## Alignment: Overall Summary

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence, and in Gateway 2, the materials meet expectations for rigor and practice-content connections.

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## Gateway 1:

### Focus & Coherence

0
7
12
14
13
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
18
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

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## Gateway 3:

### Usability

0
22
31
38
25
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

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Gateway One Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for focus and coherence. For focus, the materials assess grade-level content and spend at least 65% of class time on major work of the grade, and for coherence, the materials have supporting content that enhances focus and coherence, an amount of content designated for one grade level that is viable for one school year, and foster coherence through connections at a single grade.

### Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
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Criterion Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for not assessing topics before the grade level in which the topic should be introduced. Overall, the materials assess grade-level content and, if applicable, content from earlier grades.

### Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meets expectations for assessing grade-level content.

The materials are organized by the Domains and Clusters delineated by CCSS. Each Cluster has a Milestone Assessment, and all assessments include multiple choice and/or multiple select. The assessments are aligned to grade-level standards, and examples include:

• In Milestone Assessment 5.MD.C, Question 16 states, “Select the units that represent volume. Select all that apply. a) square centimeters ; b) $$ft^2$$ ; c) inches ; d) $$mm^3$$.
• In Milestone Assessment 5.OA.A, Question 1 states, “Where can parentheses be placed in the following expression to make it equivalent to 33? $$5+4×10-3$$. a) $$(5 + 4) × 10 - 3$$ ; b) $$5 + (4×10) - 3$$ ;  c) $$5+4×(10-3)$$ ;  d) No parentheses needed.”
• In Milestone Assessment 5.NBT.A, Question 9 states, “Which decimal is between 4.2 and 4.3?  a) 4.24;  b) 4.03;  c) 4.17; d) 4.32.”
• In Milestone Assessment 5.NF.B, Question 16 states, “Lizette is making friendship bracelets out of string. Each bracelet requires $$\frac{1}{6}$$ yard of string, and she has 8 yards of string. She plans to sell each bracelet for $2. If she uses all of her string and sells every bracelet she makes, how much money will she have? a)$48 ; b) $96 ; c)$84 ; d) $56.” ### Criterion 1b Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade. 4/4 + - Criterion Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for devoting the majority of class time to the major work of the grade. Overall, the materials spend at least 65% of class time on major work of the grade. ### Indicator 1b Instructional material spends the majority of class time on the major cluster of each grade. 4/4 + - Indicator Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for spending a majority of instructional time on major work of the grade. • The approximate number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 126 out of 178, which is approximately 71%. • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 24 out of 33 lessons, which is approximately 73%. • The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is 25 out of 36, which is approximately 69%. A day level analysis is most representative of the instructional materials because this represents the class time that is devoted to major work of the grade including reviews, domain intensives, and assessments. As a result, approximately 71% of the instructional materials focus on major work of the grade. ### Criterion 1c - 1f Coherence: Each grade's instructional materials are coherent and consistent with the Standards. 7/8 + - Criterion Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for coherence. The materials have supporting content that enhances focus and coherence, an amount of content designated for one grade level that is viable for one school year, and foster coherence through connections at a single grade. The materials are partially consistent with the progressions in the Standards. ### Indicator 1c Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 2/2 + - Indicator Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. Examples of connections between supporting content and major work of the grade include: • 5.MD.A.1, Treacle Treatment connects to 5.NBT.7 and 5.NF.2 as students convert measurements that involve operations with decimals and fractions. In the Practice Printable, Question 4 states, “The total weight of three kittens is 14 ounces. Kitten 1 weighs $$\frac{1}{4}$$ pound. Kitten 2 weighs 5.5 ounces. How many ounces does Kitten 3 weigh?” • 5.MD.B.2, Anesthesia Outcome connects to 5.NF.4 as students complete problems using operations with fractions using data they’ve plotted on a line graph. In the Practice Printable, Question 1 states, “The data shows the weight of the largest watermelons featured at the county fair this year. All measurements are rounded to the nearest $$\frac{1}{4}$$ pound. a) Complete the line plot displaying the watermelon weights. b) “How much do the three heaviest watermelons weigh all together?” • 5.MD.C.5c, Polly Packs connects to 5.OA.A as students write and evaluate expressions to solve volume problems. In the Practice Printable, Questions 4-6 state, students see a graphic of an irregular shape and “calculate the total volume of each figure”. Question 4 is a 3-dimensional “L” with 5 side measurements identified. Students are expected to break the shape into rectangular prisms to determine the volume. ### Indicator 1d The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades. 2/2 + - Indicator Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations that the amount of content designated for one grade level is viable for one year. The suggested amount of time and expectations for teachers and students of the materials is viable for one school year as written and would not require significant modifications. As designed, the instructional materials, with assessments, can be completed in 145-178 days. • There are five domains which contain a total of 33 lessons. Lessons are designed to take three to four days each, leading to a total of 99-132 lesson days. • There are 15 days for Major Cluster Intensives. • There are 31 assessment days including 10 days for review, 10 spiral review days in the Distributed Practice Modules, and 11 Milestone Assessments. The Scope and Sequence Chart in the Teacher Edition provides pacing information. A lesson is designed for 60 minutes. ### Indicator 1e Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades. 1/2 + - Indicator Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 partially meet expectations for being consistent with the progressions in the standards. The instructional materials clearly identify content from prior and future grade levels and use it to support the progressions of the grade-level standards. In the Detailed Lesson Plan, prerequisite standards are identified in every Lesson Plan Overview. Examples include: • 5.NF.B.3, Much Ado About Honey identifies “Prerequisite Standards 3.OA, 4.MD, 4.OA” and Cluster Connections including “Direct Connection: In Much Ado About Honey, the fairies use five jars of honey as a visual fraction model to show how to divide a whole number by a whole number. Cross-Cluster Connection: This activity connects 5.NF.B to 6.RP.A as students will calculate unit rate from rates in the $$\frac{a}{b}$$.” • In 5.G.A.1, Avalanche Rescue Training, the Cross-Cluster Connection states, “This activity connects 5.G to 6.NS, 7.RP, 8.EE, 8.G and 8.F as it provides students with the foundation necessary for future work with the coordinate plane as it relates to graphs of proportional and nonproportional relationships, functions and transformations.” The instructional materials do not always attend to the full intent of the grade-level standards. Each lesson addresses one grade-level standard and no standard is absent from the materials. Lessons are three to four days long, and all students complete the same work. However, there are limited opportunities within each lesson to practice the content of the standards. Opportunities for practice include: Math Simulator, one to four questions; Practice Printable typically has six to ten questions; Clicker Quizzes include six questions; and the teacher can assign a specific domain in Test Trainer Pro. Since all standards are given the same attention, students have limited opportunities to engage in extensive work with grade-level problems to meet the full intent of all grade-level standards. Examples where the full intent is not attended to include: • In 5.NF.A.2, Acre Acquisition, students do not use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. In the Practice Printable there is only one problem that has includes estimating with a benchmark fraction and none that have students justify reasonableness, Question 3, “Jackson and Loren decided to grow their hair out all summer. Jackson’s hair grew $$\frac{5}{12}$$ of an inch, while Loren’s grew $$\frac{3}{4}$$ of an inch. How can you use benchmark fractions to easily tell whose hair grew more over the summer?” • In 5.NBT.2, The Power of 10!, students do not explain patterns of zeros of the product when multiplying a number by powers of 10, nor do students explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. There are no problems in the Practice Printable that require students to explain any process or pattern. The Test Trainer Pro and Simulation Trainer are designed to provide additional, grade-level work, but all of the items for these two features are not available for review. • In Test Trainer Pro, primarily used as a daily warm-up, there is no way for teachers to assign specific content other than a domain of standards. • In Simulation Trainer, the content matches the lesson, but students can provide any number as an answer, then watch the steps worked out (no words) in a solution video. They’re presented with the same question again and can put in the correct answer, then watch the same solution again. If they get it correct the first time, they also watch the solution video. The next questions are not novel, but the same situation with new numbers. If students miss one, it resets them to the beginning, no matter where they were in the assignment. It is possible that some students would never complete a Simulation Trainer. The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. In the Detailed Lesson Plan for every lesson under the Lesson Plan Overview, the Cluster Connection—Cross-Cluster Connection— includes an explanation on how prior learning connects to grade-level work. Examples include: • In 5.MD.C.4, Shipment Shenanigans activity states, “This activity connects 5.MD.C to 3.MD.C as students build upon their knowledge of measuring areas by counting unit squares to develop an understanding of volume by counting unit cubes.” • In 5.NF.A.1, Hay, students use knowledge from Grade 4 about equivalent fractions. Practice Printable Questions one through four state, “For each set of fractions, write equivalent replacement fractions with a common denominator.” • Prior learning is referenced in Lesson Notes such as in 5.MD.A.1, Treacle Treatment, in the Instructions, At a Glance, Gladys states, “Your students will connect measurement and conversion skills learned previously in 4.MD.A.1 to the content of this standard.” ### Indicator 1f Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. 