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4.4C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15

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4.4C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15

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4.4H solve one- and two-step  problems involving division, including interpreting remainders

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4.4H solve one- and two-step  problems involving division, including interpreting remainders

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Khan Academy: Multiplying 2-Digit by 2-Digit Numbers

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Khan Academy: Multiplying 2-Digit by 2-Digit Numbers

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In this video, we're going to multiply 36 times 27. So we're multiplying a two-digit number times another two-digit number. And the way that we're going to tackle it is we're going to first multiply 36 times 7, figure out what that is. Then we're going to multiply 36 times 20, figure out what that is, and then add those two numbers together. And what I want to do is first do this, just show you the process for how to multiply these two numbers. And then I'm going to do it again where we're going to think a little bit more about what the different numbers represent. So first let's start with the process. So I'm going to multiply 36 times 7 or 7 times 36. So I can start in the ones place. 7 times 6 is 42. Write the 2 down here. And then the 4, which represents 40, I can put in the tens place. 7 times 3 is 21, plus 4 is 25. So I could write the 25 right over here. There's no place to carry this 2, so I just wrote the 2 right over here in the hundreds place. Now let's move over. So let me clean this up so we don't get confused. So we just figured out what 7 times 36 is. It is 252. Now let's worry about what 36 times 20 is. And so what we're going to do is we're going to throw a 0 right over here, because we're now going to multiply 36 times something in the tens place. This isn't just a 2. This is a 20. So let's just go with the digits right now and then we'll think about it in terms of place value the second time around. 2 times 6 is 12. Write the 2 right over here. Carry the 1. 2 times 3 is 6, plus 1 is 7. So we just figured out that 36 times 20 is 720. And just think about what would've happened if we didn't put the 0 here. Then we would have figured out that 36 times 2 is 72, but this 2 isn't just a 2. This is a 20. So 36 times 20 is 720. And now we can add these two things because 36 times 27 is the same thing as 36 times 20 plus 36 times 7. So let's add these two numbers together. 2 plus 0 is 2. 5 plus 2 is 7. 2 plus 7 is 9. And we get 972. Now I'm going to do this exact same problem again. But this time, I'm going to really talk about what these digits represent. Hopefully the first pass, you kind of saw the process for doing it. Now we're going to think about what these digits actually represent. So we're going to multiply 36 times 7. So 7 times 6 is 42. We would write the 2 in the ones place, and then the 40 we can write in the tens place. This 4 represents 40. 7 times 30 is 210, plus 40 is 250. And we already had that 2 in the ones place, so we get 252. 36 times 7 is 252. Now let's clean this up. Now let's multiply-- 20 times 6 is going to give us 120. So let's write the 20 in the tens place, and then carry the 100, or carry the 1, which represents 100. Now, 2 times-- or I should say 20 times 30 is going to give you 600, plus one more 100 is going to give you 700. So we just figured out that 36 times 20 is 720. The 7 is in the hundreds place, 2 in the tens place. And then we can add again. And just like we did the last time, we got 972.

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Multiplying 2-digit numbers (video) | Khan Academy

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In this video, we're going to multiply 36 times 27. So we're multiplying a two-digit number times another two-digit number. And the way that we're going to tackle it is we're going to first multiply 36 times 7, figure out what that is.

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Khan Academy: Multiplying with an area model

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Khan Academy: Multiplying with an area model

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Multiplying with area model: 16 x 27 (video) | Khan Academy

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Sal uses an area model to multiply 16x27.

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Super Teacher Worksheet: multiplying 2-digit by 2-digit practice

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Super Teacher Worksheet: multiplying 2-digit by 2-digit practice

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4.2B Place Value Review (Teacher sign up for a free account):

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4.2B Place Value Review (Teacher sign up for a free account):

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Find and create gamified quizzes, lessons, presentations, and flashcards for students, employees, and everyone else. Get started for free!

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Khan Academy: Adding and subtracting decimal

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Khan Academy: Adding and subtracting decimal

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Adding and subtracting decimals word problem | Decimals | Pre-Algebra | Khan Academy

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4.4C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15

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4.4C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15

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Review from 3rd grade Division -  3.4K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts.

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Review from 3rd grade Division -  3.4K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts.

