St. Brigid/Our Lady of Hope Regional School
Curriculum Resources
English Language Arts and Mathematics
St. Brigid/Our Lady of Hope Regional School follows the New York State Learning Standards for English Language Arts and Mathematics in grades Pre-Kindergarten through 8. Qualified students in grade 8 take the Algebra I Regents Course and Regents Exam. We are pleased to report that all the 8^{th} graders who took the Algebra I Regents Exam in June passed the exam, many with distinction.
The curriculum that we follow can be found at these links on the New York State Education Department New York State Next Generation ELA Learning Standards
New York State Next Generation Mathematics Learning Standards
A Parent's Guide to the New York State Next Generation ELA & Math Learning Standards
Mathematics Grades 6 through 8 and Algebra 1
6th Grade Mathematics
Students will use ratio language to describe the relationship between two quantities. They will create unit rates and explain its relationship to ratios. They will use ratios and unit rates to solve real-world problems. Students will create ratio tables relating whole-number measurements. They will find a rule for the table and calculate missing values. Students will solve unit rate problems. They will find percent of a quantity as a ratio out of 100. They will find a part of a whole given a percent. They will convert measurement units within a measurement system. They will employ dimensional analysis to change units.
Students will fluently divide multi-digit numbers using the standard algorithm. They will fluently add, subtract, multiply and divide decimals using the standard algorithm for each operation. Students will find the quotient of fractions and solve word problems by utilizing this skill. Students will fluently add, subtract multiply and divide rational numbers. They will solve word problems using all four operations with whole number, decimals and fractions. Students will graph rational numbers on a number line. Students will employ the order of operations when solving.
Students will find the greatest common factor of two whole numbers. They will use the distributive property to express the sum of two whole numbers and use the greatest common factor to factor an expression. They will find the least common multiple of two whole numbers less than or equal to 12.
Students will explore integers and use positive and negative numbers to represent quantities in real-world contexts. They will extend a number line to include negative numbers; they will graph integers on a number line. Students will understand opposite values and will be able to graph them on a number line. They will recognize that the opposite of an opposite is the number itself.
Students will be able to graph ordered pairs on a coordinate plane. They will be able to draw a coordinate plane, label the axes and quadrants. Students will understand that the signs of the numbers in the ordered pair determine their location in the quadrants on a coordinate plane. Students will solve real-world problems by graphing on a coordinate plane and find the distance between two points on the graph.
Students will interpret statements of inequality as a description of the numbers’ position on a number line, they will write, interpret and explain statements of order for rational numbers in real-world contexts. Students will understand that absolute value is the distance that a rational number is from zero on a number line. They will calculate absolute value and explain the meaning of the solution. They will compare values using absolute value.
Students will write and evaluate numerical expressions with while number exponents. They will evaluate expressions with variables. Students will evaluate expressions given specific values for the variables. They will solve given formulas for volume and surface area. Students will identify an unknown in a verbal expression and define a variable and write an algebraic expression. Students will use math terms including variable, coefficient, constant, sum, difference, product, quotient, and factor in an equation. Students will recognize parts of an expression or equation in parentheses as a single entity.
Students will use the distributive property to simplify expressions. They will use the properties of operations to simplify expressions. They will identify equivalent expressions. Students will use a given set of solutions to substitute and solve equations. They will use variables to represent the unknown in an equation.
Students will write and solve one-step equations. They will write inequalities and recognize that unlike equations, inequalities will have an infinite number of solutions. Students will read and interpret word problems containing two quantities to determine the independent and dependent variable in each case.
Students will find the are of triangles, trapezoids and other polygons by decomposing the shapes into triangles and quadrilaterals. Students will find the volumes of right rectangular prisms with whole, decimal and fractional edge lengths. Using a coordinate plane, students will graph coordinates for the vertices of polygons; they will apply the techniques learned here to real-world problems. Students will represent three-dimensional figures using nets of triangles and quadrilateral to find the surface area of these figures. Students will use area and volume models to explain perfect squares and cubes.
Students will recognize statistical questions and understand that statistics is used to gain information about a population by examining a sample of the population. They will determine if the sample is representative of the population given. Students will explore sample sizes and determine if it is large enough to show valid inferences about a population. Students will understand that a set of quantitative data can be explored to determine the shape, center and spread of the data. They will create dot plots and histograms and report about the results shown in the graph. They will calculate the range and measures of center. They will discuss outliers, and their effect on the graph. They will use the range and the measures of center to describe the data. They will choose the measure that accurately depicts the model.
