Archive for the ‘National Education Standards’ Category

5th Grade National Language Arts Standards

Thursday, September 9th, 2010

Achieve100’s Study Cards and Practice Tests support these National Language Arts Standards for 5th Grade.

5th Grade National Language Arts Standards

5th Grade Foundational Reading Skills Standards

  • Know and apply grade-level phonics and word analysis skills in decoding words.
  • Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology to read accurately unfamiliar multisyllabic words in context and out of context.
  • Read with sufficient accuracy and fluency to support comprehension.
  • Read on-level text with purpose and understanding.
  • Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.
  • Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

 5th Grade Reading Standards for Literature

  • Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.
  • Determine a theme of a story, drama, or poem from details in the text, including how characters in a story or drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text.
  • Compare and contrast two or more characters, settings, or events in a story or drama, drawing on specific details in the text.
  • Determine the meaning of words and phrases as they are used in a text, including figurative language such as metaphors and similes.
  • By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 4–5 text complexity band independently and proficiently.

5th Grade Reading Standards for Informational Text

  • Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.
  • Determine two or more main ideas of a text and explain how they are supported by key details; summarize the text.
  • Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text.
  • Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5 topic or subject area.
  • By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 4–5 text complexity band independently and proficiently.

5th Grade Language Standards

Achieve100 supports these speaking and writing standards by helping students understand the respective words, meanings and use in literature and informational text.

  • Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
    • Explain the function of conjunctions, prepositions, and interjections in general and their function in particular sentences.
    • Form and use the perfect verb tenses.
    • Use verb tense to convey various times, sequences, states, and conditions.
    • Recognize and correct inappropriate shifts in verb tense.
    • Use correlative conjunctions.
  • Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
    • Use punctuation to separate items in a series.
    • Use a comma to separate an introductory element from the rest of the sentence.
    • Use a comma to set off the words yes and no, to set off a tag question from the rest of the sentence, and to indicate direct address .
    • Use underlining, quotation marks, or italics to indicate titles of works.
    • Spell grade-appropriate words correctly, consulting references as needed.
  • Use knowledge of language and its conventions when writing, speaking, reading, or listening.
    • Expand, combine, and reduce sentences for meaning, reader/listener interest, and style.
    • Compare and contrast the varieties of English used in stories, dramas, or poems.
  • Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 5 reading and content, choosing flexibly from a range of strategies.
    • Use context as a clue to the meaning of a word or phrase.
    • Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word.
  • Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
    • Interpret figurative language, including similes and metaphors, in context.
    • Recognize and explain the meaning of common idioms, adages, and proverbs.
    • Use the relationship between particular words to better understand each of the words.
    • Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships. 

4th Grade National Language Arts Standards

Thursday, September 9th, 2010

Achieve100’s Study Cards and Practice Tests support these National Language Arts Standards for 4th Grade.

4th Grade National Language Arts Standards

4th Grade Foundational Reading Skills Standards

  • Know and apply grade-level phonics and word analysis skills in decoding words.
  • Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology to read accurately unfamiliar multisyllabic words in context and out of context.
  • Read with sufficient accuracy and fluency to support comprehension.
  • Read on-level text with purpose and understanding.
  • Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.
  • Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

4th Grade Reading Standards for Literature

  • Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.
  • Determine a theme of a story, drama, or poem from details in the text; summarize the text.
  • Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text.
  • Determine the meaning of words and phrases as they are used in a text.
  • By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently.

4th Grade Reading Standards for Informational Text

  • Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.
  • Determine the main idea of a text and explain how it is supported by key details; summarize the text.
  • Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text.
  • Determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area.
  • By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.

4th Grade Language Standards

Achieve100 supports these speaking and writing standards by helping students understand the respective words, meanings and use in literature and informational text.

  • Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
    • Use relative pronouns and relative adverbs.
    • Form and use the progressive verb tenses.
    • Use modal auxiliaries to convey various conditions.
    • Order adjectives within sentences according to conventional patterns.
    • Form and use prepositional phrases.
    • Produce complete sentences, recognizing and correcting inappropriate fragments and run-ons.
    • Correctly use frequently confused words.
  • Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
    • Use correct capitalization.
    • Use commas and quotation marks to mark direct speech and quotations from a text.
    • Use a comma before a coordinating conjunction in a compound sentence.
    • Spell grade-appropriate words correctly, consulting references as needed.
  • Use knowledge of language and its conventions when writing, speaking, reading, or listening.
    • Choose words and phrases to convey ideas precisely.
    • Choose punctuation for effect.
  • Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies.
    • Use context as a clue to the meaning of a word or phrase.
    • Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word.
  • Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
    • Explain the meaning of simple similes and metaphors in context.
    • Recognize and explain the meaning of common idioms, adages, and proverbs.
    • Demonstrate understanding of words by relating them to their opposites and to words with similar but not identical meanings.
  • Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being and that are basic to a particular topic.

