8th Grade - Gateway 3

The instructional materials for Match Fishtank Grade 8 meet the expectations that there is a clear distinction between problems and exercises in the materials.

There are eight units in each grade level. Each unit presents lessons in a consistent structure. During the Anchor Problems, which include guided instruction, step-by step procedures, and problem solving, students work on examples and problems to learn new concepts. The second half of each lesson uses a Problem Set, which contains a variety of exercises, allow students to independently master and demonstrate their understanding of the material. Each lesson concludes with a Target Task intended for formative assessment. For example,

• Unit 1, Exponents and Scientific Notation, Lesson 2, Anchor Problems, students   “Evaluate numerical and algebraic expressions with exponents using the order of operations.” through guided instruction. In the Problem Set Guidance, (EngageNY Mathematics Grade 6 Mathematics,Module 4, Topic B, Lesson 6, Problem Set), students are given additional problems for independent practice and mastery of this skill.  Exercise 2 asks students to analyze the expression $$4 + 9^2 \div 3 \times 2 - 2$$.  “What operation is evaluated first? What operations are evaluated next? What operations are always evaluated last? What is the final answer?” 
• Unit 2, Solving One-Variable Equations, Lesson 4,Anchor Problems, students “Write and solve multi-step equations to represent situations, with variables on one side of the equation.” through guided instruction. In the Problem Set Guidance, (EngageNY Mathematics Grade 8 Mathematics, Module 4, Topic A,  Lesson 5, Examples, Exercises, and Problem Set), they are given additional problems allowing for independent practice and mastery. Example 1: “One angle is five degrees less than three times the degree measure of another angle. Together, the angles measures have a sum of 143°. What is the measure of each angle?” 
• Unit 4, Functions, Lesson 4, Anchor Problems, students “Represent functions with equations” through guided instruction. In the Problem Set Guidance, (EngageNY Mathematics Grade 8 Mathematics, Module 5, Topic A, Lesson 4,  Problem Set), they are given additional problems allowing for independent practice and mastery. Example 3 asks students, “You have just been served freshly made soup that is so hot that it cannot be eaten. You measure the temperature of the soup, and it is 210°F. Since 212°F is boiling, there is no way it can safely be eaten yet. One minute after receiving the soup, the temperature has dropped to 203°F. If you assume that the rate at which the soup cools is constant, write an equation that would describe the temperature of the soup over time.”
• Unit 5, Linear Relationships, Lesson 3, Anchor Problems, students “Compare proportional relationships represented as graphs.” In the Problem Set Guidance,  (Open Up Resources, Grade 8 Unit 3 Practice Problems, Lesson 4, Problems 1 and 2), students are given additional problems for independent practice and mastery of this skill. Problem 1, “A contractor must haul a large amount of dirt to a work site. She collected information from two hauling companies. EZ Excavation gives its prices in a table. Happy Hauling Service gives its prices in a graph. [A picture of a line graph shows the cost of dirt] How much would each hauling company charge to haul 40 cubic yards of dirt? Explain or show your reasoning. Calculate the rate of change for each relationship. What do they mean for each company? If the contractor has 40 cubic yards of dirt to haul and a budget of $1000, which hauling company should she hire? Explain or show your reasoning.”
• Unit 8, Bivariate Data, Lesson 2, Anchor Problems, students “Create scatter plots for data sets and make observations about the data.” In the Problem Set Guidance, (Open Up Resources Grade 8 Unit 6 Practice Problems, Lesson 2), students are given additional problems for independent practice and mastery of this skill. Problem 1 asks students, “In hockey, a player gets credited with a “point” in their statistics when they get an assist or goal. The table shows the number of assists and number of points for 15 hockey players after a season. Make a scatter plot of this data. Make sure to scale and label the axes.”

The instructional materials reviewed for Match Fishtank Grade 8 meet the expectations that the design of assignments is intentional and not haphazard.

The lessons follow a logical, consistent format that intentionally sequences assignments, provides a natural progression, and leads to full understanding for students. For example:

• In the Anchor Problems, students are introduced to concepts and procedures through a problem-based situation. They are guided through the problem solving process via a series of Guiding Questions provided for teachers.
• In the Problem Set Guidance: This portion of instruction connects to the problem learned previously and is the substance of the lesson. It includes a list of suggested resources (including links to resources) or problem types for teachers to create a problem set aligned to the objective of the lesson. Teachers are encouraged to create a set of problems that best work for the needs of their students or for that particular lesson. 
• Each lesson concludes with an independent Target Task designed to cover key concepts from the lesson and formatively assess student understanding and mastery.

