Instructional Timeline for 7th grade Honors
Unit 1
Testing and classroom procedures (1 week)
Order of operations and properties review (1 week)
Operations with Integers (3 weeks)
Rational Number Operations (2 weeks)
Utah Core Standard(s):
• (7.NS.1)
• (7.NS.2)
• (7.NS.3)
Add and Subtract Integers
• Use a concrete model to add integers
• Use a concrete model to subtract integers
• Find the sums of integers accurately without a model
• Find the differences of integers accurately without a model
• Solve contextual problems involving adding or subtracting integers
Multiply and Divide Integers
• Use a concrete model to multiply integers
• Use a concrete model to divide integers
• Use rules for multiplying and dividing integers accurately
• Add, subtract, multiply and divide integers fluently
• Solve contextual problems involving integers
Operations with Fractions and Decimals
• Estimate the sum, difference, product or quotient of rational numbers
• Find the sum or difference of rational numbers fluently
• Find the product or quotient of rational numbers fluently
• Solve contextual problems involving rational numbers
• Explain why division by zero is undefined
Unit 2 – Expressions and Equations (3 weeks)
Utah Core Standard(s):
• (7.EE.1)
• (7.EE.2)
• (7.EE.3)
• (7.EE.4)
Properties of Arithmetic
• Combine like terms with rational coefficients
• Use the Distributive Property to expand linear expression with rational numbers
• Identify properties of arithmetic to justifying work when manipulating expression
• Write numeric and algebraic expressions to represent contexts
• Identify and explain the meaning of a given expression and its component parts
Solving Algebraic Equations
• Solve multi-step linear equations including rational numbers in a variety of forms fluently
• Use properties of arithmetic to create an argument or critique the reasoning of others
Unit 3 – Ratio and Proportion (4 weeks)
Utah Core Standard(s):
• (7.RP.1)
• (7.RP.2)
• (7.RP.3)
Unit Rates
• Compute the unit rate for either unit
• Compare two rates to determine equivalence or to contrast differences
• Use unit rate to find a missing quantity
• Identify the constant of proportionality from a table, graph, equation, diagram or context
Proportional Relationships
• Determine whether two quantities are in a proportional relationship
• Explain the meaning and significance of the points (0,0) and (1,y/x)
• Write an equation to represent a relationship that is proportional
• Explain why a relationship is or is not a proportional relationship
Solve World Problems
• Analyze the representations of a proportional relationship to solve world problems
• Fluidly transition between part : part and part : whole relationship statements
• Write and solve a proportion to find missing values
• Explain the difference between probability and odds
• Solve multi-step problems involving percent using proportional reasoning
Unit 4 – Rational Number Equivalence (4 weeks)
Utah Core Standard(s):
• (7.NS.2d)
• (7.NS.3)
• (7.SP.5)
• (7.SP.6)
• (7.EE.3)
Fraction, Decimal and Percent Conversions
• Draw models to show equivalence among fractions
• Find the percent of a quantity using a model
• Express and convert between rational numbers in different forms
• Compare rational numbers in different forms
• Solve contextual problems involving rational numbers in different forms
Investigate Chance Processes
• Understand and apply likelihood of a chance event as between 0 and 1
• Use appropriate fractions, decimals and percent to express probabilities
• Approximate probability by collecting data on a chance process
• Calculate theoretical probability on a chance process for simple events
• Predict the approximate frequencies for chance events given the theoretical probability
Solve Percent Problems
• Find a percent or fractional portion of a whole number with or without a model
• Solve contextual problems involving percent increase and decrease
• Develop numeric expressions from percent and fraction models
Unit 5 – Geometric Figures (4 weeks)
Utah Core Standard(s):
• (7.G.1)
• (7.G.2)
• (7.G.4)
• (7.G.5)
• (7.G.6)
Triangles
• Know the Triangle Angle Sum Theorem
• Explain the side length requirements of a triangle
• Explain the requirements for constructing a unique triangle
• Construct a triangle and know if it's a unique triangle given specific criteria
Scaled Drawings
• Draw a scaled version of a polygon given lengths and a scale factor
• Find a measure of a scaled object given the scale factor and measure from the original
• Find the scale factor between objects that are proportional
• Use proportional reasoning to explain whether or not two objects are similar
• Find the scale factors for perimeter or area for proportional objects
Circles
• Explain the relationship between diameter of a circle and its circumference and area
• Explain the algorithm for finding circumference or area of a circle
• Find the circumference or area of any circle given the diameter or radius
• Find the diameter or radius of any circle given the circumference or area
Angle Relationships
• Identify vertical, complementary and supplementary angles
• Find the measures of angles that have a relationship to a known angle
• Apply angle relationships to find missing angle measure
Unit 6 – Real World Equations and Inequalities (3 weeks)
Utah Core Standard(s):
• (7.EE.2)
• (7.EE.3)
• (7.EE.4)
• (7.G.5)
World Problems
• Use variables to create equations that model world problems
• Solve world problems leading to multi-step linear equations
