## Achievement First Mathematics

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### Overall Summary

The materials reviewed for Achievement First Mathematics Grade 7 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.

###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

### Focus & Coherence

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

##### Indicator {{'1a' | indicatorName}}

Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Assessment questions are aligned to grade-level standards. No examples of above grade-level assessment items were noted. Each unit contains a Post-Assessment which is a summative assessment based on the standards designated in that unit. The assessments contain grammar and/or printing errors which could, at times, interfere with the ability to make sense of the materials.

Examples of assessment items aligned to grade-level standards include:

• Unit 1 Assessment, Question 13, “Shonte’s bank statement shows that her balance is $25.40. She has an outstanding bill of$65.99 that she has to pay immediately in order to avoid paying a fine. What will her account balance show after she pays her bill?” (7.NS.3)

• Unit 5 Assessment, Question 1, “Talik walked \frac{1}{2} of a mile in \frac{1}{4} of an hour. Cedric walked \frac{3}{4} of a mile in \frac{3}{4} of an hour. If these rates remain constant, which of the following statements is true? a) The two boys would walk the same distance in the same amount of time. b) Cedric would walk \frac{1}{2} mile in less time than Talik. c) Talik would walk \frac{1}{2} mile in less time than Cedric. d) Who walks faster depends on how far they walk.” (7.RP.1)

• Unit 6 Assessment, Question 12, “There were 48 cookies and 40 brownies in a jar on Monday. The next day, the number of cookies in the jar increased by 25%, and the number of brownies in the jar decreased by 10%. Find the overall percent change in goodies in the jar to the nearest whole number.” (7.EE.3)

• Unit 8 Assessment, Question 2, “Eight of the 32 students in your seventh-grade math class have a cold. The student population is 450. Your classmate estimates that 112 students in the school have a cold. a) Is this a reasonable conclusion to draw from the data? Explain why or why not. b) Describe a survey plan you could use to better estimate the number of students who have a cold. Include all necessary parts of the plan for creating a fair sample and collecting data.” (7.SP.1)

• Unit 9 Assessment, Question 14, “A 3D figure was sliced perpendicular to its base and the plane section that resulted was a triangle. The figure was then sliced horizontally and the plane section that resulted was a square. What is the name of one 3D shape from which the plane section could have come from? Explain on the lines below.” (7.G.3)

##### Indicator {{'1b' | indicatorName}}

Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Each lesson provides State Test Alignment practice, Exit Tickets, Think About It, Test the Conjecture or Exercise Based problems, Error Analysis, Partner Practice, and Independent Practice, which all include grade-level practice for all students. The Partner and Independent Practice provide practice at different levels: Bachelor, Masters and PhD. Each unit also provides Mixed Practice, Problem of the Day, and Skill Fluency practice. By the end of the year, the materials address the full intent of the grade-level standards. Examples include:

• Unit 1, Lesson 11, Exit Ticket, students solve real-world problems by adding and subtracting rational numbers. “Death Valley sits at an elevation of 212\frac{3}{4} feet below sea level and the temperature at noon is 119.5 degrees. Mt. Humphrey’s (the tallest point in Arizona) has an elevation of 13,918\frac{9}{10} feet and the temperature at the top is -19.07 degrees. What is the change in elevation and temperature between the two locations?” (7.NS.1d)

• Unit 3, Lesson 3, Independent Practice, Question 9 (PhD level), students understand how quantities are related by rewriting an expression in different forms. “Pretend that you are a test maker. Create four multiple choice answers (one has to be correct) for the problem below. Explain the error that each answer choice addresses. Write an equivalent expression for -4n-3(-2n+3).” (7.EE.2)

• Unit 4, Lesson 20, Exit Ticket Question 1, students use the formula for the area of a circle to solve problems. “The base of John’s coffee cup has a circumference of 12\pi cm. Exactly how much space does the base of the coffee cup take up?” (7.G.4)

• Unit 6, Lesson 13, Interaction with New Material, Question 1, students use proportional relationships to solve percent problems. “Magdalena works at a clothing store and makes both an hourly wage of $8.00 and gets paid a commission rate of 5% on the total cost of all the sales she makes. During her 4-hour shift, only one customer purchased clothing. They bought 2 scarves that normally cost$15 each but were on sale for ‘Buy 1, get 1 50% off’.  How much money did she earn during her shift?” (7.RP.3)

#### Criterion 1.2: Coherence

Each grade’s materials are coherent and consistent with the Standards.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.

##### Indicator {{'1c' | indicatorName}}

When implemented as designed, the majority of the materials address the major clusters of each grade.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6.5 out of 10, which is approximately 65%.

• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 95 out of 140, which is approximately 68%.

• The number of minutes devoted to major work (including assessments and supporting work connected to the major work) is 7825 out of 12,600 (90 minutes per lesson for 140 days), which is approximately 62%.

A minute-level analysis is most representative of the materials because of the way lessons are designed, where 55 minutes are designated for the lesson and 35 minutes are designated for cumulative review each day, so it was important to consider all aspects of the lesson. As a result, approximately 62% of the materials focus on major work of the grade. However, because 62% is close to the benchmark and both other measures met or exceeded the benchmark, Grade 7 meets the requirements for spending the majority of class time on major clusters.

##### Indicator {{'1d' | indicatorName}}

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Although connections are rarely explicitly stated, problems clearly connect supporting and major work throughout the curriculum. Examples where supporting work enhances major work include:

• Unit 4, Lesson 9, supporting standard 7.G.4 enhances the major work of 7.EE.4. Students represent and solve multi-step geometric problems using a complex equation. Independent Practice Question 5 (Master level), “A hexagon has six congruent sides and each side length is \frac{1}{2}n+2. What is the measure of one of the side lengths if the perimeter is 25?”

