# ClassK12

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*Not Yet Rated*

- phonics

- addition
- fractions
- geometry
- subtraction

###### Pros

Excellent CCSS alignment, strong teacher tools, and great bilingual math content make for useful individualized practice.###### Cons

There's not much to hold students' attention once they get past the novelty of online practice.###### Bottom Line

A great tool for practice, but it's not likely to keep kids engaged for the long haul.Detailed reports on students available, and each student can be assigned different subjects by grade level.

Students may initially enjoy practicing with these tools, but there's not much here to really engage them.

Great online practice with good supporting help text, but there's nothing revolutionary or especially adaptive.

Lessons and quizzes are easy to use, and there's an excellent option to learn in Spanish.

Teachers will find ClassK12 effective for students who need some extra practice. The Spanish math lessons will be particularly helpful for teachers looking to make sure their Spanish-speaking students keep up with math concepts. Students who finish early may enjoy working ahead on more advanced concepts. ClassK12 allows for easy differentiation, and the reports will help teachers analyze areas where students may need additional support. Teachers can also download concept worksheets for easy review.

Read More Read LessClassK12 is a Web-based collection of online lessons and quizzes for grades 1 through 5. Teachers create classes on the website and assign students either Language Arts or Math at various grade levels, with support for students who learn in Spanish. The tool is aligned with Google Classroom, allowing you to assign topics or have students hand them in through that portal. There are also excellent reports that break down a student's progress in each area.

Once setup is complete, students log in and complete the assignments. They will see all subjects assigned to them and choose the specific area they wish to work on. They are able to select practicing a skill or completing assessments in that area. All activities are basic fill-in-the-blank or multiple-choice questions.

Read More Read LessClassK12 provides very thorough practice with excellent Common Core State Standards alignment. Many teachers will also appreciate the alignment with Google Classroom. However, it's unfortunate that students can see the level assigned to them (a grade 4 student working on grade 2 math will have to click on "grade 2 math" rather than a less-obvious or less-discouraging title). In addition, students will be unlikely to find the activities very engaging -- these are basically online worksheets.

There are a couple of games students can play, but they're not particularly exciting and they don't relate to any math or ELA concepts; they're just padding. Students can also earn coins for completing activities, but they don't currently do anything. Students may eventually be able to purchase digital stickers with them, but even that is unlikely to motivate them for very long.

Read More Read Less## Key Standards Supported

## Language | |

L.K: Conventions of Standard English | |

L.K.1 | Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. |

L.K.1b | Use frequently occurring nouns and verbs. |

L.K.1c | Form regular plural nouns orally by adding /s/ or /es/ (e.g., dog, dogs; wish, wishes). |

L.K.1e | Use the most frequently occurring prepositions (e.g., to, from, in, out, on, off, for, of, by, with). |

L.K.2a | Capitalize the first word in a sentence and the pronoun I. |

L.K.2b | Recognize and name end punctuation. |

L.K.2d | Spell simple words phonetically, drawing on knowledge of sound-letter relationships. |

L.1: Conventions of Standard English | |

L.1.1b | Use common, proper, and possessive nouns. |

L.1.1c | Use singular and plural nouns with matching verbs in basic sentences (e.g., He hops; We hop). |

L.1.1d | Use personal, possessive, and indefinite pronouns (e.g., I, me, my; they, them, their, anyone, everything). |

L.1.1e | Use verbs to convey a sense of past, present, and future (e.g., Yesterday I walked home; Today I walk home; Tomorrow I will walk home). |

L.1.1g | Use frequently occurring conjunctions (e.g., and, but, or, so, because). |

L.1.1h | Use determiners (e.g., articles, demonstratives). |

L.1.1i | Use frequently occurring prepositions (e.g., during, beyond, toward). |

L.1.2a | Capitalize dates and names of people. |

L.1.2b | Use end punctuation for sentences. |

L.1.2d | Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words. |

L.2: Conventions of Standard English | |

L.2.1a | Use collective nouns (e.g., group). |

L.2.1b | Form and use frequently occurring irregular plural nouns (e.g., feet, children, teeth, mice, fish). |

L.2.1c | Use reflexive pronouns (e.g., myself, ourselves). |

L.2.1d | Form and use the past tense of frequently occurring irregular verbs (e.g., sat, hid, told). |

L.2.2a | Capitalize holidays, product names, and geographic names. |

L.2.2d | Generalize learned spelling patterns when writing words (e.g., cage → badge; boy → boil). |

