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Q1: What is the relation between multiplication and division?
Ans: Multiplication and division are arithmetic operations which are inverse to each other. Multiplication is used to find out total number of objects within equal groups while division is used to identify number of objects in each equal group or number of equal groups. If 3 x 6 = 18 then 18 ÷ 3 = 6 or 18 ÷ 6 = 3.
Q2: How do you teach division?
Ans: Distributing something fairly into equal groups is called division.The first introduction to division will be sharing groups of objects into equal groups and teaching how to write division sentences. For example; dividing 12 items among 4 persons equally is a share of 3 with each which can be mathematically expressed as 12 ÷ 4 = 3. Then the children should be taught that division and multiplication are inversely related.
Q3: What is a division fact?
Ans: Division facts are the division number sentences related to times tables. Therefore: 30 ÷ 3 = 10, 27 ÷ 3 = 9 and 24 ÷ 3 = 8 are all division facts for the three times table.
Division originated from the word “divide”, which means to separate the given value or objects in groups or arrays. These groups are mainly of equal size. To learn division, various techniques involving subtraction and multiplication are implemented.
Like other basic math operations, “division” equations are written using some operators. These operators are:
The numbers used in a division equation are identified by the terms; dividend, divisor, and quotient.
A division equation using these three operators and terms can be written as follows:
= 7 (Dividend = 14, divisor = 2 and quotient = 7)“Division” is a basic math essential after learning addition, subtraction, and multiplication. The skill is useful in fluently comprehending other math concepts of geometry, measurements and data interpretation. The projected learning outcomes of division exercises in grade-3 are as follows:
1. Learning & outcome:
Based on day-to-day examples of distributing foods and objects such as fruits, candies, pencils and others, kids learn about division as a form of repeated subtraction. Another approach to learn division is finding the missing value using a multiplication table or multiplier in an equation. Also, methods like measurement model and partition model help kids to understand the process of division. The projected learning outcomes of division exercises in grade-3 are as follows:
2. Required math skills: For solving division problems, formal counting knowledge up to 10,000 is required. Other skills entail basic math operations such as addition, subtraction, and multiplication (with a single-digit number, 2-digit number and higher). With the help of multiplication tables, kids perform short division fluently.
3. Engagement: Adhering to the common core math standards, SplashLearn learning games for grade-3 focus on nurturing a deep-rooted understanding of the concept. With a playful theme-based interface to engage kids, illustrative worksheets and exercises boost confidence to excel in math through home schooling.
In this model, a set of objects is given to kids. With the defined number of groups, kids need to distribute the objects so that each group contains an equal number of items.
For example, Tim got 15 candies for his birthday to share with his two friends. How many candies will each one of them get?
Reference image: Kids will divide the candies equally to find out how many candies each one will get. In this case, each one of them will get 5 candies.
In this model of “division”, a fixed number of objects are assigned to each group. The number of groups remains unknown. To evaluate this number, repeated subtraction is used.
For example, a sack of gifts has 20 gifts. How many kids will get the gifts if each one of them is getting 2 gifts?
To obtain the result, “2” is subtracted from “20” till 0 is left.
A line plot is also helpful in repeated subtraction. For each subtraction, one jump is recorded. The total number of jumps is the resultant answer/quotient. This method is also known for its “counting back” technique for performing “division”.
To divide a number by 2, different methods can be used. Initially, kids need to determine whether a number can be divided by 2 or not? The knowledge of even and odd numbers are used to solve math expressions with divisor as 2.
Any dividend with its last digit ending in 0, 2, 4, 6 and 8 can be divided by 2. Also, partition model and measurement model can be applied to solve the problem.
For example:
To divide a number by 5, kids can recall the multiplication table of 5. All the numbers in the table end with either “5” or “0”. Thus, to divide a two-digit number by 5; use the multiplication table or partition the objects in a group of 5 each.
For example:
To divide a number by ten, the easiest method is to use a “base 10 block”. Using a base 10 block, partition the number in the set of “tens”.
If a number has fixed number of “tens” without any “ones”, then the number can be divided by 10.
To divide a number by any number other than 2, 5 and 10, use the multiplication table of the number or follow the measurement model on a line plot.
To divide a number by 4, objects can be arranged in an array with each row containing 4 objects. Count the rows to compute the result.
Similarly, in the following examples, different methods can be used to divide a number by a single digit number.
As the kids learn about different models of division such as partition and measurement models, solving one-step word problems is an easy task. With logical reasoning and abstract thinking, kids can determine the dividend and the divisor. The mathematical expressions for word problems can be written with either division operators or multiplication operators.
For example, a box of walnuts has 27 pieces. How many walnuts will each student get if there are total 9 students in the class?
Word problems on division are instrumental in nurturing reasoning skills of kids. With practice, kids learn to compute expressions verbally and mentally.
For example, if two boxes hold 4 pencils each then total pencils are 8 (4x2). If 3 boxes hold 8 pencils each, and total pencils are 24 (8x3). Then 32 pencils can be arranged in 8 individual boxes with 4 pencils each.
Another application of framing a division expression is in solving math problems involving groups and arrays.
To write division sentences for word problems involving groups, visual observation and partitioning are highly effective skills. For example, a book rack has 12 books. 4 books are issued to each student. How many students can get the total 12 books issued together?
To solve this word problem, kids can visually partition the books in 3 groups with each having 4 books as follows.
Reference image: Distribution of equal number of books amongst students
“Arrays” are also implemented for the division to solve word problems. In a schematic layout, the objects are distributed in groups of equal size. Kids learn to arrange objects in equal size rows or columns by using arrays for the division.
For example, the teacher arranged 20 students in a new classroom. Each row has 4 students. How many rows are there in total within the classroom?
To solve this, place the students in rows with 4 students each.
The required mathematical expression will be:
(20 should be divided by which number so that each row gets exactly 4 students)
The visual representation of the problem can be pictured as follows:
Reference image: 20 students, sitting in 5 rows with 4 students in each row.
Like addition and subtraction (reverse addition), multiplication and division are also closely associated. The relationship between the two operations can be easily established by interchanging the operators and the places of the numbers.
For example:
To understand it further, a multiplication table chart is useful. As, 6 x 3 = 18 and 3 x 6 = 18, then kids can establish a relationship as:
Reference image: The multiplication table of single digit number (1 to 9) is used for multiplication and short division
Grade-3 division concepts are one of the fundamental aspects to learn other math concepts. This “division” operations are used in representing fractions, the conversion of time and data as well as drawing geometric figures with multiple angles.
“Division” as a basic math skill for grade-3 is introduced to kids to stimulate the reasoning capability. With a logical approach to visualize a word problem in numbers, fast math practice is nurtured by performing mental computation using subtraction and multiplication. Proficiency in the short and long “division” and identifying arithmetic patterns is essential to foster other math concepts of measurement and geometry in later grades.
Interactive and theme-based fun learning games for SplashLearn offer a well-drafted curriculum to prevent skill loss during summer vacation and practice skills to excel in math. Scrutinized worksheets teach the skills without any math fear and common core math curriculum is followed to assist in homeschooling the kids.
