Burlington Middle School
7th Grade Essential Learning Targets
Content Standard	Benchmark	Essential Learning Target	Indications for Success
Content Standards:  Indicates the broad knowledge and skills students should be acquiring within the Colorado K-12 Standards	Benchmark:  Tactical descriptions of the knowledge and skills students will acquire within each grade level range	Essential Learning Targets (ELTs):  Defined as the skills, content, and concepts, aligned with standards and benchmarks determined to be "nonnegotiable" areas for proficiency attainment by all students so that they are prepared for the next year/level of education.  The highest cognitive level is determined using an appropriate taxonomy.	Success Criteria:  Clarifies understanding of the ELT, describes indicators for achievement, and informs the selection of appropriate formative and summative assessments.
	Assessment Objectives:  Specific knowledge and skills measured by CSAP for each grade level
Standard 1:  Students develop number sense and use numbers and number relationships in problem solving situations and communicate the reasoning used in solving these problems.	1.1a  Recognize and use equivalent representations of positive rational numbers.	Essential Learning Target:  Apply the properties of number systems to analyze and model relationships.	Success Criteria:
	1.1b  Use models to represent integers.		Recognize equivalent representations of positive rational numbers.
	1.4a  Use the relationships among fractions, decimals and percents including the concepts of ratio and proportion in problem solving situations.		Demonstrate and explain how to divide things equally using fractions, decimals, and percents.
			Create and compare models for rational numbers and integers.
			Graphically represent commonly used fractions in problem-solving situations.
			Determine and simplify ratios in problem solving situations.
			Solve proportions in problem solving situations.
			Use percents to compute values in problem solving situations.
Page 1 of 5
	Written 11-09-08		Brian Campbell
Burlington Middle School Seventh Grade ELT's
Content Standard	Benchmark	Essential Learning Target	Indications for Success
Standard 2:  Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.	2.1a  Represent, describe, and analyze numeric or geometric patterns involving common positive rational numbers or integers using tables, graphs, rules, or symbols.	Essential Learning Target:  Recognize and analyze patterns to create general rules when investigating problems.	Success Criteria:
			Identify and extend linear and nonlinear patterns in a table.
			Generate rules for linear patterns.
			Analyze and extend geometric patterns involving rotations.
			Solve problems by creating tables and graphs when given an algebraic rule.
	2.2a  Solve problems by representing and analyzing patterns involving positive rational numbers or integers using tables, graphs, or rules.		Predict and describe how a change in one quantity results in a change of the other quantity in a linear relationship.
			Recognize how changing one dimension of a rectangle affects its area and perimeter.
			Write a context for a given linear equation.
			Use a table of values to compute unit rate           (T chart).
	2.5a  Solve simple linear equations in problem solving situations using a variety of methods (informal, formal, or graphic)	Essential Learning Target:  Apply algebraic procedures to solve simple linear equations in problem solving situations.	Substitute a given number for a variable in a formula to compute a value.
			Extrapolate a linear graph to solve a problem.
			Use a linear function given in context to solve a problem.
			Create and use guess and check tables to solve problems.
			Translate written words into algebraic equations and expressions.
	2.5b  Translate written words to algebraic equations and expressions and translate algebraic equations and expressions into written words.		Translate algebraic equations and expressions into written words.
			Matching a situation to its algebraic expression.
			Writing a context for a given linear equation
Page 2 of 5
	Written 11-09-08		Brian Campbell
Burlington Middle School Seventh Grade ELT's
Content Standard	Benchmark	Essential Learning Target	Indications for Success
Standard 3:  Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.	3.1a  Construct a histogram or stem and leaf from a set of given data	Essential Learning Target:  Create histograms and stem and leaf plots from a given data set.	Success Criteria:
			Construct data displays:
			Bar graphs
			Line graphs
			Frequency tables
			Histograms
			Stem and Leaf plots
			Construct stem and leaf plots to solve a problem.
	3.1b  Read, interpret, and draw conclusions from histograms, circle graphs, stem and leaf plots, and scatter plots.	Essential Learning Target:  Analyze histograms, circle graphs, stem and leaf plots, and scatter plots to draw conclusions.	Read, interpret, and draw conclusions from histograms, circle graphs, stem and leaf plots, and scatter plots.
			Select the correct type of graph to represent given data.
			Choose the circle graph that best represents the given data.
			Interpret circle graphs using percents
			Use information on a histogram to make accurate predications
			Recognize and identify misleading graphs
