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Long Division with Whole Numbers | Single Digit Divisors | 5th Grade Math

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Long Division- Dad, Mom, Sister, Brother, Rover/Repeat

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Long Division- Dad, Mom, Sister, Brother, Rover/Repeat

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MGSE5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm (or other
strategies demonstrating understanding of multiplication) up to a 3-digit by 2-digit factor.

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MGSE5.NBT.6 Fluently divide up to 4-digit dividends and 2-digit divisors by using at least one of
the following methods: strategies based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and explain the calculation by using
equations or concrete models. (e.g., rectangular arrays, area models)

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Algorithm
• Distributive Property
• Dividend
• Divisor
• Equation
• Exponents
• Expression
• Measurement Division (or repeated subtraction)
• Multiplicand
• Multiplier
• Order of Operations
Partition Division (or fair-sharing)
• Partial Product
• Partial Quotient
• Product
• Properties of Operations
• Quotient
• Remainder

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Use the standard algorithm for multiplication

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In this lesson, you will learn to multiply using the standard algorithm.

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Multiplying Whole Numbers with Mr J.! Part 1

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Multiplying Whole Numbers with Mr J.! Part 1

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Multiplying Whole Numbers (Part 1) | 5th Grade Math

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Multiplying Whole Numbers with Mr J. Part 2

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Multiplying Whole Numbers with Mr J. Part 2

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Multiplying Whole Numbers (Part 2) | 5th Grade Math

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Multiplying Whole Numbers with Mr J- Mastery Check

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Multiplying Whole Numbers with Mr J- Mastery Check

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Multiplying Whole Numbers (Mastery Check) | 5th Grade Math

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STEPS TO USING STANDARD AlGORITHM w/multiplication

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STEPS TO USING STANDARD AlGORITHM w/multiplication

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Strategies!

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Multiplication is considered as a repeated addition. The multiplication tables and multiplication charts enable us to do this repeated addition in an efficient and fast way. Multiplication definition can also be considered as the inverse of division. There are multiple uses of multiplication in everyday life. In real life situations, also often the use of division and multiplication skills is required. For example, while handling money, sharing items between friends and cutting food into portions children are being introduced to the basics of the concepts of multiplication and division. Since they are introduced to the idea so early, they should be able to gain confidence in the subject and utilize these skills to solve problems in the later part of their life too.

Properties of Multiplication

Multiplication properties can also be used as strategies to multiply and divide. Examples:

If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.)

3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.)

Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Math Multiplication Games for 5th Grade

There are various math aids through which how to do multiplication can be taught to preschool kids. Two most fun multiplication games and math activities that can help children practice multiplication are multiplication bingo and multiplication snap.

Multiplication Bingo

This is a 2 or more-players multiplication facts games in which there are different BINGO sheets and a problem deck containing multiple multiplication problems. Bingo sheets have random numbers written in a 5 X 5 multiplication grid.

Each participant gets a BINGO sheet. Shuffle the problem deck and turn out one problem. Kids should solve the problem in their heads, then check their sheet to see if the answer is there. When a child has the answer her sheet, she can draw an "X" over it or place a counter on the correct box. The first player to have five correct answers in a row vertically, horizontally, or diagonally shouts out 'BINGO' and wins the game.

Multiplication Snap

The rules of times tables snap are simple. There are two sets of cards, one containing the 'times tables questions', and the other containing the 'answers'. At the start of the game, the cards should be shuffled, and distributed evenly to the players. The players keep their cards face down in a stack.

One by one, they take the top card from their stack and place it on a pile in the middle. When the card just placed matches the one before it, the players should call SNAP! and slap their hand on top of the middle pile. The first player to do this gets to keep all the cards in the pile. Some matches will be easy - for example if 24 is played on top of 24. Other matches will require knowledge of times tables - for example if 7x7 is played on top of 49. The most interesting matches of all will be when two matching question cards are played, for example, if 4x9 is played on top of 12x3.The winner is the player with the most cards left at the end.

Other multiplication math games to recall multiplication tables and multiplication drills and to do multiplication problems are:

Times What?

A deck of cards is needed to play this game. Take out 2 random cards from the deck. (example 2 and 4), Multiply the numbers (example: 2 x 4 = 8). The product is the number of points you keep. Repeat 4 more times. The player that has the most points after 5 turns win.