• Unit 5, Lesson 12, supporting standard 7.G.1 enhances the major work of 7.RP.2. Students understand a special kind of proportional relationship in scale drawings as either a reduction or the enlargement of a two-dimensional picture and determine the constant of proportionality that relates scale drawings as the scale factor. Independent Practice Question 6 (PhD level), “On a blueprint for an apartment building, the height of the door is 4 inches tall. The actual door is 84 inches high. If the rest of the blueprint follows this exact same scale, what would be the actual dimensions of a room that is 10 inches long and 18 inches wide on the blueprint? Express your answer in terms of feet (12 inches = 1 foot).”

• Unit 7, Lesson 6, supporting standard 7.SP.6 enhances the major work of 7.RP.2. Students develop uniform and non-uniform probability models and use proportional reasoning to predict the approximate relative frequency of outcomes (based on theoretical probability). Independent Practice Question 6 (Master level), “Yasmine has a bag of snacks that contains 40% Cheetos, 25% Doritos, 10% Fritos, and 25% pretzels. a) If she reaches into the bag and grabs one snack, and does so 15 times, how many Cheetos do you expect her to get?  b) Yasmine likes all the types of snacks except for Doritos. If she grabs a total of 40 snacks, about how many times will she get a type of snack that she likes?”

• Unit 10, Lesson 1, supporting standard 7.G.5 enhances the major work of 7.EE.4. Students define complementary and supplementary angles and determine the measurement of a missing angle by writing a simple equation. Partner Practice Question 5 (Master level), students are given a diagram of two intersecting lines and a ray coming out at 90\degree and asked, “In the diagram below, angle ABE is 90\degree. Angle EBD measures 3x and angle DBC measures 2x – 10. What are the measures of angles EBD and DBC?”

##### Indicator {{'1e' | indicatorName}}

Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. For example:

• Unit 3 Curriculum Review, Problem of the Day 3.1, students solve real-world and mathematical problems involving the four operations with rational numbers (7.NS.A) when they analyze proportional relationships (7.RP.A). Problem of the Day 3.1, Day 1, “Mr. Milliken is baking a cake for his upcoming wedding! He is going to start with a layer of cake, then a layer of icing, and so on, until the cake is finished with a layer of icing.  When finished, each layer of cake is 1\frac{1}{5} inches tall and each layer of icing is \frac{2}{5} of an inch tall. Mr. Milliken uses 1\frac{1}{4} cups of sugar for one layer of cake and one layer of icing together.  Ms. Nichols wants the cake to be 16 inches tall. How much sugar will Mr. Milliken use in creating this cake?”

• Unit 3, Lesson 4 connects 7.NS.A and 7.EE.B as students use the full range of rational numbers when they solve algebraic expressions and equations. Independent Practice, Question 10 (PhD level), “Are the expressions -4.5n+3\frac{1}{2}r-2.25r-(-2\frac{3}{4}n) and 1\frac{1}{4}(1.4n+r) equivalent? Prove it using two different methods.”

##### Indicator {{'2d' | indicatorName}}

The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade. Overall, there is an emphasis on the application aspect with the conceptual component of rigor being slightly less represented; however, each aspect of rigor is demonstrated throughout the curriculum. The materials often demonstrate a combination of aspects of rigor within single lessons and even single problems.

All three aspects of rigor are present independently throughout the program materials. Examples include:

Conceptual Understanding:

• Unit 1, Lesson 7, THINK ABOUT IT!, students use number lines to demonstrate conceptual understanding of subtracting integers. “Model and evaluate the addition and subtraction expressions on an open number line. a) 25 + (-37); b) 25 - 37. Explain a generalized rule that you could use to subtract integers without the aid of a number line.” (7.NS.1)

Fluency and Procedural Skill:

• Unit 4, Lesson 18, Exit Ticket, Question 2, students demonstrate fluency regarding the area of a circle by both estimating and finding the exact measure. “What is the exact and approximate area of a circle with a diameter of 6 feet? For the approximate area, round your answer to the nearest tenths place.” (7.G.4)

Application:

• Unit 4, Lesson 10, Independent Practice, Question 2 (Bachelor Level), students apply their knowledge about multi-step real world problems to find the winner of the reading contest. “Aaliyah and Yohance are having a competition to see who can read more pages over the coming weekend. Aaliyah has bet Ms. Solomon that she’ll read 50 more pages than Yohance. Both scholars read at an average rate of 40 pages per hour. Yohance says that he’s going to read for 7.5 hours this weekend. How many hours will Aaliyah need to read for in order to fulfill her promise of reading 50 more pages than Yohance?” (7.EE.4)

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

• Unit 2, Lesson 5, Partner Practice, Question 2 (Master Level), students demonstrate both conceptual understanding and procedural skill as they use a number line and an expression to represent division of rational numbers. “A submarine starts at the surface and then descends to a depth of 250 feet below sea level. It took the submarine 5 minutes to complete this dive. How many feet can the submarine dive in 1 minute? Draw a model and write an expression to solve.” (7.NS.2)

• Unit 5, Problem of the Day 5.1, Day 2, students demonstrate fluency and application with operations on rational numbers. “A water well drilling rig has dug to a height of –60 feet after one full day of continuous use. a) Assuming the rig drilled at a constant rate, what was the height of the drill after 15 hours? b) If the rig has been running constantly and is currently at a height of –143.6 feet, for how long has the rig been running? c) A snake is \frac{3}{4} the current distance underground of the rig and a spider is \frac{4}{5} of the same distance. How far away are the snake and the spider?” (7.NS.3)

• Unit 3, Lesson 2, Independent Practice, Question 8 (PhD level), students apply their conceptual understanding of variables to write and solve equations in real-world situations. “You and your friend made up a basketball shooting game. Every shot made from the free throw line is worth 3 points, and every shot made from the half-court mark is worth 6 points. Write an equation that represents the total amount of points, P, if f represents the number of shots made from the free throw line, and h represents the number of shots made from half-court. Explain the equation in words.”  (7.EE.4)

#### Criterion 2.2: Math Practices

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). However, there is no intentional development of MP5 to meet its full intent in connection to grade-level content.