2/2 + - Indicator Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. There are no student learning targets/objectives labeled as such. However, since each lesson has a specific standard in its title that is also referenced during the lesson, these “objectives” are visibly shaped by the CCSSM cluster headings. Examples include: • The objective of lesson 5.OA.A.1 states, “Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols,” is shaped by 5.OA.A, “Write and interpret numerical expressions.” • The objective of lesson 5.NF.B.5 states, “Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication,” is shaped by 5.NF.B, “Apply and extend previous understandings of multiplication and division to multiply and divide fractions.” • The objective of lesson 5.MD.C.4 states, “Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units,” is shaped by 5.MD.C, “Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.” Examples of problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important include: • In 5.MD.C.5b, Phil & Ned’s Excellent Assignment, the major work of cluster 5.MD.C connects to the major work of 5.NBT.B as students solve volume problems involving multi-digit numbers and decimals. In the Practice Printable, Question 2 states, “Joshua is making a pan of fruit gel. He needs to add 150 inches of hot water to the gelatin. The rectangular pan has a length of 10 inches, a width of 7 inches and a height of 2 inches. Will there be enough room in the pan to add the water?” • In 5.NF.B.4a, The Horse Doctor, the major work of cluster 5.NF.B connects to the major work of 5.NBT.B as students apply their understanding of multiplication and division of fractions to problems involving operations on multi-digit numbers and decimals. The teacher example states, “$$\frac{4}{5}$$ means we will take 4 parts of the whole when it is divided into 5 equal parts. 2 hours (or 120 minutes) divided into 5 parts is 24 minutes per part. 4 of those parts is 96 minutes.” • In 5.MD.C.5c, Polly Packs, the major work of 5.MD.C connects to the major work of 5.NBT.B as students use their understanding of volume to perform operations with multi-digit whole numbers. In the Practice Printable, Question 7 states, “Elijah is building a sandcastle made up of two rectanguar prisms stacked atop one another. He has 504 cubic inches of sand. He knows the bottom prism will be 15 inches long, 8 inches wide and 3 inches tall. If he uses all the same, what could be the dimensions of the top rectangular prism?” ### Gateway Two ## Rigor & Mathematical Practices #### Meets Expectations + - Gateway Two Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for rigor and practice-content connections. The instructional materials meet expectations for rigor by developing conceptual understanding of key mathematical concepts, giving attention throughout the year to procedural skills, spending sufficient time working with engaging applications of mathematics, and balancing the three aspects of rigor. The materials meet expectations for practice-content connections as they: identify and use the Standards for Mathematical Practice (MPs) to enrich mathematics content; attend to the full meaning of each practice standard; provide opportunities for students to construct viable arguments and critique the reasoning of others; assist teachers in engaging students to construct viable arguments and analyze the arguments of others; and explicitly attend to the specialized language of mathematics. ### Criterion 2a - 2d Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application. 8/8 + - Criterion Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for rigor. The instructional materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, spend sufficient time working with engaging applications of mathematics, and do not always treat the three aspects of rigor together or separately. ### Indicator 2a Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. 2/2 + - Indicator Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. Examples of problems and questions that develop conceptual understanding across the grade level include: • In 5.MD.C.3a-b, Cubicle Dudes, the Teacher Instruction and the Practice Printable include several diagrams and drawings of unit cubes packed into rectangular prisms to determine the volume. • In 5.NF.B.3, “In Much Ado About Honey, the three fairies Beeblossom, Coyote, and Columbina are fighting over five jars of honey. King Oberon appears and commands that they stop arguing and share the honey evenly among them. The data provided is an image of the three fairies looking at the five jars of honey.” During the Teacher Instruction, visual models are used to further develop this concept, and the teacher guides students to imagine sharing eight pizzas among five friends and putting four pounds of flour equally into six containers. • In 5.NF.B.6, Water in the World, an example is “Multiplication of fractions may not be as intuitive for students as multiplication of whole numbers, so using diagrams when discussing the problems in this lesson may be helpful. In Water in the World, Kate is doing a true public service announcement, bringing awareness to the water crisis. She points out that in the United States, very few of us have trouble accessing clean water. However, around the globe there are millions of people who do not have access to clean water, and many of those are children. The data provides the fraction of the world population without access to clean water, as well as the fraction of the population who are children.” During the Teacher Instruction, the teacher works with the students to create a visual model of $$\frac{1}{3}$$ times $$\frac{1}{8}$$. • In 5.NBT.A.1, The Traveling Suitcase, instruction includes a visual display of movements along a place value line showing how multiplying by a power of 10 results in a different place value. “As a digit shifted spots, it became clear a digit in one place represents 10 times as much as it represents in the place to its rights and $$\frac{1}{10}$$ of what it represents in the place to its left.” Examples where students independently demonstrate conceptual understanding throughout the grade include: • In 5.NBT.A.6, Hardtack, Practice Printable, Question 7 states, “Jacqueline wrote 1,152 pages during the first 12 months of college. Assuming she wrote the same number of pages each month, how many pages did she write each month? Solve by using equations, rectangular arrays, and/or area models.” • In 5.NF.B.4a, The Horse Doctor, Practice Printable, Question 2 states, “Draw a visual fraction model to represent $$\frac{5}{12}× 3$$, then write the product on the line below.” • In 5.G.B.3, Squaring Off, Practice Printable, Question 9 states, “Isaiah says that a parallelogram is a square. Dominique says a parallelogram is not a square. Draw and describe a figure Isaiah might use to prove he is correct. Draw and describe a figure Dominique might use to prove she is correct.” ### Indicator 2b Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency. 2/2 + - Indicator Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for attending to the standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency throughout the grade level in the Math Simulator, examples in Teacher Instruction, Cluster Intensives, domain specific Test Trainer Pro and the Clicker Quiz. Examples include: • In 5.MD.A.1, Treacle Treatment, the teacher demonstrates conversion factors and ratios to change units. The teacher is instructed to say, “Let’s calculate each conversion. We’ll start by finding the conversion information between each pair of units. Now we can start with the given information and then set up the ratios so that the given units cancel out, leaving us with the desired units.” • In 5.NF.A.1, Hay, the Teacher Instruction includes examples of different ways students could identify common denominators including listing multiples, multiplying the denominators by each other, and using prime factorization to identify the least common multiple. • In 5.NBT.B.5, O’Hara’s Oversized Order, the Teacher Instruction walks students through examples of multiplying using the standard algorithm: first to solve $$36×720$$, then $$567×54$$, and finally $$3152×251$$. There is also a “worked example” video provided by a “student” to refresh the skills when students work independently. Examples of students independently demonstrating procedural skills and fluencies include: • In 5.NBT.B.5, O’Hara’s Oversized Order, the Clicker Quiz includes six questions, including two questions that include error analysis, for multiplication practice. The Practice Printable includes two problems with the directions, “Estimate each product first. Find the actual product by using the standard algorithm. Use your estimate to check the reasonableness of the product.” There are three word problems, and one requires error analysis by stating, “Diana made an error on one of her homework problems. Circle Diana’s error, and redo the problem correctly.” • In 5.MD.A.1, Treacle Treatment, the Practice Printable has several problems for students to complete independently such as Question 3, “Bruno is 1.75 meters tall. How tall is Bruno in: millimeters? centimeters? kilometers?” • In 5.NF.A.1, Hay, the Practice Printable provides several opportunities by adding daily feed logs for 4 animals, where amounts have unlike denominators. Questions 1-4 state, “For each set of fractions, write equivalent replacement fractions with a common denominator,” and Questions 