School & District Info

Early Childhood

General Program Info

School & District Info

Standards & Instruction

General Learning Info

School & District Info

Grants and Funding

* * CDE will be closed on Monday, May 27 for the Memorial Day holiday. * *

# Instructional Unit Samples - Mathematics

Hello,

Below are the teacher-authored instructional unit samples in mathematics. Each of these units represents the work of a team of Colorado educators to translate one curriculum overview sample into a full instructional unit with learning experiences, teacher and student resources, assessment ideas, and differentiation options. To learn more about the unit development process and the unique aspects of the mathematics units, please consider watching one or more of the  instructional unit webinars.

Each of the units posted here was authored by a team of Colorado educators. As examples, they are intended to provide support (or conversation/creation starting points) for teachers, schools, and districts as they make their own local decisions around the best instructional plans and practices for all students.

You can also view a complete list of the mathematics curriculum overview samples and an instructional unit template to begin constructing your own Colorado Academic Standards-based units.

Raymond Johnson
Mathematics Content Specialist

## High School

### Algebra I Unit Title: Power to the Variable (Lake County School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: This unit focuses on a formal introduction to exponential functions. The students start with exploring exponential growth through geometric sequences that either grow or decay. As the students learn about geometric sequences, they continually compare them to arithmetic sequences, building to linear and exponential functions. Student fluency with these functions improves through multiple experiences with tables, graphs, equations and contexts. Then students examine the differences in the growth rates of linear, exponential, and polynomial functions leading to a formal proof of how linear functions grow by constant differences and exponential functions grow by common factors.

### Algebra II Unit Title: Logarithmic Log Jams (Lake County School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: This unit focuses on the exponential functions that are embedded in our everyday financial lives. Students explore credit card debt, interest rates, and the time it takes for investments to double in value. As they explore these topics, they are motivated to solve exponential equations, necessitating the introduction of logarithms. The students become fluent in rewriting expressions using logarithms and in solving for unknown variables in the exponent using logarithms. In addition, the students explore continuously compounded interest and discover one of the most important numbers in mathematics, e.

### Algebra II Unit Title: Survey Says... (Lake County School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: This unit focuses on inferring conclusions about a population from samples. Students explore normal distributions and the concept of quantifying “normal”. The concept of normal distributions provides the foundation for making inferences about a population from sample means and standard deviations.  The unit then looks at the different ways to collect data about a population. Finally, students investigate simulation the use of simulations to test the validity of statistical conclusions and hypotheses. Throughout this unit students will explore how statistics are used to make policy decisions and engage in the process of creating policies that impact their life.

### Integrated Math 2 Unit Title: Reproducing Bacterial Rabbits (Mesa County Valley School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: This unit focuses on exponential functions embedded in our everyday financial lives.  Students explore credit cards, loans and savings accounts.  As they explore these topics, they are motivated to solve exponential equations and become fluent in interpreting exponential expressions by using the properties of exponents to rewrite expressions. Students are introduced to the concept of the mathematical constant e, through the context of continuously compounding interest.  Students also explore the attributes of classes of functions including their inverses, which introduce the concept of a logarithm.  Students will further explore classes of functions and the impact of multiplying or adding a constant in the next unit and the concept of logarithm is developed further in Integrated III.

### Mathematics 1 Unit Title: Transform the World (South Routt School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Instructional Unit with Embedded Extended Evidence Outcomes  (Word or PDF) | Unit Storyboard

Unit Description: This unit investigates transformations, congruence, and proof. Students begin with informal explorations of rigid transformations.   Students then use precise mathematical definitions of rotations, translations and reflections to determine if each of these rigid transformations is a function. The transformation work of this unit leads students to develop formal proofs about congruency, parallel lines, triangle relationships, and parallelograms.

### Mathematics 3 Unit Title: Survey Says... (Lake County School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: This unit focuses on inferring conclusions about a population from samples. Students explore normal distributions and the concept of quantifying “normal”. The concept of normal distributions provides the foundation for making inferences about a population from sample means and standard deviations.  The unit then looks at the different ways to collect data about a population. Finally, students investigate simulation the use of simulations to test the validity of statistical conclusions and hypotheses. Throughout this unit students will explore how statistics are used to make policy decisions and engage in the process of creating policies that impact their life.

### Unit Title: Walk the Line (Lake County School District, South Routt School District, and Greeley School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: In Walk the Line, students explore representations of proportional and linear relationships. The authors of this unit begin by having students explore different representations of a proportional relationship and then move their understandings of proportional relationships to linear relationships.  A major focus of this unit includes an investigation with slope and similar triangles. Lastly, students will be solving a variety of one-variable linear equations that have one, none, and infinitely many solutions.

