The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. The lessons include problems and questions that develop conceptual understanding throughout the grade-level. Examples include:

• Unit 2, Lesson 9, Session 2, “Connect It”, Problem 4, students develop conceptual understanding by using and comparing models of dividing fractions by fractions (6.NS.1).  “How can you show the quotient $\frac{4}{6}\div\frac{1}{6}$ with a bar model? How is using a bar model similar to showing the quotient with a number line? How is it different?”

• Unit 5, Lesson 19, Session 4, “Try It”, students develop conceptual understanding with teacher guidance: “Which of these three expressions are equivalent? $3(x+2)+2x$; $2+4(x+1)+x$; $2(3+3x)-2x$” Teacher guidance helps facilitate discussion and makes connections for using properties of operations to rewrite expressions (6.EE.3). Teacher prompts include: “How does each expression change from one step to another? Why is each step necessary?”

• Unit 6, Lesson 25, Session 1, “Model It”, Problem 1, students develop conceptual understanding of absolute value of rational numbers (6.NS.7) by describing distances of objects below and above sea level. “A scientist standing on the deck of a boat flies a drone to study wave patterns. A scuba diver uses a camera to explore a sea cave. The table shows the elevations of four objects relative to sea level. (The table shows the following objects and their elevations: Camera -20 ft., Cave floor -30 ft., Drone 20 ft., Boat deck 5 ft.) a. Use the number line to show the elevations of the objects from the table. Label each object at its elevation. b. Which objects are the same distance from sea level? How far from sea level are they? c. Another object is 3 ft from sea level. Is the object’s elevation positive, negative, or could it be either? Explain.”

The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade with the use of visual models, real world connections, mathematical discussion prompts, concept extensions, and hands-on activities. Examples include: 

• Unit 2, Lesson10, Session 3, “Apply It”, Problem 9, students demonstrate conceptual understanding of dividing fractions by fractions in real world situations (6.NS.1). “It takes Francisco $\frac{5}{6}$ minute to upload a video to his blog. How much of one video can he upload in $\frac{1}{2}$ minute? Show your work.” 

• Unit 3, Lesson 12, Session 1, “Model It”, Problem 4, students demonstrate conceptual understanding of ratio relationships (6.RP.1) by explaining the difference in units. “Explain how the ratios of 5 tacos for every 2 guests and 2 tacos for every 5 guests are different. Include a model in your explanation.” 

• Unit 6, Lesson 23, Session 2, “Model It”: Vertical Number Lines, Problem 3, students demonstrate conceptual understanding of negative numbers and plot numbers and their opposites on a number line (6.NS.5 and 6.NS.6). “a. Use a rational number to label each point on the number line. b. What is the opposite of each number you wrote on the number line? c. Plot points at -1.75 and $-\frac{3}{4}$.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Within each lesson, there is a Session that provides additional practice for students to have in class or as homework. Additionally, many lessons include a Fluency & Skills Practice section. Examples include: 

• Unit 1, Lesson 5. Session 2, Apply It, Problem 9, students develop procedural skill and fluency with evaluating numerical expressions with whole number exponents (6.EE.1). “On the Lucky Five game show, Troy wins $5 if he answers one question correctly. Each time he answers another question correctly without making a mistake, the amount of money he wins is multiplied by 5. Troy answers 6 questions correctly without making a mistake. His winnings are represented by the expression $5^6$. How much money does Troy win? Show your work.” 

• Unit 2, Lesson 7, Session 3, Practice, Problems 1 and 2, students develop procedural skill and fluency with multiplication of multi-digit decimals. “A green rope is 60.5 m long. Each meter of the rope has a mass of 0.052 kg. What is the total mass of the green rope? Show your work.” Problem 2, “Find $0.102\times7.3$. Show your work.” (6.NS.3)

• Unit 4, Lesson 18, Session 2, Fluency Skills and Practice contains multiple problems for students to develop procedural skill and fluency with finding percent of a number (6.RP.3c) such as Problem 6, “Find the percent of the number: 75% of 80.”

Materials provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade level. Within each lesson, students engage with practice problems independently at different sections of the lesson. Examples include: 

• Unit 1, Lesson 5, Session 4, Apply It, Problem 4, students demonstrate procedural skill and fluency with evaluating multiple expressions involving whole-number exponents (6.EE.1). “Which expressions have a value of 100 when $m=5$? Select all that apply. $2m^2+50$; $(2m)^2+50$; $(m+5)^2$; $m^3\div5\cdot4$; $4m^2$; $(4m)^2$.”

• Unit 2, Lesson 8, Session 2, Practice, Problem 2, students demonstrate procedural skill and fluency with fluently dividing multi-digit numbers using the standard algorithm. (6.NS.2) “Platon’s mom buys a car using a loan. She repays the loan by paying $22,032 in 48 equal monthly payments. How much is each payment? Show your work.” 

• Unit 5, Lesson 21, Session 4, Practice, Problem 5, students demonstrate procedural skill and fluency with solving multi-digit division problems using the standard algorithm. (6.NS.2) “Neva is training for a race. This week, she bikes 5.5 times as far as she runs. Her total distance running and biking this week is 26 mi. How far does Neva run this week? Show your work.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for being designed so teachers and students spend sufficient time working with engaging applications of the mathematics. 

Engaging routine and non-routine applications include single and multi-step problems. Examples include:

• Unit 2, Math in Action, Session 2, Discuss Models and Strategies, students engage with a non-routine application problem by finding the volume of right rectangular prisms with fractional edge lengths by packing it with unit cubes with fractional edge lengths (6.G.2). “Alberto wants to set up an aquarium for the science club. Read the information he finds about aquarium ecosystems. Then suggest a tank, a number of guppies, and an amount of gravel for Alberto to use to set up his aquarium.” 

• Unit 4, Lesson 16, Session 2, Develop, Try It, students engage with a routine application problem by using unit rates (6.RP.3) to solve real-world problems. “Ashwini jogs on the track at her school. She uses a watch to track her progress. At this rate, how long will it take her to jog 16 laps?” There is a picture of a watch that says “15 minutes, 6 laps.” 

• Unit 7, Lesson 30, Session 2, Develop,Try It, students engage with a non-routine application problem by using a set of data to answer a statistical question (6.SP.2). “Elizabeth records the number of points her favorite basketball team scores in each game. She predicts that the team will score about 120 points in its next game. Is Elizabeth’s prediction reasonable? Display Data Set: Points Scored in a way that supports your answer.” There is a picture of the data set included.

Materials provide opportunities for students to independently demonstrate routine and non-routine applications of the mathematics throughout the grade level. Examples include:  

• Unit 2, Lesson 11, Session 4, Apply It, Problem 9, students demonstrate a non-routine application problem by identifying the dimensions and find volume of a right rectangular prism when given an edge length of a cube as a fraction (6.G.2). “Give the dimensions of a right rectangular prism that can be filled completely with cubes that have edge lengths of $\frac{1}{2}$in. Explain how to use the cubes to find the volume of the prism.”

• Unit 5, Math in Action, Session 1, Try Another Approach, students demonstrate a non-routine application problem by using variables to represent two quantities that change in relationship to each other (6.EE.9). “The cheerleaders, marching band, football team, and school mascot purchase new uniforms. The packing slip shows the total amount each team pays and provides information about tax and shipping charges. Choose one type of uniform. Write and solve an equation to find the price of one uniform before shipping and tax.” 

• Unit 6, Lesson 26, Session 5, Apply It, Problem 2, students demonstrate a routine application problem by drawing a graph and writing an inequality to model possible values of a given situation (6.EE.5). “Each week, Patrick buys more than 2 pounds of apples. Apples cost $1.37 per pound. Draw a graph that represents the possible amounts of money, m, that Patrick spends on apples in a week. Then write an inequality that represents your graph.Show your work.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade. The Understand lessons focus on developing conceptual understanding. The Strategy lessons focus on helping students practice and apply a variety of solution strategies to make richer connections and deepen understanding. The units conclude with a Math in Action lesson, providing students with routine and non-routine application opportunities.

