Sophia Learning
Sophia: Multiplying Radical Expressions With the Distributive Property
Students learn how to use the distributive property to multiply radical expressions. Detailed examples are provided that show the process.
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: 3.oa Symmetry of the Addition Table
The goal of this task is to help students understand the commutative property of addition by examining the addition facts for single digit numbers. Aligns with CCSS.Math.Content.3.OA.D.9 Identify arithmetic patterns, and explain them...
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: Using Volume Associative Property of Multiplication
The purpose of this task is for students to use the volume of a rectangular prism to understand the associative property of multiplication. Aligns with 5.MD.C.5.a.
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....
Sophia Learning
Sophia: Product Property of Radicals
Explore how to solve radical equations using the product property of radicals. Check for understanding with a quiz.
McGraw Hill
Glencoe Mathematics: Quiz on Properties of Equaltiy
This site is a short on line quiz covering the properties of equality. The topics covered include operations and equivalence relations.
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 Patterns in the Multiplication Table
The goal is to look for structure and identify patterns in the multiplication table and then try to find the mathematical explanation for this. Aligns with CCSS.Math.Content.3.OA.D.9 Identify arithmetic patterns, and explain them using...
Illustrative Mathematics
Illustrative Mathematics: 3.oa Making a Ten
This task builds on that knowledge by asking them to study more carefully the make-a-ten strategy that they should already know and use intuitively. Aligns with CCSS.Math.Content.3.OA.D.9 Identify arithmetic patterns, and explain them...
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: 4.oa Multiples of 3, 6, and 7
This task investigates divisibility properties for the numbers 3, 6, and 7. Aligns with 4.OA.C.
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 students 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
In 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...