The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. 

Lessons are designed to support students to explore and develop conceptual understanding of grade-level mathematics. For example, students develop conceptual understanding:

• In Lesson 6, Session 1, Explore, Problem 1 states, “Look at the place value models for whole numbers. Write the missing factor in each equation to show how ones, tens, hundreds, and thousands are related.” Equations include, “1,000 = __x100, 100 = __ x10, and 10= __ x 1.”  Students use pictures of place value blocks and decimal grids to show how place values are related. (5.NBT.1) 
• In Lesson 18, Session 2, Develop, Try It states, “Jared, Monica, and Heather have 5 hallways to decorate for the student council. If they share the work equally how much will each student decorate.” Students use pictures or number lines to solve problems involving fractions or mixed numbers. (5.NF.3)  
• In Lesson 22, Session 1, Explore, Try It states, “Grayson lives $$\frac {4}{5}$$ mile from the park. He already walked $$\frac {3}{4}$$ of the way to the park. How far has Grayson walked? Use a visual fraction model to show your thinking.” Students have access to a math toolkit which lists, “fraction tiles or circles, fraction bars, fraction models, grid paper, number lines, index cards and multiplication models.” (5.NF.B.6)

In the Student Worktext and during Interactive Practice, students have opportunities to independently demonstrate conceptual understanding. For example:

• In Lesson 7, Session 2, Develop, Practice with Powers of 10, Problem 6 states, “Describe how the placement of the decimal point changes when you multiply a number by a power of ten. How is this the same or different for division?” (5.NBT.2)
• In Lesson 20, Session 3, Practice Tilling a Rectangle to Find Area, Problem 4 states, “Danah has a rectangular strawberry patch in her garden. Its border is $$\frac {7}{8}$$ yard wide and $$\frac {3}{2}$$ yards long. Use a visual model to find the area of Danah’s strawberry patch. Then write an equation to describe your model. Show your work.” (5.NF.4)
• In Lesson 31, Student Worktext, Session 2, Develop, Practice with the Coordinate Plane, Problems 5, 6, and 7, students use a table and the coordinate plane to help them understand how to plot points. 
• In Interactive Practice, Find Volume Using Unit Cubes, students use unit cubes to find the volume, first finding the number of cubes in a layer and then the number of layers to find the volume. (5.MD.4)
• In Interactive Practice, Divide Decimals, students reason about place value and decimals before dividing based on what they know about multiplication and division of single digit numbers. (5.NBT.7)

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meets expectations that they attend to those standards that set an expectation of procedural skill and fluency. 

The instructional materials include problems and questions, interactive games, and math center activities that develop procedural skill and fluency throughout the grade. Students have opportunities to develop procedural skills and fluency for Cluster 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths). For example, in Classroom Resources:

• In Lesson 15, Session 3, Refine, Apply It, Problem 3 states, “What is the product of 2 and 0.73?” “Kendall chose (B) as the correct answer. How did she get that answer?” Students need to analyze the solution and identify the error in a procedural problem. (5.NBT.7)
• The materials include an online game platform with interactive games for students to build procedural skills and fluency. For example, Grade 5 students can play the game “Match” which allows them to strengthen skills in the area of computation (5.NBT.5, 5.NBT.6). In this game, students are tasked with solving addition, subtraction, multiplication, or division problems and finding a card that has a matching solution. 

5.NBT.5 (Fluently multiply multi digit whole numbers using the standard algorithm) requires students to develop grade level fluency. This standard is addressed in several lessons, including:

• In Student Worktext, Lesson 4, Session 4, Refine, Apply It, students use the standard algorithm for multiplication to solve problems. Problem 3 states, “A certain washing machine uses 29 gallons of water for each load of laundry washed. How many gallons of water would the washing machine use for 156 loads of laundry? Show your work.” 
• In Unit 1, Math in Action, Session 2, Persevere On Your Own states, “Beau plans to bring his recycled robots to the fair. Guests can buy tickets to play with the robots. Beau needs to rope off an area of the fairgrounds to keep his robots in sight. Read his notes. Robot Area Notes: The area should be rectangular. It needs to be more than 100 feet long and less than 100 feet wide. The area needs to be between 7,500 and 10,000 square feet.” Solve It states, “Describe an area that Beau can rope off his robots.”

The instructional materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade level. Within each lesson, there are Fluency and Skills Practice pages that children complete on their own. In addition, there are Learning Games and Math Center Activities that engage students with fluency practice. Examples of when students get opportunities to independently demonstrate procedural skill and fluency are:

• In Lesson 3, Session 4, Refine, Problem 2 states, “The rectangular prism shown below has a volume of 42 cubic meters. What is the length of the prism? Show your work.” The height and width are given. 
• In Lesson 10, Fluency and Skill Practice, Problem 3 states, “2.31 + 2.075.” 
• In Lesson 26, Fluency and Skill Practice, Problem 4 states, “Kareem has a pencil that is 13.5 centimeters long and a crayon that is 87.5 millimeters long. How many millimeters longer is the pencil than the crayon? (1 centimeter = 10 millimeters).”
• Math Center Activities are provided for students to work together in partnerships to develop procedural skill and fluency. In Lesson 4, Equivalent Multiplication Expressions, students take turns determining if the multiplication expression given in the header of the table are equivalent to the expressions listed in the table.