Multiplication Quiz

It is a board game with the objective to reach the finish point. The game has varied note cards of multiplication facts. The first player gets to study the note card with five facts on it for 30 seconds. After which player 2 will quiz the first player. If player 1 answers three or more problems correct, they can roll the dice and move the game piece the number shown on the dice. If two or less are answered correct, player 2 rolls the dice and moves. These steps are repeated till one of the players reaches the finish point.

Multiplication Game

The materials required to play this game are a game board, game pieces, and 2 dice. The objective is to be the first one to reach the end of the game board. The player who starts first rolls the two dice and multiplies the two numbers that appear (Example: Roll 4 on one dice and 5 on the other. That would equal 20.) The number of spaces moved is determined by the chart provided with the game. The second player repeats the same. Continue until a player reaches the end of the game board.

Building on 4th-grade math multiplication, students begin by decomposing numbers into base ten units in order to find products of single-digit by multi-digit numbers. Students use the distributive property and multiply using number disks to model. Practice with number disks is used for multi digit multiplication problems with recordings as partial products. Finally, the partial products method, the standard algorithm, and the area model are compared and connected by the distributive property

5th-grade math gives students the opportunity to apply their new multiplication skills to solve multi-step multiplication word problems and multiplicative comparison problems.

Multiplication by 10, 100, and 1,000

Children examine multiplication patterns when multiplying numbers by 10, 100, and 1,000. Reasoning between multiplication arrays and written sums on multiplication worksheets allows kids to see the role of place value units in multiplication. The multiplicative comparison is carried forward to grade 5 in the context of area and in the context of both calculations and multiplication word problems

Multiplication practice is required to develop procedural fluency. Children should especially learn the multiplication tables by representing it through multiplication table charts. Multiplication facts can be taught to kids by means of multiplication rap.

Multiplication Strategies for 5th Graders

1. Using Number Disks

Let us use the number disk method to find the product of 3 x 10. Suppose there is a group of 3 ones. Now multiply 3 ones by ten i.e. just move each disk over to the tens place and get 3 tens. Draw an arrow indicating that the disks shift one place to the left, label it × 10 and write 3 ones × 10 = 3 tens. How to multiply the result further by 10? Do the same thing again. Move them one more place into the hundreds and get 3 hundreds.

Number disks can also be used to represent products when multiplying by a two-digit number. For example Solve 15 × 10

2. Using Area Model

This model can be used to represent two-digit multiplication problems and find the solution through easy visual representation. Let us see how to multiply 10 by a two-digit multiple of 10. Example: Solve 50 × 40

Area model can also be used to represent the product of a two-digit multiple of 10 by a two-digit number. For example: Find the product of 60 and 34 using an area model.

First, draw an area model to represent 60 × 34 and then write the expressions that solve for the area of each rectangle. The area of the small rectangle is 6 tens times 4 and the area of the larger rectangle is 6 tens times 3 tens. Now add the areas: 240 + 1,800 = 2,040. Hence, 60 × 34 = 2,040.

3. Using Place Value Chart

Let us solve double digit multiplication of 40 ×

Other ways to write the expression are:

40 × 22 = (4 × 10) × 22

40 × 22 = 4 × (10 × 22)

40 × 22 = 10 × (4 × 22)

Express 22 on the place value chart. 10 × 22 is 2 hundreds and 2 tens.

Show 4 times as many i.e. draw disks to show 3 more groups of 2 hundreds 2 tens.

You will get: 8 hundreds and 8 tens. Therefore, 4 × (10 × 22) = 880 or 40 × 22 = 880.

Next let kids see that they can conceive the problem as 40 times 22, without breaking the process into the two steps of multiplying by 4 and 10 in whatever order as below:

4. Using Partial Products

Partial product method can be used to Multiply two-digit by two-digit numbers. This method pre-requires the area model. To find the product of 23 and 31 first draw an area model to represent 23 × 31 and then write the expressions that solve for the area of each rectangle. The area of each rectangle gives partial products. Summation of all partial products yields the final area. In this example, the area model gives 4 smaller rectangles with partial areas as- 9 tens, 3 ones, 6 hundreds and 2 tens. The sum is 6 hundreds, 11 tens and 3 ones. 11 tens can be regrouped as 1 hundred and 1 tens. Hence, the final sum will be 713. That means that 23 × 31 = 713.