Finding Geometric Unknowns
• Write and solve equations given a diagram of intersecting lines
• Write and solve equations to find the measure of a missing angle in a triangle
• Write and solve equations to find the radius or diameter of a circle
• Write and solve equations to find unknown lengths, perimeter, or area of polygons
Inequalities
• Use symbols of inequality to model situations in which solution are > or < a given value
• Use variables to create inequalities that model world problems
• Solve world problems leading to linear inequalities
Unit 7 – Probability and Statistics (2 weeks)
Utah Core Standard(s):
• (7.SP.1)• (7.SP.2)• (7.SP.3)• (7.SP.4)• (7.SP.5)• (7.SP.6)• (7.SP.7)• (7.SP.8)
Making Predictions
• Develop a probability model and use it to find the probability of events
• Compare probabilities from a model to observed frequencies
• Explain possible sources of discrepancies if the agreement is not good
Explain the probability of a compound event as the fraction of outcomes in the sample space for which the compound event occurs
• Represent sample spaces for compound events using organized lists, tables, and tree diagrams
Random Sampling
• Use random sampling to obtain a sample from a population
• Explain random sampling procedures that produce samples that can represent population values
• Create appropriate plots of collected data to provide a visual representation of the samples
• Compare samples of the same size from a population in order to gauge the variation in the samples
• Use variation to form an estimate of range of where a population value might lie
• Make predictions about a population based on samples
Comparing Two Populations
• Make comparisons of data distributions by estimating the center and spread from a visual inspection of data plots
• Compare two populations by calculating and comparing numerical measures of center and spread
• Calculate the mean absolute deviation as a measure of spread of a population
Measure the distance between the centers of two populations of similar variability using the MAD as a unit of measure
Unit 8 – Measurement of Solids and Cross-Sections (3 weeks)
Utah Core Standard(s):
• (7.G.3)
• (7.G.4)
• (7.G.6)
Surface Area and Volume
• Give an informal derivation of the relationship between area and circumference of a circle
Solve world and mathematical problems involving area, volume, and surface area of various two- and three dimensional objects
Cross-Sections
• Describe the two-dimensional figures that result from sliding a three-dimensional figures
• Solve world and mathematical problems involving volume and surface area of various three dimensional objects.
*This timeline is subject to change and may include additional topics as time allows.
Unit 1
Testing and classroom procedures (1 week)
Order of operations and properties review (1 week)
Operations with Integers (3 weeks)
Rational Number Operations (2 weeks)
Utah Core Standard(s):
• (7.NS.1)
• (7.NS.2)
• (7.NS.3)
Add and Subtract Integers
• Use a concrete model to add integers
• Use a concrete model to subtract integers
• Find the sums of integers accurately without a model
• Find the differences of integers accurately without a model
• Solve contextual problems involving adding or subtracting integers
Multiply and Divide Integers
• Use a concrete model to multiply integers
• Use a concrete model to divide integers
• Use rules for multiplying and dividing integers accurately
• Add, subtract, multiply and divide integers fluently
• Solve contextual problems involving integers
Operations with Fractions and Decimals
• Estimate the sum, difference, product or quotient of rational numbers
• Find the sum or difference of rational numbers fluently
• Find the product or quotient of rational numbers fluently
• Solve contextual problems involving rational numbers
• Explain why division by zero is undefined
Unit 2 – Expressions and Equations (3 weeks)
Utah Core Standard(s):
• (7.EE.1)
• (7.EE.2)
• (7.EE.3)
• (7.EE.4)
Properties of Arithmetic
• Combine like terms with rational coefficients
• Use the Distributive Property to expand linear expression with rational numbers
• Identify properties of arithmetic to justifying work when manipulating expression
• Write numeric and algebraic expressions to represent contexts
• Identify and explain the meaning of a given expression and its component parts
Solving Algebraic Equations
• Solve multi-step linear equations including rational numbers in a variety of forms fluently
• Use properties of arithmetic to create an argument or critique the reasoning of others
Unit 3 – Ratio and Proportion (4 weeks)
Utah Core Standard(s):
• (7.RP.1)
• (7.RP.2)
• (7.RP.3)
Unit Rates
• Compute the unit rate for either unit
• Compare two rates to determine equivalence or to contrast differences
• Use unit rate to find a missing quantity
• Identify the constant of proportionality from a table, graph, equation, diagram or context
Proportional Relationships
• Determine whether two quantities are in a proportional relationship
• Explain the meaning and significance of the points (0,0) and (1,y/x)
• Write an equation to represent a relationship that is proportional
• Explain why a relationship is or is not a proportional relationship
Solve World Problems
• Analyze the representations of a proportional relationship to solve world problems
• Fluidly transition between part : part and part : whole relationship statements
• Write and solve a proportion to find missing values
