# i-Ready

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- using supporting evidence
- vocabulary
- letter or word recognition
- phonics
- reading comprehension

- subtraction
- addition
- division
- fractions
- geometry
- measurement
- multiplication
- patterns

- using and applying technology

- analyzing evidence
- asking questions

###### Pros

It's a one-stop shop for deep CCSS data collection and differentiated instruction in math and literacy.###### Cons

The variety of options and plethora of data could be overwhelming for teachers in search of a more streamlined solution.###### Bottom Line

Quality, responsive instruction and the deep dive into data make this a strong contender for blended classrooms.The dashboard provides access to reports and learning tasks. Teachers can customize most of the learning environment from the dashboard.

Younger kids will enjoy the animated instruction and tasks, but the characters, themes, and instructions may skew a bit too young for older students. The student home page is easy to navigate; lessons require frequent interaction.

The program adapts to student progress and offers a comprehensive way to address Common Core math and literacy skills. Even though they're a bit cartoonish, the animated characters are diverse and lend personality to the experience.

Each learning task is modeled for students, with verbal feedback based on their answers. For both teachers and students, help is available on every screen. In terms of data, students can see an overview, while teachers can dive in deep.

It's best to use i-Ready 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 i-Ready 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 i-Ready station, where students rotate through, while others work on activities and/or 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. Lastly, keep in mind that you could also use individual i-Ready lessons, projected for the whole class, as part of your own instruction around a topic.

Read More Read Lessi-Ready is a set of CCSS-based diagnostic and instructional tools for both math and English. Upon starting the program, students take an adaptive placement test. i-Ready then uses this data to create individualized instructional pathways for each student. Teachers can let i-Ready 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 fine-grained control over the lessons taught as well as the overall scope and sequence for their students. Additionally, i-Ready offers teachers an exhaustive 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. Within both subjects, the program relies on graphic organizers that students will complete.

Read More Read Lessi-Ready 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. i-Ready's question types align well with what kids might encounter on Common Core assessments. It's reasonable to see i-Ready as a test-prep solution, though this emphasis could give pause to teachers looking for a more holistic learning experience.

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 an exhaustive range of data. Though i-Ready was designed to make student data easily actionable, the sheer amount of data offered could make it less so for some teachers -- it will depend on the amount of time they're able to devote. Overall, i-Ready delivers learning content in an engaging and rigorous way. This combination will likely serve kids well if -- and here's the catch -- teachers use i-Ready with fidelity alongside their own quality classroom instruction.

Read More Read Less## Key Standards Supported

## Reading Informational | |

RI.3: Range of Reading and Level of Text Complexity | |

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: Range of Reading and Level of Text Complexity | |

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: Range of Reading and Level of Text Complexity | |

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.9-10: Range of Reading and Level of Text Complexity | |

RI.9-10.10 | 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.11-12: Range of Reading and Level of Text Complexity | |

RI.11-12.10 | 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. |

## Counting And Cardinality | |

K.CC: 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. |

Count To Tell The Number Of Objects. | |

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. |

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). |

## Geometry | |

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 |

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: 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. |

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: 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: 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. |

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. |

6.G: Solve Real-World And Mathematical Problems Involving Area, Surface Area, And Volume. | |

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 real-world 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 real-world 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 real-world and mathematical problems. |

6.G.4 | Represent three-dimensional 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 real-world and mathematical problems. |

7.G: Draw, Construct, And Describe Geometrical Figures And Describe The Relationships Between Them. | |

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 two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. |

Solve Real-Life And Mathematical Problems Involving Angle Measure, Area, Surface Area, And Volume. | |

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 multi-step problem to write and solve simple equations for an unknown angle in a figure. |

7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. |

8.G: Solve Real-World And Mathematical Problems Involving Volume Of Cylinders, Cones, And Spheres. | |

8.G.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. |

Understand And Apply The Pythagorean Theorem. | |

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 real-world 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. |

Understand Congruence And Similarity Using Physical Models, Trans- Parencies, Or Geometry Software. | |

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 two-dimensional 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 two-dimensional figures using coordinates. |

8.G.4 | Understand that a two-dimensional 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 angle-angle 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: 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?” |

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”). |

## 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.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; 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. |

2.NBT.9 | Explain why addition and subtraction strategies work, using place value and the properties of operations.3 |

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. |

5.NBT: 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. |

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 | Read, write, and compare decimals to thousandths. |

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. |

K.NBT: Work With Numbers 11–19 To Gain Foundations For Place Value. | |

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: 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. |

## Number And Operations—Fractions | |

5.NF: 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 | 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 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. |

5.NF.7.c | Solve real world problems involving division of unit fractions by non-zero 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 1/3-cup servings are in 2 cups of raisins? |

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 |

4.NF: 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.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? |

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. |

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. |

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 | 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: Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems. | |

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 real-world 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: Analyze Proportional Relationships And Use Them To Solve Real-World And Mathematical Problems. | |

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. |

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