Literacy Essential Skills

• Writing:

  • Construct simple sentences. 

  • Capitalize I, capitalize beginning letter, use periods.

  • Write a narrative with events in order

  • Write about a topic with some information about the topic

  • Identify a topic and write an opinion about the topic

• Reading Behaviors:

  • Use sounds and pictures to decode words.

  • Demonstrate one-to-one correspondence.

  • Retell familiar stories with key details.

  • Understand concepts of print, including that print conveys a message and is organized from left to right and from top to bottom.

• Phonics:

  • Recognize letters and their sounds.

  • Read and write CVC (consonant, vowel, consonant) words including words with sh, th, ch. 

  • Segment and blend words.

  • Recognize kindergarten grade high-frequency words.

Math Essential Skills

• Counting and Cardinality:

  • Count by ones and tens up to 100.

  • Write and represent numbers from 0 to 20.

• Operations and Algebraic Thinking:

  • Understand that addition is putting together and adding to.

  • Understand that subtraction is taking apart and taking from.

  • Identify number pairs to 5.

• Numbers in Base Ten:

  • Compose and decompose numbers from 11- 29 into tens, ones, and some further ones.
    
    

Literacy Essential Skills

Writing

• Write complete sentences.

• Write narratives with a beginning, middle, and end.

• Write about topics with supporting facts and a conclusion.

• Reading Behaviors:

  • Use strategies for unknown words, such as starting at the left of the word, reading each letter, blending the sounds together and chopping the word into syllables.

  • Build reading stamina by being able to read for 20-30 minutes.

  • Comprehend stories with sequence and main idea.

• Comprehension:

  • Retell a story by including what occurs in the beginning, middle and end.

  • Be able to identify a topic of a story and the details that are connected to it.

• Phonics:

  • Read and write words with phonics patterns including digraphs, beginning blends, common endings (-ing, -ed, -s, -er), and short and long vowel sounds.

  • Recognize first grade high-frequency words.

Math Essential Skills

• Operations and Algebraic Thinking:

  • Solve word problems using addition and subtraction within 20. 

  • Fluently add and subtract within 10.

• Numbers and Operations - Base Ten:

  • Count to 120, starting at any number less than 120.

  • Understand that the two digits of a two-digit number represent amounts of tens and ones. 

  • Given a two-digit number, mentally find 10 more or 10 less than the number without having to count. 

  • Add within 100 and when doing so understand that in adding two-digit numbers, tens are added to tens and ones are added to ones; and sometimes it is necessary to compose a ten.

Literacy Essential Skills

• Writing:

  • Write a narrative with a beginning, middle and end that includes details to describe characters.

  • Write an expository and an opinion about a topic with supporting facts and definitions to develop/prove a point and include a conclusion.

  • Expand on a single sentence through elaboration and word choice.

  • Organize and group similar information together on a page.

• Reading Behaviors:

  • Choose appropriate books.

  • Build reading stamina by being able to read for 20-30 minutes.

  • Track comprehension across longer texts.

  • Use strategies for unknown words, such as blending the sounds together, chopping the words into syllables, separating the base word from the prefix/suffix, and rereading to determine if it makes sense.

• Comprehension:

  • Identify story elements such as the setting, characters, problem and solution.

  • Retell a story sequence of important events.

  • Identify a character’s feelings with evidence from the text.

  • Identify text features such as headings, captions and glossaries and their purpose in informational text.

• Phonics:

  • Read and write words with blends, digraphs, and long vowel patterns.

  • Recognize second grade high-frequency words.

Math Essential Skills

• Operations and Algebraic Thinking:

  • Fluently add and subtract within 20.

  • Use addition and subtraction within 100 for word problems involving one- and two-steps.

• Numbers and Operations - Base Ten:

  • Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones. 

  • Skip count by 5s, 10s, and 100s within 1,000.

  • Read and write numbers to 1,000.

  • Add and subtract within 1,000 and when doing so understand that one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens and hundreds.

• Geometry:

  • Partition circles and rectangles into two, three, or four equal shares and describe the shares using the words halves, thirds, a half of, a third of, etc., and describe the whole as two halves, three thirds, or four fourths.