##### Indicator {{'2e' | indicatorName}}

Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The Standards for Mathematical Practice are identified and incorporated within mathematics content throughout the grade level. The Mathematical Practices are listed in the Unit Overviews as well at the beginning of each lesson. There are instances where the Unit Overview gives a detailed explanation of the MPs being addressed within the unit, but the lessons do not cite the same MPs.

There is intentional development of MP1 to meet its full intent in connection to grade-level content. Examples include:

• Unit 1, Lesson 11, THINK ABOUT IT!, students use any estimation or an integer operation strategy to solve a problem and determine if their solution makes sense. “Maggie said that she could determine the answer to the problem below by just estimating the answer and comparing it to the given answer choices. Do you agree with Maggie? If so, explain and use estimation to prove she is correct. If not, explain and solve the problem to determine the actual answer. Dominic jumped from a height of 14.3 feet above the surface of a pool. He traveled 18.7 feet straight down into the water. From there he traveled up 25.55 feet to the top of the biggest water slide at the pool. What is the height of the tallest waterslide? a) -55.55; b) -29.55; c) 21.15; d) 55.55.”

• The Unit 2 Overview outlines the intentional development of MP1. “ In lessons 4, 10, and 11, students apply their understanding of rational number multiplication and division to multi-step problems and persevere in solving them. Students focus on identifying the appropriate starting point and appropriate rule to solve the problem. Students make sense of problems and persevere in solving them in most lessons, but MP1 is specifically emphasized in Unit 2 by pushing students to apply and evaluate their rules for rational number multiplication and division in multi-step and challenging problems to push understanding.”

• Unit 4, Lesson 19, Independent Practice, Question 7 (PhD Level), students solve an unrehearsed and unfamiliar problem by decoding information to work backwards. The problem, “Explain how you would be able to determine the area of a circle if you were given the circumference. Draw a diagram and provide an example in your explanation.”

There is intentional development of MP2 to meet its full intent in connection to grade-level content. Examples include:

• The Unit 2 Overview outlines the intentional development of MP2. “In lessons 6, 7, 8, and 9 students build on their abstract understanding of the connection between multiplication and division by identifying how to rewrite a division problem as multiplication, rewriting as multiplying by the reciprocal (multiplicative inverse) of the divisor, and rewriting numbers as terminating or repeating decimals. Lesson 12 concludes the unit by having students apply their understanding of multiplication and division rules to mathematical inequality statements with constraints on p and q. While students reason abstractly and quantitatively in most lessons, Unit 2 emphasizes MP2 with the use of rewriting expressions to deepen their reasoning, such as rewriting division as multiplication and to create rules for rational number multiplication and division.”

• Unit 5, Lesson 3, Partner Practice, Question 2 (Bachelor Level), students determine what numbers and quantities mean in a relationship. “The table below shows the relationship between the cost of renting a movie (in dollars) to the number of days the movie is rented. Read each statement below the table and determine if it is true or false. a) Dollars represents the independent variable; b) The relationship between the cost and the number of days is proportional because 6\div2=3 and 9\div3=3; c) The relationship between the cost and the number of days is not proportional because the values do not increase in order; d) The relationship between the cost and the number of days is proportional because there is a CoP of \frac{1}{3}.”

• In Unit 8, Lesson 4, Independent Practice, Question 1 (Bachelor Level), students analyze a dot plot, then find a solution using the data to determine if the quantity is reasonable.. “Consider the distribution below. Part A: Describe the distribution of the data Part B: Describe the variability of the data. Part C: What would you expect the distribution of a random sample of size 10 from this population to look like?”

##### Indicator {{'2f' | indicatorName}}

Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

There is intentional development of MP3 to meet its full intent in connection to grade-level content. Examples include:

• The Guide to Implementing AF Math describes Error Analysis lessons as one way to address MP3. “Purpose: Through the use of error analysis, guided questioning and discussion students will identify and fix a common misconception related to a skill they learned the previous day. These are sequenced so that after a particularly complex conceptual lesson or a lesson involving a skill that surfaces a common misconception, students get another focused at bat to either fix their misunderstanding or deepen their reasoning around key mathematical concepts and viable strategies to guide them away from making the same error. These lessons start with analyzing fictional student work and are structurally based off of the Standards for Mathematical Practice 3.”

• Unit 1, Lesson 9, Independent Practice #7 (PhD Level), students add and subtract rational numbers. “Using the multiple choice question below, determine which two answer choices that you can immediately eliminate without doing any calculations. Explain how you were able to eliminate those answer choices. Evaluate: -4.5 - (-1\frac{4}{5}) - (-2.1) + 4\frac{1}{2}. a) -12.9; b) 12.9; c) -5.7; d) 5.7.”