All three aspects of rigor are present independently throughout each grade level. Examples include:

• Unit 1, Lesson 4, Session 4, Apply It, Problem 4, students develop conceptual understanding by using variables to represent numbers while writing expressions and solving mathematical problems (6.EE.2, 6.EE.6). “In a video game, players start with a score of 100 points. They earn 8 points for each gold coin and 25 points for each gem they find. Isaiah finds 3 gold coins and 2 gems. Write and evaluate an algebraic expression to find Isaiah’s score. Use c for the number of gold coins found and g for the number of gems found. Show your work.”

• Unit 3, Lesson 13, Session 2, Practice, Problem 5, students practice procedural skills and fluency while solving real world problems with ratios and rates (6.RP.3). “A manager of a clothing store always orders 2 small T-shirts and 3 large T-shirts for every 4 medium T-shirts. The manager plans to order 24 medium T-shirts. How many small T-shirts and large T-shirts should the manager order? Show your work.” 

• Unit 5, Lesson 19, Session 2, Apply It, Problem 10, students apply the properties of operations to generate equivalent expressions (6.EE.3) by solving, "A company sells fruit cups in packs of 4. The packs currently weigh 20 oz. The company plans to reduce the weight of each cup by n oz. The expression 20-4n represents the new weight, in ounces, of a pack of fruit cups. Rewrite the expression for the new weight as a product of two factors. Show your work." 

Multiple aspects of rigor are engaged simultaneously to develop students' mathematical understanding of a single unit of study throughout the grade level. Examples include: 

• Unit 2, End of Unit, Unit Review, Performance Task, students attend to conceptual understanding and application as they apply their understanding of volume (6.G.2) and dividing fractions by fractions (6.NS1.) to solve a real-world problem. “Geraldine supplies number cubes to companies that make board games. Each number cube measures $\frac{3}{4}$ inch on each edge. For shipping, the number of cubes can be packed into any of the boxes shown.” Images of three boxes are shown labeled with their dimensions $(4in\times4 in\times4in$; $4in\times3$ $\frac{1}{2}in\times2in$; $2\frac{1}{2}in\times6\frac{1}{4}in\times2\frac{1}{2}in)$. “Geraldine receives an order for 780 number cubes. First, she needs to know the maximum number of cubes she can fit in each box. Then she needs a packing plan for the order. Remember: only whole cubes can be packed. Design a packing plan for Geraldine. Your plan must include the following requirements: the maximum number of cubes that can fit into each box is identified, the fewest number of boxes is used to pack the 780 number cubes, no box is packed with fewer than half the total number of cubes it can hold.”

• Unit 4, Math in Action, Session 2, Discuss Models, students attend to conceptual understanding, procedural skill and fluency, and application as they use ratio and rate reasoning (6.RP.3) in a real-world situation. “Astronauts Francisco and Mei are going on a spacewalk. Their main task is to install two new cameras on the outside of the International Space Station (ISS). After they complete their main task, they will perform get-ahead tasks. Read the information about the get-ahead tasks, and then look at the data about the astronauts’ oxygen levels. Assume that Francisco and Mei continue to use oxygen at the same rate. Assign each of them a get-ahead task. Then show that each astronaut has enough oxygen to complete his or her assigned task and return to the airlock at the ISS. What models can you use to help you determine how much time Francisco and Mei can each spend on a get-ahead task without running out of oxygen? Is there more than one possible get-ahead task for each astronaut? How do you know?” Given: Get-ahead task list with required times; time that main task is completed; amount of oxygen each had after main task. 

• Unit 7, Lesson 33, Session 2, Apply It, Problem 9, students attend to procedural skill and fluency and conceptual understanding while summarizing numerical data sets in relation to their context (6.SP.5). “The lists show the number of grams of fat in the subs sold at two sandwich shops. Juan’s Subs: 24, 5, 52, 12, 15, 10, 4, 26, 45, 6; Efia’s Subs: 28, 13, 18, 12, 13, 15, 16, 18, 10, 7. How can you use the data to support the argument that the subs at Efia’s shop have less fat than the subs at Juan’s?”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

The Mathematical Practices are embedded within the instructional design, found in the Teacher Toolbox under Program Implementation. The Teacher’s Guide includes “Standard of Mathematical Practice in Every Lesson” which states, “Through a dedicated focus on mathematical discourse, the program blends content and practice standards seamlessly into instruction, ensuring that students continually engage in developing the habits of the mathematical practices.” The Table of Contents and the Lesson Overview both include the Standards for Mathematical Practice for each lesson. In the Student Worktext, the Learning Target also highlights the MPs that are included in the lesson. 

There is intentional development of MP1: Make sense of problems and persevere in solving them, in the Try It problems, where students are able to generate their own strategies to solve the problem. Teachers are provided with guidance to support students in making sense of the problem using language routines such as Co-Craft Questions and Three Reads. Examples include: 

• Unit 2, Lesson 11, Session 1, Try It, students make sense of the relationship between edge lengths and volume when a large cube is packed with smaller cubes in order to find the volume of a right rectangular prism. “Jiro has some small cubes that are all the same size. He puts the small cubes together to make a large cube, as shown. What is the volume of each small cube?” 

• Unit 5, Math in Action, Session 2, students analyze the relationship between dependent and independent variables using graphs and tables and write an equation to model a real-world problem. “Track and Field Training. A coach plans workouts for several groups of athletes on the track and field team. Read the coach’s plans for how each group should complete a 400-meter lap around the track. Choose one group and make a table and a graph to analyze the relationship between distance, d, and time t, for that group. Then write an equation that models the relationship.” Data about the speed and distance of each group is included in the problem. In the Reflect section, students discuss how to make sense of the problem. “Use Mathematical Practices - As you work through the problem, discuss these questions with a partner. Make Sense of Problems - Which variable is the dependent variable and which is the independent variable? Explain.”

• Unit 7, Lesson 30, Session 1, Try It, students display data in dot plots on a number line and summarize numerical data sets in relation to their context. “The parks department can add one new program to its summer camp. The data shows the ages of children who have signed up. Based on “Data Set: Ages in Years”, which age group should get the new program?” 

There is intentional development of MP2: Reason abstractly and quantitatively, in the Try-Discuss- Connect routines and in the Understand lessons. Students reason abstractly and quantitatively, justify how they know their answer is reasonable, and consider what changes would occur if the context or the given values in expressions and equations are altered. Additionally, teachers are provided with discussion prompts to analyze a model strategy or representation. Examples include: 

• Unit 3, Lesson 12, Session 1, Model It, Problem 2, students understand the concept of a ratio and use ratio language to describe a relationship between two quantities as they solve, “You can also use a ratio to compare two quantities. One way to describe a  relationship between ratios is to use the language for every or for each. a. In Eldora’s lab group, there are 3 test tubes for every 1 student. Complete the model to show this ratio relationship. b. Use your model to complete these sentences that use ratio language. For every 1 student, there are ____ test tubes. There are ____ test tubes for each ____. There is ____ student for every ____ test tubes.” 

• Unit 3, Lesson 14, Session 1, Try It, students deconstruct data in the problem and then reconstruct data in a table using equivalent ratios. “Hasina is making green tea lattes.  She steams milk to mix with hot tea. Hasina has 12 fl oz of hot tea. Based on the ratio in the recipe, how much milk does Hasina need to steam?” A ratio of “Green Tea Latte, 4:3, Tea:Milk” is provided for the problem.

• Unit 7, Lesson 29, Session 1, Model It, Problem 1, students reason quantitatively with numerical data sets in relation to their context. “Keiko is on her school’s track team. She collects data to answer this question. How high did members of the track team jump in yesterday’s high jump event? Complete the dot plot to show Keiko’s data.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for supporting the intentional development of MP3: “Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.” 

