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Illustrative Mathematics

Representing Half of a Circle

For Teachers 2nd - 4th Standards
Geometric shapes make great visual models for introducing young mathematicians to the concept of fractions. Looking at a series of four circles, students are asked to determine whether or not one half of each circle is shaded. To support...
Assessment
Carolina K-12

Practice Test of Economics

For Students 9th - 12th Standards
From scarcity and supply and demand to entrepreneurship and the stock market, here you'll find a multiple-choice assessment that includes 34 questions covering all the major concepts of a traditional economics course. 
Lesson Plan
EngageNY

Systems of Equations Leading to Pythagorean Triples

For Teachers 8th Standards
Find Pythagorean Triples like the ancient Babylonians. The resource presents the concept of Pythagorean Triples. It provides the system of equations the Babylonians used to calculate Pythagorean Triples more than 4,000 years ago. Pupils...
Lesson Plan
Illustrative Mathematics

Ratio of Boys to Girls

For Teachers 5th - 7th Standards
How many boys are in the class? Here is an introductory exercise describing ratios. The commentary shows different ways learners can approach the problem, using a tape diagram of boys to girls and using a table. The activity includes...
Assessment
Mathed Up!

Area of Sector and Length of Arcs

For Students 9th - 12th Standards
Viewers learn how to apply proportional reasoning to find area of sectors and arc lengths with a video that starts off explaining how to find the areas of circle sectors and the lengths of arcs. Scholars then practice solving problems...
Assessment
Achieve

Spread of Disease

For Students 9th - 12th Standards
Viruses can spread like wildfire, and mathematics can model the speed of infection. Given a function, scholars analyze it to describe the spread of a disease within a stadium. Learners find the initial number infected and the maximum...
Assessment
1
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Balanced Assessment

Frosting on the Cake

For Students 9th - 12th Standards
Party planners need algebra too! Here, pupils decide the perfect size of a cake based on available ingredients. They use the concepts of area and perimeter to make their conclusions.
Lesson Plan
EngageNY

When Can We Reverse a Transformation? 1

For Teachers 11th - 12th Standards
Wait, let's start over — teach your class how to return to the beginning. The first lesson looking at inverse matrices introduces the concept of being able to undo a matrix transformation. Learners work with matrices with a determinant...
Lesson Plan
EngageNY

Characteristics of Parallel Lines

For Teachers 8th Standards
Systems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines...
Lesson Plan
EngageNY

The Geometric Effect of Some Complex Arithmetic 2

For Teachers 11th - 12th Standards
The 10th lesson in a series of 32, continues with the geometry of arithmetic of complex numbers focusing on multiplication. Class members find the effects of multiplying a complex number by a real number, an imaginary number, and another...
Lesson Plan
EngageNY

Equivalent Ratios Defined Through the Value of a Ratio

For Teachers 6th Standards
Ratios may not be created equal, but they are equivalent. Pupils learn the theorem relating equivalent ratios and equal values in the eighth segment in a series of 29. Classmates use the theorem to determine whether ratios within...
Lesson Plan
EngageNY

Geometric Interpretations of the Solutions of a Linear System

For Teachers 8th Standards
An intersection is more than just the point where lines intersect; explain this and the meaning of the intersection to your class. The 26th segment in a 33-part series uses graphing to solve systems of equations. Pupils graph linear...
Lesson Plan
EngageNY

Sampling Variability and the Effect of Sample Size

For Teachers 7th Standards
The 19th installment in a 25-part series builds upon the sampling from the previous unit and takes a larger sample. Pupils compare the dot plots of sample means using two different sample sizes to find which one has the better variability.
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Curated OER

Patterns in the Multiplication Table

For Teachers 3rd - 4th Standards
Explore patterns in the multiplication table in order to deepen your third graders' understanding of this essential skill. Implement this activity as a whole-class lesson plan, allowing students to work in pairs or small groups to...
Lesson Plan
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Illustrative Mathematics

The Intersection of Two Lines

For Teachers 7th - 9th Standards
Here is an introduction to solving simultaneous linear equations. Start by drawing a line through two points. Create a second line which goes through the intersecting point. Background knowledge of how to find the equation of a line and...
Assessment
Los Angeles County Office of Education

Assessment for the California Mathematics Standards Grade 5

For Students 5th Standards
Test young mathematicians' knowledge with an assessment aligned to California's fifth grade state standards. The exam covers a multitude of concepts including fractions and decimals, positive and negative numbers, measurement; and...
Assessment
Los Angeles County Office of Education

Assessment For The California Mathematics Standards Grade 6

For Students 6th Standards
Test your scholars' knowledge of a multitude of concepts with an assessment aligned to the California math standards. Using the exam, class members show what they know about the four operations, positive and negative numbers, statistics...
Lesson Plan
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Teach Engineering

Applications of Linear Functions

For Teachers 7th - 9th Standards
It's not so straightforward — lines can model a variety of applications. Pupils experience linear relationships within the context of science, including Hooke's and Ohm's Laws. Class members got a taste of motion and speed from the...
Lesson Plan
Illustrative Mathematics

The Sign of Solutions

For Teachers 7th - 9th Standards
Positive or negative, zero or no solution, are all possibilities for the solution of a linear equation. Here the resource gives examples of linear equations in one variable and their type of solutions. The resource comes with commentary...
Lesson Plan
EngageNY

First Consequences of FTS

For Teachers 8th Standards
Challenge the young mathematicians to find the exact coordinates of a dilated point. The fifth segment in a 16-part series introduces the class to the converse of the Fundamental Theorem of Similarity. Scholars use the theorem to...
Lesson Plan
EngageNY

The Converse of the Pythagorean Theorem

For Teachers 8th Standards
Is it a right triangle or not? Introduce scholars to the converse of the Pythagorean Theorem with a lesson that also provides a proof by contradiction of the converse. Pupils use the converse to determine whether triangles with given...
Lesson Plan
EngageNY

Interpreting and Computing Division of a Fraction by a Fraction—More Models

For Teachers 6th Standards
Use a unit approach in developing a fraction division strategy. The teacher leads a discussion on division containing units, resulting in a connection between the units and like denominators. Pupils develop a rule in dividing fractions...
Lesson Plan
EngageNY

Associated Ratios and the Value of a Ratio

For Teachers 6th Standards
Do ratios have values? The seventh lesson in a series of 29 introduces the value of a ratio. Pupils create associated ratios to a given ratio. They also describe the fraction associated to the ratio as the value of the ratio.
Lesson Plan
EngageNY

From Ratio Tables to Equations Using the Value of a Ratio

For Teachers 6th Standards
Use the value of a ratio to set up equations. The teacher leads a discussion on determining equations from ratio tables in the 13th portion of a 29-part series. Pupils determine which of two equations to use to find the solution....

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