Saturday, June 15, 2024, 12:45 PM
Site: Learnbps
Course: BPSS (MAT) Mathematics Standards (S-MAT)
Glossary: Seventh Grade Math
M

MAT-07.EE

BPSS-MAT logoDomain (EE)

Expressions and Equations

Narrative for the (EE) Expressions and Equations

The standards with the Expressions and Equations domain require students to (1) use properties of operations to generate equivalent expressions and (2) Solve real-world and mathematical problems using numerical and algebraic expressions and equations.  

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-07.EE.01

7th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: Use properties of operations to generate equivalent expressions

MAT-07.EE.01 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Student Learning Targets:

Skills Domain (Performance) Targets

  • I can apply the properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
  • I can use the distributive property
  • I can combine like terms in an expression or equation
  • I can simplify a polynomial expression
  • I can multiply polynomials

 

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

Vocabulary

  • Like Terms
  • Distributive Property

 

MAT-07.EE.02

7th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: Use properties of operations to generate equivalent expressions

MAT-07.EE.02 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

Student Learning Targets:

Knowledge Targets

  • I can identify the commutative property

  • I can identify the associative property

  • I can identify the distributive property

Reasoning Targets

  • I can use properties to simplify and evaluate expressions.

  • I can manipulate expressions to make equivalent expressions while problem solving.

     

Rubric - Resources

MAT-07.EE.03

7th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: Use properties of operations to generate equivalent expressions

MAT-07.EE.03 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Student Learning Targets:

Knowledge Targets

  • I can recognize a reasonable estimate
  • I can explain the steps in order to find estimated results

Reasoning Targets

  • I can estimate using fractions, decimals, percents, and integers

Skills Domain (Performance) Targets

  • I can convert between decimals, fractions, and percents.
  • I can apply properties of operations to calculate with numbers
  • I can convert a word problem into a mathematical sentence

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites:

This standard is addressed in all sections of the book.

 

MAT-07.EE.04

7th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: Use properties of operations to generate equivalent expressions

MAT-07.EE.04 Use variables to represent quantities in a real-world or mathematical problem, and construct simple 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 the 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.

Student Learning Targets:

Knowledge Targets

  • I can identify a variable.
  • I understand the meaning of expression and equation.

Reasoning Targets

  • I can write equations to represent real-world problems.
  • I can write inequalities to represent real-world problems.

Skills Domain (Performance) Targets

  • I can solve equations.
  • I can solve inequalities.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

Vocabulary

  • equation
  • inequality

 

MAT-07.EE.04.a

7th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: Use properties of operations to generate equivalent expressions

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

MAT-07.EE.04.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 the algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Student Learning Targets:

Knowledge Targets

  • I can use a variable to represent an unknown quantity

Reasoning Targets

  • I can compare the algebraic solution to an arithmetic solution

Skills Domain (Performance) Targets

  • I can write a simple algebraic equation of the form px + q = r where p, q, and r are specific numbers to represent a real-world problem.
  • I can use inverse operations and the properties of equality to solve word problems leading to equations of the form px + q = r, where p, q, and r are specific numbers
  • I can use inverse operations and the properties of equality to solve word problems leading to equations of the form p(x + q) = r where p, q, and r are specific numbers

 

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

 Vocabulary

  • Equation
  • Inverse operations
  • variable

 

MAT-07.EE.04.b

7th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: Use properties of operations to generate equivalent expressions

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

MAT-07.EE.04.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.

For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Student Learning Targets:

Knowledge Targets

  • I can name the inequality signs.

Reasoning Targets

  • I can write a simple algebraic inequality in the form px+q=r where (p, q, and r) are specific numbers to represent a real-world problem.
  • I can interpret the solution set in relation to the problem.

Skills Domain (Performance) Targets

  • I can use inverse operations and the properties of inequality to solve word problems leading to inequalities of the form px + q > r where p, q, and r are specific numbers.

Resources

Websites

  • www.khanacademy.org
    • Try searching solving inequalities, graphing inequalities
  • www.bigideasmath.com
    • This concept is found in Chapter 2

Vocabulary

  • Inequality

 

MAT-07.G

BPSS-MAT logoDomain (G)

Geometry

Narrative for the (G) Geometry

The standards within the Geometry domain require students to (1) draw, construct, and describe geometrical figures and describe the relationship between them and (2) solve real-world and mathematical problems involving angle measure, area, surface area, and volume.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-07.G.01

7th Grade MAT Targeted Standards
Domain (G) Geometry
Cluster: Draw, construct and describe geometrical figures and describe the relationships between them

MAT-07.G.01 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Student Learning Targets:

Skills Domain (Performance) Targets

  • I can use scale drawing to determine the actual dimensions and area of geometric figure

Product Targets

  • I can use a different scale to reproduce a similar scale drawing

Proficiency Scale

Link to the Proficiency Scale

Web Resources

MAT-07.G.02

7th Grade MAT Targeted Standards
Domain (G) Geometry
Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them.