Literacy Essential Skills

• Writing:

  • Write a narrative in an organized sequence with descriptive details and dialogue.

  • Write an opinion about the topic with organized reasons and supporting details.

  • Organize and group similar information together on a page and use appropriate paragraphing structure.

• Reading Literature and Informational Text:

  • Identify story elements (character, setting, problem rising action, climax, and resolution), understand their role in the story, and use them to retell the story.

  • Describe a character using their character traits and motivations with support from the text. 

  • Identify the main idea and determine the important details, leaving out personal opinions and insignificant details.

  • Use evidence to support claims.

• Word Study:

  • Apply phonics and word analysis skills when decoding words.

Math Essential Skills

• Operations and Algebraic Thinking:

  • Fluently multiply and divide within 100 and be able to recall from memory the products of two one-digit numbers.

  • Represent and solve problems involving multiplication and division within 100.

• Numbers and Operations - Base Ten:

  • Fluently add and subtract within 1,000.

  • Round whole numbers to the nearest 10 or 100.

• Numbers and Operations - Fractions:

  • Understand a unit fraction (1/b) as the quantity formed by 1 part when the whole is partitioned into b equal parts, and a fraction a/b as a quantity formed by a unit fractions.

  • Identify and label fractions on the number.

  • Compare fractions by reasoning about their size.

Literacy Essential Skills

• Writing:

  • Write organized narratives and opinions with developed characters and logical reasoning. 

  • Use transitional words, dialogue, quotations, and definitions when appropriate.

• Reading Literature and Informational Text:

  • Increase vocabulary to describe character traits using evidence from the text.

  • Identify story elements (with the addition of theme, protagonist and antagonist), understand their role in the story, and use them to retell the story.

  • Determine themes and main ideas and provide evidence to support.

  • Synthesize information from multiple sources.

• Word Study:

  • Apply phonics and word analysis skills when decoding words.

Math Essential Skills

• Operations and Algebraic Thinking:

  • Solve multi-step word problems with whole numbers using the four operations.

• Numbers and Operations - Base Ten:

  • Fluently add and subtract within 1,000,000 using the standard algorithm.

  • Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

  • Read, write and compare multi-digit whole numbers.

• Numbers and Operations - Fractions:

  • Add and subtract mixed numbers with like denominators.

  • Multiply a fraction by a whole number.

Literacy Essential Skills

• Writing

• • Write organized narratives and opinions with developed characters and logical reasoning.

  • Use quotations, descriptive details, and text features such as headings when appropriate.

• Reading Literature and Informational Text:

  • Determine a theme using character’s actions and responses supported by evidence from the text.

  • Identify and interpret figurative language.

  • Identify two or more main ideas and supporting details when summarizing a text.

  • Synthesize information from multiple sources.

• Word Study:

  • Apply phonics and word analysis skills when decoding words.

Math Essential Skills

• Operations and Algebraic Thinking:

  • Use parentheses, brackets, or braces in numerical expressions and evaluate.

  • Solve multi-step real-world problems.

  • Fluently multiply multi-digit numbers.

• Numbers and Operations - Base Ten:

  • Add, subtract, multiply and divide whole numbers and decimals up to the thousandths place.

  • Round decimals to any place.

• Numbers and Operations - Fractions:

  • Add, subtract, multiply, and divide fractions with unlike denominators and mixed numbers.

Literacy Essential Skills

• Writing:

  • Write arguments, informative/explanatory texts, and narratives using evidence.

  • Gather and assess information from print and digital sources, cite sources.

  • Draw evidence from literary or informational texts to support analysis, reflection and research.

• Literacy Habits:

  • Read a wide variety of texts independently and with support.

  • Use text evidence to support ideas.

  • Develop and revise writing by planning, revising and editing.

  • Determine the meanings of words using strategies such as Latin/Greek roots/affixes and figurative language.

• Reading Literature and Informational Text:

  • Cite textual evidence, determine themes and central ideas.

  • Analyze plot development and evaluate word meanings and author's perspective.