	3.2a  Given a display of data determine the mean, median, mode and range.	Essential Learning Target:  Analyze measures of central tendency to determine and justify which best represents a given data set.	Given a data set successfully determine mean, median, mode and range and be able to identify any outliers.
			Recognize the effects of outliers on a data set
			Identify and justify which central tendency best represents the data.
	3.7a  Determine the number of possible outcomes for a given event using a variety of strategies, such as:  tree diagrams, or organized lists.	Essential Learning Target:  Determine the number of outcomes for a given event.	Use counting strategies to determine all possible outcomes for given events.
			Determine the probability of a simple event.
			Determine the number of combination of two independent events:
			Tree diagrams
			Area models
			Organized lists
Page 3 of 5
	Written 11-09-08		Brian Campbell
Burlington Middle School Seventh Grade ELT's
Content Standard	Benchmark	Essential Learning Target	Indications for Success
Standard 4:  Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.	4.3a  Identify and compare similar shapes using ratio, proportion, or scale factor.	Essential Learning Target:  Apply ratio and proportion to solve problems involving similar figures.	Success Criteria:
			Write a part to whole ratio and communicating the reasoning used in comparing areas.
			Determine missing lengths on similar shapes
			Use a scale factor to find size and in deciding whether or not models are to scale.
			Determine ratios of given areas.
			Work with fractional scale factors to enlarge or reduce size.
	4.4a  Construct a coordinate graph and plot ordered integer pairs in all four quadrants.	Essential Learning Target:  Apply knowledge of integers to plot ordered pairs in all four quadrants.	Plot and label ordered pairs on a coordinate plane in all four quadrants.
			Approximate the coordinates of a point on a non-grid coordinate system.
			Identify coordinates of a given points
			Apply knowledge of coordinate graphing to a real world situation
	4.5b  Solve problems involving the areas of circles, triangles, and parallelograms, including surface area and volume without being given the formulas.	Essential Learning Target: Develop and apply the formulas for area and perimeter of polygons and circles to solve problems.	Compare areas of different figures and explain their relationship.
			Determine area of circular sections in a given situation.
			Find the area of polygons and circles in a problem-solving situation.
			Apply the formulas to find perimeter and area of polygons using a ruler.
	4.6a  Use reflections, translations, and/or rotations to determine congruence between two figures.	Essential Learning Target:  Determine congruence between figures by applying transformations.	Identify transformations of 2 dimensional figures.
			Translate points on a grid.
			Transform a geometric figure in the coordinate plane.
			Use transformations to determine congruence between figures.
			Recognize a figure that has been changed by a given transformation.
Page 4 of 5
	Written 11-09-08		Brian Campbell
Burlington Middle School Seventh Grade ELT's
Content Standard	Benchmark	Essential Learning Target	Indications for Success
Standard 5:  Students use a variety of tools and techniques to measure, apply the results in problem-solving situations and communicate the reasoning used in solving these problems.	5.6 Select and use appropriate units and tools to measure to the degree of accuracy required in a particular problem-solving situation	Essential Learning Target:  Use correct measurement tools in order to measure accurately.	Success Criteria:
			Use a protractor to measure an angle.
			Correctly use a ruler to measure to 1/8 of an inch
			Correctly use a metric ruler to measure to the nearest millimeter.
Standard 6:  Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithemtic, paper-and-pencil, calculators in problem solving situations and communicate the reasoning used in solving these problems.	6.1a  Use Concrete materials or pictures to explain how ratios, proportions, and percents can be used to solve real world problems.	Essential Learning Target: Use/Create a picture to determine the correct ratio, proportion, percent, and decimals.	Success Criteria:
			Use pictures to determine commonly used decimals and percents
			Convert between fractions, decimals, and percents
			Use commonly used percentages in a problem-solving situation.
			Determine and use scale factor and proportion to find distances from a picture.
	6.2a  Apply order of operations including exponents	Essential Learning Target:  Apply order of operations to compute whole numbers, fractions, mixed numbers, decimals, and exponents.	Add, subtract, multiply and divide:
			Whole numbers
			Mixed numbers
			Fractions
			Decimals
	6.2b  Add, subtract, multiply and divide positive rational numbers or integers.		Integers
			Identify order of operations
			Evaluate exponents
			Use the order of operations to evaluate an expression involving whole numbers
	6.4b  Solve problems involving positive rational numbers and/or integers.	Essential Learning Target:  Apply Appropriate computation methods and order of operations to solve problems.	Computing with fractions and using ratios and proportions in problem-solving situations.
			Use different unit rates to determine cost.
			Solve problems by estimating with rational numbers.
Page 5 of 5
	Written 11-09-08		Brian Campbell