• Unit 4, Lesson 13, Error Analysis Lesson, THINK ABOUT IT!, students use variables to create equations. “Compare and contrast Scholar A’s work and Scholar B’s work on yesterday’s exit ticket question. Is either scholar correct? Use numbers and/or words to justify your answer on the lines below.”

• Unit 5, Lesson 14, Independent Practice #2 (Bachelor Level), students solve problems involving scale. “Mark claims that he can multiply that area of Rectangle A by 4 to get the correct area of Rectangle B. Do you agree with him? Explain and prove your answer.”

• Unit 6, Lesson 13, Independent Practice #4 (Master Level), students use proportional relationships to solve percent problems. “Justin wants to buy a new IPod that costs $250. When he gets to the Apple store, he sees that they are having a sale for 15% off all IPods. He then has a coupon that takes an additional 15% off the discounted price. Justin thinks that he can figure out the cost of the iPod by finding 30% of$250 and then subtracting that from $250. Do you agree or disagree with his claim? Explain.” • Unit 7, Lesson 8, Independent Practice, Question 4 (Master Level), students approximate the probability of an event. “Tishanna is experimenting with the same bag of pens. She randomly pulls a pen out of the bag 30 times, records the color, and replaces the pen. Her results are shown below. Step A: Now make a prediction for how many times Tishanna would pick a red pen, if she conducted 60 trials of the experiment. Step B: Which prediction are you more confident in – the prediction in question # 3, or the prediction you made in question #4? Why? Explain.” ##### Indicator {{'2g' | indicatorName}} Materials support the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The materials reviewed for Achievement First Mathematics Grade 7 partially meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Students are provided with occasions to develop their own task pathways, but have limited opportunities to choose tools. There is intentional development of MP4 to meet its full intent in connection to grade-level content. Examples include: • Unit 1, Lesson 8, Partner Practice, Question 3 (Master Level), students are asked to model by creating a situation. “Write a word problem that could be expressed by the expression 45 – 75 + 52 and draw a model to help solve.” • Unit 2, Lesson 4, Think About It, “Marcus is downloading albums in iTunes to update his playlists which is sorely needed. He buys 8 albums at$9 apiece. How much money is in his bank account if he started the day with $71 in his account? Draw a model and write an expression before solving.” • Unit 3, Problem of the Day 3.2, students generate their own solution pathway to solve a real-world problem. “Shania and her friends want to figure out what their scholar dollar average was last week. Shania earned$23, Anna had $45, Dominique had the highest check with$98, and Nandita’s read -$8. Vivian’s scholar dollar average was 2 times worse than Nandita’s. What is the average scholar dollar earnings for the five scholars?” • Unit 4, Lesson 10, students “represent and solve multi-step real world problems using a complex equation.” Think About It, “Ted is planning a vacation this summer. The resort he wants to stay at charges$125.25 per day plus tax. Ted books the trip for three days and it costs him 422.25. How much did Ted pay in taxes per day of his vacation?” Students engage in MP4 to solve real-life situations. There is no intentional development of MP5 to meet its full intent in connection to grade-level content because students rarely choose their own tools. Examples include: • Throughout the year, 12 lessons, all in Geometry, identify MP5 as a focus, so there is limited exposure to the practice. • Students are rarely given choice in tools to solve problems. Unit 1, Lesson 1, Independent Practice Question 3 (Bachelor Level), “Jamie’s bank account currently has a negative balance of -2 dollars. How much money will be in her account if she deposits 8 dollars?” Instead of being able to choose a tool, a number line is given, suggesting that this is the correct tool to use. • Lack of intentional development of MP5 is seen in misaligned identification in the Unit Overviews and lessons. The Unit 8 Overview, “In lessons 5, 6 and 7, students can choose from different tools such as tables, organized lists, etc. to represent their data in a meaningful way in order to efficiently calculate the mean and MAD of a sample set.” However, in Lesson 5, students are provided with tables and organized lists to interpret data. Partner Practice Question 1 (Bachelor Level), “The table shows the number of minutes Katie and Danielle trained for a cross-country run. a. Where does the data overlap? What does that mean in the context of this data?” They are not asked to choose from different tools to represent their data in a meaningful way. ##### Indicator {{'2h' | indicatorName}} Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. There is intentional development of MP6 to meet its full intent in connection to grade-level content. Many problems present students with the opportunity to attend to precision within the mathematics and the reasoning of the answer. Examples include: • Unit 2, Lesson 6, Partner Practice, Question 2 (Bachelor Level), students attend to precision when rewriting a division problem as a multiplication problem and solving. “Use multiplication to prove that the quotient of -10 ÷ 5 is negative and justify your reasoning.” • Unit 5, Lesson 10, Exit Ticket Question 2, students attend to precision as they compute unit rates with ratios of fractions. “$$3\frac{1}{3}$$ lb. of turkey costs10.50. What is the price per pound of turkey?”

• Unit 8, Lesson 6, Independent practice, Question 1 (Bachelor Level), students attend to precision as they compute unit rates with ratios of fractions. “Rachel and Molly are in the same science class. Rachel’s scores on her first three science quizzes were 79, 86, and 90. Molly’s scores were 70, 78, and 80. Calculate the means and the mean absolute deviations of the quiz scores.”

The instructional materials attend to the specialized language of mathematics. The materials use precise and accurate mathematical terminology. Examples include:

• At the beginning of each lesson plan, there is a section labeled “Key Vocabulary” for the teacher. Unit 4, Lesson 4, Key Vocabulary,

• “Equation: two expressions set equal to one another.

• Variable: a letter used to take the place of an unknown value.