5th Grade National Mathematics Standards

Thursday, September 9th, 2010

Achieve100’s Study Cards and Practice Tests support these National Mathematics Standards for 5th Grade.

5th Grade National Mathematics Standards

Operations and Algebraic Thinking

Write and interpret numerical expressions.

  • Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
  • Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them

Analyze patterns and relationships.

  • Generate two numerical patterns using two given rules.
  • Identify apparent relationships between corresponding terms.
  • Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

Number and Operations in Base Ten

Understand the place value system.

  • Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
  • Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
  • Read, write, and compare decimals to thousandths.
    • Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.
    • Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
  • Use place value understanding to round decimals to any place.
  • Perform operations with multi-digit whole numbers and with decimals to hundredths.
  • Fluently multiply multi-digit whole numbers using the standard algorithm.
  • Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
  • Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Number and Operations—Fractions

Use equivalent fractions as a strategy to add and subtract fractions.

  • Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
  • Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
  • Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
  • Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
  • Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).
  • Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
  • Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
    • Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.
    • Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.
    • Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
  • Interpret multiplication as scaling (resizing), by:
    • Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
  • Solve real world problems involving multiplication of fractions and mixed numbers.
  • Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
    • Interpret division of a unit fraction by a non-zero whole number. Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division.
    • Interpret division of a whole number by a unit fraction, and compute such quotients.
    • Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.

Measurement and Data

Convert like measurement units within a given measurement system.

  • Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real world problems.

Represent and interpret data.

  • Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
  • Use operations on fractions for this grade to solve problems involving information presented in line plots.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

  • Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
    • A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
    • A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
  • Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
  • Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
  • Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.
  • Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
  • Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Graph points on the coordinate plane to solve real-world and mathematical problems.

  • Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates.
  • Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
  • Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Classify two-dimensional figures into categories based on their properties.

  • Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category.
  • Classify two-dimensional figures in a hierarchy based on properties.

4th Grade National Mathemetics Standards

Thursday, September 9th, 2010

Achieve100’s Study Cards and Practice Tests support these National Mathematics Standards for 4th Grade.

4th Grade National Mathematics Standards

Operations and Algebraic Thinking

Use the four operations with whole numbers to solve problems.

  • Interpret a multiplication equation as a comparison.
  • Multiply or divide to solve word problems involving multiplicative comparison.
  • Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.
  • Represent these problems using equations with a letter standing for the unknown quantity.
  • Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
  • Gain familiarity with factors and multiples.
  • Find all factor pairs for a whole number in the range 1–100.
  • Recognize that a whole number is a multiple of each of its factors.
  • Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number.
  • Determine whether a given whole number in the range 1–100 is prime or composite.

Generate and analyze patterns.

  • Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Number and Operations in Base Ten – Generalize place value understanding for multi-digit whole numbers.

  • 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. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
  • Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
  • Use place value understanding to round multi-digit whole numbers to any place.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

  • Fluently add and subtract multi-digit whole numbers using the standard algorithm.
  • Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.
  • Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Number and Operations – Fractions

Extend understanding of fraction equivalence and ordering.

  • Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
  • Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2.
  • Recognize that comparisons are valid only when the two fractions refer to the same whole.
  • Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

  • Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
  • Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
  • Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition  by an equation. Justify decompositions, e.g., by using a visual fraction model.
  • Add and subtract mixed numbers with like denominators.
  • Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
  • Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
    • Understand a fraction a/b as a multiple of 1/b..
    • Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
    • Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed?

Understand decimal notation for fractions, and compare decimal fractions.

  • Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.
  • Use decimal notation for fractions with denominators 10 or 100.
  • Compare two decimals to hundredths by reasoning about their size.
  • Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Measurement and Data

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

  • Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
  • Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
  • Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Represent and interpret data.

  • 4. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

Geometric measurement: understand concepts of angle and measure angles.

  • Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
    • An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
    • An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
  • Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
  • Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.

Geometry

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

  • Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
  • Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size.

Recognize right triangles as a category, and identify right triangles.

  • Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

3rd Grade National Mathematics Standards

Thursday, September 9th, 2010

Achieve100’s Study Cards and Practice Tests support these National Mathematics Standards for 3rd Grade.

