Illustrative Mathematics
Illustrative Mathematics: Assessing Reading Numbers
This activity assesses the student's ability to identify written numbers. One-on-one with a student, the teacher shows the numbers 1-10, one number at a time, in random order. The student should say the correct number that is being...
Illustrative Mathematics
Illustrative Mathematics: Assessing Counting Sequences Part Ii
This activity is designed to determine the appropriate instructional level for a student in a one-on-one interaction with the teacher. It assesses the students understanding of counting, specifically "number after".
Illustrative Mathematics
Illustrative Mathematics: Assessing Counting Sequences Part I
This activity is designed to determine the appropriate instructional level for a student in a one-on-one interaction with the teacher. It assesses the student's understanding of counting, specifically counting forward from a given number.
Illustrative Mathematics
Illustrative Mathematics: Counting Cup
Students will count counters, draw a picture of the counters, and record the number in a booklet. A list of materials and how to put together the booklet is included. This activity is most effective if initially it is done daily with all...
Illustrative Mathematics
Illustrative Mathematics: Choral Counting
This can be a daily activity to reinforce learning number sequences. The teacher will need a 100 chart or large number line and a pointer. As a whole group, have students chant the counting sequence starting with one to thirty, using the...
Illustrative Mathematics
Illustrative Mathematics: Bags of Stuff
This activity is a good practice for counting objects. Students will count pre-filled bags of objects and record their answers. Examples are included in this lesson. This activity can become a daily 10-minute routine with the students...
Illustrative Mathematics
Illustrative Mathematics: F Tf Foxes and Rabbits 3
Students are presented with two graphs that show the populations of foxes and rabbits in a national park over a 24-month period. This is the third Foxes and Rabbits task. In this more realistic problem, students must find functions that...
Illustrative Mathematics
Illustrative Mathematics: F Tf Foxes and Rabbits 2
Students are presented with a table that shows the populations of foxes and rabbits in a national park over a 12-month period. This is the second Foxes and Rabbits task. In this problem, students must find trigonometric functions that...
Illustrative Mathematics
Illustrative Mathematics: F Tf Sum and Difference Angle Formulas
The goal of this task is to have students derive the addition and subtraction formulas for cosine and tangent, and the subtraction formula for cosine, from the sum formula for sine. Aligns with F-TF.C.9.
Illustrative Mathematics
Illustrative Mathematics: F Tf Trig Functions and the Unit Circle
The purpose of this task is to help students make the connection between the graphs of sin t and cos t and the x and y coordinates of points moving around the unit circle. Students have to match coordinates of points on the graph with...
Illustrative Mathematics
Illustrative Mathematics: F Tf Special Triangles 1
Using known facts about the unit circle and isosceles triangles together with the Pythagorean Theorem, students can derive the sine and cosine of special angles. Aligns with HSF-TF.A.3.
Illustrative Mathematics
Illustrative Mathematics: F Tf Properties of Trigonometric Functions
The goal of this task is to use the unit circle and rigid transformations in order to establish some fundamental trigonometric function identities. Aligns with F-TF.A.2 and F-TF.A.4.
Illustrative Mathematics
Illustrative Mathematics: F Tf Trigonometric Ratios and the Pythagorean Theorem
The purpose of this task is to use the Pythagorean Theorem to establish a fundamental trigonometric identity for an acute angle. The reasoning behind this identity is then applied to calculate a cosine for a given obtuse angle. Aligns...
Illustrative Mathematics
Illustrative Mathematics: F Tf Trigonometric Functions for Arbitrary Angles
The purpose of this task is to examine trigonometric functions for obtuse angles. Aligns with F-TF.A.2.
Illustrative Mathematics
Illustrative Mathematics: F tf.a, F bf.b.3 Exploring Sinusoidal Functions
In this task, students explore the effect that changing the parameters in a sinusoidal function has on the graph of the function. Aligns with F-TF.A and F-BF.B.3.
Illustrative Mathematics
Illustrative Mathematics: F Tf, F if as the Wheel Turns
In this task, students use trigonometric functions to model the movement of a point around a wheel and through space. Students also interpret features of graphs in terms of the given real-world context. Aligns with F-TF.B.5 and F-IF.B.4.
Illustrative Mathematics
Illustrative Mathematics: F Tf Special Triangles 2
Using known facts about the unit circle and isosceles triangles together with the Pythagorean Theorem, students can derive the sine and cosine of special angles. Aligns with HSF-TF.A.3.
Illustrative Mathematics
Illustrative Mathematics: F Tf Finding Trig Values
For this task, young scholars are give values for sin, cos, or tan, and use them to find the missing value as well as the quadrant of the angle. Aligns with HSF-TF.C.8.
Illustrative Mathematics
Illustrative Mathematics: F Tf.1 What Exactly Is a Radian?
For this task, young scholars use a piece of string or another tool to measure the radius of the circle and then mark off the corresponding arc length on the unit circle as many times as they need to for 0, 1, 2, 3, 4, 5, and 6 radians....
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
Young scholars 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,...