MAT-07.G.02 Draw (freehand, with ruler and protractor, and with technology) geometric shapes from given conditions. Focus 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.

Student Learning Targets:

  • I can determine when three specific measurements will result in one unique triangle, more than one possible triangle or no possible triangle.
  •  I can draw a geometric shape with specific conditions.
  • I can construct a triangle when given three measurements (3 sides lengths, 3 angles, or combinations of side and angle measurements
Rubric - Resources

MAT-07.G.03

7th Grade MAT Targeted Standards
Domain (G) Geometry
Cluster: Draw, construct and describe geometrical figures and describe the relationships between them

MAT-07.G.03 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms

Student Learning Targets:

  • I can name the two-dimensional figure that represents a particular slice of a three-dimensional figure.
Rubric - Resources

Vocabulary:

Right Rectangular Prism

MAT-07.G.04

7th Grade MAT Targeted Standards
Domain (G) Geometry
Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

MAT-07.G.04 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Proficiency Scale

This standard is taught and evaluated in conjunction with 7.G.6.

Resources

Websites

Vocabulary

  • circle
  • circumference
  • radius
  • diameter
  • pi

MAT-07.G.05

7th Grade MAT Targeted Standards
Domain (G) Geometry
Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

MAT-07.G.05 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Student Learning Targets:

  • I can state the relationship between supplementary, complementary and vertical angles.
  • I can use angle relationships to write algebraic equations for unknown angles.
  • I can use algebraic reasoning and angles relationships to solve multi-step problems. 

Vocabulary:

Supplementary Angles, Complementary Angles, Vertical Angles, and Adjacent Angles

Rubric - Resources

MAT-07.G.06

7th Grade MAT Targeted Standards
Domain (G) Geometry
Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

MAT-07.G.06 Solve real-world and mathematical problems involving area of two-dimensional figures composed of polygons and/or circles including composite figures

 

Solve real-world and mathematical problems involving surface area of prisms and cylinders, including composite solids.

 

Solve real-world and mathematical problems involving volume of right prisms, including composite solids.

Student Learning Targets:

Knowledge Targets

  • I can identify the faces of a solid

Skills Domain (Performance) Targets

  • I can calculate the area of polygons and circles
  • I can calculate the volume of right prisms
  • I can calculate the surface area of right prisms
  • I can calculate the surface area of cylinders

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

Vocabulary

  • volume
  • surface area
  • prism
  • cylinder
  • regular polygon
  • right prism
  • composite solid

 

MAT-07.NS

BPSS-MAT logoDomain (NS)

The Number System

Narrative for the (NS) The Number System

The standards within the Number System domain require students to apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-07.NS.01

7th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

MAT-07.NS.01 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

  • a. Describe situations in which opposite quantities combine to make 0.
  • b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
  • c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show 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.
  • d. Apply properties of operations as strategies to add and subtract rational numbers.

Student Learning Targets:

Knowledge Targets

  • I can plot integers and rational numbers on a number line.

Reasoning Targets

  • I can represent addition and subtraction problems on a number line.

Skills Domain (Performance) Targets

  • I can add and subtract integers.
  • I can add and subtract rational numbers.

Resources

Websites

Vocabulary

  • integer
  • rational number
  • absolute value
  • opposite

 

MAT-07.NS.01.a

7th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

MAT-07.NS.01.a Describe situations in which opposite quantities combine to make 0.

For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

Student Learning Targets:

Knowledge Targets

  • I know that opposite numbers combine to make zero.

Reasoning Targets

  • I can describe situations where opposite numbers combine to make zero.

Resources

Websites

Vocabulary

  • opposite

 

MAT-07.NS.01.b

7th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

MAT-07.NS.01.b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Student Learning Targets:

Knowledge Targets

  • I can show that a number and its opposite are additive inverses.

Reasoning Targets

  • I can represent addition of rational numbers on a vertical or horizontal number line using the sign of the value being added to determine direction.
  • I can describe sums of rational numbers in real world contexts.

Resources

Websites

Vocabulary

 Positive, Negative, Opposite, Additive Inverse, Absolute Value, Integer, Rational Numbers.

MAT-07.NS.01.c

7th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

MAT-07.NS.01.c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show 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.