5-10 state, “Find the sum or difference.” All problems begin with unlike denominators. ### Indicator 2c Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade 2/2 + - Indicator Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for being 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 problems, presented in a context in which mathematics is applied. Examples of students engaging in routine application of skills and knowledge include: • In 5.NF.B.6, Water in the World, Practice Printable, Question 1 states, “Below is a recipe for Nana’s Banana Muffins. How much of each ingredient is needed to make $$\frac{1}{4}$$ of the recipe?” The recipe has five ingredients: three are whole number amounts, one is a unit fraction amount, and one is a non-unit fraction amount. • In 5.MD.A.1, Treacle Treatment, Practice Printable, Question 5 states, “Annette, Adriana and Sasha are all training for an upcoming race. Annette ran 1.5 kilometers; Adriana ran $$\frac{2}{5}$$ of a kilometer; and Sasha ran 1,600 meters. How many total meters did they run?” • In 5.NF.C.7c, Fairy Fractions, Practice Printable, Question 11 states, “Terri has 18 pounds of dog food for her dog, Migs. One serving for Migs is $$\frac{1}{6}$$ of a pound, and he is supposed to eat 2 servings each day. How many days will the dog food last?” • In 5.OA.A.2, Liftie Lesson, Practice Printable, Question 5 states, “Carla has 8 baseball cards. She gives 3 to her sister, and then goes to the store and doubles the number of cards she has. Write an expression to represent how many cards she has.” Examples of students engaging in non-routine application of skills and knowledge include: • In 5.NF.A, S’mores, “Matty, Lucia, and Keshia are buying supplies to make s’mores on an upcoming camping trip. They each have specific recipes they follow to make their perfect s’more. Matty uses $$\frac{1}{2}$$ bar of chocolate, Lucia uses $$\frac{1}{4}$$ bar of chocolate, and Keshia uses $$\frac{1}{3}$$ of a bar of chocolate. They each plan to eat 3 s’mores. a) How many bars of chocolate should they each buy? b) Will there be any chocolate bar left over? If so, how much? c) If they did not want to have any chocolate left over, yet they each want to eat an equal number of s’mores using their own favorite recipe, how many s’mores would they have to eat? How many chocolate bars would they buy? Once you are confident in your solution, draw a picture to show your reasoning. Be ready to present and explain your drawing.” • In 5.MD.C.5c, Polly Packs, Practice Printable, Question 7 states, “Elijah is building a sandcastle made up of two rectangular prisms stacked atop one another. He has 504 cubic inches of sand. He knows the bottom prism will be 15 inches long, 8 inches wide and 3 inches tall. If he uses all the sand, what could be the dimensions of the top rectangular prism?” • In 5.NF.B.7c, Fairy Fractions, Practice Printable, Question 5 states, “A giraffe typically spends $$\frac{4}{5}$$ of a day standing, walking, and eating. After one week, how many “days” has a giraffe spent standing, walking, and eating?” ### Indicator 2d Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade. 2/2 + - Indicator Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. Examples of the three aspects of rigor being present independently throughout the materials include: • In 5.NF.B.5a, Sweet Success!, students develop conceptual understanding of comparing the size of a product to the size of one factor on the basis of the size of the other factor. In the Practice Printable, Question 1, “Without doing the calculations, circle the greater value. a) $$25$$ or $$\frac{2}{5}×25$$; b) $$3\frac{1}{4}×45$$ or $$\frac{1}{4}×25$$; c) $$\frac{1}{3}×2$$ or $$1\frac{1}{3}×2$$; d) $$\frac{4}{5}×\frac{1}{2}$$ or $$\frac{1}{2}$$.” In Question 2, “Look at Problem C from Question 1 above. Explain how you knew which was the greater value without doing the calculation.” • In 5.NBT.A.4, Round and Round, students develop procedural skills related to rounding numbers. During the Immersion Problem students answer, “How is DJ Mastermind doing these calculations in his head?” During the resolution video, DJ Mastermind explains the procedure for rounding numbers. The procedure is developed during the Teacher Instruction, and as students have opportunities to practice during the Simulation Trainer; the Practice Printable, Question 7, students “Round 14.256 to the nearest hundredth.”; and Clicker Quiz, “What is 11.98 rounded to the nearest tenth of a second?” • In 5.MD.C.4, Shipment Shenanigans, students engage in application problems related to volume. Throughout the lesson students try to answer “What is the volume of the truck?” The lesson narrative explains, “In Shipment Shenanigans, Bud and Lou are loading a truck full of boxes that are cubes, each measuring 1-foot by 1-foot by 1-foot. As soon as the truck is loaded, they get a call from the boss asking for the volume of the truck. Neither Bud nor Lou counted the number of boxes as they loaded the truck, so the only thing left to do? Unload and recount! The data provided is an image of the truck, showing the individual boxes stacked up inside.” Additionally, in the Practice Printable, Question 6 states “Jillian works at a shoe store. The store received a shipment of children’s boots for the upcoming season. The shipment came in one large box full of smaller shoeboxes. How many shoeboxes were inside the shipping box?” Examples of multiple aspects of rigor being engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study include: • In 5.NF.B.3, Much Ado About Honey, students solve application problems using their conceptual understanding about division. In the Practice Printable, Question 7 states “The girls’ swim team is having an end of the year celebration. There are 8 girls on the team and they ordered 6 pizzas to share. How much pizza will each girl get if they split all pizzas evenly? Draw a representation to show your thinking.” • In 5.NBT.B.6, Hardtack, students use procedural skills of long division while solving application problems. The Resolution video teaches the partial quotients method for long division in the context of solving a real-world problem about how many hardtack biscuits there are for each crew member. Students use the partial quotients method in additional application problems such as the Clicker Quiz, “The Castillo family always goes camping in the summer. The four of them share a tent. The tent floor is 4,508 square inches. How much space does each family member get?” ### Criterion 2e - 2g.iii Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice 10/10 + - Criterion Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for practice-content connections. The materials: identify and use the Standards for Mathematical Practice (MPs) to enrich mathematics content; attend to the full meaning of each practice standard; provide opportunities for students to construct viable arguments and critique the reasoning of others; assist teachers in engaging students to construct viable arguments and analyze the arguments of others; and explicitly attend to the specialized language of mathematics. ### Indicator 2e The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade. 2/2 + - Indicator Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for identifying the Standards for Mathematical Practice and using them to enrich mathematics content within and throughout the grade level. The materials reference the Mathematical Practices (MPs) throughout the Philosophy and Planning sections, and the materials indicate connections to the MPs. Examples include: • In the Teacher’s Guide, mathematical practices are addressed in the Major Cluster Curriculum Components, Cluster Intensives, and the Teacher-Created Intensive, which is “Additional math problems developed by MidSchoolMath teachers and leading math experts such as Dan Meyer, Jo Boaler, and MathShell that emphasize the Standards for Mathematical Practice.” • In the Teacher’s Guide, Practices & Protocols: Standards for Mathematical Practice states, “A primary goal of the MidSchoolMath curriculum structure is to ensure that it supports the Standards for Mathematical Practice, not only in “extra” activities, but embedded in the curriculum pedagogy of each component. Use of the practices can be greatly enhanced by simple instructional moves.” • In the Teacher’s Guide, Protocols to Support Standards for Mathematical Practice includes, “To support the Standards for Mathematical Practice, MidSchoolMath has compiled a “Top 10” bank to include protocols (or instructional moves) that teachers use to structure learning experiences to deepen the understanding of the SMP. Recommended protocols for each lesson are found in the Detailed Lesson Plans with teacher instructions to implement.” The protocols are directly related to the MPs they best support. • In the Teacher’s Guide, Detailed Lesson Plans, the Domain Review references, “A Domain Review also supports the Standards for Mathematical Practice,” and “Complete the Domain Review by reading one or more of the Standards for Mathematical Practice and ask them to reflect on their work throughout the day.” • Each Detailed Lesson Plan, Lesson Plan Overview, includes one to three MPs and describes how the lesson connects to the MPs. • In addition, each Detailed Lesson Plan includes a specific tip from Jo Boaler that provides guidance about how to connect the MPs with the lesson. Examples where the MPs are connected to grade-level content include: • In 5.NF.A.1, Hay, Lesson Plan Overview, “MP2: “Reason abstractly and quantitatively. Students will be able to connect a visual model with a numeric representation of equivalent fractions when adding. In Resolution, after students have had an opportunity to apply strategies to the problem, students are simultaneously shown visual diagrams of the hay bales transforming to correspond to the mathematical process of equivalent fractions for adding. In Student Reflection, students use words and numbers, along with a strong visual representation, to build brain pathways that encourage students' ability to decontextualize and contextualize and reason abstractly and quantitatively.” • In 5.MD.C.5b, Phil & Ned’s Excellent Assignment, Lesson Plan Overview, “MP4: Model with Mathematics. In Immersion, students begin the modeling process as the problem is unstructured during this phase. Students sketch a luxury doghouse which helps them conceptualize what a ‘foundation’ is, and helps them determine what they need to know to solve the problem and what strategies they might use. During Resolution students are encouraged to think about the modeling process, specifically