L.3: Conventions of Standard English | |

L.3.1a | Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences. |

L.3.1b | Form and use regular and irregular plural nouns. |

L.3.1c | Use abstract nouns (e.g., childhood). |

L.3.1d | Form and use regular and irregular verbs. |

L.3.1e | Form and use the simple (e.g., I walked; I walk; I will walk) verb tenses. |

L.3.1f | Ensure subject-verb and pronoun-antecedent agreement.* |

L.3.1h | Use coordinating and subordinating conjunctions. |

L.3.2 | Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. |

L.3.2d | Form and use possessives. |

L.3.2e | Use conventional spelling for high-frequency and other studied words and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness). |

L.3.2f | Use spelling patterns and generalizations (e.g., word families, position-based spellings, syllable patterns, ending rules, meaningful word parts) in writing words. |

L.4: Conventions of Standard English | |

L.4.1a | Use relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why). |

L.4.1b | Form and use the progressive (e.g., I was walking; I am walking; I will be walking) verb tenses. |

L.4.1c | Use modal auxiliaries (e.g., can, may, must) to convey various conditions. |

L.4.1e | Form and use prepositional phrases. |

L.4.1g | Correctly use frequently confused words (e.g., to, too, two; there, their).* |

L.4.2a | Use correct capitalization. |

L.4.2d | Spell grade-appropriate words correctly, consulting references as needed. |

L.5: Conventions of Standard English | |

L.5.1 | Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. |

L.5.2 | Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. |

## Counting And Cardinality | |

K.CC: Know Number Names And The Count Sequence. | |

K.CC.1 | Count to 100 by ones and by tens. |

K.CC.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). |

K.CC.3 | 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. | |

K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. |

K.CC.5 | 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. | |

K.CC.6 | 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.1 |

K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. |

## Geometry | |

K.G: Identify And Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, And Spheres). | |

K.G.1 | 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. |

K.G.2 | Correctly name shapes regardless of their orientations or overall size. |

K.G.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three- dimensional (“solid”). |

Analyze, Compare, Create, And Compose Shapes. | |

K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). |

K.G.5 | Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. |

K.G.6 | Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?” |

1.G: Reason With Shapes And Their Attributes. | |

1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. |

1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.4 |

2.G: Reason With Shapes And Their Attributes. | |

2.G.1 | 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. |

2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. |

2.G.3 | 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. |

3.G: Reason With Shapes And Their Attributes. | |

3.G.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. |

4.G: Draw And Identify Lines And Angles, And Classify Shapes By Properties Of Their Lines And Angles. | |

4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. |

4.G.2 | 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. |

4.G.3 | 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. |

5.G: Graph Points On The Coordinate Plane To Solve Real-World And Mathematical Problems. | |

5.G.1 | 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). |

5.G.2 | 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. | |

5.G.3 | Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. |

5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. |

## Measurement And Data | |

K.MD: Describe And Compare Measurable Attributes. | |

K.MD.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. |

Classify Objects And Count The Number Of Objects In Each Category. | |

K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.3 |

1.MD: Measure Lengths Indirectly And By Iterating Length Units. | |

1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. |

Tell And Write Time. | |

1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. |

Represent And Interpret Data. | |

1.MD.4 | 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. |

2.MD: Represent And Interpret Data. | |

2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put- together, take-apart, and compare problems4 using information presented in a bar graph. |

Measure And Estimate Lengths In Standard Units. | |

2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. |

2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. |

2.MD.3 | Estimate lengths using units of inches, feet, centimeters, and meters. |

2.MD.4 | 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. | |

2.MD.5 | 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. |

2.MD.6 | 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. | |

2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. |

3.MD: Represent And Interpret Data. | |

3.MD.3 | 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. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. |

3.MD.4 | 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. |

Solve Problems Involving Measurement And Estimation Of Intervals Of Time, Liquid Volumes, And Masses Of Objects. | |

3.MD.1 | 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, e.g., by representing the problem on a number line diagram. |

3.MD.2 | 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, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.7 |

Geometric Measurement: Understand Concepts Of Area And Relate Area To Multiplication And To Addition. | |

3.MD.5.a | 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. |

3.MD.5.b | 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. |

3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). |

3.MD.7.a | 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. |

3.MD.7.b | Multiply side lengths to find areas of rectangles with whole- number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. |

3.MD.7.d | 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. | |

3.MD.8 | 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. |

4.MD: Solve Problems Involving Measurement And Conversion Of Measurements From A Larger Unit To A Smaller Unit. | |

4.MD.1 | 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. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... |

4.MD.2 | 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. |

4.MD.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. |

Represent And Interpret Data. | |

4.MD.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. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. |