There is intentional development of MP3 to meet its full intent in connection to grade-level content. In the Discuss It routine, students are prompted with a question and a sentence frame to discuss their reasoning with a partner. Teachers are provided with guidance to support partners and facilitate whole-class discussion. Examples include:

• Unit 1, Math in Action, Session 1, Try Another Approach, Reflect, Critique Reasoning, students critique a partner’s solution to designing pens for hens that meet certain criteria (i.e. “all pens will be the same size and hold the same number of hens, each pen should be at least 4 feet high, and there should be at least 8 square feet of floor space per hen.”)  “Do the pens your partner described meet the requirements from Juan’s teacher? Explain.”

• Unit 4, Lesson 16, Session 3, Teacher Edition, Model It, Facilitate Whole Class Discussion, provides guidance for teachers to help students construct viable arguments to defend their problem solving strategies. “Call on students to share selected strategies. Remind listeners to be specific when explaining why they disagree with a speaker's idea.” 

• Unit 5, Lesson 20, Session 3, Apply It, Problem 1, students determine if the reasoning of another makes sense and justify their response. “Greg says that x could represent a value of 3 in the hanger diagram. Do you agree? Explain your reasoning.” The problem is accompanied with a hanger diagram with three x’s on one side and six 1’s on the other side. 

• Unit 7, Math in Action, Session 2, Persevere on Your Own, Reflect, Critique Reasoning, students critique a partner’s solution to using measures of center and variability to make conclusions about a data set. “What did your partner conclude about the word lengths in the first round of both spelling bees? Is your partner’s conclusion supported by the data sets? Explain.”

• Teacher Toolbox Program Implementation Support, Teacher’s Guide, Standards for Mathematical Practice in Every Lesson, SMPs are integrated in the Try-Discuss-Connect routine. “Discuss It begins as student pairs explain and justify their strategies and solutions to each other. Partners listen and respectfully critique each other’s reasoning (SMP 3). To promote and support partner conversations, the teacher may share sentence starters and questions for discussions. During this time, the teacher is listening in to peer conversations and reviewing student strategies, identifying three or four strategies to discuss with the whole class in the next part of Discuss It.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for supporting the intentional development of MP4: “Model with mathematics;” and MP5: “Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.” 

There is intentional development of MP4: “Model with Mathematics” to meet its full intent in connection to grade-level content. Many problems present students with the opportunity to use models to solve problems throughout the materials. Examples include:

• Unit 1, Lesson 6, Session 2, Connect It, Problem 3, students connect a tree factor model to a given situation. “How many blankets and how many flashlights will be in each kit if Akio uses the GCF as the number of kits? Where do you see these amounts in the equations under the factor trees?”

• Unit 2, Lesson 9, Session 1, Model It, Problem 3, students write a division equation to model a situation. “Zhen starts with a board that is $\frac{3}{2}$ feet long. She cuts it into pieces that are each $\frac{1}{4}$ foot long for her stacking game. a. Complete the model to show how many pieces Zhen cuts her board into.” A blank tape diagram that is divided into 3 sections and labeled as $\frac{3}{2}$ is included. b. “Write a division equation that represents your model and shows how many pieces Lin cuts her board into. What related multiplication equation does your model represent?”

• Unit 6, Math In Action, Session 2, Solve It, students model a situation using inequalities. A table is included with 4 different ceramic pottery samples along with the least and greatest estimated age in years for each sample. “Find a solution to the Estimating Ages of Artifacts problem. Choose a sample. Write an inequality to represent the possible ages of the sample based on the least age given in the table. Then graph the inequality. Write an inequality to represent the possible ages of the sample based on the greatest age given in the table. Then graph the inequality. List three possible years in which the ceramic could have been made. Give an early estimate, a middle estimate, and a late estimate.” In the Reflect section, students are prompted to discuss with a partner. “Use a Model. How could you show the possible estimated ages of the ceramic sample using a single number line?”

• Unit 7, Lesson 32, Session 2, Teacher Edition, Differentiation: Reteach, Hands-On Activity, students are guided by the teacher to demonstrate why the mean can be thought of as a balance point. The students use counters and rulers to label a number line above each value to represent the data. Teachers ask, “What is the mean of this data? Have students move each counter to above 4, keeping track of how many units they move each counter.” Teachers then ask, “What do you notice about the total units the counters to the left of 4 had to move and the counters to the right of 4 had to move to get to 4?” 

There is intentional development of MP5: “Use appropriate tools strategically to meet its full intent in connection to grade-level content.” Many problems include the Math Toolkit with suggested tools for students to use. Examples include:

• Unit 1, Lesson 2, Session 3, Teacher Edition, Model It, Differentiation: Extend, provides guidance for teachers to engage students in MP5 as they recognize both the insight to be gained from different tools/strategies and their limitations. “Prompt students to compare the advantages and disadvantages of each strategy? Ask: What are the advantages and disadvantages of using decomposition and addition to find the area of the logo? Listen For: The decomposition strategy allows you to use simple calculations to find the area, but you may find it difficult to decompose the logo into familiar shapes. Ask: What are the advantages and disadvantages of composing a rectangle around the logo and then subtracting the areas of the right triangles? Listen For: With this strategy, you can find the area of a rectangle, which is a simple calculation. However, more calculations are needed to subtract the areas of the triangles from the total area. Generalize: Encourage students to explain how they might choose an appropriate strategy when solving area problems. Students may state that they use the method that is the most efficient for the given shape, or they may state that they like to use the same strategy to solve all types of area problems.”

• Unit 3, Lesson 13, Session 2, Try It, students can choose from a variety of tools to demonstrate understanding of ratios. “The ratio of picnic tables to garbage cans in a new national park should be 8:3. The park design shows plans for picnic tables in a small campground and a large campground. How many garbage cans should there be in each campground?” The number of picnic tables in each campground is provided, 40 in a small campground and 120 in a large campground. The math toolkit includes: connecting cubes, counters, double number lines and grid paper.

• Unit 6, Lesson 28, Session 2, Connect It, Problem 7 students reflect on the models and strategies they use in the Try It to find distance in the coordinate plane. “Think about all the models and strategies you have discussed today. Describe how one of them helped you understand how to solve the Try It problem.” The teacher’s edition states, “Have all students focus on the strategies used to solve the Try It. If time allows, have pairs discuss their ideas.”

• Unit 7, Lesson 31, Session 3, Teacher Edition, Differentiation: Deepen Understanding, provides prompts for students to recognize both the insight to be gained from different tools/strategies and their limitations. “Prompt students to consider when and how box plots are useful representations of data. Ask: What are some advantages to using a box plot to display a data set?...Why is the median not directly in the middle of the box plot?... What are some disadvantages to using a box plot to display a data set?”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for supporting the intentional development of MP6: “Attend to precision;” and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

There is intentional development of MP6: “Attend to Precision,” to meet its full intent in connection to grade-level content. Many problems present students with the opportunity to attend to precision within the mathematics and the reasoning of the answer. Examples include: 

• Unit 2, Math in Action, Session 1, Reflect. Students explain the results of their calculations. “Be Precise: Would it make sense to round the results of your calculations to get your final answer? Why or why not?” The students solve how many grains of salt it takes to grow one salt crystal. The problem uses decimals as the side length on a cube. 

• Unit 3, Math in Action, Session 2, students use and label graphs to compare ratios. “Josephine and her family set goals for how much water to drink compared to other beverages. Choose two family members. Use ratio tables to determine who will drink more water compared to other beverages. Make a graph that Josephine's family could use to see how the two goals compare.” The text includes the amount of water in ounces each family member drinks compared to other beverages. For example, Josephine drinks “10 ounces of water for every 5 ounces of other beverages.” The question in the Problem-Solving Tips box reminds students to attend to precision, “How will you label the axes of your graph?”