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. 

Examples of opportunities for students to engage in routine and non-routine application of mathematical skills independently and to demonstrate the use of mathematics flexibly in a variety of contexts in Classroom Routines include: 

• In Unit 2, End of Unit Assessment, Problem 5 states, “Janet buys $$1\frac{1}{4}$$ yards of cloth. She uses $$\frac{3}{8}$$ yard for a craft project. How much cloth, in yards, does Janet have left? Show your work."
• In Lesson 22, Session 2, Develop, Try It states, “Brandon’s mother left $$\frac{3}{4}$$ of a pizza on the counter. If Brandon eats $$\frac{2}{3}$$ of the leftover pizza, how much of the whole pizza did Brandon eat?” 
• In Unit 3, Math Center Activity, Real-World Multiplication Situations, students are given four word problems where fractions and mixed numbers are required to be multiplied in order to find the solution. Specifically, “Robert bought a box of 36 pencils. He placed $$\frac{1}{9}$$ of them in his desk drawer. He placed $$\frac{3}{4}$$ of the pencils left in the box in a storage cabinet. He gave the rest of the pencils to his sister. How many pencils did he give to his sister?”
• In Lesson 26, Fluency and Practice states, “Cassie has $$10\frac{1}{2}$$ feet of string to make 15 beaded bracelets. She needs 9 inches of string for each bracelet. Does she have enough string to make all the bracelets? Explain (1 ft = 12 inches).”

The instructional materials include multiple opportunities for students to engage in non- routine application of mathematical skills and knowledge of the grade level. 

For example, in Classroom Resources:

• In Unit 2, End of Unit, Unit Review, Performance Task states, “You have a movie theater gift card worth $40, so you invite a friend to go to the movies with you. Your friend challenges you to spend the exact value of the gift card. Find at least one way to do so by choosing from the items listed below.” A table is provided listing things for purchase and their prices.
• In Unit 3, Math in Action, Session 2, Solve It states, “A local nursery hears about the shrub planting project that G.O. and his neighbors are planning. The nursery gives them 50 pounds of compost to use. G.O. reads about using compost on a website. ‘When you plant a shrub, it can help to mix the soil with some compost. You can use a scoop of compost for each shrub. An average scoop of compost is between $$\frac{1}{4}$$ and $$\frac{1}{2}$$ pound.’ About how many shrubs can G.O. plant with the compost that the nursery gave him?”
• In Unit 4, Math in Action, Session 2, Preserve on Your Own states, “Sweet T is planning a BBQ for 50 people. There will be 2 different kinds of protein and 3 side dishes on the menu. Here are his choices, including amounts to estimate per person. Protein: Choose from ground beef, chicken, steak, or salmon. Estimate 6 to 8 ounces per person. Sides: Baked Beans, 2-3 ounces per person; Coleslaw, 3-4 ounces per person; Potato Salad, 4-5 ounces per person; Grilled vegetables: 3-4 ounces per person; Rice: 1:2 ounces per person. What food and how much of each should Sweet T make?”

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. The instructional materials address specific aspects of rigor, and the materials integrate aspects of rigor.

All three aspects of rigor are present independently throughout the program materials. For example:

• In Lesson 15, Session 2, Develop, students develop conceptual understanding for multiplying decimals. Try It states, “Padma bought 3 pounds of grapes.  Each pound of grapes costs $2.75. How much money did Padma spend on grapes?”  
• In Lesson 4, Fluency and Skills Practice, students use procedural skill and fluency when multiplying multi-digit whole numbers using the standard algorithm. There are 15 multi-digit whole number multiplication problems, including, “580 x 30;” “1,236 x 55;” and “2,409 x 23.” 
• In Lesson 22, Session 4, Develop engages students in application. Problem 7 states, “Lily paints 3 trees for a wall mural. The middle tree is $$2\frac{1}{2}$$ ft tall. The tree on the left is ¾ as tall as the middle tree. The tree on the right is $$1\frac{3}{4}$$ times as tall as the middle tree. How tall is each tree? Show your work.” 

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example:

• In the game platform students are given the opportunity to practice skills that simultaneously work on conceptual understanding and build fluency. For example, the game “Bounce” focuses on placing decimals on a number line. Students use a number line to move a ball to its correct location based on the given decimal. 
• In Lesson 14, Session 2, Develop combines conceptual understanding, procedural skill, and application.  Students solve word problems involving addition and subtraction of fractions, mixed numbers, and decimals. Apply It, Problem 7 states, “Tim’s bean sprout grew $$3\frac{3}{8}$$ inches. Teegan’s bean sprout grew $$2\frac{3}{4}$$ inches. How many more inches did Tim’s bean sprout grow than Teegan’s? Estimate to tell if your solution is reasonable. Show your work.”

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations that the instructional materials carefully attend to the full meaning of each practice standard. Overall, the materials attend to aspects of the mathematical practices (MPs) during different lessons throughout the grade, so when taken as a whole, the instructional materials attend to the full meaning of each MP.

