    • Tree diagram
    • Compound probability
    • Simulation
    • Sample space
    • Event
    Knowledge:
    Students know:
    • how the sample space is used to find the probability of compound events.
    • A compound event consists of two or more simple events.
    • A sample space is a list of all possible outcomes of an experiment.
    • how to make an organized list.
    • how to create a tree diagram.
    Skills:
    Students are able to:
    • find probabilities of compound events using organized lists, tables, tree diagrams and simulations
    • Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.
    • For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.
    • Design a simulation to generate frequencies for compound events.
    • Use a designed simulation to generate frequencies for compound events.
    Understanding:
    Students understand that:
    • the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
    • A compound event can be simulated using an experiment.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.16.1: Define simple events and compound events.
    M.7.16.2: Discover when to add or multiply events to find probability of compound events.
    M.7.16.3: Recall how to find the probability of simple events.
    M.7.16.4: Demonstrate adding and multiplying fractions.
    M.7.16.5: Recognize how to obtain a common denominator when adding fractions.
    M.7.16.6: Recall how to add fractions with like denominators.
    M.7.16.7: Define simulation, frequency, and compound events.
    M.7.16.8: Recall how to find the probability of compound events.
    M.7.16.9: Create a tree diagram including all possible outcomes.
    M.7.16.10: Choose appropriate model to display outcomes (tree diagram, organized list, or table).
    M.7.16.11: Identify the desired outcomes in model. M 7.16.12: Create and use a simulation to illustrate compound events.
    M.7.16.13: Recall when to add or multiply events to find probability of compound events.
    M.7.16.14: Recall how to find the probability of simple events.
    M.7.16.15: Demonstrate adding and multiplying fractions.
    M.7.16.16: Recognize how to obtain a common denominator when adding fractions.
    M.7.16.17: Recall how to add fractions with like denominators.
    M.7.16.18: Recall how to construct a table.

    Prior Knowledge Skills:
    • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
    • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
    • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
    • Generate equivalent fractions.
    • Recall how to read a graph or table.
    Geometry and Measurement
    Construct and describe geometric figures, analyzing relationships among them.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 2
    Lesson Plans: 1
    Classroom Resources: 1
    17. Solve problems involving scale drawings of geometric figures, including computation of actual lengths and areas from a scale drawing and reproduction of a scale drawing at a different scale.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Solve problems involving scale drawings.
    • Use a scale factor to reproduce a scale drawing at a different scale.
    • Determine the scale factor for a scale drawing.
    Teacher Vocabulary:
    • Scale drawing
    • Reproduction
    • Scale factor
    Knowledge:
    Students know:
    • how to calculate actual measures such as area and perimeter from a scale drawing.
    • Scale factor impacts the length of line segments, but it does not change the angle measurements.
    • There is a proportional relationship between the corresponding sides of similar figures.
    • A proportion can be set up using the appropriate corresponding side lengths of two similar figures.
    • If a side length is unknown, a proportion can be solved to determine the measure of it.
    Skills:
    Students are able to:
    • find missing lengths on a scale drawing.
    • Use scale factors to compute actual lengths, perimeters, and areas in scale drawings.
    • Use a scale factor to reproduce a scale drawing at a different scale.
    Understanding:
    Students understand that:
    • scale factor can enlarge or reduce the size of a figure.
    • Scale drawings are proportional relationships.
    • Applying a scale factor less than one will shrink a figure.
    • Applying a scale factors greater than one will enlarge a figure.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.17.1: Define scale, scale drawings, length, area, and geometric figures.
    M.7.17.2: Locate/use scale on a map.
    M.7.17.3: Identify proportional relationships.
    M.7.17.4: Recognize numeric patterns.
    M.7.17.5: Recall how to solve proportions.