The instructional materials for Match Fishtank Grade 8 meet the expectations that the instructional materials prompt students to show their mathematical thinking in a variety of ways. For example:

• Unit 2, Solving One-Variable Equations, Lesson 3. Students justify each step in solving a multi-step equation with variables on one side of the equation.
• Unit 4, Functions, Lesson 12: Students sketch graphs of functions given qualitative descriptions of the relationship.
• Unit 7, Pythagorean Theorem and Volume, Lesson 3: Students use number lines to compare values of irrational numbers.
• Unit 8, Bivariate Data, Lesson 4: Students use a best fit line to make predictions about the data.

The instructional materials reviewed for Match Fishtank Grade 8 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The series includes a variety of suggestions for physical manipulatives, and links to physical, as virtual manipulatives, For example:

• Unit 3, Transformations and Angle Relationships, Lesson 1, Anchor Problem 2. Students use shapes to investigate congruent/non-congruent shapes. 
• Unit 4, Functions, Lesson 1, Anchor Problem 1 uses survey questions and letter cards to introduce the “concept of a function by juxtaposing the clarity of a function next to the confusion of a non-function.”
• Unit 7, Pythagorean Theorem and Volume, Lesson 5, Problem Set Guidance: MARS Formative Assessment Lesson for Grade 8 Translating between Repeating Decimals and Fractions. This includes a card matching activity to build procedural fluency in converting between decimals and fractions. 

The instructional materials for Match Fishtank Grade 8 meet the expectations that materials provide teachers with quality questions for students.

In the materials, Facilitator Notes for each lesson includes questions that are included in Anchor Problem Notes for the teacher to guide students' mathematical development and to elicit students' understanding. The materials indicate that questions provided are intended to provoke thinking and provide facilitation through the mathematical practices as well as getting the students to think through their work. For example:

• Unit 3, Transformations and Angle Relationships, Lesson 3, Anchor Problem and Guiding Questions 3: “How can you answer this question without using a coordinate plane? What are the two pieces of information needed to describe a translation, and how can you see them in the coordinate points? What is the connection between the variables x and y and the movements horizontally and vertically?”
• Unit 4, Functions, Lesson 7, Anchor Problem and Guiding Questions 2: “What inputs does it make sense to use for this function? How many are appropriate to include in your table? Does the rate of change between any two points stay the same, or does it change?”
• Unit 5, Linear Relationships, Lesson 6, Anchor Problem 1 and Guiding Questions: “How did you determine your order without doing any calculations? Discuss your order with a peer. Do you have the same order? How did you each determine your order? Will you change your order based on your conversation? What measurements are important to consider when finding slope? How do you use those measurements to determine slope? Explain how to find the steepness of any staircase that climbs a distance of y feet over a distance of x feet. How does this relate to the concept of slope?”
• Unit 6, Systems of Linear Equations, Lesson 6, Anchor Problem 1 and Guiding Questions : “Do you have an equation that is already solved for either x or y? Why do you need an equation solved for either x or y? How can you rewrite one of the equations to be in this form? Is there more than one way to approach this problem? Which way is the easiest or most efficient?”

The instructional materials reviewed for Match Fishtank Grade 8 meet the expectations for containing a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials also include teacher guidance on the use of embedded technology to support and enhance student learning.

All lessons include a Tips for Teachers section.  This section provides teachers with resources and an overview of the lesson but provides little guidance on how to present the content. Due to the nature of the materials in a virtual format, there are no concrete student materials. For example: 

• In Unit 4, Functions, Lesson 3, Tips for Teachers: “Lessons 3 and 4 focus on functions represented in tables, equations, and verbal descriptions. In Lesson 3, students analyze these representations to make sense of the relationships between the quantities (MP.2). They use their understanding of unit rate and constant of proportionality to determine the rate of change between quantities. They consider what a starting or initial value means in context of a situation, and how to determine these values from a table or equation.”