3rd Grade National Mathematics Standards

Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division.

  • Interpret products of whole numbers as the total number of objects.
  • Interpret whole-number quotients of whole numbers.
  • Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.
  • Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Understand properties of multiplication and the relationship between multiplication and division.
  • Apply properties of operations as strategies to multiply and divide.
  • Understand division as an unknown-factor problem

Multiply and divide within 100.

  • Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division.
  • By the end of Grade 3, know from memory all products of two one-digit numbers.
  • Solve problems involving the four operations, and identify and explain patterns in arithmetic.
  • Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity.
  • Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
  • Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

Number and Operations in Base Ten

Use place value understanding and properties of operations to perform multi-digit arithmetic.

  • Use place value understanding to round whole numbers to the nearest 10 or 100.
  • Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
  • Multiply one-digit whole numbers by multiples of 10 in the range 10–90.

Number and Operations – Fractions

Develop understanding of fractions as numbers.

  • Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
  • Understand a fraction as a number on the number line; represent fractions on a number line diagram.
    • Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
    • Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
  • Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
    • Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
    • Recognize and generate simple equivalent fractions by using a visual fraction model.
    • Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
    • Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.

Measurement and Data

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

  • Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes.
  • Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6
  • Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units.

Represent and interpret data.

  • Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.
  • Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units — whole numbers, halves, or quarters.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

  • Recognize area as an attribute of plane figures and understand concepts of area measurement.
    • A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
    • A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
  • Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
  • Relate area to the operations of multiplication and addition.
    • Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
    • Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
    • Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c.
    • Use area models to represent the distributive property in mathematical reasoning.
    • Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
    • Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
  • Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Geometry

Reason with shapes and their attributes.

  • Understand that shapes in different categories  may share attributes, and that the shared attributes can define a larger category.
  • Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

2nd Grade National Mathematics Standards

Thursday, September 9th, 2010

Achieve100’s Study Cards and Practice Tests support these National Mathematics Standards for 2nd Grade.

2nd Grade National Mathematics Standards

Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.

  • Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.

Add and subtract within 20.

  • Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Work with equal groups of objects to gain foundations for multiplication.

  • Determine whether a group of objects (up to 20) has an odd or even number of members; write equations to express an even number as a sum of two equal addends.
  • Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends

Number and Operations in Base Ten

Understand place value.

  • Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; Understand the following as special cases:
    • 100 can be thought of as a bundle of ten tens — called a “hundred.”
    • The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
  • Count within 1000; skip-count by 5s, 10s, and 100s.
  • Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
  • Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Use place value understanding and properties of operations to add and subtract.

  • Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
  • Add up to four two-digit numbers using strategies based on place value and properties of operations.
  • Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.
  • Understand that in adding or subtracting threedigit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
  • Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
  • Explain why addition and subtraction strategies work, using place value and the properties of operations.

Measurement and Data

Measure and estimate lengths in standard units.

  • Estimate lengths using units of inches, feet, centimeters, and meters.
  • Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Relate addition and subtraction to length.
  • Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
  • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.

Work with time and money.

  • Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
  • Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

Represent and interpret data.

  • Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
  • Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple puttogether, take-apart, and compare problems4 using information presented in a bar graph.

Geometry

Reason with shapes and their attributes.

  • Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
  • Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
  • Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

1st Grade National Mathematics Standards

Thursday, September 9th, 2010

Achieve100’s Study Cards and Practice Tests support these National Mathematics Standards for 1st Grade.

1st Grade National Mathematics Standards

Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.

  • Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.
  • Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20.

Understand and apply properties of operations and the relationship between addition and subtraction.

  • Apply properties of operations as strategies to add and subtract.
  • Understand subtraction as an unknown-addend problem.
  • Relate counting to addition and subtraction.
  • Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums.

Work with addition and subtraction equations.

  • Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.
  • Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.  

Number and Operations in Base Ten

Extend the counting sequence.

  • Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Understand place value.

  • Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones — called a “ten.” The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
  • Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Use place value understanding and properties of operations to add and subtract.

  • Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

  • Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
  • Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Measurement and Data

Measure lengths indirectly and by iterating length units.

  • Order three objects by length; compare the lengths of two objects indirectly by using a third object.
  • Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

Tell and write time.

  • Tell and write time in hours and half-hours using analog and digital clocks.

Represent and interpret data.

  • Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Geometry

Reason with shapes and their attributes.

  • Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes; build and draw shapes to possess defining attributes.
  • Compose two-dimensional shapes or three-dimensional shapes to create a composite shape, and compose new shapes from the composite shape.
  • Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.
  • Describe the whole as two of, or four of the shares.
  • Understand for these examples that decomposing into more equal shares creates smaller shares.