• Speaking and Listening:

  • Engage in discussions, build on ideas with evidence, ask/respond to questions.

• Language:

  • Use language conventions effectively.

  • Determine or clarify meanings of words using context clues, syntax, and affixes/roots.

Math Essential Skills

• The Number System:

  • Divide fractions by fractions

  • Compute fluently with multi-digit numbers and find common factors and multiples.

  • Apply understanding of numbers to rational numbers. 

• Ratios and Proportional Relationships:

  • Describe a ratio relationship between two quantities.

  • Apply ratio and rate reasoning in real-world scenarios.

• Expressions and Equations:

  • Write, evaluate, and simplify numerical expressions with whole-number exponents.

  • Read, write and evaluate expressions with variables.

  • Solve one-variable equations and inequalities.

  • Identify and generate equivalent expressions.

• Geometry:

  • Solve problems involving area, surface area, and volume.

  • Use the coordinate plane to draw polygons given coordinates for the vertices.

  • Represent three-dimensional figures using nets.

• Statistics and Probability:

  • Recognize a statistical question and understand that a set of data collected to answer the statistical question has a distribution that can be described by its center, spread and overall shape.

  • Recognize that a measure of center summarizes all of its values with a single number.

  • Summarize data using measures and displays.

Literacy Essential Skills

• Writing:

  • Write arguments with reasons and evidence, informative/explanatory texts, and narratives.

  • Gather information, assess credibility, cite sources.

  • Draw evidence from literary or informational texts to support analysis, reflection and research.

• Literacy Habits:

  • Read various genres independently and with support.

  • Use text evidence to support conclusions.

  • Determine the meanings of words using strategies such as Latin/Greek roots/affixes and figurative language.

  • Write in response to literature, informational text, poetry, video, audio and other live versions of text.

• Reading Literature and Informational Text:

  • Use textual evidence to analyze meanings, themes, and plot development.

  • Analyze dialogue and character viewpoints, assess author's purpose and point of view.

  • Determine the meaning of words and phrases as they are used in a text and how the specific word choice affects the meaning and tone.

• Speaking and Listening:

  • Engage in discussions, support ideas with evidence, ask/respond to questions.

• Language:

  • Use language conventions effectively.

  • Determine or clarify meanings of words using context clues, syntax, and affixes/roots.

Math Essential Skills

• The Number System:

  • Add, subtract, multiply, and divide rational numbers.

  • Represent operations on number lines.

• Ratios and Proportional Relationships:

  • Compute unit rates, understand and apply proportional relationships.

  • Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal descriptions of proportional relationships.

  • Represent proportional relationships by equations.

  • Explain the meaning of a point (x, y) on a graph of a proportional relationship in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate.

  • Solve multistep ratio and percent problems.

• Expressions and Equations:

  • Add, subtract, factor, and expand linear expressions.

  • Solve equations and inequalities with rational coefficients.

  • Graph the solution set of an inequality and interpret it in the context of the problem.

  • Construct simple equations and inequalities using variables.

  • 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. 

• Geometry:

  • Solve problems involving scale drawings, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

  • Describe two-dimensional figures that result from slicing three-dimensional figures.

  • Write and solve simple equations for an unknown angle involving supplementary, complementary, vertical and adjacent angles.

  • Calculate area, volume and surface area of two- and three-dimensional objects.

• Statistics and Probability:

  • Understand statistical questions, summarize data, and make inferences.

  • Understand that the probability of a chance event is a number between 0 and 1.

  • Develop and use a probability model.

  • Find probabilities by using organized lists, tables, tree diagrams and simulations.

Literacy Essential Skills

• Writing:

  • Write arguments with reasons and evidence.

  • Write informative/explanatory texts with organized content.

  • Write narratives with effective technique, relevant descriptive details, and well-structured event sequences.

  • Develop a thesis or claim with facts, definitions, details, quotations, or other information and examples.

  • Gather information, assess credibility, cite sources.

• Literacy Habits:

  • Read a variety of genres independently and with support.

  • Cite evidence from multiple sources, evaluate arguments.

