Advanced Common Core Math Explorations: Ratios, Proportions, and Similarity
Mindprint Rating
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Skills
Mindprint Expert Review
Pros
- The book provides authentic, multi-layered problems for strong middle school math students to apply learned concepts and develop critical thinking skills.
- The book provides layers of support and detailed answers for teachers to ask students probing questions and help them in independent exploration and problem solving.
- The book encourages students to approach problems from multiple perspectives which will challenge flexible thinking as well as abstract reasoning skills.
Considerations
- Students and teachers might feel out of their comfort zones with some of the problems, and this book might require more advanced teacher preparation especially since problems are not ordered by difficulty.
- The pages intended to be photocopied for students are very full and offer insufficient space for problem solving.
- Given the nature of the problems, the book has relatively limited drawings to help students envision the solution.
Mindprint Expert Review
This advanced math workbook is designed for teachers to provide deeper level problem solving activities for advanced or gifted middle school students. Teachers will need to refer to Table 1 to see how each chapter correlates to the Common Core Standards for ratios, proportions and similarity. The book provides step-by-step teacher guidance on how to support students for the deepest understanding. Each of the ten chapters is an exploration of a real-world problem that is sub-divided into three stages with multiple problems per stage. Students will tackle real world problems, such as determining the size of bicycle gears, estimating the height of a transmission tower, and calculating distances among planets. The book comes with detailed teacher goals, recommendations on how to present the explorations, question prompts to guide students without telling them what to do, and multiple detailed approaches for each problem so students can improve their flexible problem solving skills. Teachers can photocopy and distribute the problem pages, though the pages will not provide sufficient space for the students to solve and answer the multi-layered questions. Overall, this book provides teachers with excellent guidance to give students authentic problem solving practice, but teachers should use their judgment as to whether the material will be suitable or too advanced for their students.
Academic Benefits
Improves academic skills
- Provides sufficient and varied types of practice problems to maximize understanding and generalization of the targeted skill/concept
- Manufacturer claims alignment with Common Core/Known Standards
- Presents educational concepts accurately
- Explains answers so students can learn from mistakes
- Better for teaching the skill to new or struggling learners
- Better for practicing or refreshing the skill
- Skills are practiced through authentic, meaningful problems (not just rote practice)
Fun
Engaging for the Mindprint recommended age range
- Appropriate for a broad age range to use and enjoy
- Subject matter and problems are relevant, interesting and authentic to students
- Includes reward stickers
- Visually stimulating and appealing (uses student-centered pictures, colors, and themes)
- Graphics and overall feel of the workbook is appropriate for the target age range
- Relative to most workbooks, fun to use from a child's perspective
- Offers ongoing, progressive challenge
- Overall - Enjoyable. Given the option, students would choose this option
Easy to Use
Understandable for children in the Mindprint recommended age range
- Provides teaching guidance for adults to support the child and set appropriate goals
- Student should be able to use independently after first use
- Specific topics/lessons are easy to find
- Presents information in multiple formats (voice over, pictures and text, etc.)
- Overall - Easy to use
Cognitive Concerns
May not be advisable for students with the following cognitive needs
- Abstract Reasoning
- Directions may be confusing for students using independently
- Word problems assume additional knowledge (conversion factors, formulas, symbols, etc.)
- Numerical Fluency
- Student will need to copy or write multi-digit math problems
- Word problems assume additional knowledge (conversion factors, formulas, symbols, etc.)
- Working Memory
- Directions may be confusing for students using independently
- Student will need to copy or write multi-digit math problems
Manufacturer Description
Stretch your students' mathematical imaginations to their limits as they solve challenging real-world and mathematical problems that extend concepts from the Common Core State Standards for Mathematics in Advanced Common Core Math Explorations: Ratios, Proportions, and Similarity. Model the solar system, count the fish in a lake, choose the best gear for a bike ride, solve a middle school's overcrowding problem, and explore the mysteries of Fibonacci numbers and the golden ratio. Each activity comes with extensive teacher support including student handouts, discussion guides, detailed solutions, and suggestions for extending the investigations. There is also a free supplemental e-book offering strategies for motivation, assessment, parent communication, and suggestions for using the materials in different learning environments.