Kindergarten National Mathematics Standards

Thursday, September 9th, 2010

Achieve100’s Study Cards and Practice Tests support these National Mathematics Standards for Pre-1st.

Kindergarten National Mathematics Standards

Counting and Cardinality

Know number names and the count sequence.

  • Count to 100 by ones and by tens.
  • Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
  • Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

Count to tell the number of objects.

  • Understand the relationship between numbers and quantities; connect counting to cardinality.
  • When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
  • Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
  • Understand that each successive number name refers to a quantity that is one larger.
  • Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

Compare numbers.

  • Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.
  • Compare two numbers between 1 and 10 presented as written numerals.

Operations and Algebraic Thinking

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

  • Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
  • Solve addition and subtraction word problems, and add and subtract within 10.
  • Decompose numbers less than or equal to 10 into pairs in more than one way.
  • For any number from 1 to 9, find the number that makes 10 when added to the given number.
  • Fluently add and subtract within 5.

Number and Operations in Base Ten

Work with numbers 11–19 to gain foundations for place value.

  • Compose and decompose numbers from 11 to 19 into ten ones and some further ones and record each composition or decomposition by a drawing or equation; understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Measurement and Data

Describe and compare measurable attributes.

  • Describe measurable attributes of objects, such as length or weight.
  • Describe several measurable attributes of a single object.
  • Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.
  • Classify objects and count the number of objects in each category.
  • Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

Geometry

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

  • Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.
  • Correctly name shapes regardless of their orientations or overall size.
  • Identify shapes as two-dimensional (lying in a plane, “flat”) or three- dimensional (“solid”).
  • Analyze, compare, create, and compose shapes.
  • Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts and other attributes. 

3rd Grade National Language Arts Standards

Thursday, September 9th, 2010

Achieve100’s Study Cards and Practice Tests support these National Language Arts Standards for 3rd Grade.

3rd Grade National Language Arts Standards

3rd Grade Foundational Reading Skills Standards

  • Know and apply grade-level phonics and word analysis skills in decoding words.
  • Identify and know the meaning of the most common prefixes and derivational suffixes.
  • Decode words with common Latin suffixes.
  • Decode multi-syllable words.
  • Read grade-appropriate irregularly spelled words.
  • Read with sufficient accuracy and fluency to support comprehension.
  • Read on-level text with purpose and understanding.
  • Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings
  • Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

 3rd Grade Reading Standards for Literature

  • Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.
  • Describe characters in a story and explain how their actions contribute to the sequence of events.
  • Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language.
  • Distinguish their own point of view from that of the narrator or those of the characters.
  • By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 2–3 text complexity band independently and proficiently.

3rd Grade Reading Standards for Informational Text

  • Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.
  • Determine the main idea of a text; recount the key details and explain how they support the main idea.
  • Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject area.
  • Use information gained from illustrations and the words in a text to demonstrate understanding of the text.
  • By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 2–3 text complexity band independently and proficiently.

3rd Grade Language Standards

Achieve100 supports these speaking and writing standards by helping students understand the respective words, meanings and use in literature and informational text.

  • Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
    • Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences.
    • Form and use regular and irregular plural nouns.
    • Use abstract nouns.
    • Form and use regular and irregular verbs.
    • Form and use the simple verb tenses.
    • Ensure subject-verb and pronoun-antecedent agreement.
    • Form and use comparative and superlative adjectives and adverbs, and choose between them depending on what is to be modified.
    • Use coordinating and subordinating conjunctions.
    • Produce simple, compound, and complex sentences.
  • Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
    • Capitalize appropriate words in titles.
    • Use commas in addresses.
    • Use commas and quotation marks in dialogue.
    • Form and use possessives.
    • Use conventional spelling for high-frequency and other studied words and for adding suffixes to base words.
    • Use spelling patterns and generalizations in writing words.
  • Use knowledge of language and its conventions when writing, speaking, reading, or listening.
  • Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies.
    • Use sentence-level context as a clue to the meaning of a word or phrase.
    • Determine the meaning of the new word formed when a known affix is added to a known word.
    • Use a known root word as a clue to the meaning of an unknown word with the same root.
  • Demonstrate understanding of word relationships and nuances in word meanings.
    • Distinguish the literal and nonliteral meanings of words and phrases in context.
    • Identify real-life connections between words and their use.
    • Distinguish shades of meaning among related words that describe states of mind or degrees of.
    • Acquire and use accurately grade-appropriate conversational, general academic, and domain-specific words and phrases, including those that signal spatial and temporal relationships.