Burlington Middle School
8th Grade Essential Learning Targets
Content Standard	Benchmark	Essential Learning Target	Indications for Success
Content Standards:  Indicates the broad knowledge and skills students should be acquiring within the Colorado K-12 Standards	Benchmark:  Tactical descriptions of the knowledge and skills students will acquire within each grade level range	Essential Learning Targets (ELTs):  Defined as the skills, content, and concepts, aligned with standards and benchmarks determined to be "nonnegotiable" areas for proficiency attainment by all students so that they are prepared for the next year/level of education.  The highest cognitive level is determined using an appropriate taxonomy.	Success Criteria:  Clarifies understanding of the ELT, describes indicators for achievement, and informs the selection of appropriate formative and summative assessments.
	Assessment Objectives:  Specific knowledge and skills measured by CSAP for each grade level
Standard 1:  Students develop number sense and use numbers and number relationships in problem solving situations and communicate the reasoning used in solving these problems.	1.1a  Recognize and use equivalent representations of positive rational numbers and common irrational numbers (demonstrate the meaning of square root and perfect squares.	Essential Learning Target: Apply equivalent number representations to demonstrate meaning of rational and irrational numbers.	Success Criteria:
			Order rational and irrational numbers
			Expand and evaluate expressions with exponents
	1.4a  Use the relationships among fractions, decimals and percents including the concepts of ratio and proportion in problem solving situations.	Essential Learning Target:  Demonstrate proportional thinking to solve problems.	Apply concepts of ratio and proportion to solve problems involving similarity.
			Apply concepts of ratio and proportion to solve problems involving scale factor.
			Apply concepts of ratio and proportion to solve problems involving unit rate.
Burlington Middle School Eighth Grade ELT's
Content Standard	Benchmark	Essential Learning Target	Indications for Success
Standard 2:  Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems	2.1a  Represent, describe, and analyze numeric or geometric patterns involving common positive rational numbers or integers using tables, graphs, verbal rules, and standard algebraic notation.	Essential Learning Target:  Analyze and extend patterns to create general rules and visual representations when investigating problems.	Success Criteria:
			Extend and generate rules for linear and non-linear number patterns.
			Develop and Explain an equation and a graph for a linear pattern.
			Recognize and extend a number pattern given in spatial form.
			Match an equation with a geometric pattern.
	2.1b  Convert from one functional representation (tables, graphs, verbal rules, and standard algebraic notation) to another.		Create an equation and graph from a table of values.
			Graph given data and draw conclusions from the information displayed.
	2.2a  Describe patterns using variables, expressions, equations, and inequalities in problem-solving situations.		Model real-world situations using patterns and equations
			Graph linear and quadratic equations
			Recognize equivalent representations of a linear pattern.
	2.5a  Solve simple linear equations in problem solving situations using a variety of methods (informal, formal and graphic).	Essential Learning Target:  Apply algebraic procedures to solve linear equations in problem solving situations.	Generate an equation from a guess and check table to solve a problem.
			Extrapolate a linear graph to solve a problem.
			Use a linear function given in a context to solve a problem.
Burlington Middle School Eighth Grade ELT's
Content Standard	Benchmark	Essential Learning Target	Indications for Success
Standard 3:  Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.	3.1a  Read and construct displays of data using appropriate techniques	Essential Learning Target:  Analyze a set of data and create the best representation including circle graphs, scatter plots, and box and whisker plots.	Success Criteria:
			Construct and interpret graphs:
			Bar graphs
			Line graphs
			Frequency tables
			Histograms
			Stem and Leaf plots
			Circle graphs
			Scatter plots
			Box and whisker plots
			Select the most appropriate display to represent a set of data.
			Use a protractor to determine percents on a circle graph.
	3.2a  Display and use measures of central tendency and measures of variability (range and quartiles) in problem solving situations.	Essential Learning Target:  Apply Measures of central tendency to solve problems.	Communicate reasoning when using measures of central tendency in problem-solving situations.