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Multiplication Games for 5th Graders Online - SplashLearn

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Looking for multiplication games for 5th graders online? Explore 5th grade multiplication games for kids to make your math practice fun. Get Started for Free!

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All Free Math Games - Multiplication.com

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Looking for free single-player and multiplayer games for learning and practicing multiplication, addition, subtraction, and division? Check out Multiplication.com's library of 100+ games, where there's something for every learner. Browse all available games here!

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Math Playground- Go Numbers & Operations Base Ten!

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Math Playground- Go Numbers & Operations Base Ten!

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Practice multiplication, fractions, decimals and algebraic reasoning with our popular math games.

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Practice multiplication, fractions, decimals and algebraic reasoning with our popular math games.

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Long Division with Whole Numbers (Mastery Check) | Single Digit Divisors | 5th Grade Math

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Long Division: Double-Digit Divisors | 5th Grade Math

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Long Division: Double-Digit Divisors (Mastery Check) | 5th Grade Math

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Long Division- Partial Quotient Strategy

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Long Division- Partial Quotient Strategy

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National Center on Intensive Intervention

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Dividing 723 ÷ 5 Using Partial Quotients

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Area Model- Long Division 1 digit divisor

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Area Model- Long Division 1 digit divisor

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Play our free Division games and learn the division facts while having fun at Multiplication.com.

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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: The first introduction to division will be sharing groups of objects into equal groups . Distributing something fairly into equal groups is called division. For example; dividing 12 items among 4 persons equally is a share of 3 with each person which can be mathematically expressed as 12 ÷ 4 = 3.
Q3: How do you write a division sentence?
Ans: We write a division sentence using the equation: dividend ÷ divisor = quotient. When we divide something equally into small groups, the complete group is called the dividend, number of items in each group is called quotient and the number of groups is called the divisor in a division sentence.

"Division" in general terms is the derivative of word "divide". As the term refers to portioning of a number, it is a form of progressive or repeated subtraction. A given number is subtracted from another number till it becomes zero or less than the subtrahend.

A division equation looks like this:

9 % 3 = 3

Dividend Divisor Quotient

A division equation can also be written as a fractional number as follows:

9 / 3 = 3 (Dividend / Divisor = Quotient)

"Division" is one of the basic math skills introduced to kids in grade 3. At this level, kids are already familiar with addition, subtraction and multiplication. With the knowledge of place value system and counting skills up to ten thousand, kids learn the division by a single digit and double-digit numbers in the pre-k curriculum.

A step next to basics of addition, subtraction and multiplication (repeated addition), division games instigate the fundamental concept systematically for the kids. Division Games on an interactive theme-equipped interface and based on real-life examples substantially boost the kids to learn.

Learning & outcome: The real challenge while learning mathematics is the application part. To nurture deep-rooted concepts with a clear understanding of the technique, immense practice is required. With division games, kids understand to equally distribute or divide objects into smaller and equal groups. Gradually, the application part of "division" for solving equations using word problems and logic puzzles helps the kids to overcome the math fear. Proficiency in the respective skill is the key to excel in math in later grades while learning advanced math.

The projected learning outcomes are:

Introduction to the concept of division (short and long division)

Understanding the process of division using different models; partition model and measurement model (using a number line)

Framing mathematical equations with different signs used for division and relating to the associated math terms

Dividing a number by another as per the technique and representing the result in the terms, dividend, divisor, and remainder

Progressing to the division of large numbers (up to 4-digit) with a 2-digit number

Comprehending the knowledge of the skill "division" in the different fields of science, mathematics, and statistics

Required math skills: As "division" is a complex and fundamental math skills; proficiency in basic math with the counting skills (up to 10,000), addition and subtraction (up to 4 digit numbers) is required. Also, the understanding of multiplication tables and "know-how" technique to form the "multiplication tables", is highly useful for the short division.

Engagement: Comprehensive division games for kids up to grade-5 are instrumental in nurturing the basic math essential. The interactive theme-based interface engages the kids and motivates them to grasp the concept within easy steps. Schematically planned as per the core math standards, math games are conducive to build confidence to excel in math.

