Report for 6th Grade
Overall Summary
The materials reviewed for Achievement First Mathematics Grade 6 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.
6th Grade
Alignment
Usability
Overview of Gateway 1
Focus & Coherence
The materials reviewed for Achievement First Mathematics Grade 6 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
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 6 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.
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Materials assess the grade-level content and, if applicable, content from earlier grades.
The materials reviewed for Achievement First Mathematics Grade 6 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 11, “Write an equivalent expression to 40 + 32 using the distributive property. The sum of two whole numbers within the parentheses should have no common factor greater than 1.” (6.NS.4)
Unit 5 Assessment, Question 6, “Manufacturer A requires 70 buttons for the manufacture of 10 shirts. Manufacturer B requires 68 buttons for the manufacture of 17 shirts. How many buttons will each require to manufacture 15 shirts?” (6.RP.3b)
Unit 7 Assessment, Question 6, “Given the set {4.2, 4.7, 5}, determine which of the values are solutions to the inequality, 4.3 + x < 9. Defend your answer by explaining why or why not for each of the values.” (6.EE.5)
Unit 9 Assessment, Question 7, “Julia is repainting her jewelry box with a length of 8 inches, a height of 5.5 inches, and a width of 3\frac{1}{2} inches. She is painting all 4 sides blue, the top purple, and she is not painting the bottom. How many square inches of each paint color does Julia need?” (6.G.4)
Unit 10 Assessment, Question 1, “For each of the following, identify whether or not it would be a valid statistical question you could ask about people at your school. Explain for each why it is, or is not, a statistical question. a) What was the mean number of hours of television watched by students at your school last night? (Yes, this is a valid statistical question because there is more than one answer and you can collect information from multiple sources.) b) What is the school principal’s favorite television program? c) Do most students at your school tend to watch at least one hour of television on the weekend?” (6.SP.1)
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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 6 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, Mixed Practice 1.3, Day 1, Question 4, students fluently subtract and multiply multi-digit decimals using the standard algorithm. “Rashad drove at an average speed of 50.55 miles per hour for 1.75 hours. He stopped at a rest stop and then drove at an average speed of 45.2 miles per hour for 2.25 hours. Did Rashad drive more miles before or after the rest stop? How many more miles?” (6.NS.3)
Unit 2 Lesson 7, Independent Practice Question 3 (Masters level), students use ratio and rate reasoning to solve percent problems. “Steven orders 8 pizzas for his birthday party. He expects that each person will eat 25% of a pizza. How many people can attend the party based on his prediction? Use a model to prove your answer.” (6.RP.3c)
Unit 6, Lesson 7, Independent Practice Question 3 (Master level), students understand that a variable can represent an unknown number. “Jeff planned to run a few miles over a certain number of weeks. He planned to run half a mile each weeknight and 4 miles on Saturday. Which expression(s) shows how many miles Jeff planned to run over a certain number of weeks. Circle all that apply. a) \frac{5}{2}+4; b) w(\frac{5}{2}+4); c) \frac{1}{2}w+4; d) \frac{5}{2}w+10; e) \frac{5}{2}+4w; f) 5w+(2)(4).” (6.EE.6)
Unit 7, Lesson 3, Independent Practice, Question 9 (PhD level), students write and solve real-world problems. “Michael bought 8 Granny Smith apples, 7 Macintosh apples, and p Red Delicious apples. She bought a total of 27 apples. Write and solve an equation that represents this problem.” (6.EE.7)
Criterion 1.2: Coherence
Each grade’s materials are coherent and consistent with the Standards.
The materials reviewed for Achievement First Mathematics Grade 6 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.
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When implemented as designed, the majority of the materials address the major clusters of each grade.
The materials reviewed for Achievement First Mathematics Grade 6 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 out of 10, which is approximately 60%.
The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 92 out of 140, which is approximately 66%.
The number of minutes devoted to major work (including assessments and supporting work connected to the major work) is 8316 out of 12,600 (90 minutes per lesson for 140 days), which is approximately 66%.
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 66% of the materials focus on major work of the grade.
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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 6 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 1, Lesson 16, supporting standard 6.NS.4 enhances the major work of 6.EE.3. Students use the distributive property to create an expression that expresses the sum of two whole numbers between 1-100 and explains how to apply the concept of factoring to the distributive property. Independent Practice Question 7 (Master level), “What values of a and b make the two expressions below equivalent? 36 + 54 = a(2 + b).”
Unit 3, Lesson 12, supporting standard 6.G.3 enhances major work standards 6.NS.6 and 6.NS.8. Students solve real-world and mathematical problems that involve points, lines, and polygons on the coordinate plane. In Independent Practice Question 4 (PhD level), students are given a coordinate graph and instructed, “Edwina is creating a diagram of her bedroom so that she can plan how to rearrange her furniture before moving anything. Use the following information below to help Edwina rearrange her room. Her room is in the shape of a rectangle. The area of her room is 86 square feet. Her bed covers 48 square feet of the floor. Her dresser covers 3 square feet of the floor. Her two night stands each have the dimensions \frac{3}{4} ft. by 1\frac{1}{4} ft. Use the information provided above and draw a plan for arranging Edwina’s furniture. Start by drawing the floor of her room. Be sure to label all vertices with coordinate pairs and label the dimensions of each figure you create.”
Unit 4, Lesson 11, supporting standard 6.NS.3 enhances major work standards 6.RP.2 and 6.RP.3. Given a unit rate, students find ratios associated with the unit rate and recognize that all ratios associated to a given unit rate are equivalent. Independent Practice #3 (Master level), “Aubrey has to type a 5-page article but only has 18 minutes until she reaches the deadline. If Aubrey is able to type at a constant rate of 0.25 page every 1 minute, will she meet her deadline? Show your work to defend your answer.”
Unit 9, Lesson 4, supporting standard 6.G.2. enhances the major standard 6.EE.7. Students apply the formulas V = lwh and V = bh to find the volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Independent Practice Question 5 (Master level), “A rectangular box is going to be filled with sand. The length of the box is 412 feet. The width 2\frac{1}{4} feet and the height is 9 feet. If sand is sold in bags of 12 cubic feet, how many bags of sand will be needed to fill the box?”