• Unit 6, Lesson 26, Session 4, Apply It, Problem 7, students attend to precision when identifying how the solutions to an inequality are related to the situation. “Aimee works up to 50 hours a month and earns $12 per hour. She wants to save more than $240 to buy a computer. The inequality $12h>240$, where h is the number of hours Aimee works this month, models this situation. Which values from 0 to 50 are solutions of the inequality? What do the solutions mean in this situation? Explain your reasoning.”

i-Ready Classroom Mathematics attends to the specialized language of mathematics. The materials use precise and accurate mathematical terminology and definitions, and the materials support students in using them. All Units include a guide to academic and content vocabulary. The Collect and Display routine is “A routine in which teachers collect students' informal language and match it up with more precise academic or mathematical language to increase sense-making and academic language development.” Teacher’s guides, student books, and supplemental materials explicitly attend to the specialized language of mathematics. Examples include: 

• Unit 3, Lesson 14, Session 3, Teacher Edition, Discuss It, provides teacher guidance to correct a common misconception when describing paint ratios with the appropriate terms. “Listen for students who think that the quantities in two ratios determine which ratio is greater. For example, they may say that 2:3 is bluer than 1:2 because $2>1$ and $3>2$. As students share their strategies, rephrase bluer and repeat the definition of ratio. Elicit discussion on how to determine who has a bluer mixture.”

• Unit 4, Lesson 15, Session 2, Teacher’s Edition, Develop Academic Language, “Why?: Support students as they craft clear explanations using precise language. How?: Remind students that using precise mathematical language and complete sentences makes explanations clearer and easier to understand. Prior to each Discuss It, work with students to develop a list of precise terms from Model It, such as rate, per minute, equivalent ratios, and ratio relationships. During Discuss It, Collect and Display authentic examples of clear explanations.”

• Unit 7, Lesson 31, Overview, Teacher Edition, Language Objectives, “Explain in writing why the median can be used as a measure of center; Summarize a data set using lesson vocabulary, including lower quartile (Q1), median (Q2), and upper quartile (Q3); Describe the variability of a data set by explaining how box plots and the IQR represent a data distribution in whole-class discussion; Demonstrate understanding of word problems by explaining how the median and IQR connect to the problem context.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards. 

The MPs are embedded within the instructional design. In the Teacher’s Guide, Front End of Book, Standard of Mathematical Practice in Every Lesson, teachers are guided “through a dedicated focus on mathematical discourse, the program blends content and practice standards seamlessly into instruction, ensuring that students continually engage in developing the habits of the mathematical practices.”

There is intentional development of MP7 to meet its full intent in connection to grade-level content. Examples include: 

• Unit 1, Lesson 6, Session 3, Teacher Edition, Differentiation: Extend, students find the least common multiple. Teachers are asked to do the following routine for MP 7: When discussing using a list of multiples to find an LCM, share with students that another method for finding the LCM of 6 and 8 is to list multiples of 8 and then check for the first number in the list that is divisible by 6. Prompt students to think about the advantages and disadvantages of this method. Ask: Why does this method work? Listen for: If a multiple of 8 is also a multiple of 6, it is divisible by 6. Ask: What is an advantage to finding the first multiple of a number that can be divided by the other number? What is a disadvantage of this method? Listen for: An advantage is that you only have to list the multiples of one of the numbers and you can stop listing multiples as soon as you find one that is divisible by the other number. A disadvantage is that you have to think about several division problems, which may be harder to do than just listing multiples would be.” 

• Unit 2, Lesson 7, Session 1, Connect It, Problem 2, students use structure of place value to add and subtract decimals. “Place value can help you add or subtract decimals. You add 25.393 and 24.138 to find Mateo’s total time. You can subtract 24.138 from 25.292 to find how much faster Mateo swims the first lap than the second lap. a. How could it help you to line up the decimals on their decimal points? b. What do you need to do before you can subtract the digits in the thousandths place in this problem? Explain. c. Complete the equation: 9 hundredths + 3 thousandths = 8 hundredths + ___ thousandths. d. How much faster is Mateo’s time for the first lap than the second lap. How did you find your answer?”

• Unit 4, Lesson 17, Session 1, Model It, Problem 4 students use structure of fractions to develop understanding of percents . “How is using a model to show a percent similar to using a model to show a fraction? Use either 50% or 10% as an example in your explanation.”

• Unit 5, Lesson 22, Session 2, Try It,  students use variables to represent two quantities in a real-world problem. “An animal reserve is home to 8 meerkats. It costs the reserve $1.50 per day to feed each meerkat. Write an equation with two variables that can be used to determine the total cost of feeding the reserve’s meerkats for any number of days.” Teachers should be asking questions that “prompt students to think about how the Try It problem describes the relationship between quantities and the two variables.” 

There is intentional development of MP8 to meet its full intent in connection to grade-level content.  Examples include: 

• Unit 2, Lesson 9, Session 2, Teacher Edition, Connect to Prior Knowledge, Start, students use repeated reasoning to make generalizations about halves and fourths in a given number. The table lists $\frac{1}{2}$, $1$, $1\frac{1}{2}$, and 2, then identifies how many halves and fourths are in each of those values. Students use the Same and Different routine to compare and contrast the number of halves and fourths using a table. The materials list possible solutions as, “There are a whole number of halves and fourths in all four numbers. There are twice as many fourths as halves in each number. There are different numbers of halves and fourths in the numbers.”

• Unit 3, Beginning of Unit, Math Background, Insights on Finding Equivalent Ratios by Multiplying and Dividing, provides teachers with a background of how students can use repeated reasoning to discover multiplicative relationships. “As students continue to use repeated addition to find equivalent ratios, they may begin to notice that each equivalent ratio is related to the original ratio by multiplication. This realization points to another way of finding equivalent ratios: Multiply both quantities in the ratio by the same nonzero number. Once they have discovered this multiplicative relationship, they can use their prior knowledge of multiplicative comparisons to solve ratio problems.” 

• Unit 4, Lesson 16, Session 2, Apply It, Problem 9, students use ratio and rate reasoning to solve real-world and mathematical problems by solving: “Anica volunteers to fold T-shirts for the runners at a marathon. She folds 8 T-shirts every 6 minutes. At this rate, how many T-shirts does Anica fold in 45 minutes? Show your work.” Teachers should “prompt students to look for the relationships between quantities in a ratio and use fractions and division to find unit rates.” 

• Unit 6, Math in Action, Session 2, Reflect, prompts students to use repeated reasoning to make a connection between elevation and negative numbers at an archeological dig site. “How is the depth of an artifact related to its elevation?” Students are provided with depths of an artifact, in meters, and asked to determine their elevations. 

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development. 

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:

• i-Ready Classroom Central, Preparing for a Unit of Instruction, “Before delivering each unit of instruction, make sure to peruse the unit-level resources in your Teacher’s Guide. Learn about the unit goals by reading the Unit Opener, take note of the vocabulary and language supports, and study the mathematics in the unit by watching the Unit Flow and Progression Video or reading the Math Background pages.” 

  • Program Overview provides the teacher with information on program components and description of i-Ready classroom Mathematics implementation. 

  • Plan is broken down into Unit, Lesson, and Session. 

  • Teach gives information on practice, and differentiation. 

  • Assess includes support for the diagnostic, reports, and data. 

  • Leadership informs the teacher on getting started, building routines, fostering discussions, making connections, and top leader actions. 

• Program Implementation includes numerous supports such as digital math tools, videos, discourse cards, vocabulary, language routines, graphic organizers, games, correlations with standards and practices, etc.

• Each unit has a Beginning of Unit document that provides the teacher with extensive information on Unit Flow and Progression, Unit Resources, Unit Opener, Unit Prepare For, Unit Overview, Lesson Progression, Prerequisites Report Overview, Professional Development, Understanding Content Across Grades, Language Expectations, Math Background, Cumulative Practice, Yearly Pacing for Prerequisites, and Unit Lesson Support. Examples include:

  • Unit Opener, Self Check, “Take a few minutes to have each student independently read through the list of skills. Ask students to consider each skill and check the box if it is a skill they think they already have. Remind students that these skills are likely to all be new to them and that over time, they will be able to check off more and more skills.”

  • Prerequisites Report Overview, “Diagnostic data generates the Prerequisites report, which helps you identify students’ prerequisite learning needs and provides guidance on how to best integrate prerequisite instruction into your grade-level scope and sequence for the year.” These are specific to current students and classes providing valuable data about entry points for students. 