    Prior Knowledge Skills:
    • Construct repeating and growing patterns with a variety of representations.
    • Continue an existing pattern.
    • Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.
    • Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.
    • Define unit rate, proportion, and rate.
    • Create a ratio or proportion from a given word problem.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 1
    Classroom Resources: 1
    18. Construct geometric shapes (freehand, using a ruler and a protractor, and using technology), given a written description or measurement constraints with an emphasis on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Determine if a unique triangle can be made when given three specific conditions of a triangle.
    • Explain why three given conditions about a triangle may result in more than one or no triangles.
    Teacher Vocabulary:
    • Construct
    • protractor
    • Angle measures
    • Constraints
    • Acute triangle right triangle
    • obtuse triangle
    • isosceles triangle
    • Scalene triangle
    • Equilateral triangle
    Knowledge:
    Students know:
    • if three side lengths will create a unique triangle or no triangle.
    Skills:
    Students are able to:
    • freehand, draw geometric shapes with given conditions.
    • Using a ruler and protractor, draw geometric shapes with given conditions.
    • Using technology, draw geometric shapes with given conditions.
    • Construct triangles from three measures of angles or sides.
    • Identify the conditions that determine a unique triangle, more than one triangle, or no triangle.
    Understanding:
    Students understand that:
    • from their experiences with constructions, what conditions are necessary to construct a triangle.
    • only certain combinations of angle and side measures will create triangles.
    • Constructing a triangle requires a specific relationship between the legs of the triangle and a specific sum between the angles of the triangle.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.18.1: Demonstrate how to use a protractor to draw an angle.
    M.7.18.2: Construct segments of a given length using a ruler.
    M.7.18.3: Recognize attributes of geometric shapes.

    Prior Knowledge Skills:
    • Model using a protractor to draw angles.
    • Measure the length of an object by selecting and using appropriate tools such as a ruler.
    • Recognize attributes of shapes.
    • Define vertex/vertices and angle.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.18 Construct and analyze a geometric figure using manipulatives.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 3
    Learning Activities: 1
    Classroom Resources: 2
    19. Describe the two-dimensional figures created by slicing three-dimensional figures into plane sections.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
    Teacher Vocabulary:
    • Two-dimensional figures
    • Three-dimensional solids
    • plane sections
    Knowledge:
    Students know:
    • the difference between a two-dimensional and three-dimensional figure.
    • The names and properties of two-dimensional shapes.
    • The names and properties of three-dimensional solids.
    Skills:
    Students are able to:
    • Discover two-dimensional shapes from slicing three-dimensional figures. For example, students might slice a clay rectangular prism from different perspectives to see what two-dimensional shapes occur from each slice.
    Understanding:
    Students understand that:
    • slicing he prism from different planes may provide a different two-dimensional shape.
    • There are specific two-dimensional shapes resulting from slicing a three-dimensional figure.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.19.1: Define two-dimensional figure, three-dimensional figure, and plane section.
    M.7.19.2: List attributes of three-dimensional figures.
    M.7.19.3: List attributes of two-dimensional figures.
    M.7.19.4: Describe the relationship between two- and three-dimensional figures.
    M.7.19.5: Recognize symmetry.

    Prior Knowledge Skills:
    • Identify that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
    • Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces.
    • Identify triangles, quadrilaterals, pentagons, hexagons, heptagons, and octagons based on the number of sides, angles, and vertices.
    • Define three-dimensional figures, surface area, and nets.
    • Select and create a three-dimensional figure using manipulatives.
    • Identify three-dimensional figures.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.19 Match two similar geometric shapes that are proportional in size and orientation.


    Solve real-world and mathematical problems involving angle measure, circumference, area, surface area, and volume.
    Note: Students must select and use the appropriate unit for the attribute being measured when determining length, area, angle, time, or volume.
    Mathematics (2019)
    Grade(s): 7
    All Resources: 3
    Classroom Resources: 3
    20. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

    a. Informally derive the formula for area of a circle.

    b. Solve area and circumference problems in real-world and mathematical situations involving circles.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Solve problems with the circumference and area of a circle.
    Teacher Vocabulary:
    • Diameter
    • Radius
    • Circle
    • Area
    • Circumference
    • π
    Knowledge:
    Students know:
    • that the ratio of the circumference of a circle and its diameter is always π.
    • The formulas for area and circumference of a circle.
    Skills:
    Students are able to:
    • use the formula for area of a circle to solve problems.
    • Use the formula(s) for circumference of a circle to solve problems.
    • Give an informal derivation of the relationship between the circumference and area of a circle.
    Understanding:
    Students understand that:
    • area is the number of square units needed to cover a two-dimensional figure.
    • Circumference is the number of linear units needed to surround a circle.
    • The circumference of a circle is related to its diameter (and also its radius).
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.20.1: Define diameter, radius, circumference, area of a circle, and formula.
    M.7.20.2: Identify and label parts of a circle.
    M.7.20.3: Recognize the attributes of a circle.
    M.7.20.4: Apply the formula of area and circumference to real world mathematical situations.

