EngageNY
Introduction to Simultaneous Equations
Create an understanding of solving problems that require more than one equation. The lesson introduces the concept of systems of linear equations by using a familiar situation of constant rate problems. Pupils compare the graphs of...
EngageNY
Geometric Interpretations of the Solutions of a Linear System
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...
EngageNY
Systems of Equations Leading to Pythagorean Triples
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...
EngageNY
Ratios of Fractions and Their Unit Rates 2
Remodeling projects require more than just a good design — they involve complex fractions, too. To determine whether a tiling project will fit within a given budget pupils calculate the square footage to determine the number of tiles...
Illustrative Mathematics
Representing Half of a Rectangle
Did you know one half of a rectangle be represented in more than one way? Young mathematicians choose the rectangles that represents one half with an instructive worksheet.
Curated OER
Literature and the Language Arts
Reading involves more than simply picking up a text and saying the words aloud. A practice guide introduces readers to key skills such as making inferences, finding the main idea or theme, and using context clues. Each skill contains a...
Concord Consortium
Gestation and Longevity
Is the gestation length of an animal a predictor of the average life expectancy of that animal? Learners analyze similar data for more than 50 different animals. They choose a data display and draw conclusions from their graphs.
Concord Consortium
Stocking the Shelves
How many ways can you stock a shelf? It's probably more than you think! Young scholars use data in a frequency table to determine how many ways to stock a shelf given a specific constraint for types of groups. They then repeat the task...
CCSS Math Activities
Smarter Balanced Sample Items: High School Math – Target G
G is for generating equations. Scholars answer eight questions covering the SBAC Claim 1 Target G high school item specifications. They write one-variable and multi-variable equations and inequalities to model relationships between...
College Board
2015 AP® Environmental Science Free-Response Questions
Less than eight percent of AP Environmental Science test takers earn the highest score possible. Help scholars improve their scores by using actual test questions on water quality and urban planning before reading sample responses that...
College Board
2014 AP® Environmental Science Free-Response Questions
Less than half of AP Environmental Science test takers pass each year. The College Board releases previous test questions covering topics from greenhouse gases to ecological succession to help scholars prepare for future assessments. Use...
College Board
2016 AP® Environmental Science Free-Response Questions
The average student scores less than three points, out of five, on the AP Environmental Science test. Most do well on the multiple choice and struggle with the free-response section. Encourage extra free-response practice with actual...
College Board
2018 AP® Environmental Science Free-Response Questions
Less than nine percent of all AP Environmental Science test takers scored a perfect five on the exam in 2018. Learn from the best answers as well as the common mistakes thanks to the College Board. Four questions from the test covering...
College Board
2015 AP® Chemistry Free-Response Questions
More than 80,000 scholars earned college credit for Chemistry with the AP exam in 2015. The College Board released the free-response questions covering topics, including moles, that often confuse scholars. They also released example...
College Board
2014 AP® Chemistry Free-Response Questions
More than half of AP Chemistry test takers earn a high enough score to get college credit. Improve that statistic by using past test questions including precipitate, molarity, and chemical equations to prepare for a future exam. The...
College Board
2017 AP® Chemistry Free-Response Questions
More than 83,000 scholars earned college credit, thus saving time and money by passing the AP Chemistry exam in 2017. Use the exact test questions covering concepts from activation energy to solubility to prepare for the upcoming...
College Board
2017 AP® Physics 2: Algebra-Based Free-Response Questions
In 2017, more than 15,000 scholars earned college credit based on their AP Physics 2 exam covering lenses, energy, and more. The College Board released the free-response questions, sample answers, and scoring guidelines from that exact...
College Board
2016 AP® Physics 1: Algebra-Based Free-Response Questions
Generally, scholars struggle on the free response portion of the AP Physics 1 exam more than the multiple-choice section. Scholars benefit from additional practice with the help of previous test questions, including questions on forces,...
College Board
2010 AP® English Language and Composition Free-Response Questions
Humorists do more than tell jokes; they also impart key messages about society. A series of free-response topics from the AP® English Language and Composition exam cover three topics, including one discussing the role of humorists....
Illustrative Mathematics
Making 22 Seventeenths in Different Ways
There is more than one way to determine a sum. Scholars demonstrate their understanding of the decomposition of fractions similar to the decomposition of whole numbers. The short task requires pupils to determine which sums of fractions...
Bowland
Hot Under the Collar
It is close enough for all practical purposes. Pupils see two methods to convert degrees Celsius to degrees Fahrenheit, one with exact numbers and another using estimation. Learners review both methods and determine when the estimation...
Illustrative Mathematics
Log Ride
The rides at a theme park always have limits on weight or number of riders. This makes a natural example of the use of inequalities to solve real-world problems. Learners explore intuitive solutions using substitution to solve the...
Illustrative Mathematics
A Pencil and a Sticker
How much do a pencil and sticker cost? Youngsters use a bar diagram to find the cost of a sticker that is twenty cents less than the cost of a pencil. Given the prices, learners must find the cost of the sticker in order to find the cost...
Illustrative Mathematics
A Bobbie Bear's Buttons
Young mathematicians help Bobbie Bear pick colored buttons out of a box as they learn how to decompose numbers less than 10 into pairs of smaller numbers. To support students with the process, consider creating a worksheet or graphic...
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