• Solution: the value that makes an equation true.

• Arithmetic approach: the approach to solving a problem that involves arithmetic only; numbers and operations.”

• The teacher is routinely prompted to use precise vocabulary such as Unit 5, Lesson 5, Connection to Learning. “Students should understand that a graph is proportional if it is linear (i.e. forms a straight line) and passes through the origin because every value of x is multiplied by the CoP (constant of proportionality) to produce the corresponding output. Students should understand that the point (0,0) must be a part of a proportional graph because no CoP can be multiplied by 0 to produce a non-zero output.”

• Unit 7, Lesson 1, Opening, Debrief, FENCEPOST #1, students use a spinner to determine probability. “Probability measures how likely an event is from impossible to certain.” The teacher shows student work who has correctly placed an x on impossible for a.) and certain for b.) and asks, “Do you agree with this scholar?” Students might say, “I agree with this scholar because for the first problem, there is no possible way for someone to spin the spinner and it to land on 5 because there isn’t a 5 on the spinner so it is impossible. For the second problem, if you spin the spinner it must land on 1, 2, 3, or 4 so it is certain that it will happen.” The teacher explains, “What you are calculating is called a probability. Probability is the likelihood of an event or outcome happening. An event is an outcome in an experiment (in this case, the ‘experiment’ is spinning the spinner and each number is an event. If you land on 1, that is an event. If you land on 2, that is an event. Etc.).”

##### Indicator {{'2i' | indicatorName}}

Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards.

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

• Unit 2, Lesson 6, Connection to Learning and Conceptual Understanding describes the structure of fraction division which teachers guide students through before they have the opportunity to practice independently. “Students understand that any division equation can be rewritten as a multiplication equation where the dividend of the division equation is equal to the product of the multiplication equation and the divisor and quotient are the factors of the multiplication equation. Students understand that because all division equations can be rewritten with multiplication that the rules for multiplying integers extends to dividing integers.”

• Unit 3, Lesson 1, Test the Conjecture, Question 1, students use repeated addition and the commutative property within expressions to understand combining like terms. “Write two expressions that are equivalent to the expression 3x + 5 + 4x + 2 and indicate the expression that is in simplest form.” Teacher prompts include, “In order to help us combine like terms, we are going to expand each term in the expression that contains a variable. How could we expand this expression? How can we group the like terms so they are with each other?”

• Unit 5, Lesson 4, Partner Practice, Question 3 (Master Level), students use structure by creating a table to discern the pattern of repeated addition. “Mary is filling out a table to keep track of how much money is in her account. On the first day of the month, she has $50. On the third day she has$150. On the 4th day, she has $200. If her account continues the same way, write an expression to determine how much money she will have on the 9th day and how long it will take her to have$n in her account.”

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

• Unit 1, Lesson 3, Exit Ticket, Question 1, students use repeated reasoning to add integers. “Evaluate the expression: (-22) + 15 + (-9) and explain how you used the generalized rules for adding integers.”

• Unit 4, Lesson 17, THINK ABOUT IT!, “For the circle below, Chandler says that there isn’t enough information to determine the circumference without measuring. Joey disagrees and says that he can write an equation to solve for the circumference. Who do you agree with and why?” The teacher states, “The circumference of a circle is equal to Pi multiplied by the diameter. What will we be able to do if our conjecture is true? We will be able to write an equation for the circumference of a circle and substitute to determine either the circumference or diameter.” Students use repeated reasoning about the relationship between circumference, diameter, and Pi.

• Unit 6, Lesson 3, AIM, students “develop the formula part = \frac{p}{100}× total using a double number line diagram.” In THINK ABOUT IT!, the teacher prompts, “The number line below shows a general percent problem with the percent, part and whole. Write an equation and solve for the part. Using your equation, describe how you can find the percent of a number.” Then the teacher, “The percent of a number is equal to the percent (as a decimal) multiplied by the total.” Students use repeated reasoning to determine the percent of a number with a double number line.

### Usability

The materials reviewed for Achievement First Mathematics Grade 7 do not meet expectations for Usability. The materials partially meet expectations for Criterion 1, Teacher Supports, partially meet expectations for Criterion 2, Assessment, and do not meet expectations for Criterion 3, Student Supports.

##### Gateway 3
Does Not Meet Expectations

#### Criterion 3.1: Teacher Supports

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

The materials reviewed for Achievement First Mathematics Grade 7 partially meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the materials, include standards correlation information that explains the role of the standards in the context of the overall series. The materials do not provide a comprehensive list of supplies needed to support instructional activities. The materials contain adult-level explanations and examples of the more complex grade-level concepts, but do not contain adult-level explanations and examples and concepts beyond the current grade so that teachers can improve their own knowledge of the subject. The materials provide explanations of the instructional approaches of the program but do not contain identification of the research-based strategies.

##### Indicator {{'3a' | indicatorName}}

Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development. Teacher guidance is found throughout the materials in the Implementations Guides, Unit Overviews, and individual lessons.

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

• The Guide to Implementing AF Math provides a Program Overview for the teacher with information on the program components and scope and sequence. This includes descriptions of the types of lessons, Skill Fluency, Mixed Practice, and Problem of the Day.

• The Teacher’s Guide supports whole group/partner discussion, ask/listen fors, common misconceptions and errors, etc.

• Each lesson includes a table identifying the steps and actions for the teacher which helps in planning the lesson and is intended to be reviewed with a coach.