Profusely illustrated practice worksheets adhering to the curriculum are best suited for homeschooling and serve as a versatile math homework help to kids.

Manipulatives used for teaching Division

Counters: As kids are familiar with the use of counters for addition and subtraction using counters, learning the technique of multiplication becomes easy. As it's a form repeated addition, using counters. "Division" using counters is the reverse process in which, instead of adding, "subtraction" is used. Division using counters is same as the partition model.

Reference image: Division using counters (without remainder), the division equation is 32 ÷ 8 = 4

Base 10 blocks: The base 10 blocks are one of the most efficient ways to comprehend the decimal number system. The smallest size block is called as 1 unit or 1 ones. Progressing further, a set of such 10 "ones" is called as 1 "ten". Ahead of tens, a block consisting 10 "tens" is called as 1 "hundred" of 100 "ones". For operation on 4-digit numbers, a block of 10 "hundreds" is used as 1 "thousand".

Reference image: Division using counters (with remainder), the division equation is 34 ÷ 8 = 4 and the remainder is 2

Though base 10 blocks are not very easy to use with the division of large numbers, but they can be used with numbers up to 100 or 1000 with two-digit numbers.

Reference image: Base 10 blocks to represent numbers

Trade 1 "ten" from 6 "tens" with 10 "ones". Now, 6 "tens" and 6 "ones" are 5 "tens" and 16 "ones".

Partition the 5 "tens" to 5 individual groups and assign the remaining 16 "ones" to the groups in equal number

Each "ten" has 3 "ones" and 1 "ones" is left, so the answer/quotient is 13 and the remainder is 1.

The division equation is 66 ÷ 5 = 13 and remainder 1

For example, divide 66 by 5.

Next section reviews the grade-wise progression of "division games".

Reference image: Grade-wise progression of "division"

In grade 3, kids learn to apply the skills of subtraction for understanding the basics of the division. Also, with the knowledge of multiplication of numbers, kids learn to form multiplication tables. With practice, other skills developed at this level are the association of the conceptual knowledge of multiplication and division to addition and subtraction. Kids also learn about portioning the number of equal size groups. The skill is useful in dividing single-digit numbers by other single-digit using pictures and counters. Other methods of division such as "measurement model" (subtracting on a number line) are also learned.

In grade 4, kids learn to divide numbers ranging from 2-digits to 4-digits with a 1-digit number. Also, division by multiples of 10 and 100 is introduced to apply the skills of representing a number up to 1 or 2 decimal places. Kids also explore the division methodology for calculating a reasonable answer to word problems (quotient) and the remainder. Proficiency in mental computation and estimation is achieved by the practice of using all 4 operations on a word problem.

In grade 5, as kids learn to divide a number by single-digit number, skills are further honed to divide a number by a 2-digit divisor. Using the knowledge of place value system, kids practice dividing a decimal number by a multiple of 10 & 100. Also, math skills to perform decimal division by representing a number in fraction form are developed.

Division, based on subtraction skills

Division with pictures - This is the basic and versatile technique to introduce division to kids in early grades. Using pictures of objects like fruits, pencils, or crayons; kids learn to arrange/divide them in equal size bundles for a fixed number of groups.

Planned math exercises help kids to master the skills and assimilate the fundamentals of the division.

Alternatively, subtract the fixed number of objects from the original set (till it becomes empty) to compute the quotient. Kids also learn to comprehend the numbers in suitable terms like dividend, divisor, and quotient to easily frame a mathematical expression on division.

Framing division sentence - To solve word problems involving division and simultaneously other math operations like addition (+), subtraction (-) or multiplication (x); students reckon the "division" equation with suitable symbols.

Count back to divide - in this division technique, kids learn to count back on the number line. Mark the "dividend" and number "0" are on the number line to start with. For each jump, as illustrated in the figure, the divisor determines the distance. Subtract it progressively to jump.

The number of jumps required to reach 0 is the "quotient".

If no jumps can be made further to reach "0" with divisor, the remaining distance is the "remainder".

For example, dividing 27 by 9 yields 3.

Equation: 27 / 9 = 3 or 27 ÷ 9 = 3

The relationship between multiplication and division - To comprehend division as the reverse of multiplication, two equations can be used to teach kids about the relationship. An equation with an unknown multiplier and other equation with an unknown divisor are used to find the unknown quantity. Kids use their addition, subtraction as well as multiplication skills (using tables or progressive addition) to find the unknown value.