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4.4F use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor

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4.4F use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor

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4.4H solve with fluency one- and two-step problems involving division, including interpreting remainders

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4.4H solve with fluency one- and two-step problems involving division, including interpreting remainders

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4.5B represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence

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4.5B represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence

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NUMBEROCK: Dividing 4-Digit by 1- Digit Numbers

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NUMBEROCK: Dividing 4-Digit by 1- Digit Numbers

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Join Stu & friends at the beach in this long division song and music video as he explains how do divide 4 digit dividends by 1 digit divisors by drawing problems into the sand with his math-e-magic wand (a piece of driftwood)! He'll be using the standard algorithm - a concept usually taught and reinforced in the 5th & 6th Grade. Pull up a beach chair, turn the volume to eleven, and have your flip flops ready, because this Caribbean tune will rock your socks off!

Copy and paste the following text onto your teacher, school, or homeschool website to give your students a chuckle.

Long Division Song Lyrics:

Verse One
First divide the dividend by the divisor:
we can fit two groups of nine into twenty four.
Multiply the nine by two, to get eighteen in the mix.
Write the eighteen and subtract, the difference is six.
Then bring down the three, and the process will repeat.
When we do long division we drop the beat.

Chorus
Divide, Multiply, Subtract, Bring Down:
that's how a quotient is found!

Verse Two
Next we divide sixty three by nine.
The quotient is seven; write it above the line.
Multiply nine by seven; we get sixty three;
then subtract the sixty three to get zero, you see.
We bring down the two, which nine does not go into
So write a zero on the line followed by remainder two

Divide multiply subtract bring down
that's how a quotient is found
Divide multiply subtract bring down
(And when there's a remainder
write "R" followed by what's left over)
that's how a quotient is found

Bridge
The remainder that's left over can be further defined:
"R2" can be written as two over nine.
Since nine is the divisor, it's the whole;
the remainder is the part, and that is it's role.
So two hundred seventy R2 is the quotient,
and two hundred seventy and two ninths is it's equivalent.

Divide multiply subtract bring down
that's how a quotient is found
Divide multiply subtract bring down
(The remainder can become the numerator,
the divisor can become the denominator.)
that's how a quotient is found

Learn More

This song targets TEKS and Common Core learning standards from both 4th Grade and 5th Grade. Look into the relevant standards here, or dig deeper into Long division here.

If you are interested in getting ideas on how to plan a robust standards-aligned Long Division with 1 Digit Divisors lesson, we recommend checking out Instructure's recommendations for common core standards 4.NBT.6, and 5.NBT.6 . These pages help break down standard language, lay out the grade-appropriate level of rigor for each concept, and offer a variety of suggestions for activities (lesson seeds) that help students achieve their learning targets.

To continue browsing Numberock's math video content library, click here. To gain access to Numberock's growing library of premium content, click here.

Steal Our Joke.

Copy and paste the following text onto your teacher, school, or homeschool website to give your students a chuckle.

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Long Division with Remainders Song with 1 Digit Divisors | NUMBEROCK

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Join Stu & friends at the beach in this long division song and music video as he explains how do divide 4 digit dividends by 1 digit divisors by drawing problems into the sand with his math-e-magic wand (a piece of driftwood)!

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The long division song works through a problem with a 1-Digit Divisor and a 3 Digit Dividend and comes out with a remainder. The animation contains a very catchy song that kids will love, and even more importantly, remember. Divide, Multiply, Subtract, Bring Down. That's how a quotient is found. Welcome to long division made easy as we go through the process step by step.

Song Lyrics:

Five Groups of Five are 29
Their Product is 25
Put That 5 Above the Line
On Top off the Line
Then Draw a Subtraction Sign
And Write the 25
The Difference is Four and There's One Step More
Bring the Eight Down Next to the Four

Divide, Multiply, Subtract, Bring Down
That's How A Quotient is Found

Divide 48 By Groups of Five
You Will Find That There Are Nine.
Put That Nine Above The Line
And Multiply Nine By Five
Then Draw A Subtraction Sign
And Write the 45
The Remainder is Three
So Write Our Three
That's How Easy Division Can Be

Divide, Multiply, Subtract, Bring Down
That's How A Quotient is Found

Divide, Multiply, Subtract, Bring Down
That's How A Quotient is Found!

And When There's a Remainder,
Write R Followed by What is Left Over
That's How A Quotient is Found!

Learn More

This song targets TEKS and Common Core learning standards from both 4th Grade and 5th Grade. Look into the relevant standards here, or dig deeper into Long division here.

