Mathematical Reasoning by The Critical Thinking
Company is a colorful, engaging, full-color activity book series that builds
strong mathematical reasoning and problem-solving skills from early childhood
through middle school. Rather than rote memorization, students actively explore
concepts through a wide variety of fun, thought-provoking activities.
The program follows a spiral approach with a Concrete → Semi-Concrete
→ Semi-Abstract → Abstract progression, helping students develop deep
understanding and critical thinking.
Key Curriculum Features:
Covers
number concepts, patterns, geometry, measurement, data analysis,
fractions, probability, and problem-solving
NCTM
standards aligned with strong emphasis on reasoning and real-world
application
Engaging,
full-color worksheets with eye-catching illustrations and hands-on
activities
Spiral
review that reinforces concepts over time
Suitable
as a core curriculum or supplement for critical thinking and skill
reinforcement
Begins
with simple readiness skills for ages 3–4 and progresses to advanced
topics through Grade 6, plus the Geometry level
Program Components:
Student
Books: Full-color, consumable activity books (Levels Beginning 1 &
2 for ages 3–4; Levels A–G for Grades K–6; Geometry also available)
Answers
provided in the back of books starting in Level B
Reproducible
for family use
Mathematical Reasoning curriculum stands out for its
fun, non-intimidating format that develops both mathematical skills and
critical thinking. It is an excellent choice for homeschool families seeking an
engaging, long-term math reasoning program that works well as a core or
supplement.
Browse all Mathematical Reasoning levels and resources below!
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Teaching Method
Traditional
Teacher-centered curriculum commonly used in classrooms that may include a text, teacher manual, tests, etc.
Charlotte Mason
A methodology based on the work of a 19th century educator who maintained that children learn best from literature (Living Books), not textbooks.
Classical
A methodology based on the Latin Trivium (three stages of learning), including the grammar stage (memorization and facts), logic stage (critical thinking), and rhetoric stage (developing/defending ideas).
Unit Study
A thematic or topical approach centered around one topic that integrates multiple subject areas.
Montessori (Discovery)
A methodology based on the work of a 20th century educator that emphasizes student and sensory-driven discovery learning and real-life applications.
Other
Other methodologies
Religious Content
Secular
Contains content contrary to common Christian beliefs (i.e. evolution).
Neutral
Avoids religious or theoretical topics or presents multiple viewpoints without preference.
Christian/Religious
Faith-based or including instructional religious content.
Learning Modality
Auditory
Learns through listening, talking out loud or reading out loud.
Visual
Learns through seeing, prefers written instructions and visual materials.
Kinesthetic/Tactile (Hands-On)
Learns through moving, doing and touching.
Multi-Sensory
Curriculum that employ a variety of activities/components.
Presentation
Sequential
Curriculum progresses through well-defined learning objectives. Emphasizes mastery before moving to the next topic.
Spiral
Topics and concepts are repeated from level to level, adding more depth at each pass and connecting with review.
Conceptual/Topical
Focus is on the “why,” often with a unifying concept as well as specific skills; coverage may be broader.
Teacher Involvement
Low Teacher Involvement
Student-led materials; parent acts as a facilitator.
Medium Teacher Involvement
A mix of teacher-led time and independent student work.
High Teacher Involvement
Teacher-led lessons; may utilize discussions, hands-on activities and working together.
Additional Materials Required
No other materials needed
Everything you need is included.
Other Materials Required
There are additional required resources that are a separate purchase.
Other Materials Optional
There are additional resources mentioned or recommended but are not absolutely necessary.