			Compute measures of central tendency from a set of data or a graph.
			Use measures of central tendency to draw conclusions about a data set.
			Determine missing data values given the mean value of the data.
	3.6a  Use a model (list, tree diagram, area model) to determine theoretical probabilities to solve problems involving uncertainty	Essential Learning Target:  Analyze theoretical probabilities to make predictions.	Determine the probability of an event using its sample space derived from:  area models, tree diagrams, and organized lists.
			Determine the probability of independent events using the sample space and the Multiplication principle.
	3.6b  Make predictions using theoretical probability in real-world problems.		Determine the probability of dependent events.
			Make predictions using theoretical probability with dependent and independent events.
Burlington Middle School Eighth Grade ELT's
Content Standard	Benchmark	Essential Learning Target	Indications for Success
Standard 4:  Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.	4.5a  Solve problems involving perimeter and area in 2 dimensions and involving surface area and volume in three dimensions.	Essential Learning Target:  Apply the formulas for volume and surface area of 3 dimensional figures.  And apply the formula for area and perimeter in 2 dimensional figures.	Success Criteria:
			Compare areas of geometric figures and relating the areas to perimeters.
			Use Pythagorean Theorem to solve a problem
			Find the  area of a 2 dimensional figure in a problem-solving situation
			Describe how a change in an object's linear dimensions affects its perimeter and area
			Construct rectangles of given area, finding minimum perimeter and explaining your answer.
	4.5b  Develop and use procedures or formulas to solve problems involving measurement (for example, distance, area, surface area, and volume of right prisms and cylinders.		Find the volume of prisms, cylinders, pyramids, and cones in problem-solving situations
			Estimate volume using the linear dimension of the given figure
			Determine surface area of a 3 dimensional object
			Determine the comparative volume of two prisms
			Use the volume of a 3 dimensional figure to find its linear measures.
	4.6a  Transform geometric figures using reflections, translations, and rotations to determine congruence.	Essential Learning Target:  Create congruent figures by applying reflections, translations, and rotations.	Success Criteria:
			Identify transformations of 2 and 3 dimensional figures.
			Translate points on a grid
			Transform a geometric figure in the coordinate plane using one or more transformations
			Use transformations to determine congruence between figures
			Recognize a figure that has been changed by a given transformation
			Define transformations used to create images of figures.
Burlington Middle School Eighth Grade ELT's
Content Standard	Benchmark	Essential Learning Target	Indications for Success
Standard 5:  Students use a variety of tools and techniques to measure, apply the results in problem solving situations and communicate the reasoning used in solving these problems.	5.2a Estimate, make and use direct and indirect measurements to describe and make comparisons (for example, use a proportion to find the height of a flag pole).	Essential Learning Target:  Use ratio, proportions, and scale factor to determine the measurement of an unknown length.	Success Criteria:
			Use appropriate measurement tools and scale factors to determine measurements.
			Measure to determine a scale factor and solve a problem.
Burlington Middle School Eighth Grade ELT's
Content Standard	Benchmark	Essential Learning Target	Indications for Success
Standard 6:  Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators in problem-solving situations and communicate the reasoning used in solving these problems.	6.1a  Use models to explain how ratios, proportions, and percents can be used to solve real-world problems.	Essential Learning Target:  Solve problems using ratios, proportions, and percents	Success Criteria:
			Use proportional thinking in problem-solving situations.
			Convert from one set of units to another.
			Use proportional reasoning to estimate distance and demonstrate how a given change can affect the result.
			Solve problems involving percents
			Scale up a recipe
			Use ratios and proportions to solve problems.
	6.2a  Apply order of operations to evaluate simple expressions with integers.	Essential Learning Target:  Apply order of operations to compute using whole numbers, fractions, mixed numbers, decimals, exponents, and integers.	Success Criteria:
			Add, subtract, multiply, and divide:
			Whole numbers
			Mixed numbers
			Fractions
			Decimals
			Integers
			Order of Operations
			Evaluate an expression using order of operations
	Written 11-09-08		Brian Campbell

