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Contemplanda

Core mathematics

Integrated Math 1

A college-prep integrated course that weaves algebra, geometry, and statistics together across a single year.

10 units · 77 lessons · 319 practice items

Integrated Math 1 is the first course on the integrated pathway, which weaves algebra, geometry, and statistics together within one year rather than teaching them in separate courses. You work through equations and inequalities, systems, sequences, linear and exponential functions and their features, then move into rigid motions and congruence, compass-and-straightedge constructions, connecting algebra with coordinate geometry, and a full unit on modeling data.

Every skill in the course runs on a mastery loop: exercises are drawn fresh from shared question banks until you can answer four in a row, and the reading on each page teaches everything the exercises ask. Interactive tools carry the work throughout, from graphing and construction canvases to statistics builders, with both semester finals drawing across the whole course.

Syllabus

Every published lesson in this course, by unit.

1Equations and inequalities7 lessons
  1. 1Equivalent expressions: combining like terms and the distributive property
  2. 2Interpreting expressions and using units to understand problems
  3. 3Explaining each step in the process of solving an equation
  4. 4Solving literal equations
  5. 5Writing inequalities to fit a context, reasoning about inequalities
  6. 6Solving absolute value equations and inequalities
  7. 7Unit 1 test
2Systems of equations and inequalities11 lessons
  1. 1An introduction to representing constraints with systems of inequalities
  2. 2Writing and solving equations in two variables
  3. 3Writing and graphing inequalities in two variables to represent constraints
  4. 4Writing and graphing inequalities and graphing the solution set to a system
  5. 5Solving systems of linear equations in two variables
  6. 6An introduction to solving systems of linear equations by elimination
  7. 7Solving systems of linear inequalities representing constraints
  8. 8Working with systems of linear equations, including inconsistent and dependent systems
  9. 9Using systems of linear equations and inequalities in a modeling context
  10. 10Unit 2 review
  11. 11Unit 2 test
3Sequences7 lessons
  1. 1Representing arithmetic sequences with equations, tables, graphs, and story context
  2. 2Arithmetic sequences and geometric sequences
  3. 3Missing terms: rate of change in arithmetic sequences and constant ratio in geometric sequences
  4. 4Comparing arithmetic and quadratic patterns
  5. 5Decreasing arithmetic sequences and interpreting equations that model linear and exponential functions
  6. 6Writing explicit rules for quadratic patterns and unit review
  7. 7Unit 3 test
4Functions8 lessons
  1. 1Comparing rates of growth in arithmetic and geometric sequences
  2. 2Introducing continuous linear and exponential functions
  3. 3Understanding and interpreting formulas for exponential growth and decay
  4. 4Focus on maximum or minimum point as well as domain and range for quadratics
  5. 5Solving exponential and linear equations
  6. 6Evaluating the use of various forms of linear and exponential equations
  7. 7Developing fluency with geometric and arithmetic sequences
  8. 8Unit 4 test
ExamSemester 1 final1 lesson
  1. 1Semester 1 final
5Features of functions11 lessons
  1. 1Using a story context to graph and describe key features of functions
  2. 2Features of functions using various representations
  3. 3Interpreting functions using notation
  4. 4Combining functions and analyzing contexts using functions
  5. 5Comparing quadratic models
  6. 6Model a situation using exponential functions
  7. 7Introduction to quadratic function graphs and their features
  8. 8Connecting transformations to quadratic functions and parabolas
  9. 9Working with vertex form of a quadratic, connecting the components to transformations
  10. 10Incorporating quadratics with the understandings of linear and exponential functions
  11. 11Unit 5 test
6Transformations, congruence, and constructions16 lessons
  1. 1Developing the definitions of the rigid-motion transformations: translations, reflections and rotations
  2. 2Examining the slope of perpendicular lines
  3. 3Determining which rigid-motion transformations carry one image onto another congruent image
  4. 4Writing and applying formal definitions of the rigid-motion transformations
  5. 5Finding rotational symmetry and lines of symmetry in special types of quadrilaterals
  6. 6Making and justifying properties of quadrilaterals using symmetry transformations
  7. 7Examining characteristics of regular polygons that emerge from rotational symmetry and lines of symmetry
  8. 8Describing a sequence of transformations that will carry congruent images onto each other
  9. 9Establishing the ASA, SAS and SSS criteria for congruent triangles
  10. 10Using ASA, SAS, or SSS to determine if two triangles embedded in another geometric figure are congruent
  11. 11Exploring compass and straightedge constructions to construct rhombuses and squares
  12. 12Exploring compass and straightedge constructions (parallels, parallelograms, equilateral triangles and hexagons)
  13. 13Construction basics
  14. 14Examining why compass and straightedge constructions produce the desired objects
  15. 15Writing procedures for compass and straightedge constructions
  16. 16Unit 6 test
7Connecting algebra and geometry6 lessons
  1. 1Use coordinates to find distances and determine the perimeter of geometric shapes
  2. 2Prove slope criteria for parallel and perpendicular lines
  3. 3Use coordinates to algebraically prove geometric theorems
  4. 4Write the equation f(t) = mt + k by comparing parallel lines and finding k
  5. 5Translating linear and exponential functions using multiple representations
  6. 6Unit 7 test
8Modeling data9 lessons
  1. 1Use context to describe data distribution and compare statistical representations
  2. 2Describe data distributions and compare two or more data sets
  3. 3Calculating and interpreting standard deviation
  4. 4Interpret two-way frequency tables and write conditional statements using relative frequency tables
  5. 5Develop an understanding of the value of the correlation coefficient
  6. 6Estimate correlation and lines of best fit; compare to calculated regression and r
  7. 7Use residual plots to analyze the strength of a linear model for data
  8. 8Unit 8 review
  9. 9Unit 8 test
ExamSemester 2 final1 lesson
  1. 1Semester 2 final