Work with division equations - To use the math skills of the division for solving word problems and puzzles, division equations are used with the unknown qualifiers. For example, how many kids can equally divide 20 apples within themselves so that each one of them gets 5 apples?

Division, using multiplication tables

For example: evaluate the unknown quantity in the following equations

To find the number, kids count the values using a multiplication table or line plots to find the number of jumps with divisor "7".

Division, based on Number and Operations in base ten

For example - divide 21 by 7

Division of a multiple of 10 by another multiple of 10 - To divide 60 by 20, consider numbers as bundles of 10s.

Division of a multiple of 100 by another multiple of 100 - To divide 800 by 400, consider numbers as bundles of 100s

Division of a multiple of 100 by another multiple of 100 - To divide 700 by 350, consider the numbers as bundles of the same block as "tens" for easy computation

700 / 350 or

70 / 35 (using base 10) for easier division and quotient "2"

To divide 18 by 3, either use multiplication table of 3 or count using partition model (6).

1. As 48 / 4 is 12, 480 can be written as 48 "ones" multiplied by 1 "tens".

2. The new equation can be 10 x (48 / 4), so answer is 10 X 12. (120)

Which division sentence will give you the closest estimate for the following?

As the number 3046 is closer to 3200 and 83 is closer to divisor 80, the correct answer can be selected by estimation of the nearest numbers.

800 / 400 or

8 / 4 in simpler terms to divide quickly for quotient "2".

60 / 20 or

6 / 2 in simpler terms to divide quickly for quotient "3".

In another example, divide 21 by 6

Using this method, students learn to calculate the remainder in later grades.

Reference image: Divide 24 by 3. Total number of jumps is 8 (quotient)

Learning games on other math skills propel kids to use multiplication as progressive addition and apply the skills in solving puzzles and word problems. With this knowledge, kids explicate to form multiplication tables for single-digit numbers and use these tables for the division.

For example, write multiplication table for 6 and 8:

Using multiplication tables, kids can divide a 2-digit number (by the respective table) by counting till the remainder is 0.

With the knowledge of base 10 blocks, decimal place value system and division equation; kids learn to divide multiples of 10 by similar numbers.

Let's game it:

Application:

"Division" as one of the fundamental math skills is extremely useful in several fields of applied maths (measurement, geometry, trigonometry) and science (chemical sciences, physics and relevant fields of anatomy). "Division of numbers" is an essential concept used in geography to rescale the distance/measurements by division (with the multiples of 10,000 and more) and draw accurate maps. To plan a navigational route, such maps are used in marine sciences and other fields.

SplashLearn Division Games Worksheet

Adhering to the common core math standards, SplashLearn institutes a well-planned curriculum using interactive worksheets. With the step-by-step introduction of complex concepts and techniques to master the associated math skills, kids learn the methods to use in later grades without any difficulty. Considering the skill-loss challenges during summer vacation or to homeschool kids for proficiency in math, comprehensive exercises are instrumental in boosting logical thinking and reasoning.

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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.

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Practice multiplication, fractions, decimals and algebraic reasoning with our popular math games.

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Common Core - State Standards Initiative

Students learn the fundamentals of geometry, measurements, and algebra as they venture into more complex mathematical concepts. Our lively math teachers break down the skills into easy-to-understand lessons in on-demand videos. Lessons are available for students who are struggling with a particular skill or who just need a refresher.

Math teachers teach students geometry, measurements, money, and algebra for the fifth-grade curriculum.

Students have instant help to learn the math skills needed for their assignments.

Teachers show students how to use the scratchpad to analyze and breakdown math problems.

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grade 5 math games free practice common core standards geometry measurement graphing numberproperties addition decimals multiplication division comparison estimation money mixedequations fractions subtraction algebra

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5th Grade Math - Fluency with fraction addition and subtraction, improve skill with fraction multiplication and division, decimal operations, developing understanding of volume.

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Long Division 3 digit by 1- Beginning- no remainders

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Long Division 3 digit by 1- Beginning- no remainders

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Long Division- 4 digit by 2 digit w/remainders

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Long Division- 4 digit by 2 digit w/remainders