Students will explore the probability of events; they will understand that the chance of an event occurring is a number between 0 and 1. They will recognize that the larger the number, the more likely the event is to happen. They will explore simple events and determine the approximate relative frequency given the probability of the event. The students will determine a probability model and use it to explore simple events like rolling a die or flipping a coin.
7th Grade Mathematics
The students analyze proportional relationships and use them to solve real world problems. They begin with unit ratios including areas, lengths and other quantities measured in different units. Proportional relationships are recognized and are also written as equations used to solve real world problems. Proportional relationships are graphed and interpreted. The topic is extended to include simple interest, tax, markups and markdowns, commissions, percent interest and decrease and percent error. The students will use their calculators to complete some of the math. They will use an online proportion calculator (BasicMath.com or Wyzant.com/resources) to practice creating proportions and
desmos.com to graph and see changes depending on the slope and y-intercepts entered.
All four operations with integer numbers are explored. Use of number lines, counters and the algorithm are employed. Online tools including didax.com and Glencoe virtual manipulatives will be used. The topic is extended to include rational numbers. All four operations are used when solving real world problems.
Properties are applied to simplify or expand algebraic expressions through addition, subtraction, and factoring. The students solve multi-step real-life and mathematical equations posed with rational numbers in any form. They compute, convert to make the units the same, and assess the reasonableness of the answers found. The students will utilize algebra tiles from mathsbot.com to practice simplifying equations to solve. The equation methods are applied to inequalities; solutions are found and graphed on number lines.
Utilizing proportions, the students explore scale models and create scale drawings at a different scale, find missing lengths and areas of scale figures. Students draw geometric figures using a ruler and given conditions; special attention is given to constraints for triangles so that the students see if they can draw a unique triangle, more than one triangle or no triangle. Students will take given figures and slice them to describe the plane sections formed. The students will use desmos.com to explore the plane figures formed through cuts.
Students will use formulas to find the circumference and area of circles. They will apply to find the surface area and volume of three-dimensional figures. They will use facts about supplementary, complementary, vertical and adjacent angles to write and solve equations and solve for an unknown variable.
In statistics and probability, the students will create box plots and find the interquartile range and determine if there are any outliers. They will examine populations and make generalizations based on samples. They will discover why random samples are the best for valid inferences. They will use measures of central tendency, mean absolute deviation and standard deviation to assess the overlap between numerical sets of data and make comparing inferences. Students will conduct trials to find the probability that an outcome will occur. They will create sample spaces and examine compound events.
8th Grade Mathematics
The students determine if numbers are rational or irrational. They convert fractions to decimals and vice versa, including repeating decimals. Using number lines, students approximate irrational numbers so that they can compare them. They use desmos.com to graph the irrational numbers to see the approximations and find better approximations.
Students will study the Laws of Exponents and use the properties to simplify expressions. They will simplify square and cube roots and solve equations involving square and cube roots. The students will express very large and very small numbers in scientific notation. They will use desmos.com to see the changes when moving the decimals for scientific notation. They will use the Laws of Exponents to compute with numbers in scientific notation. Calculators will be utilized as well.
Students will graph proportional relationships and interpret the unit rate as the slope of the graph. They will compare and contrast the steepness of the lines. They will use similar triangles to prove that slope is the same for the entire length of the line. Using desmos.com they will examine different lines and see the changes in steepness. They will utilize the slope formula and the slope-intercept formula to graph lines on the coordinate plane.
Students will solve linear equations in one variable. Equations will be one, two and multi-step; students will need to apply the distributive property and collecting like terms before they can solve. They will find one, none or infinitely many solutions to the given problems. The students will use algebra tiles and virtual algebra tiles on mathsbot.com to gain understanding of the process required to solve.
Students will analyze and solve systems of linear equations using graphing, substitution and elimination. They will use desmos.com to see the solutions as they are graphed. They will find one, none and many solutions to the systems.
Students will understand that functions are rules that assign each input to exactly one output; they will graph functions and look at graphs to determine if they are functions. Functions will be expressed as graphs, tables, and linear equations; they will be represented in different ways and compare the functions. Using points on a graph or a table of values, students will find the rate of change and the initial value. They will interpret graphs, and determine extrema, increasing and decreasing, linear or nonlinear and maximums and minimums. They will sketch graphs based on verbal information given.
Students will rotate, reflect and translate figures. They will determine if two figures are congruent by using a series of transformations to obtain the second from the first. They will recognize that corresponding sides and angles of congruent figures are congruent. They will determine if two figures are similar if the second can be obtained from the first by a series of translations, relations, reflections and dilations. The students will understand that corresponding sides and angles of similar figures are in proportion.