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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 6 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. Examples include:
Unit 4, Lesson 7 connects the work with decimal operations (6.NS.A) with the work of one variable equations (6.EE.B) as students draw a model and use substitution to check their work. Independent Practice, Question 4 (Master level), ”$$\frac{1.05}{k}=3.5$$.”
Unit 7 Curriculum Review, Problem of the Day 7.1 connects interpret and compute quotients of fractions (6.NS.A) with ratio concepts and reasoning (6.RP.A) as students create and compare equivalent ratios in a table using fractions and decimals. Problem of the Day 7.1, Day 2, “Edgar and Teri are each driving from their house to Disneyland for a vacation. Edgar is driving at a rate of 75.5 miles every 2.5 hours and Teri is driving at a speed of 41\frac{2}{5} miles every 1\frac{1}{5} hours. Fill out both ratio tables and graph the equivalent ratios representing each drivers’ speed to determine how much farther has Teri driven than Edgar after 5 hours and 30 minutes?”
Unit 10, Lesson 2 connects 6.SP.A and 6.SP.B as students create dot plots and describe the distribution of data in the dot plot in terms of center and variability. In the Partner Practice, Question 2 (Master Level), “At a local hospital, babies in the intensive care unit are given 24-hour attention from doctors and nurses. The staff records the amount of milk babies drink each hour in order to ensure that they are eating properly. The amount of milk consumed by the babies is recorded: 3\frac{1}{2} oz; 3\frac{3}{4} oz; 2\frac{3}{4} oz; 22 oz 3.5 oz; 3 oz; 4\frac{1}{4} oz; 3.75 oz; 3\frac{1}{2} oz; 2\frac{3}{4} oz. a) Create the dot plot below. b) Are there any clusters in the data set? c) Are there any peaks in the data set? d) Is the data symmetrical? How do you know? e) Are there any gaps in the data set? f) What is the spread of the values in the data set? g) What value best represents the center? What does the value mean in the context of the problem?”
Students’ work with ratios and proportional relationships (6.RP.A) is combined with their work in representing quantitative relationships between dependent and independent variables (6.EE.C). In Unit 4, Lesson 10 students develop 6.RP.A by using information from a ratio table and placing the ratios on the coordinate plane. In Unit 7, Lessons 9-12 students develop 6.EE.C when working with dependent and independent variables and graphing them. Students work in both domains independently though there is an implied connection between Unit 7 and the previous learning with proportional reasoning in Unit 4 when student graph relationships.
Examples where the materials miss the opportunity to connect two or more clusters in a domain or two or more domains in a grade:
Plotting rational numbers in the coordinate plane (6.NS.C) is part of analyzing proportional relationships (6.RP.A). Students work on these independently and no connections are made between the domains. In Unit 3, Lesson 13, students learn about graphing rational numbers but there is no connection to RP work. In Unit 4, Lesson 9, students graph proportional relationships on the coordinate plane but there is no connection with rational numbers.
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Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
The materials reviewed for Achievement First Mathematics Grade 6 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
The materials relate grade-level concepts explicitly to prior knowledge from earlier grades. This can be found in the progressions descriptions listed above, but also often focuses explicitly on connecting prior understanding. Examples include:
The Unit Overview includes “Previous Grade Level Standards and Previously Taught and Related Standards” which describes in detail the progression of the standards within each unit. In Unit 3, “Prior to 6th grade, students learned to represent positive rational numbers on a number line (3.NF.2 and 4.NF.6) and to plot points in the first quadrant of the coordinate grid (5.G.A). Students have also compared and ordered positive rational numbers, including decimal fractions (5.NBT.3b) and fractions (4.NF.2). This prior knowledge of location on a number line, coordinate geometry, and ordering positive numbers is fundamental for students being introduced to negative rational numbers for the first time in this unit.”
Each Unit Overview provides a narrative for the teacher that introduces the student learning of the unit and the background students should have. In Unit 10, Overview, Statistics and Probability – Representing and Analyzing Data, “Prior to this unit, students have had little exposure to statistics. Throughout their elementary schooling, however, they do talk about data analysis in each grade. While their study of measuring, representing, and interpreting data starts in 1^{st} grade, I will quickly review the previous three years. In 3^{rd} grade (3MDB), students generate, represent, and interpret data in bar graphs. In 4^{th} (4MD4) and 5^{th} (5MD2) grades, students represent and interpret data using line/dot. Unit 10 is the first time students learn about statistical questions and measures of center and variability. They also learn about new graphical representations – the box plot, frequency table, and histogram. On account of this, the unit focuses the majority of the time on these topics in order to develop students’ understanding of statistical representations and analysis.”
Each lesson includes a “Connection to Learning and Conceptual Understanding” section that relates to prior knowledge. In Unit 1, Lesson 11 Connection to Learning, “More directly, students learn to find factor pairs of numbers between 1 and 100, and identify numbers as prime or composite in 4th grade (4.OA.4). Ss (students) build directly off of this foundational knowledge in this lesson. FENCEPOST #1: Factors are numbers that you multiply together to get a product. FENCEPOST #2: Common factors are factors shared by two numbers.”
In the Scope and Sequence Detail from the Implementation Guide, the Notes + Resources column for some lessons includes a lesson explanation that makes connections to prior learning. In Unit 6, “Students have been taught the order of operations in 5th grade. The inclusion of exponents into the process is new.”
In the Scope and Sequence Detail from the Implementation Guide, there are additional progression connections made. The Cumulative Review column for each unit provides a list of lesson components and the standards addressed. Prior (Remedial) standards are referenced with an “R” and grade level standards are referenced with an “O.” In Unit 2, The Number System- Dividing Fractions, “Skill Fluency (4 days a week): 6.NS.3 (O)* Division, 6.NS.2 (O), 6.NS.4 (O)* GCF,LCM, Distributive Prop. Mixed Practice (3 days a week): 5.NBT.3 (R), 5.NBT.4 (R), 6.NS.3 (O), 6.NS.1 (O).”
