Illustrative Mathematics
Illustrative Mathematics: N q.a.3, N q.a.1, N q.a.2: Weed Killer
The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout. Aligns with N-Q.A.3, N-Q.A.1, and N-Q.A.2.
Illustrative Mathematics
Illustrative Mathematics: A Sse Radius of a Cylinder
Given the height and volume of a certain cylinder, Jill uses the volume formula to compute its radius. If a second cylinder has the same volume as the first, but is 100 times taller, what is its radius? Aligns with A-SSE.A.1.
Illustrative Mathematics
Illustrative Mathematics: A Sse Mixing Fertilizer
A landscaping company prepares two mixtures of fertilizer. In this task, students investigate what happens to the value of an expression when a quantity is changed. Aligns with A-SSE.A.1 and A-SSE.A.1.b.
Illustrative Mathematics
Illustrative Mathematics: F Tf, G Co, Trigonometric Identities and Rigid Motions
The purpose of this task is to apply translations and reflections to the graphs of the functions f(x)=cos x and g(x)=sin x in order to derive some trigonometric identities. There are also rotations 180 degrees about points on the x-axis...
Illustrative Mathematics
Illustrative Mathematics: A Apr Egyptian Fractions Ii
In this task, learners will rewrite fractions as a sum of distinct unit fractions. To solve the problem, students will rewrite a simple rational expression and will need to study the arithmetic of these unit fractions with a variable in...
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 Delivery Trucks
This task asks students to analyze four expressions to determine what each represents in terms of the problem's context, which is about two trucks delivering different amounts of sand in different numbers of trips. Aligns with A-SSE.A.1...
Illustrative Mathematics
Illustrative Mathematics: A Sse the Bank Account
For this task, students are asked to interpret equations representing a bank account's balance where the interest is compounded monthly versus yearly. Aligns with A-SSE.A.1 and A-SSE.A.1.a.
Illustrative Mathematics
Illustrative Mathematics: A Sse Mixing Candies
This task about a box of chocolates has students use the given equations to answer questions about weight and price, as well as interpret the expressions in the equations. Aligns with A-SSE.A.1 and A-SSE.A.1.a.
Illustrative Mathematics
Illustrative Mathematics: Which Is Heavier?
Students will learn the concept of weight by practicing weighing items on a balance scale and recording their results. Students can record their answers on the black line masters included in the Illustrated Mathematics lesson "How Heavy?".
Illustrative Mathematics
Illustrative Mathematics: Comparing Numbers
This task is a fun partner game in which students practice making two-digit numbers, decide which is greater, and write the appropriate comparison symbolically.
Illustrative Mathematics
Illustrative Mathematics: G Co Origami Regular Octagon
After successive folds of a piece of origami paper, a student must explain why the shape made is a regular octagon. Aligns with G-CO.A.3 and G-CO.D.12.
Illustrative Mathematics
Illustrative Mathematics: G Co, G Srt Seven Circles I
In this task, seven pennies are placed in a circle so that they are all touching one in the center and their neighbors. The question is whether this will work with other equally-sized circles. Aligns with G-SRT.C and G-CO.C.10.
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 C, G Co Tangent Lines and the Radius of a Circle
In this task, students are shown a circle with center O and point P on the circle. L is a line that is a tangent to the circle at P. They must show that line OP is perpendicular to line L. Aligns with G-C.A.2, G-CO.A, and G-CO.C.9.
Illustrative Mathematics
Illustrative Mathematics: G Co Inscribing an Equilateral Triangle in a Circle
Suppose we are given a circle of radius r. The goal of this task is to construct an equilateral triangle whose three vertices lie on the circle. Aligns with G-CO.D.13.
Illustrative Mathematics
Illustrative Mathematics: G Co Inscribing a Hexagon in a Circle
In this task, students inscribe a regular hexagon inside a circle and compare its area to that of the circle. Aligns with G-CO.D.13.
Illustrative Mathematics
Illustrative Mathematics: G Co Building a Tile Pattern by Reflecting Octagons
This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral. The focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square....
Illustrative Mathematics
Illustrative Mathematics: G Co Points Equidistant From Two Points in the Plane
In this task, students are shown a line segment that is bisected at a right angle by a second line. They are asked to prove statements about this geometric construction. Includes a GeoGebra worksheet that can be used by the instructor to...
Illustrative Mathematics
Illustrative Mathematics: G Co Midpoints of Triangle Sides
The goal of this task is to use similarity transformations to relate two triangles. The triangles are obtained by taking midpoints of two sides of a given triangle. Aligns with HSG-CO.C.10.
Illustrative Mathematics
Illustrative Mathematics: G Co Defining Perpendicular Lines
Three students have proposed three ways to describe when two lines are perpendicular. Students are asked to analyze their statements. Aligns with G-CO.A.1.
Illustrative Mathematics
Illustrative Mathematics: G Co Midpoints of the Sides of a Paralellogram
Suppose that ABCD is a parallelogram and that M and N are the midpoints of lines AB and CD respectively. Students are asked to prove that MN=AD, and that the line MN is parallel to line AD. Aligns with G-CO.C.11.
Illustrative Mathematics
Illustrative Mathematics: G Co Parallelograms and Translations
In this task, young scholars apply the definition of a parallelogram in the context of a geometric construction. Aligns with G-CO.C.11.
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