  • Under the Prepare column, there is a Unit and Lesson Support document that provides multiple On-the-Spot Teaching Tips for each Unit. These tips provide information on what to reinforce from prior learning promoting scaffolding to current content.

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Throughout each lesson planning information, there is narrative information to assist the teacher in presenting student materials throughout all phases of the unit and lessons. Examples include:

• Program Implementation, Teaching & Learning Resources, Discourse Cards, provides instruction on how to use the Math Discourse Cards. “These questions and sentence starters provide a way to engage all students in meaningful mathematical conversations. These cards will help students initiate, deepen, and extend conversations with partners, small groups, or the whole class. Each card has two questions or sentence starters on it-one on the front and one on the back. With each question, be sure to have students explain their reasoning for their response.”

• Unit 2, Lesson 8, Session 1, Teacher Edition, Connect It, Problem 3, “How is using the standard algorithm similar to using partial quotients to divide a three-digit number by a one-digit number? How is it different?” The teacher’s edition provides guidance for the teacher in the Exit Ticket, “Look for understanding that the standard algorithm does not use zeros as placeholders in the quotient; instead each part of the quotient is written in its corresponding place value as the division occurs. Error Alert: If students struggle to identify the place value of each digit in the quotient of the standard algorithm and place the digits of the quotient in the wrong position, then have them organize their work on grid paper to maintain alignment. Provide place-value charts so students can match the digits in their quotients to the corresponding place values.”

• Unit 3, Lesson 13, Session 2, Teacher Edition, Apply It, students answer questions about equivalent ratios. The Teacher’s Edition provides guidance for the teacher, “For all problems, encourage students to use a model to support their thinking. Allow some leeway in precision; drawing number lines with equal spacing between tick marks can be difficult, and precise measures are not necessary to determine a solution to the problem.”

• Unit 4, Beginning of Unit, Unit Prepare For, teachers are provided with guidance in using the graphic organizer included for students. This includes guidance in analyzing the term “comparing ratios” and how to build academic vocabulary throughout each lesson in the unit. “Next, have students meet with a partner to share ideas and add new information to the organizer. Circulate and validate responses and clarify any misconceptions.”

• Unit 5, Lesson 22, Session 2, Teacher Edition, Develop, Discuss It, teachers are prompted to support partner discussion. “After students work on Try It, encourage them to respond to Discuss It with a partner. If students need support in getting started, prompt them to ask each other questions such as: In your equation, how did you represent the number of days? The cost for a day? How can you organize the information to find a pattern? How can you test whether your equation makes sense?” Common Misconception: “Listen for students who are not precise when defining variables. For example, students may say d = dollars, instead of d = dollars to feed 8 meerkats for n days. As students share their strategies, have partners discuss and reinforce understandings of variables and the need for precise descriptions of the meaning of variables.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for  containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject. 

The Beginning of Unit section for every unit provides an abundance of information for teachers, including sections to support teachers with adult-level understanding of the content:

• Math Background includes Unit Themes, Prior Knowledge, and Future Learning. In the Math Background, as well as throughout the teacher materials, there are insights on the concepts taught, Common Misconceptions, and Error Alerts to watch for when students are incorrectly applying skills. 

• Lesson Progression links each lesson within the current unit to a prior and future lesson so teachers know what students need to know to be successful with the current work as well as what the current work is preparing students for. This is important for a teacher’s complete understanding of how to scaffold and bridge the current content. For example, Unit 3, Lesson 13, Lesson Overview, Teacher Edition, Find Equivalent Ratios - Full Lesson, Learning Progression:

  • “In Grade 5, students extended their use of multiplication to scale a quantity, which means to increase or decrease by multiplying a factor. In the previous lesson, students were introduced to the concept of ratio, ratio notation, and ratio language. They compared quantities and examined relationships using ratios. 

  • In this lesson, students merge their understanding of multiplication as scaling and ratio concepts to identify and generate equivalent ratios. Students find missing values in tables of equivalent ratios and solve problems using double number lines or tables. They represent ratios as ordered pairs and then graph them as points in the coordinate plane. 

  • Later in Grade 6, students will use tables to compare ratios, and they will apply their understanding of ratio to the ideas of rate and unit rate. They will analyze relationships between dependent and independent variables using graphs. In Grade 7, students will apply ratio reasoning to explore proportional relationships and calculate probabilities.”

• Understanding Content Across Grades provides explanations of instructional practices as well as information about necessary prior knowledge and concepts beyond the current course for teachers to improve their own knowledge of the subject. For example, Unit 2, Beginning of Unit, Understanding Content Across Grades related to Lesson 7:

  • Prior Knowledge: “Insights on: Adding and Subtracting Decimals. Students learn to add and subtract decimals using the same variety of models and strategies they used to add and subtract whole numbers. Common Error - When students add and subtract decimals using the standard algorithm, they may line the numbers up by the end digits, rather than by place- value. A place-value chart is an excellent tool to help students focus on the value of each digit.” This information is accompanied by example problems worked out using a number line, a 100s place value grid, and the algorithm. 

  • Current Lesson, “Insights on: Adding, Subtracting, and Multiplying Decimals. Multiplying Decimals - When multiplying decimals, students use both decimal and fractional forms of the factors to make sense of the placement of the decimal point in the product.” This information is accompanied by an example problem worked out using the relationship between decimals and fractions to understand decimal multiplication.

  • Future Learning, “Insights on… Understanding addition with positive and negative numbers. Students use integer chips to observe a key difference between adding two numbers with different signs and adding two numbers with the same sign. When the addends have different signs, they can cancel out zero pairs. When the addends have the same sign, all the chips are of the same type, so there are no zero pairs.” This is accompanied by an example problem solved using integer chips.

• Each lesson includes a Reteach section with several pages called “Tools for Instruction” that provide explicit teacher guidance related to the current work and to prerequisite skills. These pages include adult explanations, step-by-step guidance for teaching, and check for understanding. For example, Unit 6, Lesson 24, Compare Positive and Negative Rational Numbers:

  • “Rational numbers are numbers that can be written as fractions. The set includes whole numbers and fractions, as well as terminating and repeating decimals, both positive and negative. Students will be familiar with number lines from early grades… Concepts such as temperature, money in a bank account, and depth below or height above sea level give context to negative numbers… Using the number line provides a base for understanding positive and negative rational numbers and operations, absolute value, and the use of all quadrants of the coordinate plane.”

  • “Step by Step: 1) Create a number line. Have the students draw a vertical number line from -10 to 10. Ask the student to draw a horizontal line at zero across the number line. Tell the student to imagine that the horizontal line is the surface of the ground. The negative numbers are below ground, and the positive numbers are above ground. 2) Compare integers on the number line. (followed by three prompts) 3) Compare positive and negative decimals. (followed by two prompts) 4) Compare positive and negative fractions. (followed by two prompts)”

  • “Check for Understanding: Have the student use the “greater than” symbol to compare -18 and -16.” Then an error analysis chart is provided: “If you observe… the student may… Then try…”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

In Program Implementation, correlation information is present for the mathematics standards addressed throughout the grade level using multiple perspectives. For example: 

• The Correlations document for Content Focus in the Common Core State Standards (CCSS) describes lesson correlation to the CCSSM through multiple lenses. The document identifies the major and supporting areas of focus within the CCSSM and corresponding lessons that address those standards. Additionally, a table is provided that correlates each lesson with the standards addressed, designating standards as “Focus”, “Developing”, or “Applied” within each lesson. 

• The Correlations Document also identifies the Standards of Mathematical Practice that are included in each lesson; one table is organized by MP, and another is organized by lesson. 

• The Unit Review Correlation identifies the associated standard and lesson to each problem within the Unit Review, along with their Depth of Knowledge level. 

• Digital Resource Correlations, Comprehension Check Correlations, and Cumulative Practice Correlations identify the lesson and a statement of the part of the standard it aligns to. 