The materials clearly identify content from future grade levels and use it to support the progressions of the grade-level standards. These connections are made throughout the materials including the Implementation Guide, the Unit Overviews, and the lessons. For example:
The end of the Unit Overview previews, “Mastery of this unit is essential to 6th grade and in future grades. In later units in 6th grade, students apply coordinate geometry when working with areas of a variety of polygons. In the 7th grade, students rely heavily on the number line to make sense of and form generalizations about rational number operations. They apply rational numbers to represent and solve real world and mathematical problems as well as to evaluate expressions and solve equations and inequalities. Additionally, students graph proportional relationships on the coordinate plane. In 8th grade, students work heavily on the coordinate plane as they learn about transformations, functions, linear equations, systems of equations, and bivariate data. Students also work with rational number operations when solving equations and systems of equations. Rational numbers and coordinate geometry continue to be integral throughout High School mathematics as well.”
Throughout the narrative for the teacher in the Unit Overview, there are descriptions of how the lessons will be used as the grade level work progresses. In the Unit 8 Overview, “In lesson 6, students use what they learned about calculating the area of a triangle to derive the formula for the area of trapezoids.”
The last paragraph of each narrative for the teacher in the Unit Overview describes the importance of the unit in the progressions. In Unit 7, “This unit is essential for 6th grade and future grades. Students will work with equations and inequalities throughout all future math courses. It is imperative in 6th grade that the conceptual foundations for equations and inequalities are deeply understood in order to set students up for more abstract manipulation and application of equations and inequalities in future grades. Students learn to represent problems with and solve multi-step equations and inequalities using inverse operations and number properties in 7th grade and continue to apply their understanding of and skills with equations and inequalities throughout the remainder of their math career.”
The narrative for the teacher in the Unit Overview makes connections to current work. In Unit 8, “Additionally, in 5^{th} grade, students used area models as a way to understand multiplication and division of whole numbers as well as multiplication of fractions. All of this work with area provides students with (a) strong base understanding of the concept from which to build as students dive deeper into their study of area in Unit 8.”
For units that correlate with the progressions document, the materials attach the relevant text so that connections are made. In Unit 7, Appendix A: Teacher Background Knowledge (after the assessment), the “6-8 Expression and Equations” progression document is included with the footnote, “‘Common Core Expressions and Equations Progressions 6-8’ by Common Core Tools. Achievement First does not own the copyright in ‘CC Expressions and Equations Progression’ and claims no copyright in this material.”
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In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.
The instructional materials for Achievement First Mathematics Grade 6 foster coherence between grades and can be completed within a regular school year with little to no modification.
As designed, the instructional materials can be completed in 140 days.
There are 10 units with 130 lessons total; each lesson is 1 day.
There are 10 days for summative Post-Assessments.
There is an Optional Cumulative Project at the end of Unit 10 on Statistics. The amount of time is not designated. Since it is optional, it is not included in the total count.
According to The Guide to Implementing Achievement First Mathematics Grade 6, each lesson is completed in one day, which is designed for 90 minutes.
Each day includes a Math Lesson (55 minutes) and Cumulative Review (35 minutes).
The Implementation Guide states, “If a school has less than 90 minutes of math, then the fluency work and/or mixed practice can be used as homework or otherwise reduced or extended.”
Overview of Gateway 2
Rigor & the Mathematical Practices
The materials reviewed for Achievement First Mathematics Grade 6 meet expectations for rigor and balance and practice-content connections. The materials reflect the balances in the Standards and help students develop conceptual understanding, procedural skill and fluency, and application. The materials make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).
Gateway 2
Criterion 2.1: Rigor and Balance
Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.
The materials reviewed for Achievement First Mathematics Grade 6 meet expectations for rigor. The 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.
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Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
The instructional materials for Achievement First Mathematics Grade 6 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
The instructional materials develop conceptual understanding throughout the grade level. Materials include problems and questions that promote conceptual learning. Examples include:
Unit 2, Lesson 1, Exit Ticket #1, students develop conceptual understanding of fraction division by modeling problems using a tape diagram. “Draw a model and evaluate the expression \frac{9}{10}\div\frac{3}{10}.” (6.NS.1)
Unit 4, Lesson 9, Partner Practice, Question 2 (Master), students develop conceptual understanding of equivalent ratios by interpreting data points in a table and a graph. “The table below shows the relationship between the number of ounces in various sized boxes of Cheerios and the number of Cheerios in the box. (Table provides 4 data points.) Using the template below (Quadrant I of a coordinate plane provided), make a graph showing the relationship between the number of ounces in a box of Cheerios and the actual number of Cheerios in the box. a) What does the point (14, 4,500) represent? How do you know? b) Are the ratios in the table equivalent? Provide two reasons for how you know.” (6.RP.3)
Unit 6, Lesson 10, Test the Conjecture #1, students develop conceptual understanding of equivalence by analyzing an equation. Teacher prompts include, “Is the following equation true? 4m + 12 = 2(m + 6). What is the question asking us to do? How do you know? How can we apply our conjecture to this problem?” (6.EE.3)
Materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Examples include:
Unit 4, Lesson 2, Independent Practice, Question 3 (Bachelor level), students demonstrate conceptual understanding of ratio relationships by creating equivalence models. “Write two ratios that are equivalent to 3:5. Use a model to prove that each ratio is equivalent.” (6.RP.3a)
Unit 6, Lesson 11, Exit Ticket, Problem 1, students demonstrate conceptual understanding of generating equivalent expressions by using properties of operations to rewrite expressions. “Without substituting a value in for x, prove that 3x+9x-2x is equivalent to 10x .” (6.EE.3)
Unit 8, Lesson 2, Independent Practice, Question 5 (Bachelor Level), students demonstrate conceptual understanding of finding area by decomposing parallelograms into triangles. “Brittany and Sid were both asked to draw the height of a parallelogram. Their answers are below. Who is correct? Explain your answer. Is there another way they could have drawn in the height? If so, draw the different way to identify the height on one of their parallelograms and explain.” (6.G.1)
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Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.
The materials for Achievement First Mathematics Grade 6 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.Although there are not many examples to practice within a lesson, students are provided opportunities to practice fluency both with a partner and individual practice, especially within exercise based lessons and the skill fluency of the cumulative review section.