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Each lesson includes anticipated challenges, misconceptions, key points, sample dialogue, and exemplar student responses. Examples from Unit 6, Ratios and Proportional Relationships: Understanding and Applying Proportional Relationships to Percents, Lesson 6 include:

• “What do we want every student to take away or do as a result of this lesson? How will a teacher know if students have met this goal? Understand: Students understand that more than one expression can be used to determine the amount after the change. Students understand that percentages are additive and can be rewritten as the sum or difference of two percentages. Students understand that the change +/- the original amount is used to determine the amount after the change. Do: Students write two equivalent expressions that can be used to find the amount after the change given a percent increase or decrease and the whole or original value.”

• “Conjecture: Multiple expressions can be used to solve the same percent increase and decrease problem. Let’s form our conjecture for today. With your partner, come up with a conjecture about what we learned about writing expressions to represent and solve percent increase and decrease problems. Students might only specify a percent increase. If this is the case, move on to the TTC #1 (Test the Conjecture) which is a percent decrease problem and come back to revise the conjecture to include percent decrease.”

• “Frame - You have just formed our conjecture for today. A percent change will increase or decrease a number and we can use this understanding to write and solve different expressions that will have the same value. Post the Conjecture in a visible place for student reference.”

• “What will we be able to do if our conjecture is true? What is the question asking us to do? How can we apply our conjecture to solve the problem? How can we represent this on a double number line? What is one expression that we can write? Why? What is another equivalent expression that we can write? Why? How can we prove that our conjecture worked? Why does this make sense? So far, does our conjecture hold up?”

• “Anticipated Misconceptions and Errors: Students might not convert the percent change into a decimal when evaluating. Students might only find the change and not the amount after the change. Students might write the expression using addition instead of subtraction (and vice versa).”

Each lesson includes a “How” section that lists the key strategies of the lesson and delineates what “top quality” work should include. Examples from Unit 6, Ratios and Proportional Relationships: Understanding and Applying Proportional Relationships to Percents, Lesson 6 include:

• “Key Strategy: Annotate the problem for quantity, whole, and percent increase/decrease. Problem is represented using a double number line. One expression is written as the whole +/- the percentage increase/decrease of the whole. Another expression is written as the sum or difference of the whole and the percent of the whole. Expressions are evaluated to show equivalence (if needed).”

• “CFS (Criterion for Success) for top quality work: Problem is annotated for quantity, whole, and percent change. DNL created and labeled. Two equivalent expressions are written to find the amount after the change. Expressions are tested to be equivalent.”

##### Indicator {{'3b' | indicatorName}}

Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

The materials reviewed for Achievement First Mathematics Grade 7 partially meet expectations for  containing adult-level explanations and examples of the more complex grade/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject. There is very little reference or support for content in future courses.

Materials contain adult-level explanations and examples of the more complex grade/course-level concepts so that teachers can improve their own knowledge of the subject. Examples include:

• The Unit Overview includes an Appendix titled “Teacher Background Knowledge” which includes a copy of the relevant pages from the Common Core Math Progression documents which includes on grade-level information.

Materials rarely contain adult-level explanations and examples of concepts beyond the current course so that teachers can improve their own knowledge of the subject. Examples include:

• The Common Core Math Progression documents in the Appendix are generally truncated to the current grade level and do not go beyond the current course. At times, they may reference how the content connects to the next grade.

##### Indicator {{'3c' | indicatorName}}

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level/series. Examples include:

• Guide to Implementing AF Grade 7, Program Overview, “Scope and Sequence Detail is designed to help teachers identify the standards on which each lesson within a unit is focused, whether on grade level or not. You will find the daily lesson aims within each unit and the content standards addressed within that lesson. A list of the focus MPs for each lesson and unit and details about how they connect to the content standards can be found in the Unit Overviews and daily lesson plans.”

• The Program Overview informs teachers “about how to ensure scholars have sufficient practice with all of the Common Core State Standards. Standards or parts thereof that are bolded are addressed within a lesson but with limited exposure. It is recommended that teachers supplement the lessons addressing these standards by using the AF Practice Workbooks to ensure mastery for all students. Recommendations for when to revisit these standards during Math Practice and Friday Cumulative Review are noted in the Practice section of each unit.”

• The Unit Overview includes a section called Identify Desired Results: Identify the Standards which lists the standards addressed within the unit and previously addressed standards that relate to the content of the unit.

• In the Unit Overview, the Identify The Narrative provides rationale about the unit connections to previous standards for each of the lessons. Future grade-level content is also identified.

• The Unit Overview provides a table listing Mathematical Practices connected to the lessons and identifies whether the MP is a major focus of the unit.

• At the beginning of each lesson, each standard is identified.

• In the lesson overview, prior knowledge is identified, so teachers know what standards are linked to prior work.

Explanations of the role of the specific grade-level/course-level mathematics are present in the context of the series. Examples include:

In the Unit Overview, the Identify the Narrative section provides the teacher with information to unpack the learning progressions and make connections between key concepts. Lesson Support includes information about connections to previous lessons and identifies the important concepts within those lessons. Examples include:

• In the Unit Overview, How do the MPs live across lessons?, “Unit 8 emphasizes MP3 by pushing students to apply their understanding of the calculations and concepts of statistics in order to compare two populations in a meaningful way. In lesson 1, students begin the unit by making arguments about the need for random sampling, designing data collection that is valid, and the process of answering a statistical question. This underlying reasoning is the foundation upon which the rest of the unit relies. In lessons 6 and 7 students begin to apply their measures of center and variability to compare two populations and must critique the reasoning of others to ensure these comparisons are accurate.”

