Illustrative Mathematics
Illustrative Mathematics: A ced.a.1: Sum of Angles in a Polygon
This problem provides students with an opportunity to discover algebraic structure in a geometric context. They will divide up polygons into triangles. The will use the sum of the angles of 180 degrees for each triangle. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: "One More" Concentration
This game is a version of the traditional memory or concentration game. Students will practice counting forward or backward depending on their skill level. Directions and materials needed are fully explained in the lesson.
Illustrative Mathematics
Illustrative Mathematics: Counting Overview
The most important factor in teaching counting is that children count things that matter to them, and that they practice often. This site gives various examples of how to incorporate counting into your classroom on a daily basis by...
Illustrative Mathematics
Illustrative Mathematics: Guess the Marbles in the Bag
Students will make their best guesses as to how many marbles are in a bag. After recording 4-5 guesses, the teacher writes the number representing the total on the board, and the students then help sort their guesses into less than,...
Illustrative Mathematics
Illustrative Mathematics: Assessing Writing Numbers
This activity assesses rather young scholars know how to correctly write numerals. The teacher will ask students to write the number that is spoken. Extra tips for this activity are included.
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 learners 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, students 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, students 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. They...