There is guidance for teachers in the forms of Guiding Questions and Notes for implementing Anchor Problems, Problem Set Guidance, and Target Tasks. Problem Set Guidance sections are optional problem sets with student facing materials. There is no student edition, so guidance for ancillary materials is not needed.

The instructional materials for Match Fishtank Grade 8 meet expectations as they explain the role of the grade-level mathematics in the context of the overall mathematics curriculum.

• Each unit opens with a Unit Summary that includes a Lesson Map and a list of grade level standards addressed within the unit along with future connections.
• Each Lesson provides current standards addressed in the lesson.
• Each Lesson provides foundational standards which are standards that were covered in previous units or grades that are important background for the current lesson.

The instructional materials for Match Fishtank Grade 8 meet the expectations that materials provide strategies for teachers to identify and address common student errors and misconceptions. 

The materials provided notes to provide teacher guidance for the Anchor Problems that addresses common misconceptions. For example:

• Unit 1, Exponents and Scientific Notation, Lesson 5, Anchor Problem 4 states,  “This Anchor Problem targets a common misconception that can happen when students over-apply a rule. They can become confused between when to add and when to multiply. Encourage students to explain the conceptual thinking behind the rule so that the concept stays connected to the procedure or rule.”
• Unit 8, Bivariate Data, Lesson 2 Tips for Teachers states, “A common misconception is to confuse causality with association. For example, students may misunderstand a relationship between two variables to imply that one variable causes another to change, when there is only evidence to show an association between the two variables. As students describe relationships between variables, ensure they use language to imply an association rather than a causal relationship (MP.6).”

The instructional materials for Match Fishtank Grade 8 meet the expectations for the materials to provide opportunities for on-going review and practice, with feedback, for students in learning both concepts and skills. 

Each lesson is designed with teacher-led Anchor Problems, Problem Set Guidance and Target Task. The lessons contain multiple opportunities for practice with an assortment of problems. The Anchor Problems provided the teacher with Guiding Questions and Notes in order to provide feedback for students’ learning. For example:

• Unit 5, Linear Relationships, Lesson 10, Anchor Problem 3, Notes, states,  “As students are playing, listen for how students are proving their matches and how other students express their agreement or disagreement. Ensure students are using appropriate vocabulary and language.”
• Unit 3, Transformations and Angle Relationships, Lesson 5, Anchor Problem 1. The Guiding Questions provided for teachers are designed to lead students to draw conclusions about what happens to the coordinate points of a figure as it is translated over the x- or y- axis. Notes: “Use this Anchor Problem to have students determine what impact reflections over axes have on coordinate points. One approach to using this Anchor Problem could be to have students work in small groups, each group with a different reflected image (like in the Anchor Problem above), and work together to answer the two questions. Then each group could share their findings with the class, observe patterns in the results from each group, and determine a general conclusion (MP.8).”

The instructional materials for Match Fishtank Grade 8 meet the expectations for the assessments to clearly denote which standards are being emphasized. 

Each unit provides an answer key for the Unit Assessment. The answer key provides each question number and the targeted standard. For example:

• Unit 6, Systems of Linear Equations, Assessment Item 11 correlates with 8.EE.8c. 
• Unit 2, Solving One-Variable Equations, Assessment Item 4 correlates with 8.EE.7b.

The instructional materials reviewed for Match Fishtank, Grade 8 meet the expectation that materials embed tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations.

Students engage in tasks throughout lessons in the Anchor Problems, Target Tasks, Problem Set Activities, the 3-Act Math Modeling, and the Mathematics Assessment Project activities all present multiple entry points for students. For example:

• Unit 1, Exponents and Scientific Notation, Lesson 4, Target Task states, “Jake believes that $$30^5/30^4 × 30 = 1$$. Do you agree with Jake? If yes, explain why he is correct. If not, then give the correct answer and an argument to convince Jake that your answer is correct.” This problem requires students to make their own assumptions and simplifications while providing students multiple entry points to begin solving. 

The instructional materials for Match Fishtank Grade 8 meet the expectations that materials provide a balanced portrayal of various demographic and personal characteristics. For example:

• Different cultural names and situations are represented in the materials, ie., Lewis, Mari, Lucas, Juan, and Kristina.
• The materials avoid pronouns, referencing a role instead, ie., the manager, a taxicab driver, a scientist, the basketball team.