Subjects
 English Language Arts
 Math
Skills
 Critical Thinking
Privacy evaluation tiers:
Meets our minimum requirements for privacy safeguards, but more research should be completed prior to use.
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Does not meet our minimum requirements for privacy safeguards, and more research should be completed prior to use.
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Fails to meet our basic requirements for privacy safeguards, which include encryption and a detailed privacy policy.
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iReady
 Privacy polices do indicate a version or effective date.
 Data are not sold or rented to third parties.
 Unclear whether data are shared for advertising and/or marketing.
 Behavioral or contextual advertising is not displayed.
 Data are not collected by thirdparty advertising or tracking services.
 Data are not used to track and target advertisements on other thirdparty websites or services.
 Third parties can use data to create ad profiles, data enhancement, and/or targeted advertisements.
Pros: It's a onestop shop for deep, wellorganized, CCSS data collection and differentiated instruction in math and literacy.
Cons: If overused, iReady will lose effectiveness; the developers recommend 45 minutes per subject per week.
Bottom Line: Quality, responsive instruction and the deep dive into data make this a strong contender for classrooms.
It's best to use iReady as a way to gather data on your students that will be helpful as you differentiate the instruction in your class. The deep dive into data can help savvy teachers target instruction, build intervention groups, and track the effectiveness of their instruction. Consider using iReady as a way to fill in gaps in students' learning or even to push some learners to the next level. Depending on your classroom setup, you could set up an iReady station where students rotate through while others work on activities and conference with you. Have your students use the reports to reflect on their learning and set goals. These reports could also be helpful when meeting with parents. Keep in mind that you could also use individual iReady lessons, projected for the whole class, as part of your instruction around a topic.
A significant issue around programs like iReady is when they're overused. Student and teacher burnout on adaptive programs like iReady can be a problem. When this happens, it's usefulness as an instructional and assessment tool is significantly diminished. iReady wasn't developed to replace teacher instruction or an already established curriculum; it's meant to be used as a supplement to teaching. The developers recommend 45 minutes per subject per week, which is best split into two or three sessions, though a teacher may need to adjust this to keep iReady effective.
Continue reading Show lessiReady is a set of CCSSbased diagnostic and instructional tools for both math and English. Upon starting the program, students take an adaptive placement test. iReady then uses this data to create individualized instructional pathways for each student. Teachers can let iReady personalize instruction on its own, or they can customize the experience for individual students, groups of students, or even an entire class. Teachers can expect to have finegrained control over the lessons taught as well as the overall scope and sequence for their students. Additionally, iReady offers teachers a range of diagnostic reports. Data is provided on growth, performance, instructional progress, and much more.
Upon finishing the diagnostic test, students' experience is friendly and includes a simplified dashboard, where they can pick a theme and a coach and even have learning material read to them. Each lesson includes a diverse cast of animated characters that walk students through every task. Lessons start with an overview of the learning objectives, followed by a guided learning experience. Kids can review lessons at any point but won't be able to skip ahead. In math, many tasks are aimed at helping kids develop conceptual understanding across a range of topics. In the reading program, students will read with the aid of a notepad, a dictionary, and some annotation tools.
iReady is a great bet for an adaptive, supplemental learning tool. Its main strength lies in the way it diagnoses students' needs, then targets personalized practice and instruction for each individual. Teachers' ability to further personalize and customize the experience is key here, whether for individual students, groups, or an entire class. As students work their way through lessons, they'll interact with animations every few minutes. This could help some kids maintain focus, though others could tire and want to just get on with the lesson. Throughout, the instant feedback to students is helpful and includes both audio and visual supports. iReady's question types align well with what kids might encounter on Common Core assessments. It's reasonable to see iReady as a testprep solution, though it does aim to teach conceptual understanding.
Nevertheless, the program offers teachers a comprehensive look at student data, giving a clear view of students' overall growth and achievement. Ideally, this will help teachers plan in a way that meets real classroom needs. Printable lesson plans are available, should teachers want them. Also, the system's reports offer a range of data. iReady clearly has spent some time making this data organized and easily accessible for teachers, allowing them to find the information they want. Overall, iReady delivers learning content in an engaging and rigorous way. This combination will likely serve kids well if  and here's the catch  teachers use iReady with fidelity alongside their own quality classroom instruction.
Overall Rating
Engagement Is the product stimulating, entertaining, and engrossing? Will kids want to return?
Students will enjoy the animated instruction and tasks with ageappropriate characters. iReady is best used sparingly, however: no more than 45 minutes per subject per week.
Pedagogy Is learning content seamlessly bakedin, and do kids build conceptual understanding? Is the product adaptable and empowering? Will skills transfer?
iReady adapts to student progress and offers a comprehensive way to address Common Core math and literacy skills. Reports provide actionable data, enabling teachers to decide on next steps for students.
Support Does the product take into account learners of varying abilities, skill levels, and learning styles? Does it address both struggling and advanced students?
Each learning task is modeled for students, with verbal and animated feedback based on their answers. For teachers and students, help is available on every screen.
Key Standards Supported
Counting And Cardinality
 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.
 K.CC.4
Understand the relationship between numbers and quantities; connect counting to cardinality.