### Unit Title: Data Daze (Burlington School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Instructional Unit with Embedded Extended Evidence Outcomes  (Word or PDF)   Unit Storyboard

Unit Description: Data Daze takes students on a journey into random sampling. Students learn to make inferences about a population based on sample data.  Students are also introduced to the idea of variation through the mean absolute deviation.  This is the first unit in which students explore the connections between samples and populations. These ideas will be extended at the high school level and linked to the concept of standard deviation.

### Unit Title: R U Proportional? (Ellicott School District and Lake County School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: Through participation in this unit, students will be able to develop a stronger understanding of personal financial literacy by applying ratios and percents to real-world situations. Learning experiences will include practice with calculations involving tax, tips, miles per gallon, rate of pay and simple interest. Concepts include proportional and non-proportional relationships, unit rate and unit cost, slope and the connection between y=kx and graphs of proportional relationships.

### Unit Title: Go Figure! (Sangre de Cristo School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: This unit focuses on the geometric concepts of perimeter, area, surface area and volume.  Students begin by working on the coordinate plane to find the perimeter and area of rectangles.  The formula for the area of a rectangle is then built upon to create a formula for the area of parallelograms and triangles.  The concept of area is then extended to surface area and nets of three-dimensional solids with rectangular and triangular bases.  Students finish the unit by exploring volumes of right rectangular prisms with fractional side lengths by connecting back to area and fraction multiplication.

### Unit Title: Fraction Reaction (Clear Creek School District and Greeley School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: This unit focuses on the relationship between fractions and each of the four operations. The unit begins by developing the concept of a fraction as the operation of division through fair share problems. A major development in this unit is the formalization of multiplication of fractions.  Students begin by modeling fraction multiplication using area and scaling models and eventually connect these models to the algorithm for multiplication.  Students also explore division of fractions through contextualized problems and informal solution strategies: this concept is formalized and the algorithm is developed during sixth grade. Finally, students apply their understandings of multiplication of fractions and fraction equivalence to the addition and subtraction of fractions with unlike denominators.

### Unit Title: Fraction Frenzy (Norwood School District and Greeley School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: In this unit students explore fractions as quantities.  Students build on their prior knowledge with whole numbers to compose and decompose fractions in multiple ways; the early development of addition and subtraction of fractions.  Students also explore the concept of finding a fraction amount of a whole number. In addition, students begin to compare fractions by recognizing the need to examine both the numerator and denominator and the importance of maintaining a consistent unit or whole.  Throughout the unit students are focusing on the quantitative, verbal and symbolic parts of a number to provide a strong foundation for the formalization of fraction operations in fifth and sixth grade.  Finally, students explore the concept of equivalent fractions and the special cases of fractions with denominators of 10 or 100 to prepare them for their work with decimals.

### Unit Title: Multiply, Divide & Conquer (Plateau Valley School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: This unit focuses on an introduction to multiplication and division concepts.  The students begin with exploring items that come in equal groups and the connections between how equal groups, repeated addition, and skip counting relate to multiplication.  Students explore multiplication and find factors in a geometric context through the construction of rectangular arrays and use these skills to problem solve.  Students then use arrays and number strings to demonstrate their understanding of the Associative and Distributive properties of multiplication.  The culmination of this unit explores patterns in the multiplication chart in order to build fluency of multiplication facts by the end of third grade.

### Unit Title: Are You Odd or Even? (Centennial School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: This unit focuses on applications of addition and subtraction within 20 and within 100.  The students start off with solving word problems with the result unknown.  Students then move to word problems with start and change unknowns and develop an understanding of how to use a number line to solve addition and subtraction problems.  Students also connect picture and bar graphs to the concepts of addition and subtraction word problems.  The culmination of this unit introduces early multiplicative ideas such as skip counting, arrays, and odds/evens.

### Unit Title: Keeping Track (Meeker School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: This unit focuses on measurement in relation to length and time.  Across the 4-week unit, students will consider the concepts of unit, zero, conservation and transitivity. Throughout the entire unit learning experiences are designed to ensure students are measuring for a purpose.  Students begin by making indirect comparisons about length (transitivity) using non-standard units.  The concept of comparison leads to students to discuss the need for standard units, which connects, to the concept of time and the unit of an hour.  Students continue their work with units of length by repeating (iterating) a standard unit without gaps or overlaps.  All of this work provides a foundation for working with a ruler.

## Kindergarten

### Unit Title: Put it Together and Take it Apart (Archuleta School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: This unit focuses on the concepts of addition and subtraction.  Across the six-week unit students begin by decomposing and composing numbers to five.  Students explore a variety of visual representations including finger patterns, five-frames, and linking cubes.  Students then connect these representations to symbolic addition and subtraction equations.  Throughout the unit students are solving word-problems by using these representations. By the end of the unit, students progress to working with numbers to ten using the same visual and symbolic representations.

### Integrated Unit Title: Shape Detectives (Thompson School District)

Instructional Unit (Word or PDF) | Unit Storyboard

Unit Description: This unit focuses on recognizing, naming, and using geometric shapes.