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...
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
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...
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
Reasoning about Multiplication and Division and Place Value, Part 1
Help your class make sense of quantities and their relationships. Given is the product of two numbers. It is up to your number crunchers to think about the quantitative relationship when the product is one-tenth or ten times the product...
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
Writing Division Expressions II
Division is division is division is division ... four different ways to write division. Scholars continue to learn about division expressions. They translate between several forms, including verbal phrases, expressions using the division...
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...
Illustrative Mathematics
How Many Servings of Oatmeal?
Here is another way to illustrate division of a whole number by a unit fraction. In this case, the problem is asking if there are so many servings per cup, how many servings are in a package of multiple cups. Learners are to model their...
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...
Illustrative Mathematics
Traffic Jam
Help your learners understand dividing with fractions by using these methods to solve. Chose from two different number lines or linker cubes. This practices "how many groups?" style division problems which help them comprehend why...
Illustrative Mathematics
Video Game Credits
Help your learners understand how to divide fractions with this visual activity. They first answer a simple inequality before dividing the fractions. Two solution choices are given to help your mathematicians understand how to solve "how...
Illustrative Mathematics
How Many Containers in One Cup / Cups in One Container?
The object is to model fraction division by asking “How many are in one group?” It is a difficult concept to understand, but developing the model that shows one cup to a certain amount of container or one container to a certain amount of...
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...
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
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...
Illustrative Mathematics
Gifts from Grandma, Variation 3
There are three money word problems in this activity, each one is set in the same context. The first asks what was the total amount grandma spent, the second how many grandchildren grandma has, and the third asks how much grandma spent...
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
Minutes and Days
Elapsed time is a skill developed by the single question that is the center of this activity. Fifth graders are asked to find out the time that is 2011 minutes after the beginning of 2011. This question addresses the standard that...
Noyce Foundation
Sewing
Sew up your unit on operations with decimals using this assessment task. Young mathematicians use given rules to determine the amount of fabric they need to sew a pair of pants. They must also fill in a partially complete bill for...
Noyce Foundation
Baseball Players
Baseball is all about statistics. Pupils solve problems related to mean, median, and range. They calculate the total weight of players given the mean weight, calculate the mean weight of reserve players given the mean weight of the...
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Long Division Worksheets
Give these worksheets to students to practice division using the standard algorithm.
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