Curated OER
Microscopes and Crystals
Students observe crystals under the microscope. In this science lesson, students compare how the crystal look like using their eyes, hand lens and microscope. They identify the type of crystal based on the amount of light they allow to...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Equivalent Expressions
In this problem, we have to transform expressions using the distributive, commutative and associative properties to decide which expressions are equivalent. Common mistakes are addressed, such as not distributing the 2 correctly. Aligns...
Illustrative Mathematics
Illustrative Mathematics: Seeing Is Believing
The purpose of this task is to help students see that 4x(9+2) is four times as big as (9+2). Though this task may seem very simple, it provides students and teachers with a very useful visual for interpreting an expression without...
Illustrative Mathematics
Illustrative Mathematics: Domino Addition
The purpose of this task is to help students understand the commutative property of addition by using dominos as manipulatives. If the teacher does not already have dominoes, they are easily found online and can be printed onto colored...
Illustrative Mathematics
Illustrative Mathematics: Counting Dots in Arrays
This task aims to show students that there is often more than one way to represent a quantity. This lesson also lays a foundation for students to understand the commutative property of multiplication.
Illustrative Mathematics
Illustrative Mathematics: Make 9
Students will make 9 in as many ways as they can by adding two numbers between 0 and 9. This is a good introduction to the commutative property.
Illustrative Mathematics
Illustrative Mathematics: 6.ns Adding Multiples
This task will provide insight to teachers on students' level of understanding when reasoning about a problem. The task asks students to examine whether the sum of two numbers that are multiples of 6 produces another multiple of 6....
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: 3.oa Addition Patterns
The purpose of this task is to study some patterns in a small addition table. Aligns with CCSS.Math.Content.3.OA.D.9 Identify arithmetic patterns, and explain them using properties of operations.
Illustrative Mathematics
Illustrative Mathematics: F Bf Exponentials and Logarithms I
The purpose of this task is to help students see the "why" behind properties of logs that are familiar but often just memorized (and quickly forgotten or misremembered). The task focuses on the verbal definition of the log, helping...
Illustrative Mathematics
Illustrative Mathematics: N rn.a.2: Checking a Calculation of a Decimal Exponent
The purpose of the task is to connect properties of fractional exponents with ordering of real numbers. Aligns with N-RN.A.2.
Illustrative Mathematics
Illustrative Mathematics: N rn.a.1: Evaluating Exponential Expressions
The goal of this task is to use properties of exponents for whole numbers in order to explain how expressions with fractional exponents are defined. Aligns with the N-RN.A.1 standard.
Illustrative Mathematics
Illustrative Mathematics: A sse.b.4: Cantor Set
This tasks requires young scholars to explore properties of the Cantor Set, which has many uncountable points, no intervals of real numbers, and has length of zero. Aligns with A-SSE.B.4.
Illustrative Mathematics
Illustrative Mathematics: G Gpe, G Co, G Srt Unit Squares and Triangles
For this task, students are shown three unit squares and two line segments connecting two pairs of vertices. They are asked to find the area of a triangle formed by intersecting lines. They can solve it using coordinate geometry or...
Illustrative Mathematics
Illustrative Mathematics: G Gmd, G Mg Tennis Balls in a Can
In this task, students investigate the volume of tennis balls and their cylindrical container, the empty space around the balls, different ways of slicing them, and what their visualizations will look like. Aligns with G-GMD.B.4 and...
Illustrative Mathematics
Illustrative Mathematics: G Mg, G Gmd Global Positioning System Ii
Satellites communicate with a GPS device and establish the distance between them and their locations. The set of points at a fixed distance from a satellite form a sphere so when the GPS receives its distance from a given satellite, this...
Illustrative Mathematics
Illustrative Mathematics: G Mg How Many Leaves on a Tree?
This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree, taking into account the tree size and the density of the leaves. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: Connor and Makayla Discuss Multiplication
The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and use this burgeoning understanding of fraction multiplication to make sense of the commutative property of multiplication in...
Illustrative Mathematics
Illustrative Mathematics: F Bf Exponentials and Logarithms Ii
The purpose of this task is to help students see that the definition of the logarithm as an exponent results in an inverse relationship between the exponential and logarithm functions with the same base. This prepares them to think about...
Illustrative Mathematics
Illustrative Mathematics: G Co Building a Tile Pattern by Reflecting Hexagons
This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh. The focus of the task is on using the properties of reflections to deduce this seven-hexagon pattern. Aligns with G-CO.B.6.
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: 7.ee Writing Expressions
In this lesson, 7th graders determine the expression using properties of operations.
Illustrative Mathematics
Illustrative Mathematics: G Mg Hexagonal Pattern of Beehives
Beehives are made of walls, each of the same size, enclosing small hexagonal cells where honey and pollen are stored and bees are raised. This problem examines some of the mathematical advantages of the hexagonal tiling in a beehive....
Illustrative Mathematics
Illustrative Mathematics: N Rn Sums of Rational and Irrational Numbers
The goal of this task is to examine sums and products of rational and irrational numbers. One important property of rational numbers is that their decimals always terminate or repeat: using a slightly different formulation, a rational...