Illustrative Mathematics
Illustrative Mathematics: G Co Origami Equilateral Triangle
The purpose of this task is to explore reflections in the context of paper folding. Each fold is associated with a line of reflection and understanding each step in the construction requires careful analysis of angles and of the...
Illustrative Mathematics
Illustrative Mathematics: G C Right Triangles Inscribed in Circles I
This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle with one side of the triangle a diameter. The fact that these...
Illustrative Mathematics
Illustrative Mathematics: G Gpe Slopes and Circles
The purpose of this task is to lead learners through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever angle AXB is a right angle. This consists of...
Illustrative Mathematics
Illustrative Mathematics: A Apr: Zeroes & Factorization: Non Polynomial
The goal of this task is to show via a concrete example that the property of polynomials is not shared by all functions when zero is involved. Aligns with A-APR.B.2.
Illustrative Mathematics
Illustrative Mathematics: A Apr Zeroes and Factorization of a General Polynomial
In this task, students investigate the properties of a polynomial of degree d > 0. The task relates to the Fundamental Theorem of Algebra. Aligns with A-APR.B.2.
Illustrative Mathematics
Illustrative Mathematics: A Apr Zeroes and Factorization of Quadratic Polynomial
This is the first of a series of problems building to an understanding of an important property of polynomial functions, that a polynomial of degree d can have at most d roots. Aligns with A-APR.B.2.
Illustrative Mathematics
Illustrative Mathematics: A Sse Sum of Even and Odd
In this task, students use the structure of an expression to find ways to rewrite it. They are asked to use the defining property of even and odd functions to manipulate expressions involving function notation and to see the structure in...
Illustrative Mathematics
Illustrative Mathematics: 4.g Defining Attributes of Rectangles & Parallelograms
At early stages of understanding of geometric shapes, 4th graders describe shapes, but do not yet characterize shapes by their properties. One example of a misconception students have at this stage is that a rectangle has two short sides...
Illustrative Mathematics
Illustrative Mathematics: 8.f Introduction to Linear Functions
This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces the properties of linear functions. Aligns with 8.F.A.3.
Illustrative Mathematics
Illustrative Mathematics: g.co Reflections and Equilateral Triangles Ii
This task examines some of the properties of reflections of the plane which preserve an equilateral triangle. The task gives students a chance to see the impact of these reflections on an explicit object and to see that the reflections...
Illustrative Mathematics
Illustrative Mathematics: N rn.a.2: Kepler's Third Law of Motion
The purpose of this task is to solve some expressions requiring fractional exponents in the modeling context of planetary motion. Aligns with N-RN.A.2.
Illustrative Mathematics
Illustrative Mathematics: 5.md,oa You Can Multiply Three Numbers in Any Order
The purpose of this task is for students to use the volume of a rectangular prism to see why you can multiply three numbers in any order you want and still get the same result. Aligns with 5.OA.A and 5.MD.C.5.
Illustrative Mathematics
Illustrative Mathematics: 6.ns Multiplication, Division and Place Value, Part 1
Sixth graders are presented with a completed multiplication equation and are asked to use it to find the answers to seven other equations. To do this, they must use their reasoning and estimation skills. Aligns with 6.NS.B.3.
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: 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: A sse.b.3: Ice Cream
This task illustrates the process of rearranging the terms of an expression to reveal different aspects about the quantity it represents. Aligns with A-SSE.B.3.
Illustrative Mathematics
Illustrative Mathematics: G Co Properties of Congruent Triangles
The goal of this task is to understand how congruence of triangles, defined in terms of rigid motions, relates to the corresponding sides and angles of triangles. Aligns with G-CO.B.7.
Illustrative Mathematics
Illustrative Mathematics: G Srt, G Mg Seven Circles Iii
In this task, students are shown circle formations where an inner circle is surrounded by a set of circles and all circles are touching. In the first situation, all circles have the same diameter. In the second, the inner circle is...
Illustrative Mathematics
Illustrative Mathematics: G Srt, G Mg How Far Is the Horizon?
Some friends are at the beach looking out onto the ocean on a clear day and they wonder how far away the horizon is. A second problem asks how far the horizon would be from the top of a mountain. Students must also answer a question...
Illustrative Mathematics
Illustrative Mathematics: G Mg Solar Eclipse
In this task, young scholars investigate why total solar eclipses are rare. They will learn that, in addition to requiring the positioning of the Sun, Moon, and Earth, the Moon can only completely block out the Sun when it is closest to...
Illustrative Mathematics
Illustrative Mathematics: G Mg Tilt of Earth's Axis and the Four Seasons
This task gives students a chance to explore the effects of the Earth's tilt and rotation using a simple geometric model of Earth-Sun interaction that shows why the seasons occur. Aligns with G-MG.A.1.
Illustrative Mathematics
Illustrative Mathematics: G Mg Toilet Roll
Picture a roll of toilet paper; assume that the paper in the roll is very tightly rolled. Assuming that the paper in the roll is very thin, find a relationship between the thickness of the paper, the inner and outer radii of the roll,...
Illustrative Mathematics
Illustrative Mathematics: G Mg How Many Cells Are in the Human Body?
About how many cells are in the human body? The purpose of this task is for learners to apply the concepts of mass, volume, and density in a real-world context. Aligns with G-MG.A.2.
Illustrative Mathematics
Illustrative Mathematics: G Mg the Lighthouse Problem
For this task, students are asked to calculate the height above sea level of a lamp on top of a lighthouse that is visible to a boat, and to examine two other interpretations of the distance from the lighthouse to the boat. Aligns with...