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Site: Learnbps
Course: BPSS (MAT) Mathematics Standards (S-MAT)
Glossary: Sixth Grade Math

MAT-06.EE

BPSS-MAT logoDomain (EE)

Expressions and Equations

Narrative for the (EE) Expressions and Equations

In the future this will contain narratives and other information about the Domain.

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-06.EE.02

6th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions.

MAT-06.EE.02 Write, read, and evaluate expressions in which letters stand for numbers.

  • a. Write expressions that record operations with numbers and with letters standing for numbers.
  • b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
  • c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Student Learning Targets:

Knowledge Targets

  • I can use a variable to represent an unknown quantity in an expression.
  • I can solve multistep problems involving properties of operations.
  • I can identify parts of an expression using mathematical terms.
  • I can identify parts of an expression as single quantities.

Reasoning Targets

  • I can translate a description into a mathematical expression.
  • I can use Order of Operations to simplify expressions that may include exponents.

Skills Domain (Performance) Targets

  • I can simplify expressions when a value is given for a variable.
  • I can solve multistep expressions involving properties of operations.

Proficiency Scale

Please refer to the proficiency scales for sub-standards MAT-06.EE.02a | MAT-06.EE.02b | MAT-06.EE.02c

Resources

Websites

MAT-06.EE.02.a

6th Grade MAT Targeted Standards

Domain (EE) Expressions and Equations
Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions

Write, read, and evaluate expressions in which letters stand for numbers.

MAT-06.EE.02.a Write expressions that record operations with numbers and with letters standing for numbers.

For example, express the calculation "Subtract y from 5" as 5-y.

Student Learning Targets:

Skill Targets

  • I can use a variable to represent an unknown quantity in an expression.
  • I can solve multi-step problems involving properties of operations.

Reasoning Targets

  • I can translate a description into a mathematical expression.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

MAT-06.EE.02.ab

6th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions

MAT-06.EE.02.ab Write expressions that record operations with numbers and with letters standing for numbers.  Identify parts of an expression using mathematical terms; view one or more parts of an expression as a single entity.

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

Proficiency Scale:

 

Rubric - Resources

MAT-06.EE.02.b

6th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions

Write, read, and evaluate expressions in which letters stand for numbers.

MAT-06.EE.02.b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

Student Learning Targets:

Knowledge Targets

  • I can identify parts of an expression using mathematical terms.
  • I can identify parts of an expression as single quantities.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

MAT-06.EE.02.c

6th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions

Write, read, and evaluate expressions in which letters stand for numbers.

MAT-06.EE.02.c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

For example, use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s =1/2.

Student Learning Targets

Reasoning Targets

  • I can use Order of Operations to simplify expressions that may include exponents.

Skills Domain (Performance) Targets

  • I can simplify expressions when a value is given for a variable.
  • I can solve multistep expressions involving properties of operations.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

MAT-06.EE.07

6th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: Reason about and solve one-variable equations and inequalities

MAT-06.EE.07 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Student Learning Targets:

Skills Domain (Performance) Targets

  • I can use inverse operations and properties of inequality to solve one-step equations using non-negative rational numbers.
  • I can write and solve equations to represent real world problems.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

MAT-06.EE.09

6th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: Represent and analyze quantitative relationships between dependent and indepenent variables

MAT-06.EE.09 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Student Learning Targets:

Knowledge Targets

  • I can recognize that a change in the independent variable (x) creates a change in the dependent variable (y).
  • I can recognize which relationships between independent (x) and dependent (y) variables are linear.

Reasoning Targets

  • I can evaluate the function (equation) for the values (input) given.
  • I can compare relationships between the independent (x) and dependent (y) using a graph (plotting ordered pairs).

Product Targets

  • I can represent a real-world problem with function rules (equations), input/output tables, and graphs.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

MAT-06.G

BPSS-MAT logoDomain (G)

Geometry

Narrative for the (G) Geometry

In the future this will contain narratives and other information about the Domain.

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-06.G.01

6th Grade MAT Targeted Standards
Domain (G) Geometry
Cluster: Solve real-world and mathematical problems involving areas, surface area, and volume

MAT-06.G.01 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Student Learning Targets:

Reasoning Targets

  • I can relate the area of triangles to the area of rectangles.

Skills Domain (Performance) Targets

  • I can visually and physically decompose and compose polygons into rectangles and triangles to determine area.
  • I can solve multi-step problems that involve finding the area of composite figures.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

MAT-06.NS

BPSS-MAT logoDomain (NS)

The Number System

Narrative for the (NS) The Number System

In the future this will contain narratives and other information about the Domain.

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-06.NS.01

6th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of multiplication and division to divide fractions by fractions

MAT-06.NS.01 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.). How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Student Learning Targets:

Reasoning Targets

  • I can interpret quotients of fractions.