• The WIDA PRIME V2 correlates the WIDA Standards Framework to examples in the material with descriptions of how they connect. 

• The English Language Arts Correlations provides a table that offers evidence of how the Common Core State Standards for English Language Arts are supported in every lesson and unit of the i-Ready Classroom Mathematics material.

In each Beginning of Unit section, there are numerous documents provided that contain explanations of the role of the specific grade-level mathematics in the context of the series. For example: 

• The Lesson Progression provides a flow chart delineating how each standard in the current lesson builds upon the previous grade levels and connects to future grade levels. This is developed in detail with examples in the Understanding Content Across Grades document. 

• There is a Unit Flow and Progression video for teachers that provides background about the content covered in the unit. 

• The Unit and Lesson Support document provides descriptions of the standards addressed in each unit with connections to prerequisites and teaching tips about prior knowledge. For example, Unit 2, Beginning of Unit, Unit and Lesson Support, the opening narrative provides the content of the unit, “In this unit, students use what they know about adding, subtracting, and multiplying decimals to hundredths to extend their understanding of computing with decimals. They learn the standard algorithm for whole number and decimal division and use both visual models and equations to divide with fractions. They will also build on their prior understanding of volume and of multiplying with fractions to find volumes of rectangular prisms with fractional side lengths.” The document continues with Instructional Support identifying specific lessons from prior grades to develop understanding, such as Unit 2, Lesson 8, “These lessons build on students’ work with multiplying fractions and dividing unit fractions in Grade 5, Unit 3: Grade 5, Lesson 22 - Multiply Fractions in Word Problems.”

• In every teacher's Lesson Overview, the Learning Progression identifies how the standard is addressed in earlier grades, in the current lesson, next lesson, and in the next grade level. For example, Unit 4, Lesson 17, Overview, Learning Progression, “In earlier grades, students used models to represent, write, and identify equivalent fractions. Earlier in Grade 6, students generated and identified equivalent ratios… In this lesson, students understand that a percent is a special type of rate in which the second quantity is 1 unit that is divided into 100 equal parts… In the next lesson, students will use their understanding of percents and models of percents to find the percent of a number and to find the whole when a percent and part are known. In Grade 7, students will choose to represent percents as fractions or decimals as they solve a variety of percent problems.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

There are thorough explanations about the instructional approaches of the program. These are easily found under Program Implementation and in Classroom Central. For example:

• Program Implementation contains “Try-Discuss-Connect Routine Resources.” This routine is embedded throughout the program, “i-Ready Classroom Mathematics empowers all students to own their learning through a discourse-based instructional routine. Lessons are divided into Explore, Develop, and Refine sessions and are taught over the course of a week. In Explore and Develop sessions teachers facilitate mathematical discourse through a Try-Discuss- Connect instructional routine.” In i-Ready Classroom Central, there are videos modeling the six steps of the Try-Discuss-Connect routine as well as an Exit Ticket.

• Program Implementation, User Guide, Protocols for Engagement describes multiple protocols and identifies the traits each protocol validates to help all students “feel accepted and included.” Further, “Protocols provide structure for activities so that all students have a chance to think, talk, and participate equally in classroom activities. Each protocol incorporates modes of communication common to one or more culture and leverages those behaviors for a particular instructional purpose.” For example, “Stand and Share: Students stand when they have something to share with the class. Validates: spontaneity, movement, subjectively, connectedness.” Protocols can be found in the Lesson Overview section of the Teacher Guide.

• Program Implementation, i-Ready Classroom Central, Building Community, Promote Collaborative Learning, has resources such as using Lesson 0 to introduce the Try-Discuss-Connect Routine and language routines, questions to support discourse, videos about sharing math ideas, ideas for promoting mathematical practices, and creating a positive mindset. 

• Program Implementation, i-Ready Classroom Central, has a link in the upper right under the search box called Explore the Resources page that has all of the additional resources organized in a list of links by category that provide abundant information, including a section called Program Overview.

Materials include relevant research sources. In Program Implementation, Supporting Research, “i-Ready Classroom Mathematics is built on research from a variety of federal initiatives, national mathematics organizations, and experts in mathematics.” A table describes 16 concepts that are embedded in the program with examples of how and where each is used, an excerpt from the research that supports it, as well as an extensive reference list. Examples include: 

• “The Concrete-Representational-Abstract (CRA) Model is a three-part instructional model that enhances students’ mathematical learning.” This model is built into all i-Ready Classroom Mathematics lessons in the Try It, Discuss It, Connect It, and Hands-On Activities. “Using and connecting representations leads students to deeper understanding. Different representations, including concrete models, pictures, words, and numbers, should be introduced, discussed, and connected to support students in explaining their thinking and reasoning.” (Clements and Sarama, 2014)

• “Collaborative learning (partner or small group) encourages students to present and defend their ideas, make sense of and critique the ideas of others, and refine and amend their approaches.” Lessons provide multiple opportunities for collaborative learning during Discuss It and Pair/Share. “Research tells us that when students work collaboratively, which also gives them opportunities to see and understand mathematics connections, equitable outcomes result.” (Boaler, 2016)

• “An instructional framework supports students in achieving mathematical proficiency and rigor within a collaborative structure to develop greater understanding of how to reason mathematically.” The Try-Discuss-Connect instructional framework is foundational in this program. “Instructional routines are situated in the learning opportunity itself, providing students with a predictable frame for engaging with the content…”  (Kelemanik, Lucenta, & Creighton, 2016)

• Program Implementation, User Guide, Routines that Empower Students identifies 9 research-based language routines. Each routine includes the purpose, the process, and which part of the Try-Discuss-Connect Routine it can be used with. For example, Say It Another Way is used with Try It, “Why: This routine helps students paraphrase a word problem or text so they know if they have understood it. It provides an opportunity to self-correct or to ask for clarification and ensures that the class hears the problem or story more than once and in more than one way.”

• Program Implementation, i-Ready Classroom Central, Explore the Resources page (near search box), Program Overview,Building Effective Mathematics Teaching Practices within Classrooms, explains how NCTM’s Effective Teaching Practices are integrated into i‑Ready Classroom Mathematics. “When teachers use the program with integrity… they naturally engage in the Top Teacher Actions. This ensures students have access to high-quality mathematics instruction every day… The intentional design of the Teacher’s Guide provides teachers with the opportunity to consistently implement NCTM’s Teaching Practices each day.”

The materials reviewed for i-Ready Mathematics, Grade 6 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. 

The Lesson Overview for the teacher provides a Materials Required column for each lesson on the Pacing Guide; additional materials are listed in the Differentiation column. Any materials that need to be printed are also provided in the Overview, such as grid paper or double number lines. For example:

• Unit 3, Lesson 13, Session 1, “Materials tab: Math Toolkit connecting cubes, counters, grid paper, Presentation Slides. Differentiation tab: 25 two-color counters per group.”

Under Program Implementation, a Manipulatives List provides a document identifying manipulatives needed for each lesson K-8. For example: 

• “Manipulatives List, Unit 3, Lesson 13, identifies connecting cubes - 60 per pair, and counters - 60 per pair.”

Program Implementation also includes digital math tools, discourse cards and cubes, activity sheets, data sets, and graphic organizers.

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

In the Teacher Toolbox, each lesson includes Assess which provides Lesson Quizzes & Unit Assessments. Lesson Quizzes, Teacher Guide lists information for each problem: tested skills, content standards, mathematical practice standards, DOK levels, error alerts, problem notes, Short Response Scoring Rubric with points and corresponding expectations, and completed problems. For example:

• Unit 5, Lesson 20, Lesson Quiz, Problem 2, “DOK 1, 6.EE.B.5, SMP 2.”