In i-Ready, Teach and Assess, Ready Classroom Mathematics, Program Implementation, Standards for Mathematics in Every Lesson, includes information on how the Standards for Mathematical Practice (MPs) are addressed within each lesson, noting that key components of lessons are designed to engage students with the MPs. Deepen Understanding provides guidance for teachers on each MP within lessons sessions. Discourse Questions are included, as well as prompts for Structure and Reasoning specifically related to MP7 (Look for and make use of structure) and MP8 (Look for and express regularity in repeated reasoning). In addition, the Try-Discuss-Connect Instructional Routines all identify the MPs. 

The instructional materials attend to the full intent of all eight Mathematical Practices. For example:

MP 1: Make sense of problems and persevere in solving them.

• In Lesson 5 , Session 4, Refine, Try It states, “A grocery store only sells eggs by the dozen. There are 12 eggs in 1 dozen. If there are 1,248 eggs in stock, how many dozens of eggs are there?” Teacher guidance states, “Make Sense of the Problem To support students in making sense of the problem, have them discuss the meaning of in stock. Ask: How many eggs are in stock at the store? How many eggs are in a dozen? What is the problem asking you to find?”
• In Lesson 25, Session 1, Explore, Try It states, “Lira finds an antique dresser that is 4 feet wide. She wants to know if it will fit in her room. She measures the space in inches. How many inches wide is the dresser? (1 foot = 12 inches).” Teacher guidance states, “Make Sense of the Problem. To support students in making sense of the problem, have them identify the measurement units involved, feet and inches.”

MP 2: Reason abstractly and quantitatively.

• In Lesson 3, Session 2, Model It and Picture It state, “Gareth has a rectangular pencil cup on his desk. The cup is 3 inches long, 2 inches wide, and 5 inches high. What is the volume of the pencil cup?” Deepen Understanding states, “Associative Property, SMP2 Reason abstractly and quantitatively. When discussing the volume formula V = l x w x h, prompt students to consider using volume to represent the associative property of multiplication.Ask, ‘How does each order for multiplying show a different way of thinking of the unit cube model as equal layers of cubes?’ Listen for: (3 x 2) x 5 = 6 x 5 shows thinking of the model as 5 layers of 6 cubes, and 3 x (2 x 5) = 3 x 10 shows thinking of it as 3 layers of 10 cubes.” 
• In Lesson 27, Session 3, Model It states, “The line plot shows the length of songs on Ron’s playlist. (Song lengths range from $$2\frac{1}{2}$$ minutes to $$4\frac{1}{2}$$ minutes) Ron adds two new songs to his playlist. His playlist is not 34 minutes in length. What are the possible lengths for the two new songs?” Deepen Understanding, Equation Models, SMP2 Reason abstractly and quantitatively states, “Discuss that the equations in Model It represent relationships among quantities in the problem and that the equations use letters for unknown quantities. Have students brainstorm questions that can be answered using data from Ron’s line plot. Ask students to decide which questions they can model with equations. Have students use letters to represent the unknowns.”

MP 4: Model with mathematics. 

• In Lesson 22, Session 2, Practice, Problem 5 states, “Write a word problem that can be solved by finding the product $$\frac{1}{6}$$ x $$\frac{3}{8}$$. Then solve your problem. Show your work.” 
• In Lesson 30, Session 3, Practice, Problem 7 states, “Shana is doing a craft project using yarn and craft sticks. She has 5 green yarn pieces and 7 blue yarn pieces. She has 3 times as many craft sticks as yarn pieces. Which expression can you use to find the number of craft sticks Shana has?”

MP 5: Choose tools strategically.

• In Student Worktext, Lesson 13, Session 1, Explore, Try It, students choose from the Math Toolkit fraction tiles, fraction circles, fraction bars, fraction models, grid paper, or number lines to solve, “Paul has $$\frac{3}{4}$$ inch long bolt. He buys a bolt that is $$\frac{1}{8}$$ inch longer and a bolt that is $$\frac{1}{8}$$ shorter than the $$\frac{3}{4}$$ inch bolt. What are the lengths of the two bolts he buys?”
• In Student Worktext, Lesson 29, Session 3, Develop, students choose from the Math Toolkit geoboards, rubber bands, tracing paper, grid paper, and rulers to solve, “Make a tree diagram to show the hierarchy of the following shapes based on their properties: rhombus, trapezoid, polygon, square, quadrilateral, rectangle, parallelogram. Use the exclusive definition of trapezoid in your diagram: a trapezoid is a quadrilateral with exactly one pair of parallel sides. Then, classify these shapes into as many categories as possible.”

MP 6: Attend to precision.

• In Lesson 9, Session 3, Develop states, “Tyson runs in a race at a track meet. One stopwatch shows his time as 11.25 seconds. Another stopwatch has his team as 11.245 seconds.” In Deepen Understanding, Number Line Model, MP6 Attend to precision states, “When discussing the number line models, prompt students to pay attention to precision in the rounding of the times. Ask: 11.245 is close to 11.25 on the second number line. Why do 11.25 seconds and 11.245 seconds not round to the same tenth of a second? Listen for: They round to different tenths of a second because 11.25 is exactly halfway between 11.2 and 11.3 so it rounds up, while 11.245 is closer to 11.2 than it is to 11.3, so it rounds down. Ask: What if you round each time to the nearest hundredth of a second? Would they still round to different times?”
• In Unit 2, Math In Action, Session 1 states, “Dog Collars: Alex is organizing a pet fair. Money from the fair will be donated to the local pet shelter. Alex’s friend Bella will have a booth at the fair.” A sign with the cost for each different size Adorable Dog Collars shows: Small $10.75, Medium $12.00, and Large $13.25. Students are given the cost to make each size collar and to “Find how much Bella makes on each collar after paying for supplies. Show a way to make at least $225 by selling collars. Include at least 5 collars of each size in your plan.” Students analyze Alex’s Solution, compare actual costs to estimated costs for supplies and discuss why precision is necessary when an exact cost is needed. 