• Explain the difference between probability and odds
• Solve multi-step problems involving percent using proportional reasoning
Unit 4 – Rational Number Equivalence (4 weeks)
Utah Core Standard(s):
• (7.NS.2d)
• (7.NS.3)
• (7.SP.5)
• (7.SP.6)
• (7.EE.3)
Fraction, Decimal and Percent Conversions
• Draw models to show equivalence among fractions
• Find the percent of a quantity using a model
• Express and convert between rational numbers in different forms
• Compare rational numbers in different forms
• Solve contextual problems involving rational numbers in different forms
Investigate Chance Processes
• Understand and apply likelihood of a chance event as between 0 and 1
• Use appropriate fractions, decimals and percent to express probabilities
• Approximate probability by collecting data on a chance process
• Calculate theoretical probability on a chance process for simple events
• Predict the approximate frequencies for chance events given the theoretical probability
Solve Percent Problems
• Find a percent or fractional portion of a whole number with or without a model
• Solve contextual problems involving percent increase and decrease
• Develop numeric expressions from percent and fraction models
Unit 5 – Geometric Figures (4 weeks)
Utah Core Standard(s):
• (7.G.1)
• (7.G.2)
• (7.G.4)
• (7.G.5)
• (7.G.6)
Triangles
• Know the Triangle Angle Sum Theorem
• Explain the side length requirements of a triangle
• Explain the requirements for constructing a unique triangle
• Construct a triangle and know if it's a unique triangle given specific criteria
Scaled Drawings
• Draw a scaled version of a polygon given lengths and a scale factor
• Find a measure of a scaled object given the scale factor and measure from the original
• Find the scale factor between objects that are proportional
• Use proportional reasoning to explain whether or not two objects are similar
• Find the scale factors for perimeter or area for proportional objects
Circles
• Explain the relationship between diameter of a circle and its circumference and area
• Explain the algorithm for finding circumference or area of a circle
• Find the circumference or area of any circle given the diameter or radius
• Find the diameter or radius of any circle given the circumference or area
Angle Relationships
• Identify vertical, complementary and supplementary angles
• Find the measures of angles that have a relationship to a known angle
• Apply angle relationships to find missing angle measure
Unit 6 – Real World Equations and Inequalities (3 weeks)
Utah Core Standard(s):
• (7.EE.2)
• (7.EE.3)
• (7.EE.4)
• (7.G.5)
World Problems
• Use variables to create equations that model world problems
• Solve world problems leading to multi-step linear equations
Finding Geometric Unknowns
• Write and solve equations given a diagram of intersecting lines
• Write and solve equations to find the measure of a missing angle in a triangle
• Write and solve equations to find the radius or diameter of a circle
• Write and solve equations to find unknown lengths, perimeter, or area of polygons
Inequalities
• Use symbols of inequality to model situations in which solution are > or < a given value
• Use variables to create inequalities that model world problems
• Solve world problems leading to linear inequalities
Unit 7 – Probability and Statistics (2 weeks)
Utah Core Standard(s):
• (7.SP.1)• (7.SP.2)• (7.SP.3)• (7.SP.4)• (7.SP.5)• (7.SP.6)• (7.SP.7)• (7.SP.8)
Making Predictions
• Develop a probability model and use it to find the probability of events
• Compare probabilities from a model to observed frequencies
• Explain possible sources of discrepancies if the agreement is not good
Explain the probability of a compound event as the fraction of outcomes in the sample space for which the compound event occurs
• Represent sample spaces for compound events using organized lists, tables, and tree diagrams
Random Sampling
• Use random sampling to obtain a sample from a population
• Explain random sampling procedures that produce samples that can represent population values
• Create appropriate plots of collected data to provide a visual representation of the samples
• Compare samples of the same size from a population in order to gauge the variation in the samples
• Use variation to form an estimate of range of where a population value might lie
• Make predictions about a population based on samples
Comparing Two Populations
• Make comparisons of data distributions by estimating the center and spread from a visual inspection of data plots
• Compare two populations by calculating and comparing numerical measures of center and spread
• Calculate the mean absolute deviation as a measure of spread of a population
Measure the distance between the centers of two populations of similar variability using the MAD as a unit of measure
Unit 8 – Measurement of Solids and Cross-Sections (3 weeks)
Utah Core Standard(s):
• (7.G.3)
• (7.G.4)
• (7.G.6)
Surface Area and Volume
• Give an informal derivation of the relationship between area and circumference of a circle
Solve world and mathematical problems involving area, volume, and surface area of various two- and three dimensional objects
Cross-Sections
• Describe the two-dimensional figures that result from sliding a three-dimensional figures
• Solve world and mathematical problems involving volume and surface area of various three dimensional objects.
*This timeline is subject to change and may include additional topics as time allows.