Illustrative Mathematics
Illustrative Mathematics: F Tf Bicycle Wheel
The purpose of this task is to introduce radian measure for angles in a situation where it arises naturally, in this case the movement of a bicycle wheel. Aligns with HSF-TF.A.1.
Illustrative Mathematics
Illustrative Mathematics: F Tf Calculations With Sine and Cosine
The goal of this task is to study some values of sin x and cos x for different angles, and to look for and then explain patterns that are seen. Aligns with HSF-TF.C.8.
Illustrative Mathematics
Illustrative Mathematics: F Tf Equilateral Triangles and Trigonometric Functions
The purpose of this task is to apply knowledge about triangles to calculate the sine and cosine of 30 and 60 degrees. Aligns with HSF-TF.A.3.
Illustrative Mathematics
Illustrative Mathematics: F Tf Hours of Daylight 1
In order to determine how effective solar panels would be at various times of the year, it is important to know the amount of daylight at a given location. Students are asked to find an appropriate function that serves as a mathematical...
Illustrative Mathematics
Illustrative Mathematics: F Le Boiling Water
Students are shown two tables of data showing the approximate boiling point of water at different elevations. Both data sets can be modeled by linear functions but with different slopes. When the tables are combined, however, students...
Illustrative Mathematics
Illustrative Mathematics: F Le Exponential Kiss
The purpose of this task is to use technology to study the behavior of some exponential and logarithmic graphs and to manipulate some explicit logarithmic and exponential expressions. Aligns with HSF-LE.A.4, F-BF.B.5, and F-IF.C.7.e.
Illustrative Mathematics
Illustrative Mathematics: F Le Dido and the Foundation of Carthage
According to ancient legend, Dido made a deal with a local ruler to obtain as much land as she could cover with an oxhide. Dido interpreted "cover" in an imaginative way and the land she obtained became the site of the important ancient...
Illustrative Mathematics
Illustrative Mathematics: F Le Choosing an Appropriate Growth Model
The goal of this task is to examine some population data for large cities from a modeling perspective. Students are asked to decide if the population data can be accurately modeled by a linear, quadratic, and/or exponential function, and...
Illustrative Mathematics
Illustrative Mathematics: Equality Number Sentences
Learners will compare the number of circles in two boxes. If they are equal, they will write a number sentence. Explanations and examples are included.
Illustrative Mathematics
Illustrative Mathematics: Biggest Number Wins
Students will practice number recognition and greater than/less than with this classic "war" game. Explanations, materials needed, and variations of play are included in this lesson.
Illustrative Mathematics
Illustrative Mathematics: Assessing Sequencing Numbers
This lesson assesses rather students can correctly order numbers. The teacher will ask the student(s) to put pre-made number cards in order from the smallest number to the biggest number or in the order they would say them if they were...
Illustrative Mathematics
Illustrative Mathematics: Find the Missing Number
Learners will solve addition and subtraction equations with different structures so that they are able to see the connections between addition and subtraction more easily.
Illustrative Mathematics
Illustrative Mathematics: Finding a Chair
This lesson includes a series of questions that can be posed by the teacher to the whole class which revolves around addition and subtraction.
Illustrative Mathematics
Illustrative Mathematics: F Le Triangular Numbers
The goal of this task is to work on producing a quadratic equation from the arithmetic context of triangular numbers. Aligns with HSF-LE.A.
Illustrative Mathematics
Illustrative Mathematics: F Le Comparing Graphs of Functions
The goal of this task is to use appropriate tools to compare graphs of several functions. In addition, young scholars are asked to study the structure of the different expressions to explain why these functions grow as they do. Aligns...
Illustrative Mathematics
Illustrative Mathematics: Fact Families With Pictures
Students will use pictorial models to write as many equations for each picture as they can. Multiple variations and extension ideas are included in this lesson.
Illustrative Mathematics
Illustrative Mathematics: Choral Counting
Using base ten blocks, students will develop the concept of ten more and ten less, moving from concrete representation to understanding of the unit of ten within ten more and ten less. Included is a detailed lesson plan with many...
Illustrative Mathematics
Illustrative Mathematics: Field Day Scarcity
Students will learn about managing money and scarcity while practicing addition and subtraction. They will be given a certain amount of money to spend at a fictitious store. Included are discussion questions about how students decided to...
Illustrative Mathematics
Illustrative Mathematics: Fact Families
As a whole class, the teacher presents students with 3 numbers on cards, such as 5, 8, and 3. The teacher asks the students to find all the ways the numbers can be put together in addition or subtraction sentences. This lesson includes...
Illustrative Mathematics
Illustrative Mathematics: Color Week
Five-year-olds need to count things that relate to them. This activity builds on their need to be included or see the relevance of their counting. Students will practice counting, writing numbers, and filling in a chart or bar graph....
Illustrative Mathematics
Illustrative Mathematics: F Le Do Two Points Determine an Exponential Function?
In this task, students investigate whether exponential functions will always be determined by two points. It complements the task "Do two points always determine a linear function?" Aligns with F-LE.A.2.
Illustrative Mathematics
Illustrative Mathematics: F Le.4 Graphene
This task provides a real-world context for examining the power of exponential growth and decay. Students experiment, at the macro level, using scotch tape to pull a chip of graphite apart into two pieces. They are asked to find about...
Illustrative Mathematics
Illustrative Mathematics: F Le a Valuable Quarter
The context of this task is that a quarter was put into a bank account in 1901 and students are asked to calculate its value in 2013 at two different interest rates. Those amounts are compared to the appreciation rate of a rare and...
Illustrative Mathematics
Illustrative Mathematics: F Le Basketball Bounces, Assessment Variation 1
This task asks young scholars to analyze a set of data about the height of a basketball for each time it bounces. They choose a model that reasonably fits the data and use the model to answer questions about the physical context. This...