    Prior Knowledge Skills:
    • Define center, radius, and diameter of a circle.
    • Identify real-world examples of radius and diameter.
      Examples: bicycle wheel, pizza, pie.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.20 Identify the radius, diameter, and circumference of a circle.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 4
    Lesson Plans: 1
    Classroom Resources: 3
    21. Use facts about supplementary, complementary, vertical, and adjacent angles in multi-step problems to write and solve simple equations for an unknown angle in a figure.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Find the values of angles using complementary and supplementary angle relationships and equations.
    • Identify angle relationships in angle diagrams involving vertical, supplementary, and complementary angles.
    • Write equations to represent relationships between known and unknown angle measurements.
    • Determine the measures of unknown angles and judge the reasonableness of the measures.
    Teacher Vocabulary:
    • Supplementary angles
    • Complementary angles
    • vertical angles
    • Adjacent angles
    Knowledge:
    Students know:
    • supplementary angles are angles whose measures add to 180 degrees.
    • Complementary angles are angles whose measures add to 90 degrees.
    • vertical angles are opposite angles formed when two lines intersect.
    • Adjacent angles are non-overlapping angles which share a common vertex and side.
    Skills:
    Students are able to:
    • write a simple equation to find an unknown angle.
    • Identify and determine values of angles in complementary and supplementary relationships.
    • Identify pairs of vertical angles in angle diagrams.
    • Identify pairs of complementary and supplementary angles in angle diagrams.
    • Use vertical, complementary, and supplementary angle relationships to find missing angles.
    Understanding:
    Students understand that:
    • vertical angles are the pair of angles formed across from one another when two lines intersect, and that the measurements of vertical angles are congruent.
    • Complementary angles are angles whose measures add up to 90o, and supplementary angles are angles whose measures add up to 180o.
    • Relationships between angles depends on where the angles are located.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.21.1: Define supplementary angles, complementary angles, vertical angles, adjacent angles, parallel lines, perpendicular lines, and intersecting lines.
    M.7.21.2: Discuss strategies for solving multi-step problems and equations.
    M.7.21.3: Identify all types of angles.
    M.7.21.4: Identify right angles and straight angles.

    Prior Knowledge Skills:
    • Model using a protractor to draw angles.
    • Draw points, lines, line segments, and parallel and perpendicular lines, angles, and rays.
    • Define vertex/vertices and angle.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.21 Classify angles as acute, obtuse, right, or straight.


    Mathematics (2019)
    Grade(s): 7
    All Resources: 4
    Classroom Resources: 4
    22. Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Find efficient ways to determine surface area of right prisms and right pyramids by analyzing the structure of the shapes and their nets.
    • Use the formulas for volume of prisms and pyramids to solve multi-step real-world problems.
    • Use the formula for volume to find missing measurements of a prism.
    Teacher Vocabulary:
    • Area
    • volume
    • Surface area
    • Two-dimensional figures
    • Three-dimensional solids
    • Triangles
    • quadrilaterals
    • polygons
    • Cubes
    • Right rectangular prisms
    Knowledge:
    Students know:
    • that volume of any right prism is the product of the height and area of the base.
    • The volume relationship between pyramids and prisms with the same base and height.
    • The surface area of prisms and pyramids can be found using the areas of triangular and rectangular faces.
    Skills:
    Students are able to:
    • find the area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
    • Use a net of a three-dimensional figure to determine the surface area.
    • Find the volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.
    Understanding:
    Students understand that:
    • two-dimensional and three-dimensional figures can be decomposed into smaller shapes to find the area, surface area, and volume of those figures.
    • the area of the base of a prism multiplied by the height of the prism gives the volume of the prism.
    • the volume of a pyramid is 1/3 the volume of a prism with the same base.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.22.1: Define volume, surface area, triangles, quadrilaterals, polygons, cubes, and right prisms.
    M.7.22.2: Discuss strategies for solving real-world mathematical problems.
    M.7.22.3: Recall formulas for calculating volume and surface area.
    M.7.22.4: Identify the attributes of triangles, quadrilaterals, polygons, cubes, and right prisms.

    Prior Knowledge Skills:
    • Recognize the formula for volume.
    • Define volume, rectangular prism, edge, and formula.
    • Evaluate the volumes of rectangular prisms in the context of solving real-world and mathematical problems.
    • Set up V=lwh and V=Bh to find volumes in the context of solving real-world and mathematical problems.
    • Discover the volume of a rectangular prism using manipulatives.
    • Define three-dimensional figures, surface area, and nets.
    • Evaluate how to apply using surface area of a three-dimensional figure to solving real-world and mathematical problems.
    • Draw nets to find the surface area of a given three-dimensional figure.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.22 Determine the area regular, two-dimensional figures. Determine the volume of rectangular prisms, limited to whole numbers.