Student Learning Targets:

Knowledge Targets

  • I can show the distance between two rational number on the number line is the absolute value of their difference
  • I can use the additive inverse to write a subtraction problem as an addition problem

Skills Domain (Performance) Targets

  • I can subtract rational numbers in real world contexts.

Proficiency Scale

Click Here to access the link to the Proficiency Scale PDF.

Resources

Websites

  • www.khanacademy.org
    • Try searching - integer addition, integer subtraction, rational numbers, rational numbers addition, rational numbers subtraction
  • www.bigideasmath.com
    • Chapter 1 - Integer addition and subtraction sections
    • Chapter 2 - Rational numbers addition and subtraction sections

Vocabulary

  • rational number
  • integer
  • absolute value
  • opposite

 

MAT-07.NS.01.d

7th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

MAT-07.NS.01.d Apply properties of operations as strategies to add and subtract rational numbers.

Student Learning Targets:

Skills Domain (Performance) Targets

  • I can add rational numbers
  • I can subtract rational numbers

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

 

Vocabulary

  • Integer
  • rational number
  • absolute value
  • opposite

 

MAT-07.NS.02

7th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

MAT-07.NS.02 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

  • a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
  • b. Understand that integers can be divided, provided that the divisor is not zero, and 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). Interpret products of rational numbers by describing real-world contexts.
  • c. Apply properties of operations as strategies to multiply and divide ational numbers.
  • d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Student Learning Targets:

Skills Domain (Performance) Targets

  • I can multiply and divide integers.
  • I can multiply and divide rational numbers. (This includes work with positive and negative fractions and decimal numbers.)

Websites

Vocabulary

 Integer, Rational Numbers, Terminating Decimals, and Repeating Decimals.

MAT-07.NS.02.a

7th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

MAT-07.NS.02.a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Student Learning Targets:

Reasoning Targets

  • I can relate the properties of multiplication of fractions to the multiplication of rational numbers.
  • I can interpret products of rational numbers by describing real world situations.

Skills Domain (Performance) Targets

  • I can use the rules for multiplying signed numbers to determine the sign of the product.

Resources

Websites

Vocabulary

  • integer
  • rational number

 

MAT-07.NS.02.b

7th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

MAT-07.NS.02.b Understand that integers can be divided, provided that the divisor is not zero, and 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). Interpret products of rational numbers by describing real-world contexts.

Student Learning Targets:

Reasoning Targets

  • I can explain why dividing by zero is undefined.
  • I can interpret quotients of rational numbers by describing real world situations

Skills Domain (Performance) Targets

  • I can use the rules for dividing signed numbers to determine the sign of the quotient.

Resources

Websites

Vocabulary

  • product
  • quotient
  • integer
  • rational number

 

MAT-07.NS.02.c

7th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

MAT-07.NS.02.c Apply properties of operations as strategies to multiply and divide rational numbers.

Student Learning Targets:

Skills Domain (Performance) Targets

  • I can multiply rational numbers using the properties of operations.
  • I can divide rational numbers using the properties of operations.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

Vocabulary

  • Integer
  • rational number
  • product
  • quotient

 

MAT-07.NS.02.d

7th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

MAT-07.NS.02.d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Student Learning Targets:

Knowledge Targets

  • I know that the decimal form of a rational number terminates or repeats.

Skills Domain (Performance) Targets

  • I can convert rational numbers into decimals using long division.

Resources

Websites

 

Vocabulary

  • decimal
  • fraction
  • rational number

 

MAT-07.NS.03

7th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

MAT-07.NS.03 Solve real-world and mathematical problems involving the four operations with rational numbers.

Student Learning Targets:

Skills Domain (Performance) Targets

  • I can add rational numbers
  • I can subtract rational numbers
  • I can multiply rational numbers
  • I can divide rational numbers
  • I can simplify expressions with absolute value elements
  • I can apply the order of operations to solve problems
  • I can write word problems into mathematical notation

Proficiency Scale

Link to Proficiency Scale 

Resources

Websites

Vocabulary

  • rational number
  • absolute value

 

MAT-07.RP

BPSS-MAT logoDomain (RP)

Ratios and Proportional Relationships

Narrative for (RP) Ratios and Proportional Relationships

The standards within the Ratios and Proportional Relationships Domain require students to analyze proportional relationships and use them to solve real world and mathematical problems.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-07.RP.01

7th Grade MAT Targeted Standards
Domain (RP) Ratios and Proportional Relationships
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

MAT-07.RP.01 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

For example, If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles per hour.