MP 7: Look for and make use of structure

• In Lesson 3, Session 3, Develop, Try It states, “Bethany has a raised garden bed. The diagram shows its measurements. All the corners are right angles. If she fills the bed to the top with soil, how many cubic feet of soil will Bethany need?” Students “Explore different ways to understand finding the volume of a solid figure by breaking it apart into two rectangluar prisms. Guidance to Support Whole Class Discussions, Compare and connect the different representations and have students identify how they are related. How does your model represent the garden bed as a combination of rectangular prisms?”
• In Lesson 15, Session 2, Develop states, “Padma bought 3 pounds og grapes. Each pound costs $2.75. How much money did Padma spend on grapes?” In Deepen Understanding, Partial Products Model, MP 7 Use structure states, “Ask: How do the factor pairs in the second row relate to the partial products model on the Student Worktext page?”

MP 8: Look for and express regularity in repeated reasoning. 

• In Lesson 21, Session 4, Refine, Problem 4 states, “You can compare the size of a product to the size of the factors in a multiplication equation if you know whether the factors are greater than, less than or equal to 1. Part A: Write a multiplication equation in which the product is greater than both of its factors. At least one factor should be a fraction. Draw a model to support your answer. Part B. Write a multiplication equation in which both factors are fractions and the product is less than both of its factors. Draw a model to support your answer.”
• In Lesson 24, Session 3, Develop states, “Alex makes 2 pounds of bread dough. He splits the dough into $$\frac{1}{4}$$ pound loaves before baking them in the oven. How many loaves does he make?” In Deepen Understanding, Equivalent Fractions, SMP8 Use repeated reasoning states, “When discussing the equation method shown in the second Model It, prompt students to consider where else they use renaming as a strategy. Ask: In your own words, how do you describe the strategy shown for dividing a whole number by a unit fraction. Listen for: You rename the whole number, 2, as the fraction $$\frac{8}{4}$$ so that the dividend and the divisor describe the same parts of a whole. You can then think of dividing 8 fourths into equal groups of 1 fourth.”

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

In i-Ready, Teach and Assess, Ready Classroom Mathematics, Classroom Resources, the Student Worktext and the Math Journal provide students with opportunities to construct arguments and critique the reasoning of others. Evidence where students have opportunities to construct viable arguments includes: 

• In Unit 1, Math In Action, Try Another Approach, students make estimates to determine how many worms will be needed to start a worm farm to recycle kitchen scraps.  After students solve the problem, students Reflect on “Make an Argument: Why did you choose the numbers you did for your estimates?”
• In Lesson 27, Session 4, Refine, Problem 7 states, “Jordan looks at the live plot above. He says the difference between the most common capacity and the least common capacity is $$\frac{1}{4}$$ gallon. He says he knows the difference without subtracting. Explain Jordan’s mistake. Then find the actual difference between the measurement.”

Evidence where students have opportunities to analyze the mathematical arguments of others includes:

• In Lesson 19, the Math Center Activity, Fraction Area Models, students work with partners to solve multiplication problems by shading factors in an area model. Students “Tell how to shade it on the model. If your partner agrees, shade and label the model. Your partner reads the second factor and tells how to shade it on the model. If you agree, your partner shades and labels the model. Work separately to find the product. If you and your partner agree, write the product on the Recording sheet. If you and your partner do not agree, work together to find the correct product.”
• In Lesson 30,  Session 2, Develop, Connect It, Problem 3 states, “Morgan says you can evaluate 6 x (32 – 8) using three steps: multiply 32 by 6, multiply 8 by 6, and subtract the two products.  Why does Morgan’s method work?”

Evidence where students constructing viable arguments and analyze the mathematical arguments of others includes:

The materials contain a “Discuss It” box throughout the lessons that provide students with discussion prompts.  Some of them engage students in constructing viable arguments and/or analyzing the reasoning of others. For example, Lesson 4, Session 3, Develop, Try It states, “Find the product 1,429 X 42”  Discuss It, “Ask your partner: Do you agree with me? Why or Why not? Tell your partner: I agree with you about…because…”

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

In i-Ready, Teach and Assess, Ready Classroom Mathematics, Program Implementation, Resources include Discourse Cards which present questions and sentence starters to engage students in mathematical discourse, including the construction of arguments and analysis of others reasoning. For example, “Can you convince your partner or others that your answer makes sense? What do you think about what another student said? Does your partner’s strategy make sense? How is your solution method the same as or different from another student’s method?”