why the process is so important. Additionally, during Clicker Quiz and Practice Printable, students will recognize that the formulas V = Bh and V = lwh can be used to solve real world problems involving volume and that the formulas ‘model’ the filling (or packing) of right rectangular prisms.” • In 5.OA.B.3, Snowfall, Lesson Plan Overview, “MP8: Look for and express regularity in repeated reasoning. In Resolution, students experience how to maintain oversight of the process, while attending to details. Students experience repeated reasoning and regularity as they focus on the patterns of snowfall over time. Students (1) describe what patterns they noticed, (2) explain whether a pattern is repeating, and (3) determine if the pattern applies to all situations or not to be able to make a generalization (a rule). This practice is reinforced by having the students watch a complimentary video in which Jo Boaler has students modeling how to look and identify patterns in real-life scenarios.” ### Indicator 2f Materials carefully attend to the full meaning of each practice standard 2/2 + - Indicator Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for carefully attending to the full meaning of each practice standard. Materials attend to the full meaning of each of the 8 MPs. Examples include: • For MP1, during the Immersion situations, students make sense of a problem and look for entry points to its solution. For example, in 5.MD.B.2, Anesthesia Outcome, the Detailed Lesson Plan states, “SMP1: Make sense of problems and persevere in solving them. Anesthesia Outcome provides a good opportunity for students to make sense of and persevere in solving problems in all three phases of The Math Simulator. During the Immersion phase, students begin this practice immediately as they are prompted to make sense of a type of task that is relatively unstructured. Encourage students to take time to develop questions and assumptions and to not feel the need to rush to try to solve the problem. In Data & Computation, students will continue to persevere by developing a plan to approach the problem, create a visual that helps students make sense of the problem, and complete the calculation. In Resolution, students share different approaches to solving the problem and even present mistakes they may have made.” • For MP2, students make sense of quantities and their relationships in problem situations through contextualizing and decontextualizing. For example, in 5.NF.B.6, Water in the World, the Detailed Lesson Plan states, “SMP2: Reason abstractly and quantitatively. As students move away from visuals and use equations to represent and solve real-world problems, they often decontextualize to calculate and then contextualize again to interpret their results. During Practice Printable, students will encounter various contexts in which they have to calculate a product and interpret the results.” Practice Printable Question 1 states, “Below is a recipe for Nana’s Banana Muffins. How much of each ingredient is needed to make of the recipe?” Students are given a recipe with five ingredients and required to calculate $$\frac{1}{4}$$ of the recipe. • For MP4, students put an authentic problem into their own words and use an appropriate strategy from the math they know to create a path to a solution. For example, in 5.MD.A.1, Treacle Treatment, the Detailed Lesson Plan states, “SMP4: Model with mathematics. During Immersion, students begin modeling with limited information, primarily just a visual to solve the problem. Because they do not know how much each bottle holds, they must make assumptions and approximations pulling references from their own experiences (milk jugs, water bottles, etc.), which helps build a personal entry point for each student. Students collaborate to create an initial solution pathway prior to having enough information to do so, realizing they may need to make adjustments and revisions later. This pathway may consist of diagrams, estimations and initial calculations.” • For MP5, students demonstrate understanding of the benefits and limitations of a variety of tools by choosing the appropriate tool for the purpose - solving problems, calculation, communication, etc. For example, in 5.NF.B.4b, Find a Field, the Detailed Lesson Plan states, “SMP5: Use appropriate tools strategically. Students choose tools to develop a strategy for solving the problem. In Immersion, students begin with a brief “tool session,” recommended by Jo Boaler, that reminds them of the various tools at their disposal at any given time. In Data & Computation, students are asked to create a visual, selecting tools of their choice. In Resolution, students complete visuals by writing a statement about how their tools were effective in helping them think about and solve the problem. In the Practice Printable, students will choose tools or representations that help them model multiplication of fractions.” • For MP6, students use appropriate vocabulary and symbols in the communication of mathematics. Their calculations are accurate and include units and labels appropriate to the context. For example, in 5.G.A.2, The Waterfall Hunter, the Detailed Lesson Plan states, “SMP6: Attend to precision. This lesson provides an opportunity for students to experience the importance of precision, especially when communicating directions. In Immersion, student pairs play “Directions for Directions” in which each student gives verbal directions to a location (without identification) while the other student draws the map. In Resolution, students re-engage in the game with a new location but with explicit directions on how to improve their directions (giving directions to directions). Between this game and the mathematical task in The Waterfall Hunter, students gain direct experience of how applying precision in units and measurements results in greater overall clarity of communication.” • For MP7, students find structure or patterns in the mathematics that leads to understanding content. For example, in 5.NF.B.5a, Sweet Success!, the Detailed Lesson Plan states, “SMP7: Look for and make use of structure. In Immersion, students begin the lesson with a 'Number Talk' designed to help them look for and make use of structure of a multiplication problem, specifically the relationship between the factors and the product. Students are not given the pattern, but rather must discern these patterns themselves. In Resolution, teacher prompts encourage students to look for structures and to reason about how they might be useful.” • For MP8, students generalize a process or discover a shortcut, through repeated reasoning or calculations that promote understanding of an algorithm or formula. For example, in 5.OA.B.3, Snowfall, the Detailed Lesson Plan states, “SMP8: Look for and express regularity in repeated reasoning. In Resolution, students experience how to maintain oversight of the process, while attending to details. Students experience repeated reasoning and regularity as they focus on the patterns of snowfall over time. Students (1) describe what patterns they noticed, (2) explain whether a pattern is repeating, and (3) determine if the pattern applies to all situations or not to be able to make a generalization (a rule). This practice is reinforced by having the students watch a complimentary [sic] video in which Jo Boaler has students modeling how to look and identify patterns in real-life scenarios.” ### Indicator 2g Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by: 0/0 ### Indicator 2g.i Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. 2/2 + - Indicator Rating Details The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. Examples of prompting students to construct viable arguments and analyze the arguments of others include: • In 5.NF.B.5b, The Beef with Beef, Practice Printable, Question 3 states, “Explain or show why $$2\frac{1}{3}×6$$ will have a product greater than 6.” Question 4 states, “Explain or show why $$\frac{2}{4}×4$$ will have a product less than 4.” Question 6 states, “Juan multiplied $$\frac{1}{2}×\frac{2}{3}$$, and he got $$\frac{2}{6}$$ or $$\frac{1}{3}$$. This confused him because he always thought that when multiplying two factors, the product would always be greater than the factors. Write an explanation to Juan and tell him why his product is smaller than the factors.” • In 5.G.B.4, It’s a Polygon World, Practice Printable, Question 2 states, “Name three shapes that are quadrilaterals. Then explain the similarities and differences in their properties.” • In 5.NBT.A.3b Puppy Playdate, Practice Printable Question 4 states, “Which is greater, 13.04 or 13.1? Explain your answer.” • In 5.G.B.3, Squaring Off, Practice Printable, Introduction Problem states, “As Poseidon and Zeus moved on to another round of “Shape Up,” another disagreement occurred. Zeus said that a parallelogram is a trapezoid, while Poseidon said that a parallelogram is not a trapezoid. Who is correct - Zeus or Poseidon? Explain how you know.” Practice Printable Question 9 states, “Isaiah says that a parallelogram is a square. Dominique says a parallelogram is not a square. a) Draw and describe a figure Isaiah might use to prove he is correct. b) Draw and describe a figure Dominique might use to prove she is correct.” • In 5.G.B.4, It’s a Polygon World, Practice Printable, Question 4 states, “Stacey said a rhombus is always a square. Joel said a square is always a rhombus. Use what you know about the properties of these shapes to explain who is correct.” • In 5.NF.B.5a, Sweet Success!, Practice Printable, Question 6 states, “Ryan said that the product of 24 and $$\frac{5}{2}$$ is less than 24 because any whole number multiplied by a fraction will be less than 24. Is he correct? Explain your answer without doing the actual calculation.” • In 5.NF.B.5b, The Beef with Beef, Practice Printable, Introduction Problem states, “Marie was grocery shopping. She came to the meat counter and asked Kenneth for$12 worth of ground pork. Ground pork was priced at $8.00 per pound. Marie suggested Kenneth start with measuring two pounds; since$12 was so much more than \$8, it would have to be at least 2 pounds of meat. Kenneth told her it would be less than 2 pounds of meat. Which one of them is correct? Explain how you know.”
• In 5.MD.C.3a-b, Cubicle Dudes, Practice Printable, Introduction Problem states, “The dudes have a new box, the volume of which they need to determine. They have agreed to use a cube with a side length of 1 inch, however they have gotten different answers. This means that one of the dudes has made a mistake in his calculation. Which dude is right? Explain how you know.”

### Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

The materials provide guidance for teachers on how to engage students with MP3. In several lessons, the Detailed Lesson Plan identifies MP3 and provides prompts that support teachers in engaging students with MP3. Examples include:

• In 5.MD.C.3a-b, Cubicle Dudes, the materials include, “ During Data and Computation, the procedure outlines setting up a mock jury where students will listen to arguments presented by three students with opposing claims to reach a final verdict. This exercise reinforces SMP3 by having students explain and justify the logic of their assumptions.” Teachers are guided to “choose three students to present one of each claim with their supporting evidence. This can be done using a document camera or other technology. Encourage them to make statements using assumptions, data and definitions that support a viable argument in logical statements: My claim is______.; My mathematical evidence is_______.; My assumptions are______.; My calculations support ______.  While the three students are prepping, group students to act as a jury to discuss the arguments presented to them. During each presentation, they may ask one clarifying question. At the end they must each agree on a verdict.”
• In 5.NF.B.3, Much Ado About Honey, the materials include, “Students construct an individual argument to show how much honey each fairy should receive using the "Sketch It!" protocol. Students are tasked with providing visual evidence to accompany computational evidence during the protocol. They share their work in small groups, justifying their conclusions. Students in the group vote on whether they believe each person's sketch and presentation would end the fairies’ argument or if the logic/visual needs to be revised. Teachers are provided with directions to help facilitate this process of analyzing arguments: Have students join in groups of three where each student is given one minute to present their sketch and create a viable argument. Other students in the group vote as to whether each sketch will end the fairies’ argument or if revision is needed to improve the argument. If revisions are needed, group members agree on one piece of feedback for the presenter.”

In most lessons, there are prompts for teachers that can be used for student reflection at the end of the lesson; however, these prompts are optional as the materials state “It is not always necessary for students to respond. The questions can simply be used to cue thinking prior to instruction.” Examples of these include:

• What did you do that was the same?
• What was different?
• What strategy do you think was more efficient? Why?