The materials develop procedural skill and fluency throughout the grade level. Examples include:
Unit 1, Lesson 11, Interaction with New Material, students develop procedural skill and fluency by finding common factors and multiples. “Ex. 1) The Ski Club members are preparing identical welcome kits for the new skiers. The Ski Club has 72 hand warmer packets and 48 foot warmer packets. What is the greatest number of identical kits they can prepare using all of the hand warmer and foot warmer packets? How many hand warmer packets and foot warmer packets will there be in each kit? ...Based on our understanding of the problem, what is our plan for solving this problem? ...Note to teacher: Ss will likely struggle to make the connection to the GCF. Push hard on Ss understanding that you are dividing each total up and make sure that students truly understand that the number of groups will be the same for both types of warmer and the size of the group will be different.” (6.NS.4)
Unit 7, Skill Fluency 7.3, Day 1, Question 5, students develop procedural skill and fluency by using substitution to make equations true. “Which equation is true if x = 5? a) 3x = 8; b) 2x = 10; c) x + 5 = 5; d) 25 - 5 = x.” (6.EE.5)
Unit 8, Skill Fluency 8.2, Day 1, Question 6, students develop procedural skill and fluency by using properties of operations to generate equivalent expressions. “What is the correct first step to take in order to simplify the expression below? [3.5 × (5 - 4.3)] + 2.7: a) Subtract 4.3 from 5; b) Multiply 3.5 by 2.7; c) Multiply 3.5 by 5.” (6.EE.3)
The materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade-level. Examples include:
Unit 1, Lesson 1, Independent Practice, Question 1 (Bachelor Level), students demonstrate procedural skill and fluency by using operations on decimals. “Evaluate each expression: a) 23 – 0.324; b) 9.3 + 19.59.” (6.NS.3)
Unit 2, Skill Fluency 2.2, Day 1, Problems 1-4, students demonstrate procedural skill and fluency by dividing multi-digit numbers. "1) 1,986 ÷ 60 = ?; 2) Solve: 80.25\div20= ?; 3) Find the quotient: 540\div0.60= ?; 4) 35.2\div5.5= ?” (6.NS.2)
Unit 6, Lesson 2, Independent Practice, Question 3 (Master Level), students demonstrate procedural skill and fluency by evaluating expressions. “Evaluate each expression: a) 24\frac{3}{5}+(4^3\times(8.2-2)); b) 6^2 + (13.5 - 5 + 2) × 2^3 + 3\frac{8}{10}” (6.EE.2c)
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Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.
The materials reviewed for Achievement First Mathematics Grade 6 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Students are given multiple opportunities to engage in real-world applications especially within exercise based lessons as well as the problem of the day in each cumulative review.
Materials include multiple routine and non-routine applications of the mathematics throughout the grade level. Examples include:
Unit 6, Mixed Practice 6.3, Day 1, Question 4, students apply skills related to solving routine problems using division of fractions. “Carla wants to know how many batches of birdseed she can make with 3\frac{1}{2} cups of sunflower seeds. She puts \frac{1}{6} cup of sunflower seeds in every batch. Carla divides 3\frac{1}{2} by \frac{1}{6} to find the answer. She says this is the same as multiplying \frac{1}{6} by \frac{7){2}. a) Is Carla correct? Why or why not? b) Using a correct method, find the solution. Show your work.” (6.NS.1)
Unit 7, Lesson 12, Partner Practice, Question 2 (Master Level), students represent and analyze routine quantitative relationships between dependent and independent variables. "Sam drove his car at a constant speed for t minutes and traveled a total of m miles. This relationship is represented in the table below. (3 data points provided, leading to 1.5t = m) If Sam drove 14.25 miles in all, how many minutes had he been traveling?” (6.EE.9)
Unit 10, Problem of the Day 10.1, Question 2 - students apply skills related to solving problems utilizing decimals in a non-routine application. "Four 6th graders are working on a project. They are going to paint a large banner and need to protect the floor. They measured the floor, which is 3.05 meters by 3.68 meters. Plastic is sold in rolls of 0.5 square meters each. How many rolls of plastic will they need to buy in order to cover the floor?” (6.NS.3)
Materials provide opportunities for students to independently demonstrate routine and non-routine applications of the mathematics throughout the grade level. Examples include:
Unit 3, Lesson 12, Independent Practice, Question 3 (Master Level), students solve real life, non-routine problems such as graphing points on the coordinate plane and using them to find area. "Mason Rice Elementary School is creating a new playground in the park behind the school. The playground’s perimeter is rectangular and is 60 feet long with a width of 15\frac{1}{2} feet. The planning committee is drafting the design of the new playground on a coordinate grid. They started by placing one corner of the park at (-8, 8). Each unit on the coordinate plane represents 1 foot. a) Plot the other three corners of the playground, label the coordinates of each corner, and connect the corners to create a rectangle. b) The committee is planning on splitting the playground diagonally in order to make two separate spaces for younger kids and older kids. Draw a line that divides the playground diagonally. How many square feet of space is the committee allocating for each part of the playground?” (6.NS.6c, 6.NS.8, 6.G.1)
Unit 4, Lesson 5 Exit Ticket, Question 2, students apply skills related to solving problems using ratio reasoning in non-routine ways. “Josh was solving the following problem: The Superintendent of Highways is interested in the numbers of commercial vehicles that frequently use the county’s highways. He obtains information from the Department of Motor Vehicles for the month of September and finds that for every 14 non-commercial vehicles, there were 5 commercial vehicles. If there were 108 more noncommercial vehicles than commercial vehicles, how many of each type of vehicle frequently use the county’s highways during the month of September? He says that he cannot solve it because \frac{108}{14} = a number with a decimal remainder. What is the mistake that Josh is making? Find the mistake, and solve correctly.” (6.RP.3a)
Unit 5, Day 2, Problem of the Day, students apply skills related to solving problems using ratio reasoning in a non-routine problem. "Gylissa and Alicia are developing a business of making and selling slime. The table below shows corresponding amounts of all ingredients they use to make their slime. Part A: If Gylissa and Alicia always use the same recipe when making slime, what are the values of x and y? Part B: Gylissa and Alicia receive a huge order of 6 cups of slime for each student in their class of 24 students. How many cups of each ingredient will they need to fill the order? Part C: Jadine and Tiarah also decide to make a slime business, but their recipe uses 6 cups of water, 8 cups of glue, and 3 cups of borax. Whose recipe will make a stickier slime? Show your work below to prove your answer.” (6.RP.3a)
Unit 7, Lesson 7, Independent Practice, Question 7 (PhD Level), students apply skills related to writing and solving routine one-step equations. "Nadia bought five food tickets that each cost x dollars and three drink tickets that each cost $2 to attend a spaghetti fundraiser at her school. She spent a total of $33.50. Write an equation that represents the cost of each food ticket.” (6.EE.7)
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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 6 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade. 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 5, Independent Practice, Question 4b (Master Level), students use models and equations to conceptualize division with the standard algorithm. "For each word problem, draw a model, write an equation, and solve the problem. b. Thomas has 575 pennies that he wants to exchange for quarters. How many quarters will he receive in exchange for his 575 pennies?" (6.NS.2)
Fluency and Procedural Skill:
Unit 6, Lesson 1, Independent Practice, Question 6 (Master Level), students develop fluency with evaluating numerical expressions that include exponents. “Evaluate the expressions: a) 90 - 5^2 × 3.5; b) 6.4 - 2^2\div2 + 0.3^2.” (6.EE.1)
Application:
Unit 7, Problem of the Day, 7.3, Day 2, students apply their knowledge about using a variable to represent an unknown in an equation to find out about fast food profits. “Wendy’s has a number of franchises, f, in Brooklyn. Each franchise makes $223 every hour. a) Write an expression to represent, m, the total amount of money all Wendy’s franchises make per hour. b) If m = 7,136 how many Wendy’s franchises are there in Brooklyn?” (6.EE.6)
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 4, Partner Practice, Question 1 (Bachelor level), students demonstrate both conceptual understanding and procedural skill as they create a model and use the standard algorithm to divide fractions. “Evaluate each expression using a model and using the algorithm: a) 2\frac{4}{5}\div\frac{2}{5}; b) 3\frac{5}{6}\div\frac{2}{3}” (6.NS.1)
Unit 3, Lesson 16, Independent Practice #2 (Master Level), students demonstrate procedural skill and application as they meet the requirements to construct a rectangle. “Construct a rectangle on the coordinate plane that satisfies each of the criteria listed below. Identify the coordinates of each of its vertices. 1) Each of its vertices lies in a different quadrant; 2) Its sides are either vertical or horizontal; 3) The perimeter of the rectangle is 28 units; 4) Using absolute value, show how the lengths of the sides of your rectangle provide a perimeter of 28 units.” (6.G.3)
Unit 4, Lesson 5, Exit Ticket, students demonstrate both procedural skill and application as they use ratio reasoning to solve real-world and mathematical problems. “For every six hot dogs that are shipped to a store, two hamburgers are shipped. Yesterday, 12 hamburgers were added making the amount of hot dogs and hamburgers shipped equal. How many hot dogs and hamburgers were shipped originally?” (6.RP.3)
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 6 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.
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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 6 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The 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:
The Unit 3 Overview outlines the intentional development of MP1. “In lessons 4 and 12, students make sense of integers in real-world contexts by translating them to a number line. In lesson 16, students solve complex, multi-step problems involving integers on the coordinate plane by making sense of real-world situations and persevering to solve them. MP 1 is a major focus of Unit 3 as students make sense of rational numbers in various contexts and persevere in solving problems and situations involving them.”
Unit 2, Lesson 10, Independent Practice Question 7 (PhD level), students find an entry point and persevere to solve a multi-step problem involving rational numbers. “Amare paid $16.50 to buy a book. The cost of the book is $$2\frac{1}{2}$$ the cost of a magazine. He bought 3 books and 2 magazines with a $50 bill. How much change should he receive?”
Unit 5, lesson 12, Independent Practice Question 7 (PhD Level), students make sense of a familiar situation in order to find a solution. “Tricia had a birthday party. During the party, she opened 36 gifts, which was 60% of all of her gifts. After the party, she opened the rest of the gifts and found that 25% of them were the same present, so she returned all but one of the duplicate gifts. How many gifts did she return? Show your work.”
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 3-5, students reason abstractly and quantitatively about situations involving the division of fractions. By utilizing the context of the problem, students reason to determine the proper division expression for the situation. In lessons 10 and 11, students reason to decontextualize word problems and translate them into expressions and equations for solving. MP 2 is a major focus of Unit 2 as students reason quantitatively about complex situations in order to translate them into mathematical situations they can solve.”
Unit 2, Lesson 3, Independent Practice Question 2 (Master Level), students have to use ratio reasoning with fractions and then put their answer back into context in order to answer the question. “Melanie is planning a hiking trip. She knows that she estimates that she will finish a liter of water every \frac{3}{4} mile that she hikes. Using the table below (given 3 trails and their distance), answer each of the following questions. a) How many liters of water will Melanie drink if she does the Lily Pond loop? b) How many liters of water will Melanie drink if she hikes to Starlight point and back?”
Unit 7, Lesson 14, Exit Ticket, students reason abstractly and quantitatively as they solve and graph the solution for one-step inequalities. “Exit Ticket: Blayton is at most 2 meters above sea level. Part A: Select all of the statements below that are true about the scenario: a) The phrase at most 2 means values less than two are included; b) The phrase at most 2 means values more than two are included; c) The value 2 would be included in the solution; d) An inequality that represents this scenario is x ≥ 2; e) 2 meters below sea level would be included in the solution set for the inequality representing this scenario. Part B: Represent Blayton’s possible elevation on a graph.”
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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 6 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
There is intentional development of MP3 to meet its full intent in connection to grade-level content. 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 2, Lesson 9, Error Analysis Lesson, THINK ABOUT IT!, students compare exit ticket responses about the magnitude of the fraction quotient in relationship to 1. Teacher prompts include, “Which scholar’s work did you agree with? Turn and tell your partner who you chose and why. Why does this relationship between the dividend and divisor make sense? What error did this scholar make? What did this scholar do to get this correct, and why was that helpful?”
Unit 6, Lesson 14, THINK ABOUT IT!, students identify equivalent expressions. “Angela drew a regular octagon (meaning all the sides are the same length) with a side length of 3p + 2. Write two equivalent expressions that represent the perimeter of the octagon. Explain how you know that the expressions that you wrote are equivalent.”
Unit 7, Lesson 5, Error Analysis Lesson, Think About It, students investigate 1-step 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 8, Lesson 6, Independent Practice, Question 4 (Master Level), students decompose shapes into triangles to find area. “Explain how you can use triangles to derive the area formula for trapezoids. Use an example to help illustrate the explanation.”
Unit 10, Lesson 5, Test the Conjecture, Question 1, students work with measures of center to understand what a single value represents. “Over the last ten days, the temperatures in Miami, Florida have been 80\degree, 78\degree, 80\degree, 76\degree, 85\degree, 84\degree, 82\degree, 79\degree, 76\degree, and 40\degree. The weatherman made an error and forgot to include the 40 degrees when finding the mean and median of the data. Should the weatherman report out the incorrect mean or the median in order to try to hide his mistake and report accurately about the weather? Prove your answer mathematically.” (6.SP.3)
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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 6 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 2, Mixed Practice 2.3, Day 3, Question 3, students apply skills related to fraction division. “Ellie ran a 1\frac{3}{4} mile special race course. Every \frac{1}{8} mile, there was an obstacle, with a final obstacle at the finish line. How many obstacles did Ellie encounter in the race? Use a model and/or words to explain your thinking.”
Unit 4, Mixed Practice 4.3, “Master Level problem, Question 3, “One type of soda machine uses 2 ounces of flavoring syrup for every 16 ounces of soda. A different soda machine uses 4 ounces of flavoring syrup for every 30 ounces of soda. Which soda machine uses less flavoring syrup? Show your work.”
In the Implementation Guide, the Problem of the Day Overview explains, “Structurally, mixed practice focuses on the Standards for Mathematical Practice 1 and 4, as students are focusing on both perseverance in problem solving and mathematical modeling. This component includes spiraled material so that students must apply previously learned skills and concepts several days, weeks, or months after the related lesson was taught.”
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, six lessons, all in Unit 10, identify MP5 as a focus, so there is very limited exposure to the practice.
Students are rarely given choice in tools to solve problems. Unit 8, Lesson 8, students calculate the area of figures given a coordinate plane. The materials list has a calculator and a handout and the coordinate grid is pre-numbered and pre-labeled. There is no opportunity to choose a tool to solve the problems.
Unit 10, MP5 is misidentified. “In lessons 5-7, students use measures of center as a tool to describe a data set. In lesson 11, students utilize range as a tool to measure variability of a data set. In lesson 13 students utilize their toolbelt of statistical tools to describe data sets. MP5 is a major focus of Unit 10 as students equip themselves with new statistical tools to help them better describe data sets and practice utilizing them in different contexts throughout the unit.” However, measures of center and statistical concepts are new content learning for Grade 6, so they cannot be used as a tool yet to support students in making mathematics more accessible.
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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 6 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
There is intentional development of MP6 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 1, Lesson 5, Question 4 (Master Level), students attend to precision when they apply the division algorithm to divide a three and four-digit dividend by a two- and three-digit divisor. “For each word problem, draw a model, write an equation, and solve the problem: a) Elise has 572 quarters that she has collected over the last several years. She wants to exchange all of her quarters for pennies. How many pennies will she receive in exchange for 572 quarters? b) b. Thomas has 575 pennies that he wants to exchange for quarters. How many quarters will he receive in exchange for his 575 pennies?”
Unit 4, Lesson 5, Independent Practice, Question 3 (Master Level), students attend to precision as they solve ratio problems involving comparisons using a tape diagram. “Review the student work below and determine whether or not it is correct. If it is correct, explain why. If it is incorrect, explain why and find the correct answer. For every 2 earrings sold at a store, 6 bracelets are sold. Today they had an earring sale and sold 12 extra earrings, making the total number of earrings and bracelets sold the same. How many bracelets did they sell in total?”
Unit 7, Lesson 5, Independent Practice, Question 1 (Bachelor Level), students attend to precision as they solve and check the solution of one-step equations using substitution. “Directions: Draw a model to solve each equation and check your answer using substitution: 14 = m - 37.”
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,
“Ratio - A comparison of a pair of non-negative numbers, A:B, which are not both 0. Units can be alike or different.
Term - 1 part of a ratio (i.e. in ratio A:B, A is a term and B is a term). Terms can represent like or unlike quantities.
Like Quantities - Two quantities with the same unit (e.g. girls and boys- both people).
Unlike Quantities - Two quantities with different units (e.g. dollars per gallon, laps per minute).
Equivalent ratio – Two ratios that express the same relationship between two terms.
Tape diagram - A diagram used to represent equivalent ratios that have the same units.”
Unit 6, Lesson 3, Exit Ticket Question 3, students are directed to use appropriate mathematical language. “When you take a taxi, the driver charges an initial fee when you start a ride and then an additional charge for every mile driven in the cab. If the total fare for a cab ride is 3.5m + 2.5 after riding for m miles, what does the 2.5 represent? Explain (use appropriate math vocabulary in your explanation).”
Unit 9, Lesson 1, Opening, Debrief, FENCEPOST #1, students utilize precise vocabulary about 3D shapes. “The shapes that you cut out of the paper are called ‘nets.’ For the first net, what solid were you able to form? How do you know?” Students might say, “I was able to form a rectangular prism. I know this is a rectangular prism because it has opposite parallel bases that are rectangles.” The next teacher prompt, “For the second net, what solid were you able to form? How do you know?” Students might say, “I was able to form a triangular prism. I know this is a triangular prism because it has opposite parallel bases that are triangles.”
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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 6 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards.
There is intentional development of MP7 to meet its full intent in connection to grade-level content. Examples Include:
Unit 6, Lesson 2, Think About It!, students analyze the structure of expressions with order of operations. “Antoine, Rosa, and Michelle are having a debate about how to evaluate an expression. Analyze their work and settle the debate by explaining: 1) Who solved correctly. 2) How you know that they solved correctly.” Students look for structure in expressions to manipulate them for efficient simplification.
Unit 6, Lesson 12, Think About It!, students learn about the structure of distributive property as a quicker route of creating equivalent expressions. “You can represent a number next to parentheses as repeated addition.” During instruction, the teacher, “The expression 2(a + 4) means, ‘$$2 × (a + 4)$$.’ Using this understanding, write two equivalent expressions to 2(a + 4) and explain how you came up with the two expressions.” Students might say, “I agree with the expression because we know that multiplication is the same as repeated addition. If we think of 2 as the number of groups and (a + 4) as the group size, then we have two groups of (a + 4), which can be written as (a + 4) + (a + 4).”
Unit 8, Lesson 1, Opening, THINK ABOUT IT!, students look for and make use of structure as they analyze the structure of each shape they are working with and reason about this structure to derive the area of it. “Louis’ teacher asked him to find the area of the parallelogram pictured below. He wasn’t sure what the area formula was for parallelograms, so he cut a right triangle off of the left side of the parallelogram and moved the triangle to the other side of the parallelogram, forming a rectangle. You can see his steps below. Assuming that what Louis did is okay, how should he find the area of the parallelogram? Show and explain in the space below.”
There is intentional development of MP8 to meet its full intent in connection to grade-level content. Examples Include:
Unit 1, Lesson 7, THINK ABOUT IT!, Debrief, students have the opportunity to generalize understanding about “multiplying a division expression by a fraction in the form of 1 does not change the quotient.” The teacher prompts, “Based on your calculations, we know that the expressions in set A are equivalent and the expressions in set C are equivalent because you can multiply the divisor and dividend each by 10 and by 100 respectively. Do you agree or disagree with this student’s explanation and work?” Students might say, “I agree with this work because the student showed that the expressions are equivalent by multiplying by a form of 1. For example, in set A, you can multiply the first expression by \frac{10}{10}, which is equal to 1, to get the second expression. For set C, you can multiply the first expression by \frac{100}{100}, which is also equal to 1 and therefore the resulting expression is equivalent to the first. For set B, the student did not multiply by a form of 1. Instead, s/he just multiplied the denominator by 10 and the quotients were not equivalent.” Students express regularity in repeated reasoning when manipulating division expressions involving decimals. They shift place value relationships to make solving these expressions easier for them.
Unit 4, Lesson 12, Independent Practice, Question 2 (Bachelor Level), students develop an understanding of repeated addition to create equivalent rates and ratios, and determine that all ratios with the same unit rate are equivalent. “A publishing company is looking for new employees to type novels that will soon be published. The publishing company wants to find someone who can type at least 45 words per minute. Dominique discovered she can type at a constant rate of 704 words in 16 minutes. Does Dominique type at a fast enough rate to qualify for the job? Explain why or why not.”
Unit 6, Lesson 1, Think About It, students have the opportunity to make sense of repeated reasoning as they evaluate exponents. “Complete the table below. Explain how you came up with the exponential expressions.” The table includes the multiplication expression, product, and exponential expression.
Overview of Gateway 3
Usability
The materials reviewed for Achievement First Mathematics Grade 6 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
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 6 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 6 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development. 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, Expressions and Equations - Algebraic Expressions, 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: As a result of this lesson, every student understands that they can write an expression to represent a real world context. They understand that the real world context and the algebraic expression represent the same thing. Additionally, students understand that they have to very specifically define the meaning of a variable used in an expression to ensure that the expression does in fact represent the real world context accurately and is interpreted correctly. Do: As a result of this lesson, every student is able to define a variable and write an expression to represent a real world context.”
“ANTICIPATED MISCONCEPTIONS AND ERRORS: Students may not define the variable clearly or may define it inaccurately. Students may switch the order of the number and variable in the expression.”
“Planner’s note: Students absolutely must understand that the expression does not correctly represent the context if the variable is not defined correctly.”
Teacher prompts: “Without using numbers, what is this problem asking us to do? How did you annotate the problem and what additional meaning did the annotations give the problem? How should we apply our KP (Key Point) to this problem? Teacher writes on the board and students write in notes. On your own, write an expression to represent this context. Be prepared to defend the expression you wrote. Do we agree with this expression? Why?”
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, Expressions and Equations - Algebraic Expressions, Lesson 6 include:
“Key Strategy/ies: Annotate the problem with margin notes (part, total, group size, and number of groups as well as operations when appropriate). Define the variable clearly. Write an expression to represent the context.”
“CFS (Criterion for Success) for top quality work: Problem is annotated with margin notes. Variable is defined clearly. Expression is written.”
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 6 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:
Unit Overviews provide thorough information about the content of the unit which often includes definitions of terminology, explanations of strategies, and the rationale about incorporating a process. Unit 5 Overview, “In lesson 8, students use double number lines to find a benchmark percent of a whole. This means that students are working with percentages that are easily converted to fractions (i.e. 10%, 20%, 25%, 50%). Students use similar strategies and reasoning to the previous lesson, and recognize that they are looking for different information. In this case, students understand that they can represent the percent as a part-to-whole ratio with 100. And, they can represent the other known whole as equivalent to 100% in the diagram and the unknown part as equivalent to the known percent. For example, when finding 25% of $40, students set up the double number line diagram below. First, they draw 40 and 100% as the wholes. Then, knowing that 25% is $$\frac{1}{4}$$, they partition the double number line into fourths. They reason that each part on the top of the diagram must represent $10 and understand that 25% of $40 is $10 because 10 goes into 40 four times, similar to 25% into 100% four times.”
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 6 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 6, 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:
Unit 6, Lesson 2, Connection To Learning and Conceptual Understanding identifies previous skills for grade level related standards, “How does this lesson connect to previous lessons? In the previous lesson, students learned how to evaluate exponential expressions. They used the order of operations to evaluate expressions with exponents, multiplication and division, and addition and subtraction. In this lesson, they incorporate grouping symbols. This directly builds off of their work with grouping symbols in 5th grade while adding exponents into the mix.”
In the Unit 8 Overview, the narrative provides skills from previous years and connects the units’ lessons. “Starting in elementary school and 5th grade students develop area concepts. Students move from building arrays to understand multiplication and division to using arrays to find the area of rectangles and squares. From there, they use their understanding of area to develop an understanding of volume by decomposing three-dimensional shapes into rectangular layers (5.MD.C.3, 5.MD.C.5). Additionally, in 5th grade students used area models as a way to understand multiplication and division of whole numbers as well as multiplication of fractions. All of this work with area provides students with strong base understanding of the concept from which to build as students dive deeper into their study of area in Unit 8.”
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 6 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 6 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.
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Materials provide a comprehensive list of supplies needed to support instructional activities.
The materials reviewed for Achievement First Mathematics Grade 6 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 5 Lesson 8, the Lesson Overview includes, “Materials: Handout.”
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 6 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 6 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 6 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 6 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. There are 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:
The Unit 3 assessment contributes to the full intent of 6.NS.7 (understand ordering and absolute value of rational numbers). Item 1, “1) Lucy's bank statement for last week shows $300 for a deposit into her checking account and –$300 for a withdrawal. (2pts) Select all statements that are true. A) The withdrawal amount is more than the deposit amount. B) The sum of the deposit and withdrawal equals $0. C) The absolute value of both the deposit and withdrawal is $0. D) The amounts of the deposit and withdrawal would be the same distance from 0 on the number line.”
The Unit 6 assessment contributes to the full intent of 6.RP.3c (use ratio and rate reasoning to solve real-world and mathematical problems). Item 12, “A clothing store offers a 30% discount on all items in the store. a) If the original price of a sweater is $40, how much money will a customer save with the discount? b) A shopper bought a shirt and saved $24 with the discount. What was the original cost of the shirt?”
Unit 9, Lesson 4, Exit Ticket, Problem 1 contributes to the full intent of 6.G.2 (find the volume of a right rectangular prism with fractional edge lengths). “Jake is filling up the fish tank below completely with water. How many cubic feet of water will he need?” The dimensions of the tank are 2\frac{1}{3} feet by \frac{2}{4} foot by 1\frac{1}{2} feet.
Assessments include opportunities for students to demonstrate the full intent of grade-level practices across the series. Examples include:
Unit 2 Assessment, Item 5, supports the full development of MP4 by modeling to represent the problem. "Barry is making pillows. He needs \frac{3}{4} of a yard of fabric to make each pillow. If Barry has 6 yards of fabric, how many pillows will he be able to make? (2 pts) a. Use a model to represent the problem and solution.”
Unit 5 Assessment, Item 10, supports the full development of MP3 (constructing arguments and critiquing the reasoning of others). "Tyler drew a double number line diagram and stated that 75% of 24 is 15. Is he correct? Explain why or why not and include your own double number line diagram as part of your justification.”
Unit 7 Assessment, Item 4, supports the full development of MP2 (reasoning abstractly and quantitatively). “Antoine ate 3 times as many apples as Jose ate on Monday and Tuesday. In total, Antoine ate 12 apples. Jose ate a certain number of apples on Monday and 4 apples on Tuesday. Write an equation that you could solve to find out how many apples Jose ate on Monday.“
Indicator {{'3l' | indicatorName}}
Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
The materials reviewed for Achievement First Mathematics Grade 6 do not provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment. This is true for both formal unit assessments and informal exit tickets.
Criterion 3.3: Student Supports
The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.
The materials reviewed for Achievement First Mathematics Grade 6 do not meet expectations for Student Supports. The materials do not provide strategies and supports for students in special populations or for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics.
The materials provide multiple extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity, and manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
Indicator {{'3m' | indicatorName}}
Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.
The materials reviewed for Achievement First Mathematics Grade 6 do not meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.
The materials do not provide specific strategies and supports for differentiating instruction to meet the needs of students in special populations.
Indicator {{'3n' | indicatorName}}
Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
The materials reviewed for Achievement First Mathematics Grade 6 meet expectations for providing extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
Materials provide opportunities for students to investigate the grade-level content at a higher level of complexity. Examples include:
Implementation Guide, philosophy of the Problem of the Day, “The typical question types selected for this component of the program are of the highest level of rigor in the program. They often cross standards, are multi-step and require a full problem-solving process in order to solve.” Problem of the Day 1, 6.2 states, “Carey goes shopping for birthday gifts for his mother. He buys her a box of chocolates for 9.97, a dozen roses for 0.83 each rose, and a stuffed animal for $28.07. If Corey wants to split the cost of all of the gifts, equally, with his 3 brothers, how much will they each pay? What percent of the total does his portion represent?”
In the Implementation Guide, the philosophy of the Mixed Practice Overview states, “[problems are] presented in mixed problem types and normally at a middle or high level of rigor. These questions are often in the form of word problems, multi-step problems, or a novel context.”
Independent Practice work in each lesson provides three levels of rigor in the lesson for student work: Bachelor, Master, and PhD work, with the PhD including the most rigorous problems.
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 6 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 6 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 3, Lesson 11, Key Learning Synthesis, “Let’s form our KP for today. With your partner, TT and come up with our key point about comparing rational numbers.”
Unit 8, Lesson 3, Test the Conjecture, students work in pairs to test the conjecture the area formula of a right triangle applies to acute triangles. “For the next 5 minutes, you’ll be working with your partner applying the conjecture that we just stamped.”
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 6 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 6 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 6 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 6 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 6 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 6 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
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 9 Overview, “The learning in this unit relies heavily on concrete and pictorial representations to solidify students’ conceptual understanding of volume and surface area. For example, when packing the solid below with cubes that have an edge length of 1⁄2 inch, students first find the number of cubes that fit in the cube. They do this by determining how many cubes fit across the length (3), how many cubes fit across the width (3), and how many cubes fit across the height (3). Students multiply the number of cubes that fit across the length, width, and height to determine that a total of 27 one-half inch cubes fit in the cube below.”
In Unit 10, Lesson 4, cubes are listed as an option for a representation of people when graphing a frequency table.
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 6 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 6 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 6 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 6 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 6 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
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Usability
1st Grade
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Usability
2nd Grade
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Usability
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.
3rd Grade
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Usability
4th Grade
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Usability
5th Grade
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Usability
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.