In Classroom Resources, Lesson 0, Understanding the Try-Discuss-Connect Instructional Routine. The Discuss routine presents opportunities to use questions and sentence starters for students to share their thinking and critique each other’s reasoning. In addition, using Compare Strategies, students discuss how representations are the same, different, and related. For example, Lesson 0, Session 2, Discuss It, Compare Class Strategies states, “Folding chairs are set up in a school auditorium for a play. There are 16 rows of chairs. Each row has 28 chairs. How many folding chairs are there? Once students share strategies and reasoning, the teacher asks “How are they the same? How are they different? How are they connected?” These instructional routines are present in every lesson.

Evidence where the instructional materials support teachers to engage students in constructing viable arguments includes:

• In Unit 3, Math in Action, Try Another Approach states, “G.O. and his neighbors clear a rectangular area $$8\frac{1}{2}$$ feet by $$6\frac{1}{4}$$ feet to plant shrubs. Now they have to decide how many shrubs to plant and how much water to use on the shrubs.” Reflect states, “Make an Argument: How could you justify the number of shrubs you suggested?”

Evidence where the instructional materials support teachers to engage students in analyzing the arguments of others includes:

• In Lesson 16, Session 1, Explore, Try It states, “Martin has $0.50.  Sara has 10 times as much as Martin. Jon has one tenth as much as Martin.  Does Sara have more money than Martin? Does Jon have more money than Martin? Explain.” Support Whole Class Discussion includes prompts for teachers such as, “How do (student name)’s and (student name)’s models show the amount of money each person has?”
• In Lesson 8, Session 2, Develop, Model It, Deepen Understanding provides teachers guidance in helping students construct arguments. It states, “When discussing the expanded forms, prompt students to justify how you can represent the same value in different ways.”

Evidence where the instructional materials support teachers to engage students in constructing arguments and critiquing the reasoning of others includes:

• In Lesson 9, Session 3, Develop, Discuss It, Support Partner Discussion states, “Encourage students to use the Discuss It question and sentence starter on the Student Worktext page as part of their discussion. Support as needed with questions such as: What evidence do you have to defend your solution? What evidence does your partner have that allows you to agree with his or her work?”

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations that materials explicitly attend to the specialized language of mathematics.

In i-Ready, Teach and Assess, Ready Classroom Mathematics, there are several resources to support teachers and students to use the specialized language of mathematics. In Program Implementation, the Academic Vocabulary Glossary identifies the vocabulary, provides a definition, and uses the word in a sample sentence organized by unit. For example, justify should be used by teachers “You must justify your answer to prove it is correct.” Encouraging educators to use precise and accurate terminology during instruction. 

In Classroom Resources, Lesson Overview, Lesson Vocabulary identifies whether there is new vocabulary or review, and key terms used in the lesson. For example in Lesson 31, Session 2, the student materials include a vocabulary box with the following: “coordinate plane a two-dimensional space formed by two perpendicular number lines called axes; ordered pair a pair of numbers (x,y), that describes the location of a point in the coordinate plane, where the x-coordinate gives the point’s horizontal distance from the origin, and the y-coordinate gives the point’s vertical distance from the origin; numerator the number above the line in a fraction that tells the number of equal parts that are being described.” 

Throughout lessons in Ready Classroom Mathematics, students are provided with Graphic organizers that assist with mathematical language to ensure students are using precise vocabulary. There are five different graphic organizers used throughout the lessons that allows students to organize learning concepts and vocabulary through definitions, illustrations, examples, etc. For example, Student Worktext, Lesson 8, Session 1 states, “Think about what you know about expanded form. Fill in each box. Use words, numbers and pictures. Show as many ideas as you can. Expanded Form: In My Own Words; My Illustrations; Example, Non-Example.”

Build Your Vocabulary is provided at the beginning of each unit to support students in learning and using precise language and terminology. For example in, Unit 3, Beginning of Unit, Build Your Vocabulary, there are review vocabulary words, “estimate, decimal, fraction and round.” The teacher’s guide provides suggestions for teachers to use with students to build math vocabulary using this page. It states, “Display, point to, and read each review word aloud. Have students repeat chorally.” The page contains a table for students to complete. Students have to compare two of the words at a time (round and estimate, fraction and decimal). They must answer “How are they similar? How are they different?” and provide an example. The teacher’s guide states, “Have students share their work in a whole class setting. If students struggle to verbalize their thinking, provide the following sentence frames as they compare and contrast round and estimate. Round and estimate are similar because they both _____. Round and estimate are different because round _____, but estimate _____.”

In the Lesson Overview, Language Objectives are included for each lesson. For example, in Lesson 7, Lesson Overview, the Language Objectives includes, “Use language of equivalent fractions to describe equivalent decimals.”

In the End of Unit, Vocabulary, Vocabulary Cards are available. The materials state, “The purpose of the vocabulary cards is to reinforce students’ understanding of the new vocabulary words in the unit as well as to provide a place for students to record any other math words and definitions that would be helpful for them in their understanding of unit concepts. Students may find it useful to draw or write examples on the vocabulary cards as they encounter the terms during the unit. you may want to make a copy of the cards and display them in a word wall in the classroom to further support students’ learning.”

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for distinguishing between problems and exercises. 