 

 

BMS Mathematics

ELT’s and Mile Markers

 

 

7^th Grade ELTs

 

Ø     Apply the properties of number systems to analyze and model relationships.

Ø     Recognize and analyze patterns to create general rules when investigating problems.

Ø     Apply algebraic procedures to solve and graph simple linear equations in problem solving situations

Ø     Create histograms and stem and leaf plots from a set of data

Ø     Analyze histograms, circle graphs, stem and leaf plots, and scatter plots to draw conclusions

Ø     Analyze measures of central tendency to determine and justify which best represents a given set of data.

Ø     Determine the number of outcomes for a given event.

Ø     Apply ratio and proportions to solve problems involving similar figures.

Ø     Apply knowledge of integers to plot ordered pairs in all four quadrants

Ø     Develop and apply formulas for area and perimeter of polygons and circles to solve problems.

Ø     Determine congruence between figures by applying reflections, translations, and rotations

Ø     Use correct measurement tools to measure accurately.

Ø     Use/Create pictures to determine the correct ratio, proportion, percent and decimals.

Ø     Apply order of operations to compute using whole numbers, signed numbers, fractions, mixed numbers, decimals, percents and exponents.

Ø     Apply appropriate computation methods and order of operations to solve problems.

 

 

 

“Mile Markers”

 

• Apply order of operations to compute using whole numbers, signed numbers, fractions, mixed numbers, decimals, percents and exponents.

 

• Apply ratio and proportions to solve problems involving similar figures.

 

• Apply algebraic procedures to solve simple linear equations

 

•  Develop and apply formulas for area, volume and perimeter of polygons and circles to solve problems.

 

• Analyze histograms, circle graphs, stem and leaf plots, and scatter plots to draw conclusions

 

 

 

8^th Grade  ELTs

 

Ø      Apply equivalent number representations to demonstrate meaning of rational and irrational numbers.

Ø      Demonstrate proportional thinking to solve problems

Ø      Analyze and extend patterns to create general rules and visual representations when investigating problems

Ø      Apply algebraic procedures to solve linear equations in problem solving situations

Ø      Analyze a set of data and create the best representation including circle graphs, scatter plots, and box and whisker plots

Ø      Apply measures of central tendency to solve problems

Ø      Analyze theoretical probabilities to make predictions

Ø      Apply the formulas for area and perimeter for 2 dimensional figures

Ø      Apply the formulas for volume and surface area of 3 dimensional figures

Ø      Create congruent figures by applying reflections, translations, and rotations

Ø      Use ratio, proportions, and scale factor to determine the measurement of an unknown length.

Ø      Solve problems using ratios, proportions, and percents

Ø      Apply order of operations to compute using whole numbers, fractions, mixed numbers, decimals, exponents, and integers.

Ø      Apply computation and estimation methods for problem solving

 

 

 

 

“Mile Markers”

 

• Apply algebraic procedures to solve linear equations in problem solving situations

 

• Analyze a set of data and create the best representation including circle graphs, scatter plots, and box and whisker plots

 

• Apply the formulas for volume and surface area of 3 dimensional figures

 

• Solve problems using ratios, proportions, and percents

 

• Apply order of operations to compute using whole numbers, fractions, mixed numbers, decimals, exponents, and integers.

 

• Apply computation and estimation methods for problem solving

 

 

 

Algebra I ELTs

 

Ø      Utilize the properties of number systems to simplify or solve algebraic or numeric representations

Ø      Create an equation that models a real world situation

Ø      Convert among multiple representations of functions

Ø      Solve, graph and simplify algebraic and linear equations/functions and Inequalities

Ø      Solve using the systems of equations (Substitution, Elimination, and Graphing)

Ø      Apply and compute operations of exponents and radicals (add, subtract, multiply, divide)

Ø      Analyze the relationships among data sets to make a reasonable prediction based on the graph and line of best fit

Ø      Apply the formulas for area and perimeter for 2 dimensional figures

Ø      Apply the formulas for volume and surface area of 3 dimensional figures

Ø      Factoring and solving polynomials and applying the quadratic equation

Ø      Determine the max, min, domain, and range of a given graph

Ø      Determine and compute the appropriate measure of central tendency given data

Ø      Apply experimental and theoretical probability to represent and solve problems involving uncertainty.

Ø      Choose and apply the appropriate method of measurement

Ø      Formulate and apply appropriate scale factor, rate, or unit rate to solve problems

Ø      Develop and communicate proportional thinking

Ø      Apply appropriate computational methods to solve multi-step problems.

 

 

 

“Mile Markers”

 

• Solve, graph and simplify algebraic and linear equations/functions.

 

• Apply and compute operations of exponents and radicals (add, subtract, multiply, divide)

 

• Analyze the relationships among data sets to make a reasonable prediction based on the graph and line of best fit.

 

• Factoring and solving polynomials and applying the quadratic equation

 

• Apply the formulas for area and perimeter for 2 dimensional figures, along with volume and surface area for 3 dimensional figures.