The materials include 10 protocols to support Mathematical Practices. Several of these protocols engage students in constructing arguments and analyzing the arguments of others. When they are included in a lesson, the materials provide directions or prompts for the teacher to support engaging students in MP3. These include:

• “I Wonder, I Notice (8-10 min): Following a completed whole-class assignment, set ground rules for peer critique, including being thoughtful, specifc [sic], and helpful (≈ 1 min). Choose a student to be “the originator” who is tasked to explain his or her approach and solution to a problem (≈ 2 min), while other students listen only. Then ask other students to ask “the originator” clarifying questions or comments that start with ‘I wonder’ and ‘I notice’ (≈ 5-6 min).”
• “Think-Pair-Share (5-6 min): Ask students to think individually about an idea and make some notes (≈1-2 min). Tell students to pair with a partner and discuss their notes (≈ 2 min). Finally, facilitate whole-class discussion by cold-calling on students to share their ideas. Consider recording ideas on a whiteboard (≈ 2 min).”
• “Lawyer Up! (12-17 min): When a task has the classroom divided between two answers or ideas, divide students into groups of four with two attorneys on each side. Tell each attorney team to prepare a defense for their “case” (≈ 4 min). Instruct students to present their argument. Each attorney is given one minute to present their view, alternating sides (≈ 4 min). Together, the attorneys must decide which case is more defendable (≈ 1 min). Tally results of each group to determine which case wins (≈ 1-2 min). Complete the protocol with a “popcorn-style” case summary (≈ 2-3 min).”
• “Math Circles (15-28 min): Prior to class, create 5 to 7 engaging questions at grade level, place on diferent [sic] table-tops. For example, Why does a circle have 360 degrees and a triangle 180 degrees? Assign groups to take turns at each table to discuss concepts (≈ 3-4 min each table).”
• “Quick Write (8-10 min): After showing an Immersion video, provide students with a unique prompt, such as: “I believe that the store owner should...”, or “The person on Mars should make the decision to...” and include the prompt, “because...” with blank space above and below. Quick writes are excellent for new concepts (≈ 8-10 min).”
• “Sketch It! (11-13 min): Tell students to draw a picture that includes both the story and math components that create a visual representation of the math concept (≈ 5-7 min). Choose two students with varying approaches to present their work (≈ 1 min each) to the class (via MidSchoolMath software platform or other method) and prepare the entire class to discuss the advantages of each model (≈ 5 min).”

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for explicitly attending to the specialized language of mathematics.

The materials use precise and accurate terminology and definitions when describing mathematics, and the materials provide instruction in how to communicate mathematical thinking using words, diagrams, and symbols.

• Each Detailed Lesson Plan provides teachers with a list of vocabulary words and definitions that correspond to the language of the standard that is attached to the lesson; usually specific to content, but sometimes more general. For example, 5.G.4 states “Classify two-dimensional figures in a hierarchy based on properties.” The vocabulary provided to the teacher in 5.G.B.4, It’s A Polygon World is, “Hierarchy: A system or organization in which figures (usually polygons) are ranked one above the other according to their properties.”
• The vocabulary provided for the teacher is highlighted in red in the student materials on the Practice Printable.
• Each Detailed Lesson Plan prompts teachers to “look for opportunities to clarify vocabulary” while students work on the Immersion problem which includes, “As students explain their reasoning to you and to classmates, look for opportunities to clarify their vocabulary. Allow students to ‘get their idea out’ using their own language but when possible, make clarifying statements using precise vocabulary to say the same thing. This allows students to hear the vocabulary in context, which is among the strongest methods for learning vocabulary.”
• Each Detailed Lesson Plan includes this reminder, “Vocabulary Protocols: In your math classroom, make a Word Wall to hang and refer to vocabulary words throughout the lesson. As a whole-class exercise, create a visual representation and definition once students have had time to use their new words throughout a lesson. In the Practice Printable, remind students that key vocabulary words are highlighted. Definitions are available at the upper right in their student account. In the Student Reflection, the rubric lists the key vocabulary words for the lesson. Students are required to use these vocabulary words to explain, in narrative form, the math experienced in this lesson. During “Gallery Walks,” vocabulary can be a focus of the “I Wonder..., I Notice...” protocol.”
• Each lesson includes student reflection. Students are provided with a list of vocabulary words from the lesson to help them include appropriate mathematics vocabulary in the reflection. The rubric for the reflection includes, “I clearly described how the math is used in the story and used appropriate math vocabulary.”
• Vocabulary for students is provided in the Glossary in the student workbook. “This glossary contains terms and definitions used in MidSchoolMath Comprehensive Curriculum, including 5th to 8th grades.”
• The Teacher Instruction portion of each detailed lesson plan begins with, “Here are examples of statements you might make to the class:” which often, though not always, includes the vocabulary with a brief definition or used in context. For example, the vocabulary provided for 5.NF.B.4a, The Horse Doctor, is “Partition” and “Product.” The sample statements provided are, “In The Horse Doctor, Dr. Equinas decides to give Bella a larger dose than is typically given to a regular-sized horse; Dr. Equinas interprets $$\frac{4}{3}$$ of 9 grams as 4 parts, when 9 grams is partitioned into 3 parts.”

## Usability

### Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
7/8
+
-
Criterion Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for being well designed and taking into account effective lesson structure and pacing. The materials distinguish between problems and exercises, have exercises that are given in intentional sequences, and have a variety in what students are asked to produce. The materials partially include manipulatives that are faithful representations of the mathematical objects they represent.

### Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for providing both problems and exercises that have purpose.

Students engage with problems and exercises through a consistent lesson structure. Students participate in a warm-up in the Test Trainer Pro daily for 10 minutes. The Math Simulator introduces the story and the essential problem with an online video during the Immersion and Data & Computation and Resolution stages. In the Detailed Lesson Plan, the teacher instructional time (8-10 minutes) provides problems for the teacher to use as examples. The student does independent online (3-7) exercises in the Simulation Trainer, with additional repetition if they miss the problems. The Practice Printable can be used as a differentiation tool, as in-class practice, or as homework. The Clicker Quiz consists of six multiple choice questions. At the end of the lesson, there is a section for a Gallery Walk and Reflection of other student work.

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for assignments being designed with an intentional sequence.

There is logic to the design because each lesson is one standard; lessons are listed in the order of the standards within each domain. In Planning the Year, the materials state, “The sequence provided in the materials is specifically designed to provide a framework to allow teachers sufficient time for teaching each standard throughout the year. Additionally, the materials are intentionally designed for students to work with more ‘concrete’ forms of mathematics prior to abstract concepts. Finally, the structure of the curriculum is sequenced to allow for completion of topics before associated summative assessments, and sequencing within lessons progresses from conceptual work to practice with exercises.”

### Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for requiring variety in what students produce.

Each lesson builds around an essential problem that is the entry point for the content. The problems always include “artifacts” that require students to work with content in a wide variety of ways including breaking codes, planning rations for trips, determining if things will fit, etc. In addition to the essential problem, the program utilizes 10 protocols that generate a variety of responses such as creating arguments, making up their own problems, sketching situations, quick writes, and more. The student reflection, found at the end of each lesson, gives students the opportunity to personalize and be creative in how they explain their understanding.

### Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 partially meet expectations for effective use of manipulatives.

The instructional materials do not include extensive use of manipulatives, and in the online materials, tools used as manipulatives are not available. In some of the lesson material, there are visual models with number lines, graphs, or bars. Students occasionally look at models and create a math equation from the representation. Overall, there are limited opportunities to use manipulatives to develop mathematical understanding.

### Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 include print materials that are not distracting or chaotic. The student workbook provides space for students to write in the workbook. There are numerous videos in various parts of the lesson which are brief and engaging to students.

However, the Math Simulator can be distracting because students have to rewatch entire videos even if they have answered the questions correctly. The students do not have the ability to fast forward through the videos even though they have seen the video previously.

### Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
4/8
+
-
Criterion Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 do not meet expectations for supporting teacher learning and understanding of the Standards. The materials contain support for planning and providing learning experiences with quality questions and contain ample and useful notations and suggestions on how to present the content. The materials do not meet expectations for containing: adult-level explanations so that teachers can improve their own knowledge of the subject and explanations of the grade-level mathematics in the context of the overall mathematics curriculum.

### Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for supporting teachers with quality questions to guide mathematical development.

There are prompts for teachers embedded throughout each section of the Detailed Lesson Plan. Many of these are generic and repeated in almost every lesson, such as, “What information are we given? What operations were used? Is the math same, just represented in a different way? What visuals did you notice were similar or different?” Some questions are consistently connected to Mathematical Practices, such as, “Would this always be true? Can you think of a situation where this would not work?” In addition, each lesson introduction poses an essential question intended to guide student learning and specific prompts related to that outcome.

### Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for containing ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials.

In the Detailed Lesson Plan pages, there is information that can help teachers understand the materials in order to present the content. In the Teacher Instruction it states, “Lectures can be developed using guidance from the Detailed Lesson Plans.” Each lesson identifies the relevant Mathematical Practices, Cluster Connections, and Common Misconceptions. In the Instruction at a Glance section, the authors give hints to help teachers provide support to students. Also provided in each lesson is a Mathematical Practice TIp from Jo Boaler to offer ideas to instructors.

In the Detailed Lesson Plan, there is a section that provides instructions to use the online Test Trainer Pro as a daily warm up. A video is provided with each lesson which sets a scene in which the essential question is asked. The Math Simulator is a “central component of Core Curriculum MidSchoolMath, designed to provide a strong conceptual foundation of the mathematical standard.”

### Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) 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.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 do not meet expectations for containing adult-level explanations so that teachers can improve their own knowledge of the subject. While the materials provide support for instruction in each lesson, they do not include adult-level explanations of the grade-level content or advanced mathematics concepts so that teachers can improve their own knowledge of the subject.

### Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 do not meet expectations for explaining the role of grade-level mathematics in the context of the overall mathematics curriculum.

The materials do not assist teachers in understanding the role of the specific course-level mathematics in the context of the overall series. There is no explanation of how the topic is developed in previous and future grades, other than a list of prerequisite standards for each lesson.

### Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 provide a list of lessons in the teacher edition, cross-­referencing the standards addressed, and a pacing guide.

Each course in this series includes a document called Planning the Year that provides the standards and pacing (number of weeks) for each lesson. There is additional standards correlation in the Scope and Sequence Chart that lists each Lesson, Domain Review, and Major Cluster Lessons throughout a year.

### Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 include a parent letter that explains the program in both English and Spanish. The how-to-help paragraph suggests that parents have the student log into the program and show the parents their work, “Try your best to listen and not be critique [sic]”, and to expect the math to be different. It also mentions the mindset of being bad at math and changing the mindset by saying they do not understand the concept “Yet”. There is no further communication for parents and no direct discussion of mathematical concepts.

### Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 explain instructional approaches used and how they are research-based in the Curriculum Structure. Examples include:

• The Clicker Quiz is “a whole-class, low-stakes test (comprising [sic] of six multiple choice math problems) facilitated through any device to enhance long-term recall of concepts and provide the teacher with real-time class evaluation data. (Research Indicator: ‘The Testing Effect’ demonstrates that learning is higher through repetitive low to no-stakes testing than through studying, and that long term recall is higher.)”
• Information on Cultural Diversity in Math - “Moving from Shallow Notions of Culture to Student-Centered Mathematics Tasks” by Toya J. Frank, Ph.D. is provided online in Resources.
• In addition, Lesson Planning for Remote Situations provides overview and essential considerations in the Resources menu online for teachers, parents, and students.

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
6/10
+
-
Criterion Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 partially meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the Standards. The materials include assessments that clearly denote which standards are being emphasized. The materials partially meet expectations for providing: strategies to gather information on students’ prior knowledge; strategies to identify and address common student errors and misconceptions; opportunities for ongoing review and practice with feedback; and assessments that include aligned rubrics and scoring guidance for teachers to interpret student performance and suggestions for follow-up.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 partially meet expectations for gathering information about students’ prior knowledge.

• Test Trainer Pro, which is intended to be used daily, automatically gathers information about students’ prior knowledge of Core Skills (from Grades 1 through 4) and the domains within the grade-level standards.
• The Detailed Lesson Plan lists prerequisite standards for each lesson, but does not provide strategies to gather information about knowledge of those standards.
• Assessing prior knowledge is not directly addressed in the Detailed Lesson Plan, but can be elicited through teacher questioning and observation.
• The lesson plan does not include suggestions for responding to answers that demonstrate lack of prior knowledge.
• There are no pre-tests available in the materials.

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
1/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 partially meet expectations for identifying and addressing common errors and misconceptions.

The Detailed Lesson Plan includes a section of “Common Misconceptions”. In the Teacher Instruction, the teacher is usually prompted to address the misconception by showing students the correct way to do the math with some detail as to why and how. The Teacher Instruction and the Practice Printables sometimes show work with a mistake based on the misconception and ask the students to decide if the example is correct and how they know, then the students work the problem correctly.

While these address common errors and misconceptions, the materials do not mention strategies to identify the common student errors and misconceptions or why students make them.

### Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
1/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 partially meet expectations for providing ongoing review and practice with feedback.

Opportunities for ongoing review include:

• The Daily Test Trainer gives students multiple-choice review questions each day.
• Distributive Practice provides two weeks of multiple-choice questions on the computer.
• Game-Based Review incorporates multiple standards.
• The Domain Review provides a short clip of four Immersion Videos from the unit. Students then complete a reflection including Story Recall, Math Concepts, and Math Connections for those four lessons. However, the majority of the materials focus on one specific standard at a time.

Opportunities for feedback include:

• Teacher prompts and questions while students work.
• The Simulation Trainer provides feedback about correct/incorrect and solution videos.
• The domain reflection includes a rubric with clear expectations.
• Students provide peer feedback during a gallery walk of student reflections.
• Formal feedback is not provided, and there is no suggested feedback for assessments related to content.

### Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
2/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for denoting which standards are emphasized on assessments.

On each Milestone Assessment, the clusters are shown below the title in the digital materials and in the footer of the PDFs, and the standards are shown below the title in the digital materials.

### Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
1/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 partially meet expectations for interpreting student performance on assessments and making suggestions for follow-up.

The assessments are multiple-choice with an answer key in the Teacher Guide. Each Milestone Assessment has a scoring rubric that is based on the percent of correct answers. The recurring suggestion for following-up with students is for them to review and correct their mistakes. Students who score advanced (80-100%) create a tutoring session for the nearing proficient. The proficient students (60-79%) create a Top-3 Tips sheet for the class. The students who are nearing proficient (40-59%) attend the tutoring session. The novice students attend a reteaching session with the teacher.

Since the questions are all multiple choice, the teacher has a limited perspective of student abilities, and it is challenging to interpret student performance. The multiple-choice aspect of the assessments also limits the ability to measure higher-level thinking.

### Indicator 3q

Materials encourage students to monitor their own progress.
0/0
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 provide very little opportunity for students to monitor their own progress. Students self-assess their understanding of each concept during the Reflection; the Reflection rubric includes Mathematical Representation where a score of 4 (Exceeds Expectations) states, “My mathematical representation shows complete understanding of the math concept.” However, there is no overall progress monitoring completed by students.

