Contemplanda
Contemplanda course syllabus
Integrated Math 1
A Contemplanda online course.
Integrated Math 1 is the first course of the integrated pathway, which teaches algebra, geometry, and statistics together each year in place of separate courses. Equations and inequalities, systems, sequences, and linear and exponential functions fill the first semester. The second semester moves to the features of functions, then rigid motions, congruence, and compass-and-straightedge constructions, then coordinate geometry and the modeling of data.
Each skill's practice draws fresh questions from shared banks until four answers in a row are correct, and nearly every problem carries hints. Interactive tools are used for many of the answers: graphs, a construction canvas, and builders for histograms, box plots, and scatterplots. Each semester ends with a final exam, and most of its questions are drawn from the same banks.
Course at a glance
- Course title
- Integrated Math 1
- Publisher
- Contemplanda
- Structure
- 8 units and 2 semester exams, over two semesters (units 1 to 4 in semester 1; units 5 to 8 in semester 2)
- Lessons
- 77 lessons: 67 teaching lessons, 8 unit tests, and 2 semester exams
- Credit
- Not awarded by Contemplanda
- Enrollment
- Through the student's school
Credit and enrollment
Contemplanda does not award high school credit. A student who wants credit for the course should ask their own school whether it will accept it.
Schools order course seats for their students by writing to info@contemplanda.com, and a student enrolls through their school.
Students enrolled through Contemplanda Direct sign in at direct.contemplanda.com. A student whose school delivers the course signs in on the school's own portal instead.
How the course works
- Practice comes one question at a time and continues until the student answers four in a row correctly. After a wrong answer, the practice keeps drawing questions.
Units and lessons
Every published lesson, by semester and unit.
Semester 1
Equations and inequalities
- Equivalent expressions: combining like terms and the distributive property
- Interpreting expressions and using units to understand problems
- Explaining each step in the process of solving an equation
- Solving literal equations
- Writing inequalities to fit a context, reasoning about inequalities
- Solving absolute value equations and inequalities
- Unit 1 testUnit test13 questions
Systems of equations and inequalities
- An introduction to representing constraints with systems of inequalities
- Writing and solving equations in two variables
- Writing and graphing inequalities in two variables to represent constraints
- Writing and graphing inequalities and graphing the solution set to a system
- Solving systems of linear equations in two variables
- An introduction to solving systems of linear equations by elimination
- Solving systems of linear inequalities representing constraints
- Working with systems of linear equations, including inconsistent and dependent systems
- Using systems of linear equations and inequalities in a modeling context
- Unit 2 review
- Unit 2 testUnit test16 questions
Sequences
- Representing arithmetic sequences with equations, tables, graphs, and story context
- Arithmetic sequences and geometric sequences
- Missing terms: rate of change in arithmetic sequences and constant ratio in geometric sequences
- Comparing arithmetic and quadratic patterns
- Decreasing arithmetic sequences and interpreting equations that model linear and exponential functions
- Writing explicit rules for quadratic patterns and unit review
- Unit 3 testUnit test12 questions
Functions
- Comparing rates of growth in arithmetic and geometric sequences
- Introducing continuous linear and exponential functions
- Understanding and interpreting formulas for exponential growth and decay
- Focus on maximum or minimum point as well as domain and range for quadratics
- Solving exponential and linear equations
- Evaluating the use of various forms of linear and exponential equations
- Developing fluency with geometric and arithmetic sequences
- Unit 4 testUnit test12 questions
Semester 1 final
- Semester 1 final49 questions
Covers all of semester 1, units 1 to 4.
Semester 2
Features of functions
- Using a story context to graph and describe key features of functions
- Features of functions using various representations
- Interpreting functions using notation
- Combining functions and analyzing contexts using functions
- Comparing quadratic models
- Model a situation using exponential functions
- Introduction to quadratic function graphs and their features
- Connecting transformations to quadratic functions and parabolas
- Working with vertex form of a quadratic, connecting the components to transformations
- Incorporating quadratics with the understandings of linear and exponential functions
- Unit 5 testUnit test18 questions
Transformations, congruence, and constructions
- Developing the definitions of the rigid-motion transformations: translations, reflections and rotations
- Examining the slope of perpendicular lines
- Determining which rigid-motion transformations carry one image onto another congruent image
- Writing and applying formal definitions of the rigid-motion transformations
- Finding rotational symmetry and lines of symmetry in special types of quadrilaterals
- Making and justifying properties of quadrilaterals using symmetry transformations
- Examining characteristics of regular polygons that emerge from rotational symmetry and lines of symmetry
- Describing a sequence of transformations that will carry congruent images onto each other
- Establishing the ASA, SAS and SSS criteria for congruent triangles
- Using ASA, SAS, or SSS to determine if two triangles embedded in another geometric figure are congruent
- Exploring compass and straightedge constructions to construct rhombuses and squares
- Exploring compass and straightedge constructions (parallels, parallelograms, equilateral triangles and hexagons)
- Construction basics
- Examining why compass and straightedge constructions produce the desired objects
- Writing procedures for compass and straightedge constructions
- Unit 6 testUnit test18 questions
Connecting algebra and geometry
- Use coordinates to find distances and determine the perimeter of geometric shapes
- Prove slope criteria for parallel and perpendicular lines
- Use coordinates to algebraically prove geometric theorems
- Write the equation f(t) = mt + k by comparing parallel lines and finding k
- Translating linear and exponential functions using multiple representations
- Unit 7 testUnit test11 questions
Modeling data
- Use context to describe data distribution and compare statistical representations
- Describe data distributions and compare two or more data sets
- Calculating and interpreting standard deviation
- Interpret two-way frequency tables and write conditional statements using relative frequency tables
- Develop an understanding of the value of the correlation coefficient
- Estimate correlation and lines of best fit; compare to calculated regression and r
- Use residual plots to analyze the strength of a linear model for data
- Unit 8 review
- Unit 8 testUnit test16 questions
Semester 2 final
- Semester 2 final59 questions
Covers all of semester 2, units 5 to 8.
Assessment
Each teaching lesson includes a graded check.
Each of the eight content units closes with a unit test of 11 to 18 questions.
Each semester closes with a final exam. The semester 1 final has 49 questions on units 1 to 4, and the semester 2 final has 59 questions on units 5 to 8.
Unit tests and semester exams are graded automatically, and all graded work counts toward the student's mastery record, which shows each skill as attempted, familiar, proficient, or mastered.
Contemplanda publishes no grade weighting for this course. A school that decides to grant credit for it also decides how the work counts toward a grade.
Academic integrity
Work in the course must be the student's own.
Answer keys for graded questions are never sent to the student's device.
Materials and technology
- Where the course runs
- In a web browser, through Contemplanda Direct or inside a school's own platform
- Textbook
- None required. The course's own lessons are the text.