Geometric Measurement: Understand Concepts Of Angle And Measure Angles. | |

4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: |

4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. |

4.MD.7 | 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, e.g., by using an equation with a symbol for the unknown angle measure. |

5.MD: Convert Like Measurement Units Within A Given Measurement System. | |

5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. |

Represent And Interpret Data. | |

5.MD.2 | 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. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. |

Geometric Measurement: Understand Concepts Of Volume And Relate Volume To Multiplication And To Addition. | |

5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. |

5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. |

5.MD.5.b | Apply the formulas V=l×w×handV=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. |

5.MD.5.c | 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. |

## Number And Operations In Base Ten | |

1.NBT: Extend The Counting Sequence. | |

1.NBT.1 | 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. | |

1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: |

1.NBT.2.a | 10 can be thought of as a bundle of ten ones — called a “ten.” b. |

1.NBT.2.b | The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. |

1.NBT.2.c | 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). |

1.NBT.3 | 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. | |

1.NBT.4 | 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. |

1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. |

1.NBT.6 | 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. |

2.NBT: Understand Place Value. | |

2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: |

2.NBT.2 | Count within 1000; skip-count by 5s, 10s, and 100s. |

2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. |

2.NBT.4 | 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. | |

2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. |

2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. |

2.NBT.7 | 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 three- digit 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. |

2.NBT.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. |

3.NBT: Use Place Value Understanding And Properties Of Operations To Perform Multi-Digit Arithmetic.4 | |

3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. |

3.NBT.2 | 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. |

3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. |

4.NBT: Generalize Place Value Understanding For Multi-Digit Whole Numbers. | |

4.NBT.1 | 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. |

4.NBT.2 | 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. |

4.NBT.3 | 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. | |

4.NBT.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. |

4.NBT.5 | 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. |

4.NBT.6 | 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. |

5.NBT: Understand The Place Value System. | |

5.NBT.1 | 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. |

5.NBT.2 | 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. |

5.NBT.3.a | Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). |

5.NBT.3.b | Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. |

5.NBT.4 | Use place value understanding to round decimals to any place. |

Perform Operations With Multi-Digit Whole Numbers And With Decimals To Hundredths. | |

5.NBT.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. |

5.NBT.6 | 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. |

5.NBT.7 | 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 | |

3.NF: Develop Understanding Of Fractions As Numbers. | |

3.NF.1 | 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. |

3.NF.2.a | 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. |

3.NF.2.b | 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. |

3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. |

4.NF: Extend Understanding Of Fraction Equivalence And Ordering. | |

4.NF.1 | 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. |

4.NF.2 | 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. | |

4.NF.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. |

4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. |

Understand Decimal Notation For Fractions, And Compare Decimal Fractions. | |

4.NF.5 | 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 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. |

4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. |

4.NF.7 | 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. |

5.NF: Use Equivalent Fractions As A Strategy To Add And Subtract Fractions. | |

5.NF.1 | 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. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) |

5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions |

Apply And Extend Previous Understandings Of Multiplication And Division To Multiply And Divide Fractions. | |

5.NF.3 | 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. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? |

5.NF.4.a | 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. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) |

5.NF.7.a | Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. |

5.NF.7.b | Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. |

## Operations And Algebraic Thinking | |

K.OA: Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From. | |

K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. |

K.OA.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. |

K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). |

K.OA.5 | Fluently add and subtract within 5. |

1.OA: Represent And Solve Problems Involving Addition And Subtraction. | |

1.OA.1 | 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, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.2 |

1.OA.2 | Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. |

Understand And Apply Properties Of Operations And The Relationship Between Addition And Subtraction. | |

1.OA.3 | Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) |

1.OA.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. |

Add And Subtract Within 20. | |

1.OA.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). |

Work With Addition And Subtraction Equations. | |

1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = � – 3, 6 + 6 = �. |

2.OA: Represent And Solve Problems Involving Addition And Subtraction. | |

2.OA.1 | 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, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 |

Add And Subtract Within 20. | |

2.OA.2 | Fluently add and subtract within 20 using mental strategies.2 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. | |

2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. |

2.OA.4 | 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. |

3.OA: Represent And Solve Problems Involving Multiplication And Division. | |

3.OA.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. |

3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. |

3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 |

Multiply And Divide Within 100. | |

3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. 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. | |

3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. |

4.OA: Use The Four Operations With Whole Numbers To Solve Problems. | |

4.OA.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. |

4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1 |

4.OA.3 | 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. | |

4.OA.4 | 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. | |

4.OA.5 | 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. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. |

5.OA: Write And Interpret Numerical Expressions. | |

5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. |

5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. |

Analyze Patterns And Relationships. | |

5.OA.3 | 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. |