There are several practice pages provided with each lesson. After receiving guidance from the teacher in the Try It section of each lesson, students can demonstrate their understanding in a variety of ways. Students solve problems to learn new mathematics in the Explore sessions of each lesson. These ideas are further developed in Develop sessions, where students solve problems in the Try It and Connect It sections. In the Refine session, students complete exercises where they apply their learning. For example:

• In Grade 5, Lesson 7, Session 1, Explore, students explore powers of ten by recognizing place value patterns with whole numbers in the Try It section. In Session 2, Develop, students use these patterns with powers of ten and decimal numbers. They practice multiplication of powers of ten and decimals. In Session 3, Refine, students apply their learning in the Apply It session, where they solve word problems. 

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for designing assignments not being haphazard and exercises given in intentional sequences. 

The sequence of lessons in each topic is designed to move from concrete and pictorial representation toward abstract work with numbers. Each unit has a Unit Flow and Progressions Video that highlights the work of the unit and how it fits in the progression of mathematics across grade levels. 

Each unit also has a Learning Progression Chart that shows which lessons are building upon and which lessons students are preparing for within the unit. Each lesson has learning progression information which highlights work done in previous grade levels, as well as the work to be done in this lesson and subsequent lessons.

Each lesson has a consistent structure that builds towards independence. For example,

• In Grade 5, Lesson 13, Session 1, Explore, the teacher is prompted to help students make sense of the problem, “Paul has a $$\frac{3}{4}$$ inch long bolt. He buys a bolt that is $$\frac{1}{8}$$ inch longer and a bolt that is ⅛ inch shorter than the $$\frac{3}{4}$$ inch bolt. What are the lengths of the two bolts he buys?” The teacher is then prompted to support partner discussion by looking for and prompting use of a common denominator and how same sized parts in addition can be used in subtraction. Finally, during Apply It and the Exit Ticket students practice and independently show their understanding.

Lessons within units build upon each other. For example: 

• In Grade 5, Unit 4 includes the following lessons and topics: Lesson 25: Convert Measurement Units, Lesson 26: Solve Word Problems Involving Conversions, Lesson 27: Make Line Plots and Interpret Data, Lesson 28: Understand Categories of Two Dimensional Figures, and Lesson 29: Classify Two Dimensional Figures.

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for having a variety in what students are asked to produce. 

Students are expected to respond to problems in a variety of ways, including produce answers, use models, drawings, and equations to support their explanations. Students are asked to justify their solutions with a partner and participate in discussions with Discuss It and Pair/Share prompts. Students respond to different problem types in the Refine section of the lessons, including short answer explanations, multiple choice, fill in the blank, and drawings. For example:

• In Grade 5, Lesson 15, Session 3, Develop, students respond to problems in multiple ways when multiplying decimals by whole numbers. There are problems where students provide solutions with explanations, multiple choice items, and an area model diagram.

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for manipulatives being faithful representations of the mathematical objects they represent. 

There are a variety of manipulatives in the Math Tool Kit available during lessons, and students are introduced to these in appropriate contexts for the concept being developed.

• In Grade 5, Lesson 2, Session 1, Explore, students use unit cubes, grid paper, dot paper and square sticky notes to find volume. 

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for providing teachers with questions that are designed to elicit students’ mathematical understanding and thinking. 

• In Grade 5, Lesson 7, Session 1, Explore, questions are posed for the teacher to ask students.  The questions are in italics and easy for the teacher to see. In Discuss It the following questions are provided: “What do you notice about the number of zeros in each product and the numbers of factors of ten? How does the value of the digit 3 in 3,000 compare to the value of the digit 3 in 30? How can you use the diagram to answer the question? What do you notice about the number of zeros in each quotient and the number of zeros in the dividend and divisor?”

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meets expectations for including ample notes and useful annotations and suggestions on how to present the content in the student edition. 

The Program Implementation tab includes a “Digital Math Tools - Support Videos” section. This section includes support videos for counters and connecting cubes, base ten introduction, base ten: add and subtract, number line, multiplication models, perimeter and area, fraction models: add and subtract, and fraction models: compare and multiply.

In Classroom Resources, guidance for teachers supports the delivery of the content, as well as information on student responses for each section of the lesson. For example: 

• In Grade 5, Lesson 25, Session 3, Develop, the teacher notes include annotations that describe the Purpose, Connect to Prior Knowledge, Make Sense of the Problem, Try It, Discuss it, Model It & Solve It, Connect It, Apply It, and a Close: Exit Ticket to assist the teachers in presenting the material to the students. Moreover, in this section there is a Deepen Understanding box that focuses on MP2. 

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for containing a teacher’s edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject as necessary. 

In Classroom Resources at the beginning of each unit, Learning Progressions, Math Background, and Unit Flow and Progression Videos provide information for teachers on mathematics and models. For example:

• In Grade 5, Unit 5, Beginning of Unit, the Unit Flow & Progression video helps teachers understand lines, rays, measures, combined angles, classifying figures and symmetry. There are visuals, common errors, and insights on each topic to deepen teachers’ knowledge of the subject. 

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for containing a teacher’s edition that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for Kindergarten through Grade 12.  