2nd Grade National Language Arts Standards

Thursday, September 9th, 2010

Achieve100’s Study Cards and Practice Tests support these National Language Arts Standards for 2nd Grade.

2nd Grade National Language Arts Standards

2nd Grade Foundational Reading Skills Standards

  • Know and apply grade-level phonics and word analysis skills in decoding words.
  • Distinguish long and short vowels when reading regularly spelled one-syllable words.
  • Know spelling-sound correspondences for additional common vowel teams.
  • Decode regularly spelled two-syllable words with long vowels.
  • Decode words with common prefixes and suffixes.
  • Identify words with inconsistent but common spelling-sound correspondences.
  • Recognize and read grade-appropriate irregularly spelled words.
  • Read with sufficient accuracy and fluency to support comprehension.
  • Read on-level text with purpose and understanding.
  • Read on-level text orally with accuracy, appropriate rate, and expression on successive readings.
  • Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

2nd Grade Reading Standards for Literature

  • Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.
  • Describe how characters in a story respond to major events and challenges.
  • Acknowledge differences in the points of view of characters, including by speaking in a different voice for each character when reading dialogue aloud.
  • Use information gained from the illustrations and words in a print or digital text to demonstrate understanding of its characters, setting, or plot.
  • By the end of the year, read and comprehend literature, including stories and poetry, in the grades 2–3 text complexity band proficiently.

2nd Grade Reading Standards for Informational Text

  • Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.
  • Identify the main topic of a multi-paragraph text as well as the focus of specific paragraphs within the text.
  • Determine the meaning of words and phrases in a text relevant to a grade 2 topic or subject area.
  • Identify the main purpose of a text, including what the author wants to answer, explain, or describe.
  • By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 2–3 text complexity band proficiently.

2nd Grade Language Standards

Achieve100 supports these speaking and writing standards by helping students understand the respective words, meanings and use in literature and informational text.

  • Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
    • Use collective nouns.
    • Form and use frequently occurring irregular plural nouns.
    • Use reflexive pronouns.
    • Form and use the past tense of frequently occurring irregular verbs
    • Use adjectives and adverbs, and choose between them depending on what is to be modified.
  • Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
    • Capitalize holidays, product names, and geographic names.
    • Use commas in greetings and closings of letters.
    • Use an apostrophe to form contractions and frequently occurring possessives.
    • Generalize learned spelling patterns when writing words.
  • Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on kindergarten reading and content.
    • Identify new meanings for familiar words and apply them accurately.
    • Use the most frequently occurring inflections and affixes as a clue to the meaning of an unknown word.
  • With guidance and support from adults, explore word relationships and nuances in word meanings.
    • Sort common objects into categories to gain a sense of the concepts the categories represent.
    • Demonstrate understanding of frequently occurring verbs and adjectives by relating them to their opposites.
    • Identify real-life connections between words and their use.
    • Distinguish shades of meaning among verbs describing the same general action by acting out the meanings.
  • Use words and phrases acquired through conversations, reading and being read to, and responding to texts.
  • Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 1 reading and content, choosing flexibly from an array of strategies.
  • Use sentence-level context as a clue to the meaning of a word or phrase.
  • Use frequently occurring affixes as a clue to the meaning of a word.
  • Identify frequently occurring root words and their inflectional forms.
  • With guidance and support from adults, demonstrate understanding of word relationships and nuances in word meanings.
  • Sort words into categories to gain a sense of the concepts the categories represent.
  • Define words by category and by one or more key attributes.
  • Identify real-life connections between words and their use.
  • Distinguish shades of meaning among verbs differing in manner and adjectives differing in intensity by defining or choosing them or by acting out the meanings.
  • Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using frequently occurring conjunctions to signal simple relationships.
  • Use knowledge of language and its conventions when writing, speaking, reading, or listening.
  • Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 2 reading and content, choosing flexibly from an array of strategies.
  • Use sentence-level context as a clue to the meaning of a word or phrase.
  • Determine the meaning of the new word formed when a known prefix is added to a known word.
  • Use a known root word as a clue to the meaning of an unknown word with the same root.
  • Use knowledge of the meaning of individual words to predict the meaning of compound words.
  • Demonstrate understanding of word relationships and nuances in word meanings.
  • Identify real-life connections between words and their use.
  • Distinguish shades of meaning among closely related verbs and closely related adjectives.
  • Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using adjectives and adverbs to describe.