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Using the calculator for division with remainder People often say that division is easily done on the calculator. Division with remainder, however, requires some common sense to sort out the answer. With a calculator using the division key: Then subtract 5 to get 0. Calculator assistance may be extremely useful with larger numbers, but experience with long division is essential to interpret the calculator display This phenomenon is common to many similar situations in mathematics.

When calculating a division, we are constantly calculating multiples of the divisor, and lack of fluency with multiplication is a significant handicap in this process. The material in this module lays the foundation for multiplication, and then division, of fractions and decimals.

Other applications of multiplication include percentages and consumer arithmetic. For example, we calculate the price of an item inclusive of GST by calculating 1. A familiarity with multiplication and the expression of numbers as products of factors paves the way for one of the major theorems in mathematics.

The Fundamental Theorem of Arithmetic states that every whole number bigger than 1 can be written as a product of prime numbers and such an expression is unique up to the order in which the factors are written.

The Fundamental Theorem of Arithmetic has far-reaching consequences and applications in computer science, coding, and public-key cryptography. Last, but not least, a strong grounding in arithmetic sets a student up for success in algebra. The division algorithm uses multiplication and subtraction.

As such, division demands that we synthesise a lot of prior knowledge. This is what makes division challenging, and for many students it is their first taste of multi-layered processes.

The ability to reflect on what you know, and implement it within a new, higher-level process is one of the generic mathematical skills that division helps to develop.

The implementation of the division algorithm is typically a multi- step process, and as such it helps to develop skills that are invaluable when students move on to algebra. The link to factors is also critical in later years. Just as the history of number is really all about the development of numerals, the history of multiplication and division is mainly the history of the processes people have used to perform calculations.

The development of the Hindu-Arabic place-value notation enabled the implementation of efficient algorithms for arithmetic and was probably the main reason for the popularity and fast adoption of the notation.

The earliest recorded example of a division implemented algorithmically is a Sunzi division dating from AD in China. Essentially the same process reappeared in the book of al Kwarizmi in AD and the modern-day equivalent is known as Galley division.

It is, in essence, equivalent to modern-day long division. However, it is a wonderful example of how notation can make an enormous difference. Galley division is hard to follow and leaves the page a mess compared to the modern layout.

The layout of the long division algorithm varies between cultures. Throughout history there have been many different methods to solve problems involving multiplication. Some of them are still in use in different parts of the world and are of interest to teachers and students as alternative strategies or because of the mathematical challenge involved in learning them.

The method is very old and might have been the one widely adopted if it had not been difficult to print. It appears to have first appeared in India, but soon appeared in works by the Chinese and by the Arabs.Circle a number that makes the sentence true. There are 4 9 36 horses in each pen.

3. Chris plants 25 pumpkin seeds in 5 equal rows.

How Debbie made this array to model a division equation. Which equation could Debbie have modeled? Mark all Write a division equation to represent the model. __ _ . Represent multiplication and division using a rectangular area model.

modeled with students. COLLABORATIVE PRACTICE Serve as small group, or partnered work. The work should promote student discourse, which allows students I am going to write down five tens and think of .

When solving a division problem by multiplying by the reciprocal, remember to write all whole numbers and mixed numbers as improper fractions. The final answer should . Number Models for 5th Grade Math Classes A number model is a math equation. By the time students complete 5th grade, they should know many number model formats and some specific formulas.

Write a division sentence and indicate the divisor, dividend, and quotient. Select one of your arrays and write two story problems that can be modeled with the array, one for multiplication and one for division.

Lesson 14 Objective: Solve division word problems with remainders. Write two division sentences for this array. S: (Write 12 ÷ 3 = 4 and 12 ÷ 4 = 3.) Continue with the following possible sequence: 5 × 2 array and 7 × 3 array.

modeled with an array.

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Grade 3: Relating Multiplication and Division: Overview