7th Grade - Gateway 3

The materials reviewed  for CK-12 Interactive Middle School Math 7 for CCSS 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.

Materials provide comprehensive guidance to assist teacher delivery of student materials. The Teacher Edition of the materials contains Teacher Notes throughout to assist the teacher in presenting the student lessons.  Examples include:

• Important information about student learning at the beginning of lessons. For example, in Lesson 7.4, Theoretical Probability Models, the Introductory Teacher Notes states, “In this lesson, we shift from experimental probability to theoretical. Students will continue to learn how to calculate theoretical probabilities and use these probabilities to estimate and predict the likelihood of outcomes. Students should continue to use what they have learned about probabilities as they work through the examples to answer questions and make predictions. (7.SP.5 & 7.SP.6) 

• Answers to all Inline Questions 

• Instructions for help with the Interactives. For example, in Lesson 1.8, Solving Multi-Step Ratio Problems, Warm-Up, the Teacher Notes for the Interactive states, “This Interactive is intended to help with the discount problem in the text above. It has three sliders: A green slider to adjust price (of the item being discounted), a red slider to change the numerator of the fraction, and a blue slider to change the denominator. As the students change the fraction, an equivalent number of boxes will appear next to the fraction to help the student visualize the percentages. The denominator dictates how many boxes appear, and the numerator dictates how many boxes are colored.  Students can set these values to match the product price and discounts in the text above, and they will see how much was discounted (ex: set the Interactive fraction to \frac{1}{4} and price to $1,200 to find the price of the discount on the refrigerator - $300 off.) (7.RP.3)

• Possible answers, further questions, and discussion ideas for the Discussion Questions are in the following examples. In Lesson 6.1, Area and Perimeter of Scale Drawings, Activity 2, the Discussion Question Teacher Notes state, “Students need to convert the scale so that both are in inches before determining the size of the model. Once the scale is all in inches, then also convert the measurements of the actual building into inches. Once everything is all in the same units, then it can be scaled down. As for the scale factor, it is reasonable. It might be a little big to bring a nearly 5-foot tall model to school, but it could work. As an extension, you could have students determine a more “reasonable” scale and then determine the dimensions of their model. Students need to explain why they chose their scale.” (7.G.1)

• Specific learning standards and objectives for each lesson

• Lesson-specific Teacher Notes

• A scope-and-sequence at the end of the Teacher Edition

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. In the Teacher Edition at the beginning of each lesson, there is an overview of the lesson to assist the teacher in planning lessons:

• Common Core Standard—the focus and prerequisite standard(s) for each lesson is listed.

• Standard for Mathematical Practice—the mathematical practice(s) for each lesson is listed as well as where in the lesson it is developed.

• Previous Learning Objectives —a majority of the lessons list these objectives and the standard(s) or grade(s) the objective is connected.

• Learning Objectives -goals for each lesson.

• Agenda - there is an agenda listed for each lesson with the allotted times for the Warm-Up, the Activities, Review Questions, Related Modalities and Adaptive Practice.

• Introductory Teacher Notes—located at the beginning of the lesson after the agenda, these notes describe what the students will be doing in the lesson. Some have helpful hints.

• Interactives—Teacher Notes for the Interactive activities give the teacher direction on how the students are to use the Interactive and helpful hints. 

• Discussion Questions -  Teacher Notes for Discussion Questions  provide possible answers and/or possible questions to ask to further the discussion. 

• Extension Activities—some of the lessons give extension activity ideas that can enhance the learning.

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. 

Instructional approaches of the program and identification of the research-based strategies can be found on the homepage, the citations for this research can be found under the “Resources” tab on the homepage. The materials state the following, “The CK-12 Interactive Middle School Math series promotes exploratory learning (Stein 2010). Each lesson contains interactive applets which actively engage students in the learning process and allow them to explore concepts in an open-ended environment (Cocea & Magoulas, 2015; Hoyles, 2018; NCTM, 20115). Inline question sets Socratically guide students to discover connections present in the interactive applets, and a list of Works Cited includes:

• Stein, R. G. (2010). Math for Teachers: An Exploratory Approach. Kendall Hunt

  Publishing Company.

• Cocea, M., & Magoulas, G. D. (2015). Participatory learner modeling design: a

  methodology for iterative learner models development. Information Sciences, 321,

  48-70.

• Schunk, D. H. (2012). Learning Theories: An Educational Perspective. Pearson.

• Hoyles, C. (2018). Transforming the mathematical practices of learners and teachers

  through digital technology. Research in Mathematics Education.

• Hoyles, C., & Lagrange, J. B. (Eds.). (2010). Mathematics education and technology:

  Rethinking the terrain. New York: Springer.

• National Council of Teachers of Mathematics. (2014). Access and equity in mathematics

  education: A position of the national council of teachers of mathematics. National

  Council of Teachers of Mathematics.