Assess, End of Unit, Unit Assessments, Teacher Guide, Forms A and B are provided and include the content item with a solution. Form A includes Problem Notes, completed problems, DOK levels, content standards, mathematical practices, Scoring Guide, Scoring Rubrics, and Responding to Student Needs. Form B appears to parallel all of the correlations provided for Form A, though it is not labeled. It is noted in the Scoring Guide, “For the problems in the Unit 4 Unit Assessments (Forms A and B), the table shows: depth of knowledge (DOK) level, points for scoring, lesson assessed by each problem, and both the CCSS standard and Mathematical Practice Standards addressed.” For example:

• Unit 1, End of Unit, Assess, Unit Assessment, Form A, Scoring Guide, Problem 5, “DOK 2, 6.G.A.1, SMP 6.”

• Unit 7, End of Unit, Assess, Unit Assessment, Form A, Scoring Guide, Problem 12, “DOK 2, 6.SP.A.2, SMP 7.”

Digital Comprehension Checks “can be given as an alternative to the print Unit Assessment. For this comprehension check, the table below provides the Depth of Knowledge (DOK), standard assessed, and the corresponding lesson assessed by each problem.” While the Comprehension Checks identify the content standards, they do not identify the mathematical practices. For example:

• Unit 1, End of Unit, Assess, Comprehension Check Correlation Guide, Problem 5, “DOK 2, 6.G.A.1.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

The assessment system provides opportunities to determine students’ learning that include teacher support for interpreting student performance in the Problem Notes and Rubrics provided, though the rubrics are generic rather than specific to the lesson. Examples include:

• Problem Notes for each problem in the Lesson Quizzes and Form A of the Unit Assessment provide guidance on steps to solve the problem and what students may have done incorrectly. For example:

  • Unit 1, Lesson 5, Assess, Lesson Quiz, Problem 2, “C is correct. Students could solve the problem by identifying that there are 2 additional factors of 3 in $3^{21}$, and $3\times3=9$. A is not correct. This answer represents the difference between the exponents. $21-19=2$. B is not correct. This answer represents the repeated factor instead of the product of the repeated factors. D is not correct. This answer represents three factors of 3 instead of two factors of 3.”

  • Unit 6, End of Unit, Assess, Unit Assessment, Form A, Problem 6, “Students could also solve the problem by considering the placement of each layaway balance on the number line and identifying the balance that is farthest from 0.” 

• Lesson Quizzes contain a Fill-in-the-Blank/Multiple Select/Choice Matrix Scoring Rubric and a Short Response Scoring Rubric. The Fill-in-the-Blank/Multiple Select/Choice Matrix Scoring Rubric states: “2 points if all answers are correct, 1 point if there is 1 incorrect answer, and 0 points if there are 2 or more incorrect answers.” The Short Response Scoring Rubric states: 2 points if the “Response has the correct solution and includes well-organized, clear and concise work demonstrating thorough understanding of mathematical concepts and/or procedures.” 1 point for “Response contains mostly correct solution(s) and shows partial understanding of mathematical concepts and/or procedures.” 0 points if the “Response shows no attempt at finding a solution and no effort to demonstrate an understanding of the mathematical concepts and/or procedures.”

• Unit Assessments contain the Extended Response Scoring Rubric (if there is an extended response question included in the assessment), Short Response Scoring Rubric, and a rubric for Fill-in-the-Blank/Multiple Select/Choice Matrix. For example, the Extended Response Scoring Rubric, a response should earn 4 points if, “Response has the correct solution(s) and includes well-organized, clear and concise work demonstrating thorough understanding of mathematical concepts and/or procedures.” This same expectation scores a 2 on the Short Response Scoring Rubric. The Fill-in-the-Blank/Multiple Select/Choice Matrix Scoring Rubric is the same as the Lesson Quizzes.

The Lesson Quizzes and Unit Assessments provide sufficient guidance to teachers to follow-up with students, although there is no follow-up guidance for the Comprehension Checks. The follow up suggestions reference previous work rather than new material. For example:

• Unit 2, Lesson 10, Assess, Lesson Quiz provides three types of differentiation for possible follow up depending on student performance: Reteach, Reinforce, and Extend. “Reteach: Tools for Instruction, Students who require additional support for prerequisite or on-level skills will benefit from activities that provide targeted skills instruction. Grade. Reinforce: Math Center Activity, Students who require practice to reinforce concepts and skills and deepen understanding will benefit from small group collaborative games and activities (available in on-level, below-level, and above-level versions). Extend: Enrichment Activity, Students who have achieved proficiency with concepts and skills and are ready for additional challenges will benefit from group collaborative games and activities that extend understanding.” The Reteach section directs teachers back to Lesson 10, Divide Fractions. The Reinforce section directs teachers back to Lesson 10, Use Fraction Division. The Extend section directs teachers back to Lesson 10, Pumpkin Pairs.

• Unit 2, End of Unit, Assess, Unit Assessment, Form A, provides a section called Responding to Student Needs. This section directs teachers back to the relevant lessons for review and where teachers can access the Review, Reinforce, and Extend options. “For students who answer problems incorrectly on the Unit Assessment, choose from the following resources on the Teacher Toolbox for additional support.””Reteach: Tools for Instruction, Multiply Multi-Digit Decimals (Lesson 7), Divide Multi-Digit Decimals (Lesson 8), Understand Division with Fractions (Lesson 9), Divide Fractions (Lesson 10). For students who exceed proficiency on the Unit Assessment, choose from the following activities on the Teacher Toolbox.””Extend: Enrichment Activities, Tacos for All! (Lesson 9), Pumpkin Pairs (Lesson 10), Turn Down the Volume (Lesson 11).”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. 

There are formative and summative assessments provided as PDFs as well as comparable assessments provided online. Lesson Quizzes and Unit Assessments provided include a variety of item types for students to demonstrate grade-level expectations. For example:

• Fill-in-the-blank

• Multiple select

• Matching

• Graphing

• Constructed response (short and extended responses)

• Technology-enhanced items, e.g., drag and drop, drop-down menus, matching 

Throughout the lessons, there are opportunities to demonstrate critical thinking, develop arguments, or apply learning in a performance task, though these are not typically on the assessments.

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

• i-Ready Classroom Central, Teach, Differentiate, has information to support the teacher in planning for all special populations. Address Unfinished Learning provides multiple links to guidance resources, data analysis resources, and instructional resources. i-Ready Personalized Instruction has resources for students who have taken the Diagnostic and will have access to online learning and instructional paths tailored to their individual needs to reinforce prerequisite skills and build grade-level skills. Support Every Learner, “Every student can excel in mathematics with the right supports. Access these resources to find ideas and strategies for organizing groups and adapting your instruction to meet the unique needs and learning styles of all students.” There are seven links related to grouping students and adapting instruction. For example:

  • Reference Sheet: Supporting Differentiated Needs before the Unit or Lesson is a 4-page document with numerous strategies including addressing prerequisites, integrating assessments, supporting English learners, and differentiating that links to practice, games, enrichment, literacy, tutorials, and more.

  • Reference Sheet: Supplemental Tools for Accessible Mathematics Instruction is a 5-page table that provides support ideas for every aspect of the lesson. For example, during Try It, a suggested support is, “Offer multiple means of representation, engagement, and action and expression such as: highlight important numbers, words, and phrases; Invite volunteers to act out the problem for the class; Offer options for how students express their ideas.” During Discuss It, “Use hand signals to agree, disagree, or share an idea.”

• In Refine, the last session of each lesson, the teacher’s edition provides suggestions to Group & Differentiate, “Identify groupings for differentiation based on the Start and problems 1-3. A recommended sequence of activities for each group is suggested below. Use the resources on the next page to differentiate and close the lesson.” Resources are suggested for groups Approaching Proficiency, Meeting Proficiency, and Extending Beyond Proficiency. 

• At the end of the Lesson Quiz in the teacher’s edition, there is a section for differentiation that provides suggestions for Reteach (Tools for Instruction), Reinforce (Math Center Activity), and Extend (Enrichment Activity). Reteach, “Students who require additional support for prerequisite or on-level skills will benefit from activities that provide targeted skills instruction.” Reinforce, “Students who require practice to reinforce concepts and skills and deepen understanding will benefit from small group collaborative games and activities (available on-level, below-level, and above-level versions).” Extend, “Students who have achieved proficiency with concepts and skills and are ready for additional challenges will benefit from group collaborative games and activities that extend understanding.” 