• Unit 10 Overview, connection to previous skills is identified. “Students wrap up the year with a geometry unit on angle relationships and triangle constructions. Prior to this unit, students have learned about the concept of angles as well as how to measure and construct angles with a protractor in 4th grade. Students studied properties of 2D shapes in 5th grade and revisited those properties in 6th grade through their study of area and surface area. In 7th grade, students revisited the topic of surface area and they also learned how to write and solve multi-step equations. These previously studied topics serve as the foundation needed to be successful in Unit 10.”

##### Indicator {{'3d' | indicatorName}}

Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

The materials reviewed for Achievement First Mathematics Grade 7 do not provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement. No evidence could be found related to informing stakeholders about the materials.

##### Indicator {{'3e' | indicatorName}}

Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials reviewed for Achievement First Mathematics Grade 7 partially meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

Materials explain the instructional approaches of the program.

• The Implementation Guide states, "Our program aims to see the mathematical practices come to life through the shifts (focus, coherence, rigor) called for by the standards. For students to engage daily with all 3 tenets, we structure our program into two main daily components: math lesson and math cumulative review. The math lessons are divided into three structural lesson types: conjecture-based lesson, exercise-based lesson, and error analysis lesson. On a given day students will be engaging in EITHER a conjecture-based, exercise-based lesson or less often an error analysis lesson. The math cumulative review component has three sub-components: skill fluency, mixed practice, and problem of the day. Three of the five school days students engage with all three sub-components of the math cumulative review. The last two days of the week have time reserved for lessons, reteach lessons, and assessments. See the diagram below followed by each category overview for more information.”

Materials do not include and reference research-based strategies.

• The materials do not explicitly name any strategies as research-based strategies.

##### Indicator {{'3f' | indicatorName}}

Materials provide a comprehensive list of supplies needed to support instructional activities.

The materials reviewed for Achievement First Mathematics Grade 7 do not meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

• Each lesson includes a list of materials, but it often does not support the teacher in preparing the lesson. For example, “Handout” is commonly named on the materials list, but there is no link provided to the document and the title of the handout is not provided. For example, in Unit 6 Lesson 5, the Lesson Overview includes, “Materials: Handout, calculator.”

##### Indicator {{'3g' | indicatorName}}

This is not an assessed indicator in Mathematics.

##### Indicator {{'3h' | indicatorName}}

This is not an assessed indicator in Mathematics.

#### Criterion 3.2: Assessment

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

The materials reviewed for Achievement First Mathematics Grade 7 partially meet expectations for Assessment. The materials identify the standards, but do not identify the practices assessed for the formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance but do not provide suggestions for following-up with students. The materials include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

##### Indicator {{'3i' | indicatorName}}

Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for Achievement First Mathematics Grade 7 partially meet expectations for having assessment information included in the materials to indicate which standards are assessed. There are connections identified for standards, but not the mathematical practices.

Materials identify the standards assessed for the formal assessments. Examples include:

• Each Unit Overview provides a chart that identifies CCSS Math Content standards for each item on the Unit Assessment. Occasionally, an individual item on the assessment identifies the standard, but in general, student-facing assessments do not include the standards.

• Each lesson includes an Exit Ticket that aligns with the standard of the lesson.

Materials do not identify the practices assessed for the formal assessments.

##### Indicator {{'3j' | indicatorName}}

Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The materials reviewed for Achievement First Mathematics Grade 7 partially meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The assessment system provides multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance but does not provide suggestions for following-up with students. Examples include:

• Assessments include an informal Exit Ticket in each lesson and a formal Unit Assessment for every unit.

• There is guidance, or “look-fors,” to teachers about what the student should be able to do on the assessments.

• All Unit Assessments include an answer key with exemplar student responses.

• The is a rubric for exit tickets that indicates, “You mastered the learning objective today; You are almost there; You need more practice and feedback.”

• There are no strategies or suggestions if students do not demonstrate understanding of the concept, and no next steps based on the results of the assessment.

##### Indicator {{'3k' | indicatorName}}

Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. There are a variety of question types including multiple choice, short answer, and constructed response. Mathematical practices are embedded within the problems.

Assessments include opportunities for students to demonstrate the full intent of grade-level standards across the series. Examples include:

##### Indicator {{'3o' | indicatorName}}

Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials reviewed for Achievement First Mathematics Grade 7 provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning; however, there are few opportunities for students to monitor their learning.

The program uses a variety of formats and methods to deepen student understanding and ability to explain and apply mathematics ideas. These include: Conjecture Based Lessons, Exercise Based Lessons, Error Analysis Lessons, and Math Cumulative Review. The Math Cumulative Review includes Skill Fluency, Mixed Practice, and Problem of the Day.

In the lesson introduction, the teacher states the aim and connects it to prior knowledge. In Pose the Problem, the students work with a partner to represent and solve the problem. Then the class discusses student work. The teacher highlights correct work and common misconceptions. Then students work on the Workshop problems, Independent Practice, and the Exit Ticket. Students have opportunities to share their thinking as they work with their partner and as the teacher prompts student responses during Pose the Problem and Workshop discussions. For each Exit Ticket, students have the opportunity to evaluate their work as well as get teacher feedback.

##### Indicator {{'3p' | indicatorName}}

Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for Achievement First Mathematics Grade 7 provide some opportunities for teachers to use a variety of grouping strategies. Grouping strategies within lessons are not consistently present or specific to the needs of particular students. There is no specific guidance to teachers on grouping students.

The majority of lessons are whole group and independent practice; however, the structure of some lessons include grouping strategies, such as working in a pair for games, turn-and-talk, and partner practice. Examples include:

• Unit 4, Lesson 8, Key Learning Synthesis, “Let’s form our key point for today. With your partner, come up with a key point for solving contextual situations that involve solving multi-step equations.”