Skills Domain (Performance) Targets

  • I can solve word problems involving division of fractions by fractions.
  • I can compute quotients of fractions.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

 

MAT-06.NS.03

6th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Compute fluently with multi-digit numbers and find common factors and multiples

MAT-06.NS.03 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Student Learning Targets:

Skills Domain (Performance) Targets

  • I can add multi-digit decimals.
  • I can subtract multi-digit decimals.
  • I can multiply multi-digit decimals.
  • I can divide multi-digit decimals using the standard algorithm for each operation

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

 

MAT-06.NS.06.c

6th Grade MAT Targeted Standards
Domain (NS) The Number System
Cluster: Apply and extend previous understandings of numbers to the system of rational numbers

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

MAT-06.NS.06.c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

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-06.RP

BPSS-MAT logoDomain (RP)

Ratios and Proportional Relationships

Narrative for (RP) Ratios and Proportional Relationships

In the future this will contain narratives and other information about the Domain.

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-06.RP.03

6th Grade MAT Targeted Standards
Domain (RP) Ratios and Proportional Relationships
Cluster: Understand ratio concepts and use ratio reasoning to solve problems

MAT-06.RP.03 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

  • a. Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
  • b. Solve unit rate problems including those involving unit pricing and constant speed.
  • c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
  • d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Student Learning Targets:

Knowledge Targets

  • I can convert ratios to percents.

Reasoning Targets

  • I can determine the relationship between two or more ratios.
  • I can determine equivalent ratios.
  • I can determine equivalent relationships between ratios.
  • I can compare equivalent ratios to find missing values in a table.
  • I can solve real world problems involving ratios and rates.
  • I can solve real-world problems involving ratios and percents.
  • I can determine if rates are equivalent.

Skills Domain (Performance) Targets

  • I can make tables of equivalent ratios relating quantities with whole-number measurements.
  • I can graph points of equivalent ratios on a coordinate plan.
  • I can calculate unit rates.
  • I can manipulate units appropriately when multiplying and dividing.
  • I can establish ratios to convert measurements within a system.

Proficiency Scale

Please refer to the proficiency scales attached to standards MAT-06.RP.3b | MAT-06.RP.3cMAT-06.RP.3d |

Resources

Websites

MAT-06.RP.03.a

6th Grade MAT Targeted Standards
Domain (RP) Ratios and Proportional Relationships
Cluster: Understand ratio concepts and use ratio reasoning to solve problems

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

MAT-06.RP.03.a Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Student Learning Targets:

Reasoning Targets

  • I can determine the relationship between two or more ratios.
  • I can determine equivalent ratios.
  • I can determine equivalent relationships between ratios.
  • I can compare equivalent ratios to find missing values in a table.

Skills Domain (Performance) Targets

  • I can graph points of equivalent ratios on a coordinate plane.

Product Targets

  • I can make tables of equivalent ratios relating quantities with whole-number measurements.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

MAT-06.RP.03.b

6th Grade MAT Targeted Standards
Domain (RP) Ratios and Proportional Relationships
Cluster: Understand ratio concepts and use ratio reasoning to solve problems

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

MAT-06.RP.03.b Solve unit rate problems including those involving unit pricing and constant speed.

For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Student Learning Targets:

Skills Domain (Performance) Targets

  • I can calculate unit rates.
  • I can solve real world problems involving ratio and rate.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

MAT-06.RP.03.c

6th Grade MAT Targeted Standards
Domain (RP) Ratios and Proportional Relationships
Cluster: Understand ratio concepts and use ratio reasoning to solve problems

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

MAT-06.RP.03.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

Student Learning Targets:

Reasoning Targets

  • I can convert ratios to percents.

Skills Domain (Performance) Targets

  • I can solve real-world problems involving ratios and percents.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

 

MAT-06.RP.03.d

6th Grade MAT Targeted Standards
Domain (RP) Ratios and Proportional Relationships
Cluster: Understand ratio concepts and use ratio reasoning to solve problems

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

MAT-06.RP.03.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Student Learning Targets:

Reasoning Targets

  • I can determine if rates are equivalent.

Skills Domain (Performance) Targets

  • I can manipulate units appropriately when multiplying and dividing.
  • I can establish ratios to convert measurements within a system.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

 

MAT-06.SP

BPSS-MAT logoDomain (SP)

Statistics and Probability

 Narrative for the (SP) Statistics and Probability

In the future this will contain narratives and other information about the Domain.

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-06.SP.05

6th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Develop understanding of statistical variability

MAT-06.SP.05 Summarize numerical data sets in relation to their context.

  • a. Reporting the number of observations.
  • b. Describing the nature of the attribute of investigation, including how it was measured and its units of measurement.
  • c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.
  • d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

 

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Websites

 

MAT-06.SP.05.c

6th Grade MAT Targeted Standards
Domain (SP) Statistics and Probability
Cluster: Develop understanding of statistical variability

Summarize numerical data sets in relation to their context.

MAT-06.SP.05.c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.

Student Learning Targets:

Skills Domain (Performance) Targets

  • I can compute mean, median, and range. I can compute interquartile range.

Product Target

  • I can make a box-and-whisker plot for a set of data.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites