6th to 8th Grade - Gateway 1

The materials reviewed for Experience Math Grades 6 through 8 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The formal assessments follow a consistent structure across grades, including Diagnostic Tasks, Topic Assessments, Online Topic Assessments (autoscorable), Parallel Topic Assessments, and Performance Tasks. Grade 6 includes sixteen Diagnostic Tasks, sixteen Topic Assessments, sixteen Online Topic Assessments (autoscorable), eleven Parallel Topic Assessments, and twelve Performance Tasks. Grade 7 includes twelve Diagnostic Tasks, twelve Topic Assessments, twelve Online Topic Assessments (autoscorable), nine Parallel Topic Assessments, and ten Performance Tasks. Grade 8 includes twelve Diagnostic Tasks, twelve Topic Assessments, twelve Online Topic Assessments (autoscorable), three Parallel Topic Assessments, and seven Performance Tasks.

Examples include:

• Grade 6, Topic 8: Multiplying and Dividing Whole Numbers and Decimals, End of Topic Resources, Topic Assessment, Question 5, “Calculate the quotient using the standard algorithm and leave the remainder as a whole number. 685 32.” (6.NS.2)

• Grade 7, Topic 1: Probability of Single Events, End of Topic Resources, Performance Task, “About \frac{1}{4} of children in America live in a one-parent household. About \frac{1}{5} of Americans speak a language other than English. About \frac{1}{8} of Americans live in California. About 110 of people are left-handed. 1. Choose one of the facts above. Tell whether you think it represents a theoretical probability or an experimental one. 2. Create a probability experiment using the fact you chose (live in one-parent household, are left-handed, speak a language other than English, live in California) to help you predict how many people in a group of 20 have the characteristic. 3. Predict the results of your experiment. 4. Conduct your experiment. Use your results to test your prediction.” (7.SP.5, 7.SP.6, 7.SP.7b)

• Grade 8, Topic 2: Powers and Roots, Planning and Resources, Diagnostic Task, Question 8, “Make squares with some of the areas below. Use square tiles. Which number of tiles can you make squares out of? 25 tiles, 100 tiles, 48 tiles, 60 tiles, 49 tiles.” (8.EE.2)

The materials reviewed for Experience Math Grades 6 through 8 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

Assessment Item Correlations documents include item analysis charts for all formal assessments in the program (Diagnostic Tasks, Topic Assessments, and Performance Tasks). Each chart contains several key components: the item number for reference, a brief description of the mathematical content assessed (“Math Content” column), the aligned Common Core State Standard (“CCSS” column) with its cluster designation, the Depth of Knowledge (“DOK” column) level indicating the required cognitive complexity (Levels 1–3), and the Standards for Mathematical Practice (“SMPs” column) that students engage in while solving the problem.

Examples include:

• Grade 6, Topic 2: Factors and Multiples, End of Topic Resources, Topic Assessment, Question 5: “If you were asked to quickly come up with a common multiple of 117 and 5, what answer might you give? Explain your thinking.” The Assessment Item Correlations to CCSS states that the standards addressed are 6.NS.4, MP.2, MP.3.

• Grade 7, Topic 10: Area and Volume, End of Topic Resources, Performance Task, Question 1, “The school’s Wildlife Club wants to sell wooden birdhouses at a craft fair. The birdhouses are shaped like pentagonal prisms. Decide the dimensions of the birdhouse they should make. What is its volume?” The Assessment Item Correlations to CCSS states that the standards addressed are 7.G.6, MP.1, MP.4, MP.6.

• Grade 8, Topic 8: The Pythagorean Theorem, End of Topic Resources, Topic Assessment, Question 11, “A box in the shape of a rectangular prism measures 12 inches length, 3 inches width, and 5 inches height. What is the diagonal length of the box? Explain.” The Assessment Item Correlations to CCSS states that the standards addressed are 8.G.7, MP.1, MP.4.

There is no standard identification provided within the assessments themselves or in the Teacher Experience Guide for each topic.

The materials reviewed for Experience Math Grades 6 through 8 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

Formal assessments include Topic Assessments with Skill and Concept Questions, Performance Tasks, and Diagnostic Tasks. Assessments evaluate both procedural skills and conceptual understanding while requiring students to engage with mathematical reasoning, problem-solving strategies, and communication skills. The online assessments provide opportunities for students to demonstrate their understanding of grade-level content standards through a variety of item types, including Drag and Drop, Fill-in-the-Blank, Matching, Multi-Select, Short Response, and Single Select.

Examples include:

• Grade 6, Topic 11: Using Algebra, End of Topic Resources, Performance Task, Question 1 states, “Create three algebraic expressions: Expression 1: Uses one variable and involves subtraction. Expression 2: Uses two variables and involves multiplication and addition. Expression 3: Uses one variable and involves division. For each expression: Draw a picture to represent each algebraic expression. Create an equivalent expression and tell why it is equivalent. Evaluate the expression using a value for the variable(s) that makes sense in that situation. Explain whether the value of the expression increases or decreases when the value of the variable(s) increases and why that makes sense.” The materials assess the full intent of 6.EE.2, 6.EE.3, MP.2, and MP.7 as students write, evaluate, and create expressions given certain criteria.

• Grade 7, Topic 3: Proportionality, End of Topic Resources, Topic Assessment, Questions 12-14 states, “12. Create a table of values and draw a graph that might be useful to show how many miles someone would travel if they drove 45 miles per hour for 213hours. 13. There are 12 baseballs in a package. Create a table of values and draw a graph to show the relationship between the number of baseballs and the number of full packages. 14. Imagine creating a graph to show the relationships between the perimeters of equilateral triangles with a certain side length. a. Why does the data line go through (0,0)? b. Why does the data line look as it does? c. Why would a graph describing the total perimeters of 3 squares and some number of triangles not go through (0,0)?" The materials assess the full intent of 7.RP.2 and MP.2 as students represent and utilize proportional relationships.

• Grade 8, Topic 5: Proportional Relationships and Slope, End of Topic Resources, Topic Assessment, Questions 12-15 states, “Imagine you have a line that goes through the origin. You choose two pairs of points on the line to connect and create \frac{rise}{run} triangles using each pair. a. Why do the \frac{rise}{run} triangles have to be either congruent or similar? b. When are they congruent? 13. Why can you use any two points on a line to determine its slope? 14. When you graph a proportional relationship with a slope of 6, why is the equation of the graph y = 6x? 15. Why does it make sense that one of these lines represents the equation y = 4x and the other represents the equation y = 4x + 5?” The materials assess the full intent of 8.EE.6 and MP.7 as students use the structure of similar triangles to justify why the slope is constant for any two points on a line and apply that relationship to derive and interpret the equations y = mx and y = mx + b.

The materials reviewed for Experience Math Grades 6 through 8 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Each lesson follows a consistent three-part structure that engages students in extensive work with grade-level problems. The three parts include Minds On, Action Task (which provides open-ended problem-solving prompts that require collaboration and critical thinking), and Consolidate Questions. Each topic includes various games and activities that may feature Academic Vocabulary, Brain Benders, Data Tasks, Making Connections Tasks, Math Talks (including Number Talks and Data Talks), and Wonder Tasks, as well as Your Turn and Additional Practice. Across the program, students have multiple opportunities to independently demonstrate their understanding of the full intent of the standards.

Examples include:

• Grade 6, Topic 9: Dividing Fractions, End of Topic Resources, Topic Your Turn, Question 8 engages students with the full intent of 6.NS.1 (Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem) as students model and solve problems involving divisions of fractions. Question 8 states, “For Questions 8 and 9, use a visual model such as a double number line or picture to solve each problem. 8. Linh read \frac{1}{3} of a book in 2\frac{1}{2} hours. How much of the book did she read in 1 hour?”

• Grade 7, Topic 9: Algebra, Lessons 1 and 2 engage students with the full intent of 7.EE.1 (Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients). In Lesson 1, Your Turn, students add or subtract expressions with integer coefficients. Question 1 states, “In Questions 1-6, add or subtract to write an equivalent expression. (4x-3) + (2x+4).” Question 8 states, “Which expression is equivalent to 4x-12y? A (-2x - 2y) - (-6x + 10y) B (-2x -2y) + (-6x + 10y) C (-2x - 2y) + (-6x - 10y) D (2x - 2y) - (-6x + 10y)” In Lesson 2, Action Task students factor and expand expressions, Questions 3-7 states, “For each expression in Questions 3-7, suggest an equivalent expression. Explain why you think your suggestion is equivalent. 3. 5c - 15e + 25d 4. 4(x-2y) 5. 6x + 8y - 2 6. x+\frac{1}{2}x 7. y + 0.05y.” 

• Grade 8, Topic 6: Functions, Lesson 1, Minds On Activity engages students with the full intent of 8.F.1 (Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output). Students examine two coordinate grids with plotted points. Graph A represents a function with four points plotted within quadrant 1, while Graph B also has four points plotted in quadrant 1, but two of the points have an x value of 4, which makes it not a function. Question 1 states, “What is the same and what is different about Graph A and Graph B?” The Teacher Guidance, After the Minds on Activity states, “Introduce the term function and talk about what makes a relationship a function. You might introduce the language of a vertical line test to see if a graph shows a function. Let students know that we can describe a function with a table of values which we graph as (input, output) ordered pairs. Help students see that in each pair of graphs in the Minds On Activity, one showed a function, and one did not.” In the Student Experience Book, Your Turn, Question 1 asks, “Why is x=8 not a function but y=8 is?” Additional Practice, Question 4 states, “Determine what numbers need to be placed in the table to make it a function.” A table with x and y values is given. The x values are 1, 1, 2, 3 and a blank that corresponds with the y value of 6. The y values are 4, a blank that corresponds with an x value of 1, 5, 6, 6.

The materials reviewed for Experience Math Grades 6 through 8 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. 

The pacing guide indicates that most lessons span about two days, with each lesson, including differentiation, taking approximately 90 to 130 minutes. Additional days are built in for review, assessment, and connecting or extension tasks. Overall, at least sixty-five percent of instructional time focuses on the major work of the grade.

In Grade 6:

• The number of topics devoted to the major work of the grade (including assessments and related supporting work) is 9 out of 16, approximately 56%.

• The number of lessons devoted to the major work of the grade (including assessments and related supporting work) is 33 out of 64, approximately 52%.

• The number of days devoted to the major work of the grade (including assessments and related supporting work, but excluding a review day) is 84 out of 142, approximately 59%.

• The number of days devoted to the major work of the grade (including assessments and related supporting work) is 93 out of 142, approximately 65%.

In Grade 7:

• The number of topics devoted to the major work of the grade (including assessments and related supporting work) is 6 out of 12, approximately 50%.

• The number of lessons devoted to the major work of the grade (including assessments and related supporting work) is 29 out of 54, approximately 54%.

• The number of days devoted to the major work of the grade (including assessments and related supporting work, but excluding a review day) is 73 out of 120, approximately 61%.

• The number of days devoted to the major work of the grade (including assessments and related supporting work) is 79 out of 120, approximately 66%.

In Grade 8:

• The number of topics devoted to the major work of the grade (including assessments and related supporting work) is 9 out of 12, approximately 75%.

• The number of lessons devoted to the major work of the grade (including assessments and related supporting work) is 39 out of 50, approximately 78%.

• The number of days devoted to the major work of the grade (including assessments and related supporting work, but excluding a review day) is 96 out of 136, approximately 71%.

The materials reviewed for Experience Math Grades 6 through 8 meet expectations that supporting content simultaneously enhances focus and coherence by engaging students in the major work of the grade. 

Materials are designed so that supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are found within Topics and Lessons. 

An example of a connection in Grade 6 includes:

• Topic 13: Rational Numbers, Student Experience Book, Lesson 3, connects the supporting work of 6.G.3 (Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems) to the major work of 6.NS.8 (Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate). Students plot the vertices of polygons in all four quadrants on a coordinate plane. Then, students use the absolute values of the coordinates to measure the lengths of the segments. Student Experience Book, Action Task states, “4. What name best fits the pool (blue quadrilateral) below? How long are its sides if each unit is a meter? Tell how you know. Include using absolute value.” An image of a pool is superimposed on a coordinate plane. Student Experience Book, Your Turn states, “6. What name best fits the quadrilateral below? How long are its sides? Use absolute value to tell how you know.” Students are given a quadrilateral drawn on a coordinate plane. 

An example of a connection in Grade 7 includes:

• Topic 12: Probability of More Than One Event, Lesson 1, Student Experience Book, connects the supporting work of 7.SP.6 (Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability) to the major work of 7.RP.3 (Use proportional relationships to solve multistep ratio and percent problems). Students use number cubes to collect data to determine probability and apply proportional reasoning to scale the results over more trials. Student Experience Book, Your Turn states, “1. You roll two number cubes. a. What is the probability that you get an even number on both cubes? b. What is the probability that the sum of the two numbers is 7? c. What is the probability that the two numbers have a difference of 1?. 2. You roll one number cube twice. What event could have a probability of \frac{10}{36}? Show how you would get this probability using a diagram or model of your choice.

An example of a connection in Grade 8 includes:

• Topic 7, Rational and Irrational Numbers, Lesson 2, Student Experience Book, connects the supporting work of 8.NS.2 (Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., 2)) to the major work of 8.EE.2 (Use square root and cube root symbols to represent solutions to equations of the form x^2=p and x^3=p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that \sqrt{2} is irrational). Students determine that whole numbers that are not perfect squares have irrational square roots and identify examples of such numbers between 50 and 200. They use this understanding to reason that the square roots of those numbers are nonterminating, nonrepeating decimals. Student Experience Book, Action Task states, “3. Whole numbers that are not perfect squares have square roots that are irrational. For example, \sqrt{2}, \sqrt{10}, and \sqrt{20} are all irrational. The decimal for \sqrt{2} begins 1.414213562373095 and continues forever without a pattern. The decimal for 10 begins 3.162277660168379 and continues forever without a pattern. The decimal \sqrt{20} begins 4.472135954999579 and continues forever without a pattern. a. Name three or four whole numbers between 50 and 100 whose square roots are irrational. b. Name three or four whole numbers between 100 and 200 whose square roots are irrational.”

The materials reviewed for Experience Math Grades 6 through 8 meet expectations for including problems and activities that connect two or more clusters in a domain, or two or more domains in a grade. 

Connections among the major work of the grade are present throughout the materials where appropriate. These connections are within Topics and Lessons.

An example of a connection in Grade 6 includes:

• Topic 14: Equations and Inequalities, Lesson 1, Student Experience Book connects the major work of 6.EE.B (Reason about and solve one-variable equations and inequalities) to the major work of 6.EE.C (Represent and analyze quantitative relationships between dependent and independent variables). Students use variables to represent numbers and write equations for word problems. Student Experience Book, Action Task states, “There are many relationships between units of time. For example, there are 60 minutes in an hour and there are 7 days in a week. If you can describe an amount of time using one unit, you can use one of these relationships to determine how many of another unit you would need to describe another unit of time. 1. Use the relationships between the units of time to answer each part. a. Describe the relationships between five pairs of time units. Choose one of the relationships you described. Model the relationship with a visual model such as a bar diagram or with algebra tiles. c. Create a table of values that represents the relationship you chose. Use the table to graph the relationship on a coordinate grid.” 

An example of a connection in Grade 7 includes:

• Topic 8: Operations with Rational Numbers, Lesson 2, Student Experience Book, connects the major work of 7.NS.A (Apply and extend previous understandings of operations with fractions) to the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations). Students solve real-world problems involving distances represented by positive and negative fractional values and write and solve equations to model the situations. Student Experience Book, Action Task states, “Jason’s family is out running errands on Saturday morning. They started at their house and made some stops. In Questions 1-3, solve each problem using any method. Then represent the situation by writing and solving an equation with positive and negative values. Explain how you could have estimated to see if your answers make sense.” Students see the following information on a map: Library - -5\frac{2}{3} miles east; Skate Park -7\frac{3}{4} miles west; Store -15\frac{3}{8} miles east. “1. How far did Jason’s family drive altogether to reach the store? 2. What was the farthest distance east of Jason’s house traveled on the trip? 3. What was the farthest distance west of Jason’s house? 4. How would your answers for Questions 1-3 change if Jason’s family did the drive in this order instead? -7\frac{3}{4} miles west, then -5\frac{2}{3} miles east, then 15\frac{3}{8} miles east from there. 5. Suppose the total distance traveled changed to 32\frac{1}{2} miles. a. How would this total distance change the last distance traveled in Question 1? b. How would that change the answer to Questions 2 and 3?” Students then answer a question about why they created their equations. Consolidate, Question 2, “When you created your equations in the Action Task, in what situations did you add? In what situations did you subtract? Why?”

An example of a connection in Grade 8 includes:

• Topic 8: The Pythagorean Theorem, Lesson 2, Student Experience Book, connects the major work of 8.EE.A (Expressions and Equations Work with radicals and integer exponents) to the major work of 8.G.B (Understand and apply the Pythagorean Theorem). Students apply the Pythagorean Theorem to determine unknown side lengths in right triangles and compute square roots. Student Experience Book, Action Task states, “4. A person uses the ladder to hang a pair of string lights from the tree to the ground. The string lights are hung 15 feet above in the tree to an anchoring point on the ground 16 feet to the left and 12 feet behind the tree. How long must the string lights be to reach the diagonal length, d, from the tree to the anchoring point in the ground? Explain.”

The materials reviewed for Experience Math Grades 6 through 8 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 provide multiple features to support coherence across grade levels. Connecting to Concepts Beyond the Grade notes at each grade and topic guide teachers to see how current instruction fits within the broader K-8 progression of learning. These notes identify how current instruction prepares students for future standards and clarify the significance of these connections by sharing the progression of mathematical understanding. For example: 

• In Grade 7, Teachers Experience Guide, Program Overview, Connecting to Concepts Beyond the Grade links the work in Grade 7 to related concepts in later grades, including Grades 8 and high school. Geometry (Topic 6) states, ​“In Topic 6 (Geometry) students explore scale drawings, geometric constructions, angle relationships, and cross-sections of three-dimensional figures. They discover important relationships like vertical angles being equal and complementary angles summing to 90°. Through informal exploration, students learn that when creating triangles with three specific angles, different triangles are possible, but they all look similar. Further, they discover that triangles constructed with the same two angles and the included side length are always congruent. In Grade 8, students formalize these discoveries through beginning studies of similarity and congruence. In high school, students develop criteria for triangle similarity and congruence. They learn that the sum of angles in any triangle is 180° and in any quadrilateral is 360°, regardless of the specific shape. Their work with scale drawings expands to include formal definitions of similarity, where one figure can be transformed into another through a dilation (enlargement or reduction). In Geometry and higher courses, transformations become powerful tools for analyzing geometric relationships, with students learning that figures are congruent precisely when one can be transformed into the other through a sequence of reflections, rotations, and translations. Understanding geometric transformations and relationships provides a foundation for coordinate geometry, vector analysis, and other advanced mathematical topics. This geometric reasoning becomes essential for modeling physical phenomena, analyzing spatial relationships, and solving complex problems across various disciplines.”

Going Back notes emphasize prior knowledge and skills that form the foundation for grade-level learning, while Going Forward notes describe how current concepts will be extended and applied in later grades. Together, these supports strengthen coherence across grade levels by helping teachers make explicit links between prior, current, and future learning. 

An example of a connection to future grades in Grade 6 includes:

• Topic 5: Percent, Teachers’ Experience Guide, Planning and Resources, Topic 5: Planning connects the comparing, estimating, and calculating percent work of Grade 6 to the future work of Grade 7, where students calculate more complex percents, including those greater than 100 percent. Teacher Experience Guide, Going Forward states, “In moving from Grade 6 to Grade 7, students extend what they learn about percents to work with percents greater than 100% and they solve more complex percent problems.”

An example of a connection to prior knowledge in Grade 6 includes:

• Topic 12: Writing and Evaluating Numeric Expressions, Teachers' Experience Guide, Planning and Resources, Topic 12: Planning connects the work of solving numerical expressions with exponents in Grade 6 to the prior work of Grade 5, where students were introduced to powers of 10. Teacher Experience Guide, Going Back states, “In Grade 5, students are introduced to whole-number exponents to denote powers of 10. Students look for and explain patterns in the number of zeros when performing operations with powers of 10.”

An example of a connection to future grades in Grade 7 includes:

• Topic 7: Multiplying and Dividing Integers, Teachers' Experience Guide, Planning and Resources, Topic 7: Planning connects multiplying and dividing integers and applying order of operations to the future work of Grade 8, where students continue to work with integers and incorporate exponents, including square and cube roots. Teacher Experience Guide, Going Forward states, “In Grade 8, students continue to use both positive and negative integers, but in the context of applying exponents to them. They will consider square roots of positive integers and cube roots of both positive and negative integers.”

An example of a connection to prior knowledge in Grade 7 includes:

• Topic 11: Collecting Data, Teachers' Experience Guide, Planning and Resources, Topic 11: Planning connects collecting useful data, choosing samples, and using them to make comparisons, and comparing populations in Grade 7 to the prior work of Grade 6, where students are introduced to statistical measures and questions. Teacher Experience Guide, Going Back states, “While students in Grade 6 begin to think about statistical measures and statistical questions, students in Grade 7 use these ideas to investigate the use of sampling and the use of statistical measures to draw conclusions.” 

An example of a connection to future grades in Grade 8 includes:

• Topic 2: Powers and Roots, Teachers' Experience Guide, Planning and Resources, Topic 2: Planning connects the powers and roots, and scientific notation work of Grade 8 to the future work in High School, where students write and evaluate expressions with rational-number exponents and graph and analyze square root and cube root functions. Teacher Experience Guide, Going Forward states, “In later grades, students write and evaluate expressions with rational-number exponents, graph and analyze square root and cube root functions.”

An example of a connection to prior knowledge in Grade 8 includes:

• Topic 10: Angle Relationships, Teachers' Experience Guide, Planning and Resources, Topic 10: Planning connects the angle relationships, dilations, and similarity, and rigid motions work of Grade 8 to the prior work in Grade 7, where students worked with scaled drawings, constructed two-dimensional shapes, solved problems involving angles, and worked with cross sections. Teacher Experience Guide, Going Back states, “In Grade 7, students solved problems involving supplementary, complementary, adjacent and vertical angles and used angle measures to construct triangles. The focus in Grade 8 is more on the consistency of angle relationships when lines are parallel, when triangles are similar, or in the sum of the interior or exterior angles of a triangle.”