Students will find the measures of angles and explain the relationships of angles formed when two parallel lines are cut by a transversal. They will determine the rules and find the relationships using mathwarehouse.com. They will find the sum of angles in a polygon and exterior angles. They will solve problems using the Pythagorean Theorem and apply it to find missing sides. The students will use the converse of the Pythagorean Theorem to prove that a given triangle is a right triangle. They will use the theorem to derive the distance formula to find the distance between two points in a coordinate system.
Students will review area and volume. They will extend their knowledge of volume to include finding the volume of cones, cylinders and spheres. They will solve real world problems involving these shapes.
Students will construct scatter plots for bivariate data analysis to determine patterns of association between two quantities. They will describe patterns, outliers, clustering, linear or nonlinear association and positive, negative or no correlation. They will use desmos.com to graph the points and examine and interpret the scatter plots. They will find lines of best fit for the scatter plots formed. Once they find the line of best fit, they will solve problems in the context of bivariate data. They will interpret the slope and y-intercept of the equation.
Algebra I
The students will use properties and operations to understand different forms of rational and irrational numbers. They will use all four operations to create equivalent forms of rational numbers. They will describe the solutions of rational and irrational operations as rational and irrational and explain. Students will use the properties to explain each step of a solution.
Students will use properties of exponents to transform expressions for exponential functions. Students will rewrite expressions involving rational exponents by using the properties of exponents. They will use technology to simplify rational exponents by raising the base to the indicated rational number and by changing the index.
Students will interpret expressions and name the parts including coefficient, terms, factors, constants and variables. The students will recognize one or more of the parts, including expressions in parentheses, as one entity. They will define variables and create expressions from given descriptions. They will simplify expressions by performing basic operations and combing like terms.
Students will understand that a function has two sets of values called the domain and range. They will define the domain and range for all functions given. They will use function notation, evaluate functions and create tables and graphs with the given information. They will recognize sequences as functions. They will recognize qualities of function graphs such as maximum, minimum, increasing, decreasing, outliers, clusters, positive and negative and be able to create graphs with a given description. They will calculate the average rate of change, slope, for a given function. They will find the slope from the graph, a table and given points by using the formula. Students will graph linear and quadratic functions and show intercepts, maxima and minima. They will graph absolute value, square root, piecewise and step-functions. They will create tables of the domain and range and graph the given pairs. They will recognize graphs based on the shapes depicted on the coordinate plane. They will graph exponential functions.
Students will write functions that describe the relationship between two quantities. They will combine functions using arithmetic operations. They will write and interpret arithmetic and geometric sequences with explicit and recursive formulas. They will solve real-world problems by creating sequences and solving for a given term.
Students will use transformations to examine the changes to graphs. They will graph functions and the transformations to explore the changes and the effects on solutions to the equations. They will describe the changes to the parent function of a graph by examining the given equation. Students will find inverse functions and write equations for them.
They will create equations and inequalities in one variable to solve for an unknown. They will use the properties to explain the steps of the solution. They will graph solutions of inequalities on a number line.
Students will rearrange formulas to solve for a given variable. They will use the given solution to solve real-world problems.
Students will create equations arising from linear, quadratic, rational and exponential functions and inequalities in one variable and use them to solve problems. Students will create equations in two variables to represent relationships between quantities; these will be graphed on coordinate planes with axes and scales labeled. Students will understand that the graph of an equation in two variables is the set of all solutions graphed in a curve, or line.
Students will distinguish between situations that can be modeled with linear, quadratic and exponential functions. Students will recognize when one quantity changes with a constant rate; they will use the intercept and slope to create a linear equation. Students will recognize when a quantity grows or decays at a constant percent rate per unit; they will use the given information to write an exponential equation. They will observe, using graphs and tables, that a quantity increasing exponentially will eventually exceed a quantity increasing quadratically or linearly. Students will construct arithmetic and geometric sequences given a graph, a description of the relationship or two input-output pairs.
Students will write and solve inequalities in two variables. They will define variables and create two equations using the descriptions given; they will solve the system and check the solutions. They will graph a system of equations to find the point of intersection on paper and using technology. Students will graph the two equations and understand that the point of intersection is the solution that satisfies both equations. They will graph the solutions of a system of inequalities by creating boundary lines and including shading to show the areas that contain the points that make the two inequalities true. They will answer questions about possible solutions. Students will solve systems of equations graphically, through substitution and elimination.
Students will compute with polynomials. They will employ all four operations to simplify quadratic expressions. They will factor quadratic expressions. They will create quadratic expressions and equations from a given description.
