EngageNY
The Euclidean Algorithm as an Application of the Long Division Algorithm
Individuals learn to apply the Euclidean algorithm to find the greatest common factor of two numbers. Additionally, the lesson connects greatest common factor to the largest square that can be drawn in a rectangle.
EngageNY
Dividing Multi-Digit Numbers Using the Algorithm
Scholars learn to divide multi-digit numbers using the standard algorithm in the 14th installment in a module of 21 parts. They get plenty of practice with the algorithm by completing a worksheet.
EngageNY
The Division Algorithm—Converting Decimal Division into Whole Number Division Using Fractions
Knowing the standard algorithm opens up a whole new world of division. Scholars learn how to convert division involving decimals to division involving whole numbers to use the standard algorithm. Knowing how to multiply with powers of...
Concord Consortium
Vending Machine
Let the resource quench your thirst for knowledge, like a vending machine that dispenses drinks. Future computer scientists develop an algorithm to identify the fewest number of coins that a vending machine could use in creating change....
College Board
2006 AP® Computer Science A Free-Response Questions
Inheritance is a programming problem. Released free-response questions allow pupils and teachers to experience the 2006 AP® exam phrases questions. The items range from the application of basic algorithms to using inheritance in a...
College Board
2004 AP® Computer Science A Free-Response Questions
What is important from the instruction? Using the questions, pupils and teachers see how the AP® Computer Science exam addresses topics. Scholars realize the importance of the case studies from the course. The released questions range...
Illustrative Mathematics
Running Time
Ever wonder why that computer image takes so long to load? Well, math is involved and provides the algorithms needed to compute the measure in nanoseconds. Young mathematicians plug the image measures into the formulas and compare the...
Illustrative Mathematics
How Many _______ Are In. . . ?
Help your learners gain meaningful understanding of dividing fractions using fraction models. The activity includes nine problems which are sequenced to show how the fraction division algorithm evolves. Have students use graph paper or...
College Board
2007 AP® Computer Science A Free-Response Questions
Stay tuned for a programming announcement. The resource contains the four free-response questions from the 2007 AP® Computer Science exam. Teachers and pupils use the questions to understand how topics appear on exams. The items cover...
EngageNY
The Division Algorithm—Converting Decimal Division into Whole Number Division Using Mental Math
Make math much simpler with mental math methods. The 16th installment in a series of 21 looks at ways scholars can apply mental math to convert division problems into easier problems with the same quotient. Multiplying or dividing both...
Illustrative Mathematics
Interpreting a Division Computation
Mathematicians show their understanding of a division problem. If a student can apply long division to a pair of numbers and determine a quotient, what other factors and multiples become apparent? The example illustrates a simple...
Illustrative Mathematics
Reasoning about Multiplication and Division and Place Value, Part 2
The learner puts reasoning and estimation to work. The directions are to place a decimal in the answer to make the equation true. Pupils are to look at the two problems, one multiplication and one division, and estimate an answer. No...
EngageNY
Describing the Center of a Distribution Using the Mean
Everyone does their fair share. The sixth segment in a 22-part unit presents the mean as a fair share. Groups build a conceptual understanding of the mean of a data set, rather than simply learn an algorithm. Learners use the...
Curated OER
Folding strips of paper
Fifth graders need concrete experiences to introduce a unit on multiplying fractions by fractions. A strip of paper is used to create a number line and represent 5/6. It is folded first in half, and then in quarters. After unfolding,...
Illustrative Mathematics
Zeroes and Factorization of a General Polynomial
These four problems will guide your class through the idea behind the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n roots. Use the division algorithm and the definition of a zero/root of a...
Illustrative Mathematics
Zeroes and factorization of a quadratic polynomial I
This activity uses the division algorithm and the definition of a zero/root of a function to guide your class to see the relationship between zeros and factors of a general quadratic, which can later be generalized to the Remainder...
College Board
2009 AP® Computer Science A Free-Response Questions
Coding and decoding is part of the work. Pupils and teachers use the released questions from 2009 to gather information on how topics show up on the AP Computer Science exam. The four questions range from the array data structure to...
College Board
2008 AP® Computer Science A Free-Response Questions
Get the code right. A detailed resource provides pupils and teachers of computer science courses with released items from the 2008 exam. Questions range from studying code in a case study to creating code to perform specific tasks....
College Board
2002 AP® Computer Science A Free-Response Questions
Find the data in an array. Questions for the 2002 AP® Computer Science exam provide opportunities for practice using their ability to use an array structure. Four questions provide different scenarios to use arrays. Pupils then create...
College Board
1999 AP® Computer Science A Free-Response Questions
Assess an array of using coding. Pupils develop code to respond to four questions dealing with arrays. The questions range from determining who in a list are seniors and generating a pattern for a quilt. The questions are the first time...
College Board
2005 AP® Computer Science A Free-Response Questions
Four free-response questions from the 2005 AP® Computer Science exam show pupils how topics appear on the test. Scholars use the questions to practice coding skills in preparation, while teachers use the items to determine what concepts...
College Board
2003 AP® Computer Science A Free-Response Questions
You deserve a C++. Released items from the last year of C++ programming for the AP Computer science course provides opportunities to practice. Pupils use the questions to develop their programming skills by finding solutions to the...
College Board
2000 AP® Computer Science A Free-Response Questions
Coding works for other fields. The free-response questions for AP Computer science require pupils to develop code to solve a problem. Problems range from creating a histogram to developing an encryption program. Teachers use the...
EngageNY
Estimating Digits in a Quotient
Boiling down any division problem to a one-digit divisor problem sure makes estimation easy. The lesson shows how to estimate division problems by using place value understanding and basic arithmetic facts to simplify the division. Some...
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