 K.CC.4.a
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.
 K.CC.4.b
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.
 K.CC.4.c
Understand that each successive number name refers to a quantity that is one larger.
 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.
 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 020 (with 0 representing a count of no objects).
Geometry
 1.G.1
Distinguish between defining attributes (e.g., triangles are closed and threesided) versus nondefining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
 1.G.2
Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles) or threedimensional 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
 1.G.3
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.
 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 samesize 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.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.
 3.G.2
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
 4.G.1
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.
 4.G.2
Classify twodimensional 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 twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry.
 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 twodimensional figures in a hierarchy based on properties.
 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., xaxis and xcoordinate, yaxis and ycoordinate).
 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.
 6.G.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems.
 6.G.2
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems.
 6.G.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems.
 6.G.4
Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems.
 7.G.1
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
 7.G.2
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
 7.G.3
Describe the twodimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
 7.G.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
 7.G.5
Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
 7.G.6
Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
 8.G.9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems.
 8.G.6
Explain a proof of the Pythagorean Theorem and its converse.
 8.G.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions.
 8.G.8
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
 8.G.1
Verify experimentally the properties of rotations, reflections, and translations:
 8.G.1.a
Lines are taken to lines, and line segments to line segments of the same length.
 8.G.1.b
Angles are taken to angles of the same measure.
 8.G.1.c
Parallel lines are taken to parallel lines.
 8.G.2
Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
 8.G.3
Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates.
 8.G.4
Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them.
 8.G.5
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
 K.G.4
Analyze and compare two and threedimensional 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?”
 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 twodimensional (lying in a plane, “flat”) or three dimensional (“solid”).
Number And Operations In Base Ten
 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.
 1.NBT.2
Understand that the two digits of a twodigit 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 twodigit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
 1.NBT.4
Add within 100, including adding a twodigit number and a onedigit number, and adding a twodigit 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 twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
 1.NBT.5
Given a twodigit 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 1090 from multiples of 10 in the range 1090 (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.1
Understand that the three digits of a threedigit 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.1.a
100 can be thought of as a bundle of ten tens — called a “hundred.”
 2.NBT.1.b
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).
 2.NBT.2
Count within 1000; skipcount by 5s, 10s, and 100s.
 2.NBT.3
Read and write numbers to 1000 using baseten numerals, number names, and expanded form.
 2.NBT.4
Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
 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 twodigit 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.
 2.NBT.9
Explain why addition and subtraction strategies work, using place value and the properties of operations.3
 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 onedigit 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.
 5.NBT.5
Fluently multiply multidigit whole numbers using the standard algorithm.
 5.NBT.6
Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit 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.
 5.NBT.1
Recognize that in a multidigit 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 wholenumber exponents to denote powers of 10.
 5.NBT.3
Read, write, and compare decimals to thousandths.
 5.NBT.3.a
Read and write decimals to thousandths using baseten 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.
 K.NBT.1
Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
 4.NBT.1
Recognize that in a multidigit 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 multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit 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 multidigit whole numbers to any place.
 4.NBT.4
Fluently add and subtract multidigit whole numbers using the standard algorithm.
 4.NBT.5
Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit 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 wholenumber quotients and remainders with up to fourdigit dividends and onedigit 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
 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 50pound 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
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
 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.4.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.
 5.NF.5
Interpret multiplication as scaling (resizing), by:
 5.NF.5.a
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.
 5.NF.5.b
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
 5.NF.6
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
 5.NF.7
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1
 5.NF.7.a
Interpret division of a unit fraction by a nonzero 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.
 5.NF.7.c
Solve real world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3cup servings are in 2 cups of raisins?
 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
 4.NF.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a.
 4.NF.3.a
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
 4.NF.3.b
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. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
 4.NF.3.c
Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
 4.NF.3.d
Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
 4.NF.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
 4.NF.4.a
Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
 4.NF.4.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. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
 4.NF.4.c
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? Between what two whole numbers does your answer lie?
 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.
 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.
 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
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
 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.
 3.NF.3.a
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
 3.NF.3.b
Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
 3.NF.3.c
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
 3.NF.3.d
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, e.g., by using a visual fraction model.
Ratios And Proportional Relationships
 6.RP.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
 6.RP.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1
 6.RP.3
Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
 6.RP.3.a
Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
 6.RP.3.b
Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
 6.RP.3.c
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
 6.RP.3.d
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
 7.RP.1
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
 7.RP.2
Recognize and represent proportional relationships between quantities.
 7.RP.2.a
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
 7.RP.2.b
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
 7.RP.2.c
Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
 7.RP.2.d
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
 7.RP.3
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Key Standards Supported
Reading Informational Text
 RI.3.10
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.
 RI.5.10
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.
 RI.8.10
By the end of the year, read and comprehend literary nonfiction at the high end of the grades 6–8 text complexity band independently and proficiently.
 RI.910.10
By the end of grade 9, read and comprehend literary nonfiction in the grades 9–10 text complexity band proficiently, with scaffolding as needed at the high end of the range.
 RI.1112.10
By the end of grade 11, read and comprehend literary nonfiction in the grades 11–CCR text complexity band proficiently, with scaffolding as needed at the high end of the range.
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