• Unit 9, Lesson 11, Debrief, “If the class votes incorrectly or close to a split down the middle, T should call on a correct and incorrect scholar and engaged the class in a debate to clear the misconception.”

##### Indicator {{'3q' | indicatorName}}

Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The materials reviewed for Achievement First Mathematics Grade 7 do not meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

Materials do not provide any resources for students who read, write, and/or speak in a language other than English to meet or exceed grade-level standards through regular and active participation in grade-level mathematics.

##### Indicator {{'3r' | indicatorName}}

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for Achievement First Mathematics Grade 7 provide a balance of images or information about people, representing various demographic and physical characteristics. Examples include:

• Lessons portray people from many ethnicities in a positive, respectful manner.

• There is no demographic bias seen in various problems.

• Names in the problems include multi-cultural references such as Mario, Tanya, Kemoni, Jiang, Paige, and Tomi.

• The materials are text based and do not contain images of people. Therefore, there are no visual depiction of demographics or physical characteristics.

• The materials avoid language that might be offensive to particular groups.

##### Indicator {{'3s' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for Achievement First Mathematics Grade 7 do not provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials do not provide suggestions or strategies to use the home language to support students in learning mathematics. There are no suggestions for teachers to facilitate daily learning that builds on a student’s multilingualism as an asset nor are students explicitly encouraged to develop home language literacy. Teacher materials do not provide guidance on how to garner information that will aid in learning, including the family’s preferred language of communication, schooling experiences in other languages, literacy abilities in other languages, and previous exposure to academic everyday English.

##### Indicator {{'3t' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for Achievement First Mathematics Grade 7 do not provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials do not make connections to linguistic and cultural diversity to facilitate learning. There is no teacher guidance on equity or how to engage culturally diverse students in the learning of mathematics.

##### Indicator {{'3u' | indicatorName}}

Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for Achievement First Mathematics Grade 7 do not provide supports for different reading levels to ensure accessibility for students.

The materials do not include strategies to engage students in reading and accessing grade-level mathematics. There are not multiple entry points that present a variety of representations to help struggling readers to access and engage in grade-level mathematics.

##### Indicator {{'3v' | indicatorName}}

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials reviewed for Achievement First Mathematics Grade 7 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Manipulatives are described as accurate representations of mathematical objects in the narrative of the Unit Overviews, and although there is little guidance for teachers or students about the use of manipulatives in the lessons, the use of manipulatives can be connected to written methods. Examples include:

• In Unit 7, Lesson 7, Interaction with New Material Example 1, students predict sample space of a probability experiment using manipulatives, “T(eacher) should have an envelope ready with the following color distribution to use as a check at the end (1 red, 2 purple, 2 green, 5  blue). Ms. Fleck conducted a probability experiment in a previous class where scholars picked a color paper out of an envelope and recorded the frequency in the table below. She doesn’t remember the amount of each color in the envelope but she does know that there are 10 pieces of paper. Determine the number of each color without opening the envelope.”

• In Unit 10 Overview, In both lessons 3 and 9, students must choose the appropriate tools to explain their reasoning for angle relationships and constructions with triangles. Students may use a variety of tools to do this, such as sketching and labeling a diagram, applying definitions (such as complementary angles or SAS), and/or using  construction tools such as a ruler or protractor.”

#### Criterion 3.4: Intentional Design

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

The materials reviewed for Achievement First Mathematics Grade 7 do not integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, or provide teacher guidance for the use of embedded technology to support and enhance student learning. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

##### Indicator {{'3w' | indicatorName}}

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials reviewed for Achievement First Mathematics Grade 7 do not integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials do not contain digital technology or interactive tools such as data collection tools, simulations, virtual manipulatives, and/or modeling tools. There is no technology utilized in this program.

##### Indicator {{'3x' | indicatorName}}

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials reviewed for Achievement First Mathematics Grade 7 do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials do not provide any online or digital opportunities for students to collaborate with the teacher and/or with other students. There is no technology utilized in this program.

##### Indicator {{'3y' | indicatorName}}

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials reviewed for Achievement First Mathematics Grade 7 have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The student-facing printable materials follow a consistent format. The lesson materials are printed in black and white without any distracting visuals or an overabundance of graphic features. In fact, images, graphics, and models are limited within the materials, but they do support student learning when present. The materials are primarily text with white space for students to answer by hand to demonstrate their learning. Student materials are clearly labeled and provide consistent numbering for problem sets. There are several spelling and/or grammatical errors within the materials.

##### Indicator {{'3z' | indicatorName}}

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for Achievement First Mathematics Grade 7 do not provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

There is no technology utilized in this program.

## Report Overview

### Summary of Alignment & Usability for Achievement First Mathematics | Math

#### Math K-2

The materials reviewed for Achievement First Mathematics Grades K-2 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Achievement First Mathematics Grades K-2 do not meet expectations for Usability, Gateway 3.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

#### Math 3-5

The materials reviewed for Achievement First Mathematics Grades 3-5 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Achievement First Mathematics Grades 3-5 do not meet expectations for Usability, Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

#### Math 6-8

The materials reviewed for Achievement First Mathematics Grades 6-8 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Achievement First Mathematics Grades 6-8 do not meet expectations for Usability, Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

## Report for {{ report.grade.shortname }}

### Overall Summary

###### Alignment
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###### Usability
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##### Gateway {{ gateway.number }}
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