Student Learning Targets:

Knowledge Targets

  • I know that a ratio is a comparison of two quantities using division
  • I can identify equivalent ratios
  • I can write a ratio in lowest terms

Reasoning Targets

  • I can create equivalent ratios
  • I can write ratios to represent practical problems

Skills Domain (Performance) Targets

  • I can calculate a unit rate.

 

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

Vocabulary

  • unit rate
  • ratio
  • rate

 

MAT-07.RP.02

7th Grade MAT Targeted Standards
Domain (RP) Ratios and Proportional Relationships
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

MAT-07.RP.02 Recognize and represent proportional relationships between quantities.

  • a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
  • b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
  • c. Represent proportional relationships by equations.
  • d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Student Learning Targets:

Knowledge Targets

  • I can understand that a proportional relationship is when two ratios are equal

Reasoning Targets

  • I can determine when a proportional relationship is being represented
  • I can determine that ratios are proportional if their cross products are equal

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

Vocabulary

  • ratio
  • proportion
  • cross products

 

MAT-07.RP.02.a

7th Grade MAT Targeted Standards
Domain (RP) Ratios and Proportional Relationships
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Recognize and represent proportional relationships between quantities.

MAT-07.RP.02.a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Student Learning Targets:

Reasoning Targets

  • I can determine if two quantities are proportional using a variety of methods (tables, graphs, diagrams, equations, or verbal description

Resources

Websites

Vocabulary

  • ratio
  • proportion
  • cross product

 

MAT-07.RP.02.b

7th Grade MAT Targeted Standards
Domain (RP) Ratios and Proportional Relationships
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Recognize and represent proportional relationships between quantities.

MAT-07.RP.02.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Student Learning Targets:

Knowledge Targets

  • I can understand that a proportional relationship is when two ratios are equal

Reasoning Targets

  • I can determine when a proportional relationship is being represented
  • I can determine that ratios are proportional if their cross products are equal

 

Websites

Vocabulary

  • ratio
  • proportion
  • cross products

MAT-07.RP.02.c

7th Grade MAT Targeted Standards
Domain (RP) Ratios and Proportional Relationships
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Recognize and represent proportional relationships between quantities.

MAT-07.RP.02.c Represent proportional relationships by equations.

For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between total cost and the number of items can be expressed as t = pn.

Student Learning Targets:

Reasoning Targets

  • I can use an equation to represent a proportional relationship.

 

Resources

Websites

Vocabulary

 

MAT-07.RP.02.d

7th Grade MAT Targeted Standards
Domain (RP) Ratios and Proportional Relationships
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Recognize and represent proportional relationships between quantities.

MAT-07.RP.02.d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Student Learning Targets:

Knowledge Targets

  • I can Identify the unit rate by using the point (1, r)

Reasoning Targets

  • I can explain what the point (0, 0) on the graph of a proportional relationship means
  • I can explain what a point (x, y) on the graph of a proportional relationship means

 

Websites

Vocabulary

 Proportional Relationship, Constant of Proportionality, Unit Rate, Equivalent Ratios, and Origin.

MAT-07.RP.03

7th Grade MAT Targeted Standards
Domain (RP) Ratios and Proportional Relationships
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

MAT-07.RP.03 Use proportional relationships to solve multistep ratio and percent problems.

Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Student Learning Targets:

Knowledge Targets

  • I know how to use proportions

Reasoning Targets

  • I can solve percent problems
  • I can solve problems involving percent of change
  • I can solve simple interest problems

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

Vocabulary

  • proportion
  • percent
  • discount
  • markup
  • interest
  • simple interest
  • percent of increase
  • percent of decrease
  • sale price

 

MAT-07.SP

BPSS-MAT logoDomain (SP)

Statistics and Probability

 Narrative for the (SP) Statistics and Probability

The standards within the Statistics and Probability domain require students to (1) use random sampling to draw inferences about a population, (2) draw informal comparative inferences about two populations, and (3) investigate chance processes and develop, use, and evaluate probability models.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-07.SP.01

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Use random sampling to draw inferences about a population

MAT-07.SP.01 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Student Learning Targets:

  • I can explain that inferences about a population can be made by examining a sample.
  • I can explain why the validity of a sample depends on whether the sample is representative of the population.
  • I can explain that random sampling tends to produce representative samples. 

Vocabulary:

Sample, Population, Validity, Generalization, Random Sample, and Representative Sample.

Rubric - Resources

MAT-07.SP.02

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Use random sampling to draw inferences about a population

MAT-07.SP.02 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Student Learning Targets:

  • I can draw inferences about a population based on data generated by a random sample.
  • I can generate multiple samples from the same population and analyze the estimates or predictions based on the variation of each sample.

Vocabulary:

Population, Sample, and Random Sample.