The Ready Classroom Mathematics materials include a “Learning Progression,” section in the teacher edition for each lesson that describes how the grade-level appropriate standard is developed in previous grades as well as how it will extend in the next grade. For example:

• In Grade 5, Lesson 1, Lesson Overview, Standards 5.MD.3a & 5.MD.3b are listed and defined. Under the Learning Progression section on the same page, there is a small paragraph about “In Grade 4,” then “in this lesson,” and then, “in the next lesson.”

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels. 

The materials in Ready Classroom Mathematics list prerequisite skills for each lesson in the Lesson overview. Prerequisite Lessons are provided with each lesson to review concepts or to provide students with instruction in areas that may be gaps in their learning. For example:

• In Grade 5, Lesson 4, the Prerequisite Lessons are: Grade 4 Lesson 11, Sessions 1-4, and Lesson 12, Sessions 1-3.

In addition to identifying prerequisite skills for each lesson, Explore, at the beginning of each lesson, connects students’ prior knowledge with the content of the lesson. In some Warm-up questions there is a tag “Prerequisite” noting that the question is assessing prior knowledge.  

The instructional materials include adaptive Diagnostic Assessments with Prerequisite  Reports found in i-Ready, Reports.

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions. 

The Ready Classroom Mathematics materials provide strategies for teachers to identify and address common student errors and misconceptions. For example,

• In Grade 5, Lesson 27, Session 1, Explore, the Common Misconception states, “Look for students who are not comfortable with identifying the values for the unlabeled tick marks.  As students present solutions, have them specify how they determined the value for the lightest tomato.”

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills. 

Over the course of a lesson, which includes multiple sessions, materials engage students with multiple activities to review, practice, and independently demonstrate the grade-level mathematical concepts and skills. 

Feedback is provided to students as they progress through the Sessions. Frequent feedback opportunities to address skills and concepts are provided in the Classroom Resources tab, within each lesson and its sessions. The Reteach - Tools for Instruction within each lesson provides teachers with sample errors and remediation strategies to address those errors. In addition, throughout the lesson sessions, potential misconceptions are highlighted with guidance for teachers to provide feedback and new opportunities for practice. For example:

• In Grade 5, Lesson 16, Reteach Tools for Instruction, Multiply Decimals, Check for Understanding states, “If you observe the student uses a correct model but finds the incorrect product, the student may not understand the difference between tenths and hundredths.  Then try reviewing models of tenths and hundredths using 10 by 10 grids.” 

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for offering ongoing formative and summative assessments that clearly denote which standard is being emphasized.

• Standards are clearly noted within the assessments found at the end of each lesson. Standards are provided alongside the questions as well as the Depth of Knowledge level. Unit Assessment Correlations are available with the question number, DOK, Standard, and Lesson. 
• A Mid-Unit Assessment is provided for longer units. Mid-Unit Assessments also provide standards correlations for each item. These can be found in the Classroom Resources tab, End of Unit, Assess, Lesson Quizzes, and Unit Assessments. 
• Formative assessments are also available:
• Lesson quizzes, exit tickets, and quick checks are provided for most lessons. These quizzes assess the specific standard(s) being taught in the lesson.
• Within the sessions are Check For Understanding supports that include a statement as to why the check is being done. The why relates back to the standard being taught in the activities for that session.

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for including aligned rubrics and scoring guidelines to support teachers in interpreting student performance and sometimes provide for follow-up instruction. 

Rubrics are provided for Mid-Unit Assessments, Unit Assessments, Unit Performance Tasks, Lesson Quizzes, and Math in Action. (grade 2 and above) The rubrics and scoring guidelines support teachers to interpret student performance. Assessment answer keys are provided alongside the questions along with the DOK level for the item. For multiple choice answers, the correct answer and explanations for incorrect choices are given, including the most common misconceptions.  

Reports from i-Ready diagnostic assessments and comprehension checks assist teachers in providing follow-up instruction for misconceptions and mathematical errors. The electronic reports also include links to assist in reteaching items missed. Within lessons, rubrics and scoring guidelines provide guidance for teachers to follow-up and, throughout Ready Classroom Mathematics, there is guidance for teachers on behaviors to look for, error alerts, and Common Misconceptions. 

• Unit Assessments include a Unit Assessment Teacher Guide that provides instructors with solutions, points possible, the exact standard covered, and the depth of knowledge (DOK) level for each item.
• The Scoring Guide for the problems in the scoring table include: DOK, points of scoring, standard addressed, and lesson assessed by each problem.
• The Scoring Rubrics includes points and expectations for short response, multiple select, choice matrix, extended response, and fill-in-the-blank items.
• Assessment Practice provides some support for follow-up by identifying standards that need further study and reinforcement. Assessment Practice Answer Key and Correlations identify the standard which each question has been designed to evaluate. 

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. 

The sessions within a lesson follow the sequence of Explore, Develop, and Refine. Within a session, there is a sequence of Start, followed by Try It, Model It, or Apply It; Discuss; Connect; and Close.

• Start is designed to build fluency or connect to prior knowledge. 
• Try It is designed to give students an opportunity to explore the concept on their own.
• Model It is designed to allow students the opportunity to explore the concept through manipulatives or drawings. 
• Apply It is designed to give students an opportunity to practice the skill on their own. 
• Discuss is designed to allow students to talk to other students about the concept and compare what they did with each other. 
• Connect It is designed to help students connect the concept to real-life. 
• Close is designed to solidify the learning for the day and to check for understanding through the use of an exit ticket. 