Students will employ different methods to solve quadratic equations. Students will solve by taking the square root of each side of the equation when appropriate. Students will be able to factor quadratic expressions. Students will solve graphically; they will use the graph to show the zeros, extreme values and symmetry. Students will solve by employing the quadratic formula. Students will be able to complete the square in a quadratic expression and use this to find the maximum or minimum value of the function. Students will identify the zeroes of a polynomial. Students will use the method completing the square to rewrite equations in vertex form.
Students will represent data with plots on a real number line by constructing dot plots, box plots and histograms. Students will use mean and median to examine the center and interquartile range and standard deviation to examine the spread of a set of data. They will examine the graph and data set for extrema which can alter the measures of center and spread.
Students will create two-way frequency tables using categorical data and interpret the conditional, joint and marginal frequencies. They will interpret the results and look for associations and trends in the data.
Students will use bivariate data to create scatterplots and describe how the data are related. They will determine if linear, quadratic or exponential models can be used to describe the data. They will use technology to find residuals to determine if a function fits the data in the graph. The students will find a line of best fit for the data that can be represented by a linear function. They will interpret the slope of the line of best fit for the data given and explain its meaning. They will compute the correlation coefficient using technology. Students will differentiate between correlation and causation.
Science
St. Brigid/Our Lady of Hope Regional School follows the Next Generation Science Standards in grades Kindergarten through 8. Qualified students in grade 8 take the Living Environment Regents Course and Regents Exam. We are pleased to report that all the 8^{th} graders who took the Living Environment Regents Exam in June passed the exam, many with distinction. NGSS is focused on helping students prepare for career and college readiness. NGSS requires an increase in inquiry-based learning, resulting in more hands-on activities.
Science Grades K-5
The science program in grades K through 8 integrates life, earth, and physical science.
Units in Kindergarten include: Living Things, Our Changing World, Weather and the Sun, and Make Things Move.
First Grade Units include: All About Plants, Animals and How They Communicate, Light and Shadows, and Sky Patterns.
Second Grade Units include: Land and Water, Properties of Materials, Earth's Changing Landscape, and Living Things and Habitats.
Third Grade Units include: Forces Around Us, Life Cycles and Traits, Different Environments, and Observing Weather.
Fourth Grade Units include: Forces and Energy, Using Energy, Our Dynamic Earth, and Information Processing and Living Things.
Fifth Grade Units include: Investigate Matter, Ecosystems, Earth's Interactive Systems, and Earth and Space Patterns.
Middle School Science
6th Grade
Earth and It's Systems
Students will:
Earth and It's Place in the Universe
Students will:
Earth and Human Activity Impact
Students will:
7th Grade
Organisms structure and properties
Students will:
Heredity inheritance and trait variations
Students will:
Biological Evolution
Students will:
Interactions, Energy and Dynamics in an Ecosystem
Students will:
8th Grade
Matter and interactions
Students will:
Forces and interactions
Students will:
Energy
Students will:
Waves
Students will:
6-8 Engineering design
Students will:
The Living Environment is a high school level Regents course that requires additional class time before school, mandated labs, and sitting for the Regents Exam that is administered in June. Students who successfully complete the course and pass the Regents Exam receive high school credit.
Lab periods are built into the master schedule for Middle School Science.
Topics covered in The Living environment Course
Social Studies
St. Brigid/Our Lady of Hope Regional school follows the New York State K-12 Social Studies Framework. The Social Studies program prepares students for college, careers, and civic life.
Information about the Social Studies Framework can be found at this URL: http://www.p12.nysed.gov/ciai/socst/documents/ss-framework-k-12-intro.pdf
Technology Education
St. Brigid/Our Lady of Hope Regional School is implementing the ISTE (International Society for Technology in Education) Standards. Our students experience a wide range of topics, from keyboarding to coding. Chromebook devices are assigned to students in grades 1 through 8, iPads to students in Nursery, Pre-K and Kindergarten. They have the use of the Google Apps for Education. With the guidance of Faculty Moderators, and using various technologies, the 7^{th} graders design and publish the school newspaper, and the 8^{th} graders design and publish the school yearbook.
Technology Scope and Sequence - Grades N through 8
The skills and competencies are intended to help students achieve success in a global community.
Rubric
The rubric itentifies at each grade level when the skills under each Key Idea are to be introduced and at which grade level they are to be mastered.
Introduce | I | Students are introduced to a topic or skill |
Develop | D | Students are given the opportunity to develop introduced skills alongside guided practice opportunities |
Reinforce | R | Skills are reinforced to a topic and students are provided with an opportunity to practice and apply |
Master | M | Students master a topic and can apply key ideas independently |
Information about the ISTE Standards can be found at this URL: https://www.iste.org/standards
From the New York State Education Department Technology and the Next Generation Learning Standards