• Program Implementation, i-Ready Classroom Central, Differentiate, Support Every Learner, Reference Sheet: Supplemental Tools for Accessible Mathematics Instruction, Accessibility and Accommodations with i-Ready Classroom Mathematics, Accessibility and Accommodations Update document which states, “To make i-Ready Classroom Mathematics accessible to the widest population of students, we offer a range of accessibility supports that may also meet the requirements of a number of student accommodations.” The table provided lists the Universal Supports, Designated Supports, and Accommodations that are both embedded and not embedded in the program. For example, embedded supports include audio support, closed captioning, calculator, zoom in/out, highlighting, and more. Available non-embedded supports include native language translation of directions, noise buffer, alternate response options, scribe, and more.

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity. 

• Each lesson has an Extend: Enrichment Activities column that provides a challenge task. For example, Unit 1, Lesson 2, Extend, Building Shapes, students are provided with a challenge question, “How can you build different polygons with given areas using triangles, rectangles, and parallelograms?” followed by related tasks such as, “What is the fewest number of triangles needed to build a 4-sided polygon with an area of 12 square units? Explain. Draw one possible way to do this.”

• Refine sessions at the end of each lesson provide recommendations for students that demonstrate understanding “Extending Beyond Proficiency” to engage in problems for reinforcement and a challenge. The number of problems is the same as the work for students who are considered to be “Meeting Proficiency.” Additional Enrichment Activities can be found online in the Small Group Differentiation Extend section. In addition, Refine sessions include at least one problem identified as DOK 3 where students utilize strategic thinking. 

• In Explore and Develop sessions in each lesson, the materials contain Differentiation: Extend, Deepen Understanding or Challenge for the lesson’s key concepts through the use of discourse with students. For example, Unit 5, Lesson 21, Session 3, Teacher Guide, Differentiation: Extend, Deepen Understanding, “Prompt students to compare differences between a hanger diagram for an addition equation and one for a multiplication equation...Ask: In what situations could a hanger diagram be used to represent addition or multiplication? When could it only represent addition?”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing strategies and support for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics. Examples include: 

• Program Implementation, i-Ready Classroom Central, Differentiate, Support All Learners, Reference Sheet: Supports for English Learners explains where to find and how to use all of the supports built into the Teacher Guide for every lesson to “address the strengths and needs of ELs” such as, Build Your Vocabulary, Connect Language Development to Mathematics, Language Objectives, Connect to Community and Cultural Responsiveness, and Connect to Language Development.

• Program Implementation, Program Overview, Integrate Language and Mathematics shows where teachers can access tips for targeted support using Language Routines in the Teacher Guide for every lesson.

• Program Implementation, Program Overview, Language Development and Discourse Support provides “support at the word/phrase, sentence, and discourse levels so that all students can engage in rigorous mathematics and communicate effectively.”

• Program Implementation, User Guide, Resources for Language Development describes nine features that are embedded in the teacher materials to “build academic language of all students, especially English learners. These supports help students learn how to communicate effectively across the language domains.”

• Program Implementation, User Guide, Routines that Empower Students provides nine language routines. “While these routines support English learners, they are designed to be used by all students as they access mathematical concepts and their growing mathematical understanding.” Three routines, in particular, are differentiated for English Learners: Act it Out, Co-Constructed Word Banks, and Stronger and Clearer Each Time. 

• Program Implementation, User Guide, Support for Academic Discourse describes “a variety of ways to support students in communicating with academic and math-specific vocabulary and language.”

• Program Implementation, Discourse Cards provide sentence starters and questions to help students engage in conversations with their partners, small groups, or the whole class such as, “Did anyone get a different answer?; What would you add to what was said?”

• All classroom materials are available in Spanish.

• Program Implementation, Multilingual Glossary is available in Arabic, Chinese, Haitian Creole, Portuguese, Russian, Tagalog, Urdu, and Vietnamese. There is a Bilingual glossary in the student textbook that includes mathematics vocabulary in English and Spanish.

• Beginning of Unit, Language Expectations is a chart that “shows examples of what English Learners at different levels of English language proficiency can do in connection with one of the Common Core State Standards (CCSS) addressed in this unit. As you plan for this unit, use these examples of language expectations to help you differentiate instruction to meet the needs of English Learners.”

• Beginning of Unit, Unit Prepare For, Build Academic Vocabulary includes a chart of academic words for the units paired with their Spanish cognates. There are three routines provided in Professional Development to support vocabulary development: Academic Vocabulary, Cognate Support, and Collect and Display. 

• Each lesson in Lesson Overview, Teacher Guide’s Full Lesson includes Language Objectives, Connect to Culture, and Connect to Language. 

• Session 1 of every lesson uses graphic organizers to help students access prior knowledge and vocabulary they will develop in the lesson. Support for Academic language is used during the “Try-Discuss-Connect Language” routines in each lesson. 

• All sessions throughout the lesson embed support including references back to previously listed items.

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Students have access to both virtual and physical manipulatives throughout the program. For example:

• Program Implementation, Digital Tools are available for students. These tools include Counters and Connecting Cubes, Base-Ten Blocks, Number Line, Multiplication Models, Perimeter and Area, and Fraction Models. Geometry Tool, Scientific Calculator, and Graphing Calculator. Also in Program Implementation, support videos are available for each of the digital tools, explaining how they may be used and their functions. 

• Program Implementation, Manipulative Kit includes algebra tiles, plastic rulers, centimeter cubes, base ten blocks, number cubes, rainbow color tiles, two color counters, and connecting cubes. A la carte items are available. The materials state that these items may only be used once, may be common to classrooms, or print options are available. A la carte items include fraction bars, tangrams, geoboards, geosolids, and rainbow fraction circle sets. 

• Program Implementation, Manipulative List by Lesson has specific manipulatives listed for each lesson. For example, Unit 6, Lesson 24 lists 1 Set of Algebra Tiles, 20 Two-color counters, and 1 Number cube per pair. There is also a Manipulative Suggestions for At-Home Use document that provides ideas for using items commonly found at home or easily created that could be used in place of the actual manipulative (e.g. Attribute Buttons and Connecting Cubes could both be replaced with Lego bricks). 

• Program Implementation, Activity Sheet Resources includes a 52-page document full of visual models such as number lines, graphs, grid paper, nets, graphic organizers, etc. These are also provided as a link in lessons where they would be expected to be a helpful resource. 

Program Implementation, Try-Discuss-Connect Routine Resources, Understanding the Try-Discuss-Connect Instructional Routine, the foundational “Try-Discuss-Connect” routine is designed to “encourage proficiency and rigor within a collaborative structure.” A primary purpose is to “expose students to a number of representations and approaches” to help them make connections, develop mathematical language and thinking, and improve written and oral communication skills. This routine helps students transition from manipulatives to written methods. For example: 

• In the Try It activity, “students have access to a variety of tools and manipulatives to use to represent the problem situation.” During the Discuss It activity, “Students present and explain their solution methods and listen to and critique the reasoning of others, models and representations.” During the Connect It activity, “Students write their answers to Connect It questions independently (or in pairs to support language production, as needed) to solidify understanding and make further connections.” 

• “Tip: If students are struggling with writing responses…. have multiple students share answers orally while writing key words or phrases on the board. Have students use these key words and phrases to write their own response to the question in their worktexts.”

• “Tip: Encourage students to represent and solve problems in more than one way to build flexibility in their thinking.”

The “Try-Discuss-Connect” routine also integrates the Concrete-Representational-Abstract (CRA) model, for example:

• Try It, “Students may use concrete, representational, or abstract strategies to solve the problem, based on their understanding of the problem or mathematical concept.”

• Discuss It, “Students who use more concrete approaches begin to make connections to representational or abstract approaches as they engage in partner discussions.”

• Connect It, “Through the Connect It questions, students connect concrete and representational approaches to more abstract understanding as they formalize their connections.”