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
8/12
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Criterion Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 partially meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The materials embed tasks with multiple entry-points and provide a balanced portrayal of various demographic and personal characteristics. The materials partially meet expectations for providing: strategies to help teachers sequence or scaffold lessons; strategies for meeting the needs of a range of learners; supports, accommodations, and modifications for English Language Learners and other special populations; and opportunities for advanced students to investigate mathematics content at greater depth.

### Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
1/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 partially meet expectations for providing strategies to help teachers make content accessible to all learners. There are some routines within the materials that help make the content accessible to all learners, but very few specific strategies to support teachers in scaffolding the lesson. For example:

• Each lesson has the same structure.
• The Immersion Video and problem provide an opportunity for students at all levels to engage in the math; however, the materials do not support the teacher with strategies to scaffold the content if students struggle.
• The Exit Ticket provides information to the teacher to determine who might join a small reteaching group, but there is limited guidance about what the teacher should do except help the students do the second side of the Practice Printable.
• The Teacher Guide describes the Top 10 Protocols and states, “For each protocol, take time to imagine the experience of all students in the classroom. For example, having one student present their work to the rest of the class could lead to only one student benefiting while most students are passively listening (or not listening at all).” Despite pointing this out, there are no strategies provided for how to scaffold the lesson to engage all students.
• The Content at a Glance in each lesson includes Pro-Tips from three teachers designed to help teachers scaffold the content such as, “Consider having students draw a visual representation of two expressions, one with no grouping symbols and one with. This will help them see how using grouping symbols can change the value of the expression.”

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
1/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 partially meet expectations for providing teachers with strategies for meeting the needs of a range of learners. The range of learners is addressed in a limited way, but specific strategies for meeting their needs are not provided. For example:

• The Teacher Guide provides suggestions when planning to teach, “Prep work: Review the Practice Printable Answer Key in the Detailed Lesson Plan. Decide on how you would like to use the Practice Printable (as a differentiation tool, as in-class practice, as homework, etc.). Consider choosing one problem of your choice for students to complete as an exit ticket for the period, with the option of using the results to group students for work the next day.“
• The instruction for differentiation is the same for every lesson, after students complete the first side of the Practice Printable, they answer an Exit Ticket: “Ask students to rate their personal understanding of the problem on a scale of 1 to 3: 1 = I need more help; 2 = I need more time, yet mostly understand; 3 = I’ve got this!” Based on their answer, when the students complete the second side of the Practice Printable, the teacher can assign a challenge for those who answered 3 and create a small reteach group for the students who answered 1, though there are no suggestions about what to do with the group.
• During the Simulation Trainer, it is suggested that students who complete the activity quickly can help the students who are struggling.
• The Teacher can assign a different grade level in the Test Trainer Pro.

### Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
2/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for providing tasks with multiple entry points.

• The opening Immersion Video and problem present a task in each lesson that provides multiple entry points with no clear route to the solution.
• The Math Simulator also provides problems with multiple entry points and a variety of solution strategies, though they only show one in their solution video.
• Beyond the initial task in each of these areas, problems repeat the same situation with new numbers.

### Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
1/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 partially meet expectations for including support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

• The materials include support, accommodations, and modifications for ELL students through pull-out boxes in the Detailed Lesson Plans.
• There are no strategies provided for making accommodations specifically for students in special populations that would allow them to regularly and actively participate in learning grade-level mathematics.
• There is a box in each lesson called Differentiation Plan with a section for Remediation, but the suggestion is to work on problems together, with the teacher, or each other. This does not provide modifications for additional support and practice for students.

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
1/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 partially meet expectations for providing opportunities for advanced students to investigate mathematics at greater depth.

• Materials include little, if any, deeper or more complex mathematics that would challenge advanced learners.
• There is a box in each lesson called Differentiation Plan with a section for Enrichment which suggests that students can move on to the Reflection or offers a problem that lets students apply the content. Some of these promote investigation that would enhance knowledge related to grade-level standards.

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 meet expectations for providing a variety of demographic and personal characteristics.

The actors in the videos are from different races and portray people from many ethnicities in a respectful manner. Names in the story problems include Kolson, Jalil, Misha, and Sonia. The settings span a wide range including rural, urban, international, and space.

### Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 provide opportunities to group students, though they are rarely delineated in the materials. The Immersion Phase allows the teacher to group students many different ways. The second side of the Practice Printable can be done as a small group. The Student Reflection has some protocols that allow for a variety of grouping strategies.

### Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 do not present opportunities for teachers to draw upon home language and culture to facilitate learning.

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0
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Criterion Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 are web-based and compatible with multiple internet browsers and include opportunities for teachers to assess student learning. Although the materials are dependent on a digital platform, students use a limited range of technology within the platform. The materials are not easily customized for individual learners or local use and provide few, if any, opportunities for teachers and/or students to collaborate with each other through technology.

### Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0
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Indicator Rating Details

The digital materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 pose an essential question during an engaging introduction video for every lesson. Students can complete and submit the three components of the essential question (Immersion, Data & Computation, and Resolution) online, and the teacher will have a digital record of completion. These phases often incorporate the Mathematical Practices.

While the program is very technology-dependent, the students use a limited range of technology. The students do not use technology as a math tool. No virtual manipulatives were found. The digital materials include opportunities to assess students' mathematical understanding and knowledge of procedural skills through Test Trainer Pro, the Math Simulator, and the Clicker Quizzes. The Clicker Quiz offers opportunities for whole class discussions of multiple choice questions.

### Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0
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Indicator Rating Details

The digital materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 are web-based and compatible with multiple internet browsers. The materials are platform-neutral and compatible with Chrome, ChromeOS, Safari, and Mozilla Firefox. Materials are compatible with various devices including iPads, laptops, Chromebooks, and other devices that connect to the internet with an applicable browser.

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0
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Indicator Rating Details

The digital materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 include opportunities for teachers to assess student learning. Examples include:

• Teachers can assign lesson problems and assessments, as well as view assessment analytics.
• The Test Trainer Pro can be assigned by the teacher by domain.
• The Domain Replay gives students a brief review of various concepts.
• The Math Simulator is designed to “provide a conceptual foundation of the mathematical standard.”
• The 6-question Clicker Quiz provides immediate feedback with the multiple choice questions.
• None of the materials allow for teachers to modify questions nor add different questions.

### Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0
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Indicator Rating Details

The digital materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 include Milestone assessments that are “a summative evaluation following each cluster per grade. They are automatically graded, yielding the percentage of items answered correctly. The math items are created to include items of varying difficulty.”

“Test Trainer Pro acts as a low-stakes, formative assessment for students to practice testing under more relaxed and stress-free conditions. It is an adaptive tool and is designed to elicit the largest gains in students' achievement possible in the shortest period of time.”

None of the digital materials are customizable.

The digital materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 provide one lesson for the student to complete for each standard.

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0
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Indicator Rating Details

The digital materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 5 provide few, if any, opportunities for teachers and/or students to collaborate with each other through technology.

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Report Published Date: 12/29/2020

Report Edition: 2020

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Please note: Reports published beginning in 2021 will be using version 2 of our review tools. Learn more.

## Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

## Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

• Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
• Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

## Key Terms Used throughout Review Rubric and Reports

• Indicator Specific item that reviewers look for in materials.
• Criterion Combination of all of the individual indicators for a single focus area.
• Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
• Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
• Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

## Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.

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