Rubric - Resources

 

MAT-07.SP.03

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: TOPIC

MAT-07.SP.03 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.

For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

Student Learning Targets:

  • I can find the difference in the mean or the median of two different data sets.
  • I can demonstrate how two data sets that are very different can have similar variabilities. 
  • I can draw inferences about the data sets by making a comparison of these differences relative to the mean absolute deviation or interquartile range of a set of data. 

Vocabulary:

Measures of Center (Measures of central tendencies)

Variability

mean

median

mode

mean absolute deviation

interquartile range.

Rubric - Resources

MAT-07.SP.04

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Draw informal comparative inferences about two populations

MAT-07.SP.04 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Student Learning Targets:

  • I can apply central measures t draw conclusions.
  • I  draw conclusions from different population samples.
  • I can make inferences about two populations.

 

Proficiency Scale

Click HERE to access the Proficiency Scale for 7.SP.4

Vocabulary:

Measures of Variability

Measures of Center

Mean

Median

Absolute Deviation

Interquartile Range

Population

Random Sample

Rubric - Resources

MAT-07.SP.05

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

MAT-07.SP.05 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Student Learning Targets:

  • I can define probabilite as a ratio that compares favorable outcomes to all possible outcomes.
  • I can recognize and explain that probabilities are expressed as a number between 0 to 1.
  • I can interpret a probability near 0 as unlikely to occur and a probability near 1 as likely to occur.
  • I can interpret a probability near 1/2, as being equally able to occur as to not occur

 

Vocabulary:

Likely

unlikely

Rubric - Resources

MAT-07.SP.06

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

MAT-07.SP.06 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

Student Learning Targets:

  • I can collect data on a chance process to approximate its probability.
  • I can use probability to predict the number of times a particular event will occur given a specific number of trials.
  • I can use variability to explain why the experimental probability will not always exactly equal the theoretical probability.

Vocabulary

Theoretical Probability

Experimental Probability

Relative Frequency

 

Rubric - Resources

MAT-07.SP.07

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

MAT-07.SP.07 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

  • a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
  • b. Develop a possibly model (which may not be uniform) by observing frequencies in data generated from a chance process.

Student Learning Targets:

Reasoning Targets

  • I can explain the difference between theoretical and experimental probability of an event

Skills Domain (Performance) Targets

  • I can find experimental probability of an event
  • I can find theoretical probability of an event

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

Vocabulary

  • probability
  • theoretical probability
  • experimental probability
  • outcome
  • event

 

MAT-07.SP.07.a

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

MAT-07.SP.07.a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

Student Learning Targets:

  • I can find the theoretical probability.
  • I can find the number of favorable outcomes.
  • I can find the number of possible outcomes.
  • I can use a proportion to solve for the total number of outcomes or favorable number of outcomes.
  • I can use theoretical probabilities to solve real-world problems.

Vocabulary

  • List
  • Event
  • Outcomes
  • Event
  • Tree diagram

 

MAT-07.SP.07.b

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

MAT-07.SP.07.b Develop a possibly model (which may not be uniform) by observing frequencies in data generated from a chance process.

For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

Student Learning Targets:

  • I can find experimental probability.

Vocabulary

  • List

 

MAT-07.SP.08

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

MAT-07.SP.08 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

  • a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
  • b. 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 with compose the event.
  • c. Design and use a simulation to generate frequencies for compound events.

Student Learning Targets:

  • I can find the theoretical Probability
  • I can find the experimental Probability
  • I can determine the relationship between experimental and theoretical probability
  • I can predict the experimental probability of an event based on the theoretical probability
  • I can determine the likelihood of an event occurring based on the probability
  • I can use organized lists tree diagrams, tables, simulations, and mathematical computations to determine the probability of compound events.

Vocabulary

Compound events

sample space

tree diagram

outcomes

favorable outcomes

simulation

Proficiency Scale

 Link to Proficiency Scale

Rubric - Resources

Khan Academy

Theoretical Probability

Marble Probability

Compound Probability using a sample space

Compound Probability using a tree diagram

Dependent Events

Big Ideas Math: Probability is found in Chapter 9 of the Big Ideas math book

MAT-07.SP.08a

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

MAT-07.SP.08a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills Domain (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can
Rubric - Resources

MAT-07.SP.08b

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

MAT-07.SP.08b 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 with compose the event.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills Domain (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can
Rubric - Resources

MAT-07.SP.08c

7th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

MAT-07.SP.08c Design and use a simulation to generate frequencies for compound events.

For example, use random digits as a simulation tool to approximate the answer to the question: if 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills Domain (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can
Rubric - Resources