Each lesson includes a Differentiated Instruction Teacher Toolbox that includes Reteach (Tools for Instruction), Reinforce (Math Center Activities), and Extend (Enrichment Activities). For example, the Lesson 1 Overview states: 

• Reteach- “Children who require additional support for prerequisite or on-level skills will benefit from activities that provide targeted skills instruction.”
• Reinforce- “Children who require additional practice to reinforce concepts and skills and deepen understanding will benefit from small group collaborative games and activities.” This is available in three versions: on-level, below-level, and above-level.
• Extend- “Children who have achieved proficiency with concepts and skills are ready for additional challenges will benefit from group collaborative games and activities to extend understanding.”

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for providing teachers with strategies to meet the needs of a range of learners. 

Each lesson provides opportunity for differentiation in small group lessons, interactive digital tutorials, support for teachers to address common misconceptions at different points throughout lessons. For example:

• The Differentiated Instruction opportunities provide support to reteach students who need additional support, reinforce learning for students who need additional practice, and extend learning for students who have achieved proficiency and are ready for further challenges.
• The Language Development sections for English Language Learners provides even more differentiated support for students who are at different levels of English proficiency.
• Community and Cultural Responsiveness activities build bridges between the mathematics students are learning to investigations of authentic contexts and issues. For example, students apply mathematics they have learned to objects and activities found in parks.

The materials also support learning with a variety of different experiences to develop connections in each lesson. For example:

• Lessons use manipulative objects such as counters and connecting cubes for hands-on experiences where students are actively applying and representing mathematics with hands-on objects.
• Partner and Whole group discussion are incorporated in all sessions to provide dialogue surrounding the mathematics being done.
• Visual representations and physical representations using mathematics manipulatives are used throughout each session.

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for embedding tasks with multiple entry points that can be solved using a variety of solution strategies or representations. 

The materials present word problems at the beginning of most lessons in the Try It part of the session, which provides multiple points of entry for students. During Model It, students can model the problem in whichever way they like. Examples of problems that provide multiple entry points, different representations, and/or solution pathways include:

• In Grade 5, Lesson 11, Session 1, Explore, Try It states, “The mass of a female hummingbird is 4.5 grams. The mass of a male hummingbird is 3.2 grams. What is the difference between the masses of the female and male hummingbirds?” 

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations to engage students in regular and active participation in learning mathematics.

In Program Implementation, Implementation Support there are resources, including:

• A Multilingual Glossary
• A Bilingual Glossary
• An Academic Vocabulary Glossary
• WIDA PRIME V2 Correlation
• Try-Discuss-Connect Routine Resources

In Classroom Resources, Teachers Edition, Language Development is identified for each lesson. This differentiated instruction chart provides guidance for teachers at three levels of differentiation that identifies specific strategies (e.g., Speaking/Writing, Reading/Writing) directly connected to lesson sessions and activities. During sessions, specific strategies target additional supports for students to support engagement in lesson activities. For example:

• Prerequisite lessons are identified for most lessons and include specific supports for ELLs.
• Develop Language includes Why (rationale for the suggestions) and How (strategies and guidance on how to engage students) sections, along with explanations as needed.  
• Discuss It provides supports for all students to engage in mathematical discourse.
• Differentiated Instruction is included for most lessons and includes activities for intervention, on-level, and challenge.
• Math Center activities provide multiple levels of content. 
• Math in Action lessons in Grade 2 and higher build background in a variety of contexts to ensure access for all.

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for providing opportunities for proficient and advanced students to participate in enrichment activities for a deeper challenge. 

In i-Ready, Teach and Assess, Ready Classroom Mathematics, Classroom Resources, Teacher, Lesson Pacing Guide includes Small Group Differentiation Activities, and highlights Extend, Enrichment Activity. These Enrichment Activities can be found during the Refine session in the lesson, and include a Challenge Activity related to the content of the lesson. For example: 

• In Grade 5, Lesson 5, Extend states, “Have students write division word problems using a three- or four-digit number for the dividend and a two-digit number for the divisor…”

The instructional materials reviewed for Ready Classroom Mathematics Grade 5 meet expectations for providing a balanced portrayal of demographic and personal characteristics representing a variety of backgrounds. 

In the Program Implementation tab, a multilingual, bilingual, and academic glossary are provided. Throughout the materials there are examples of animated pictures of children that have varied skin tone, features, hair color, and hair types such as pictures of children with brown skin and black hair, light skin and blond hair, and brown skin and brown hair. Pictures with more than one child show interactions between children with varied skin and hair colors such as one with light brown skin and black hair and the other with dark brown skin and black hair. The pictures of objects included are pencils, cars, soccer balls, footballs, apples, bananas, crayons, goldfish, rocks, flowers and other objects commonly known to most students. A variety of names representing different ethnic and cultural backgrounds are used, including:  Rosa and Ryan, Nick and Nora, Dave and Ari, Roberto and Rena, Fran and Pete, Gabe and Rose, Darious, Sam, Lexi, Paco, Julija, Lana, and Kyle.