• National Council of Teachers of Mathematics. (2015). Strategic use of technology in

  teaching and learning mathematics: A position of the national council of teachers of

  mathematics. National Council of Teachers of Mathematics.

• Wolf, D., Lindeman, P., Wolf, T., & Dunnerstick, R. (2011). Integrate Technology with

  Student Success. Mathematics Teaching in the Middle School, 16(9), 556-560.”

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

The Interactives in the lessons are designed to replace any extra materials. There is a comprehensive list of supplies needed for the optional activities included at the beginning of the Teacher Edition under the Resources tab. The materials listed are provided for the lessons that need extra supplies for optional activities  (Note: the quantity listed is per student unless otherwise noted.) Examples include:

• In Lesson 1.7, Interpreting Graphs of Proportional Relationships, Warm-up Activity, Proportional Relationships in Art: Ruler and Tape Measure.

• In Lesson 6.2, Area and Circumference of Circles, Activity 1, Parts of a Circle: Ruler Access, Tape Measure Access, and Access to other measuring tools if desired.

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations for including an assessment system that provides multiple opportunities throughout the grade 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 and most of the assessments provide sufficient suggestions for following-up with students. Examples include:

• Every lesson has Adaptive Practice Questions which generate a report with the number correct, difficulty of the questions, time spent and mastery level.

• Answer keys are provided for all Inline Questions, Discussion Questions, and End of Chapter assessments. 

• Each of the End of Chapter Assessments contains a rubric to assist the teacher in scoring student work. Each problem is given a 1-5 score and is correlated with the CCSS. Rubrics are provided for End of Chapter Assessments only. Scoring rubrics provide information on student performance but do not include suggestions for the teacher to follow up. 

• Statistics are given through reports to the teacher on each assessment component students take. The Skill Meter gauges student understanding and skill based question-by-question and is color-coded so teachers can quickly ascertain student understanding:

  • Beginning - new to concept (red)

  • Exploring - starting to understand (orange) 

  • Developing - demonstrating familiarity (yellow)

  • Proficient - understands core concept (light green)

  • Mastery - deep, demonstrated understanding (dark green)

• The Class Insights function uses the Skill Meter to give information on individual students and the entire class, by placing students on a quadrant analysis graph based on their skill level and engagement. The Class Insights function also has the Teacher Assistant which, “uncovers your students’ learning gaps and misconceptions, giving you (the Teacher) personalized insights on where you (the Teacher) can intervene effectively.” The Teacher Assistant provides suggestions for following-up with students through the “Insights and Recommendations” section. Examples of suggestions include:

  • Recommending specific “PLIX” activities to help students with low skill levels improve their skill levels.

  • Noting which students are doing exceptionally well on the current concept, and suggesting new concepts to keep those students challenged.

  • Information about the top question(s) students answered incorrectly, with the recommendations for students to review the following question(s) and the related paragraphs.

  • Information on which students are not reaching the goal of 10 correct answers on the Adaptive Practices, and recommending to remind students to complete that goal.

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

The assessments regularly provide opportunities for students to demonstrate the full intent of grade-level standards and practices through a wide variety of assessment types, such as multiple choice, drag and drop, matching, short answer, true/false, computational response, and discussion response. Students use different types of modalities to demonstrate their understanding in assessment, including short answer explanations and multi-layered questions. The Inline Questions and Review/Quiz Questions are connected to standards and practices. The End of Chapter Assessments have the content standards identified on the answer keys.

The materials reviewed for CK-12  Interactive Middle School Math 7 for CCSS meet expectations for providing manipulatives, both virtual and physical. They are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The materials provide suggestions and/or links for virtual and physical manipulatives that support the understanding of grade-level concepts. Manipulatives are accurate representations of the mathematical objects they represent and are sometimes connected to written methods. Physical manipulatives, while not included with the series, are listed in the beginning of the Teacher Edition under the Resource tab. The use of physical manipulatives is minimal.

Each lesson contains several Interactives where students use virtual manipulatives to gain an understanding of the math standard they are learning. They include a variety of manipulatives such as: graphs, x-y tables, number lines, coordinate planes, GeoGebra Interactives, word matching problems, tape diagrams, dice and playing cards. Examples include:

• In Lesson 1.1, Unit Rate and Proportionality, Activity 3, students are understanding rates as a ratio. It states, “If a car travels 300 miles in 5 hours, how far does it travel in 1 hour? How far does a car travel in 1 hour if it travels 350 miles in 5 hours? Drag the car back and forth to determine how many miles the car drives in one hour.  When looking at the point value for the car, the x-value is the hours, and the y-value is the miles.“ (7.RP.1)

• In Lesson 6.2, Area and Circumference of Circles, Activity 1, students use the Interactive to discover parts of a circle. It states, “Students will be practicing labeling the parts of a circle: radius, center, diameter, and circumference. At the bottom are draggable words that students can place on the black line next to the appropriate part. If a work is placed in the wrong spot, it will turn red.” (7.G.4)