  • Determine the meanings of words using strategies such as Latin/Greek roots/affixes and figurative language.

• Reading Literature and Informational Text:

  • Use textual evidence to analyze explicit and inferred meanings.

  • Identify themes and analyze development, interpret word meanings.

  • Compare viewpoints of characters and authors. 

  • Assess the author's point of view or purpose.

• Speaking and Listening:

  • Engage in collaborative discussions, build on the ideas of others, express ideas while providing evidence, pose and respond to questions that connect ideas, and elaborate with relevant observations and ideas.

  • Adapt speech to different contexts.

• Language:

  • Apply language arts conventions effectively.

  • Determine or clarify meanings of words using context clues, syntax, and affixes/roots.

Math Essential Skills

• The Number System:

  • Understand rational and irrational numbers, approximate irrational numbers.

• Expressions and Equations:

  • Work with radicals and exponents, evaluate square and cube roots.

  • Use scientific notation, graph and interpret proportional relationships, solve linear equations.

• Functions:

  • Understand and compare properties of functions.

  • Construct a function to model a linear relationship between two quantities and determine the rate of change or initial value. 

  • Describe the functional relationship between two quantities by analyzing a graph.

• Geometry:

  • Experiment with transformations, understand congruence and similarity.

  • Describe the effect of dilations, translations, rotations and reflections.

  • Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

  • Explain and apply the Pythagorean Theorem. 

  • Calculate volumes of geometric shapes.

• Statistics and Probability:

  • Describe data distributions, compare data sets, fit data to normal distributions.

  • Represent relationships between variables with scatter plots.

Algebra Essential Skills

• The Number System:

  • Use properties of rational and irrational numbers. Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

  • Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. 

  • Rewrite expressions involving radicals and rational exponents using the properties of exponents.

  • Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

  • Interpret the structure of expressions. Interpret expressions that represent a quantity in terms of its context.

  • Interpret parts of an expression, such as terms, factors, and coefficients.

  • Interpret complicated expressions by viewing one or more of their parts as a single entity.

  • Write expressions in equivalent forms to solve problems. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

  • Factor a quadratic expression to reveal the zeros of the function it defines

• Algebra:

  • Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

  • Use the properties of exponents to transform expressions for exponential functions.

  • Write expressions in equivalent forms to solve problems, ie: compound interest

  • Perform arithmetic operations on polynomials. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

  • Understand the relationship between zeros and factors of polynomials.

  • Use polynomial identities to solve problems.

  • Rewrite rational expressions. Rewrite simple rational expressions in different forms.

  •  Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions..

  •  Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

  • Create equations that describe numbers or relationships. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

  • Understand solving equations as a process of reasoning and explain the reasoning. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

  • Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

  • Solve equations and inequalities in one variable. Solve quadratic equations in one variable. 

  • Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form. 

  • Solve quadratic equations square roots, completing the square, the quadratic formula and factoring.

  • Solve systems of equations., graphically  and algebraically. 

  • Represent and solve equations and inequalities graphically. Explain why the x-coordinates of the points where the graphs of the equations

    •  y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values.  Also, where f(x) and/or g(x) are linear,  rational, absolute value, exponential, and functions

• Functions:

  • Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range

  • Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 

  •  Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

  • Interpret functions that arise in applications in terms of the context, a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship increasing, decreasing, positive, or negative, etc.

  • Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval

  • Graph linear and quadratic functions and show intercepts, maxima, and minima.

  • Graph piecewise-defined functions, including step functions and absolute value functions.

  • Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available.

  • Use the process of factoring and completing the square in a quadratic function to show zeros.

  • Use the properties of exponents to interpret expressions for exponential functions.

  • Write a function that describes a relationship between two quantities.

  • Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations.

  • Find inverse functions.

  • Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

  • Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.

• Statistics and Probability

  • Summarize, represent, and interpret data on a single count or measurement variable. Represent data with plots on the real number line (dot plots, histograms, and box plots).

  • Summarize, represent, and interpret data on a single count or measurement variable. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

  • Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

  • Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.

  • Summarize categorical data for two categories in two-way frequency tables.

  • Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.