If you are interested in getting ideas on how to plan a robust standards-aligned long division lesson, we recommend checking out Instructure's recommendations for common core standards 4.NBT.6, and 5.NBT.6 . These pages help break down standard language, lay out the grade-appropriate level of rigor for each concept, and offer a variety of suggestions for activities (lesson seeds) that help students achieve their learning targets.

To continue browsing Numberock's math video content library, click here. To gain access to Numberock's growing library of premium content, click here.

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Numberock's Long Division Song | Divide, Multiply, Subtract, Bring Down

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This upbeat Long Division Song, set on a farm, works through a problem with a 1-Digit Divisor and a 3 Digit Dividend.

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QUIZIZZ: Division with Remainders                               

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QUIZIZZ: Division with Remainders                               

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Find and create gamified quizzes, lessons, presentations, and flashcards for students, employees, and everyone else. Get started for free!

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Khan Academy: Multiplication with Arrays

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Khan Academy: Multiplication with Arrays

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So, I have several groups of these ball-looking things. And let's think about how many balls are in each group. We have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 12. And what I want to do is think about the different ways of dividing these 12 balls into different numbers of groups. So, for example, I could view these 12 balls as one, so that's 1 group of 3, 2 groups of 3, 3 groups of 3, 4 groups of 3. So I could view 12 as being 4 groups of 3. And the way that we would write that is that 12 is equal to 4 groups of 3. Or another way of reading this is that 12 is equal to 4 times 3. If I have 1, 2, 3, 4 groups, and in each of those groups I have 1, 2, 3, objects, I'm going to have a total of 12 objects. But that's not the only way we can get to 12. We could also view it as 3 groups of 4. So, let's look at that. So we could have it as 1 group of 4, 2 groups of 4, 3 groups of 4. So now we could view 12 as being 3 groups of 4. Or we could say-- let me get the right tool out-- that 3 times 4 is equal to 12. So, whether we're doing 4 times 3 or 3 times 4, they're both going to be equal to 12. 4 groups of 3 is 12, 3 groups of 4. But we don't have to stop there. We could also view 12 as, well, we could view it as 2 groups of 6. Let's look at that. So this is 1 group of 6 right over here. So, that's one 1 of 6. That's another group of 6. So, once again, we could view this as 2 times 6. 2 times 6 will also get us a 12. Well, what about doing it as 6 groups of 2? Well, we can draw that out, too-- 6 groups of 2. So that's 1 group of 2. Let me do that in a different color. Let me do it in this purple color. We have 1 group of 2, 2 groups of 2, 3 groups of 2, 4 groups of 2, 5 groups of 2, and 6 groups of 2. So once again, this is all different ways of writing 12, something equivalent to 12. We could write 6 times 2-- 6 groups of 2-- 6 times 2 is also equal 12. But we don't have to stop there. We could also literally view 12 as 1 group of 12. So how would that look? So 1 group of 12. So this whole thing is just 1 group of 12 here. So we could literally say 1 times 12 is equal to 12. We have one entire group of 12. 1 times 12 is equal to 12. And we could think of it the other way around. We could view this as 12 groups of 1. Let me draw that. So 12 groups of 1. This is 1 group of 1, 2 groups of 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12-- 12 groups of 1. So we could also write 12. 12 groups, and in each one, I have 1. Well, that's still going to get me to 12.

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Multiplication with arrays (video) | Khan Academy

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So, I have several groups of these ball-looking things. And let's think about how many balls are in each group. We have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 12. And what I want to do is think about the different ways of dividing these 12 balls into different numbers of groups.

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Quizlet: Multiplying 2-Digit by 2-Digit Numbers

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Quizlet: Multiplying 2-Digit by 2-Digit Numbers

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Khan Academy: Multiplication Word Problems

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Khan Academy: Multiplication Word Problems

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Multiplication word problem: soda party (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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4.5A represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity

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4.5A represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity

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Learn Zillion: Represent multiplication using arrays 

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Learn Zillion: Represent multiplication using arrays 

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In this lesson, you will learn how to represent multiplication by using arrays.

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3.5B represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

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3.5B represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

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4.4H solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders

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4.4H solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders

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4.4D - use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

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4.4D - use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

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This song will show you how you can use input/output tables and number expressions to create number patterns following a given rule. The NUMBEROCK crew are given a series of numbers as they make predictions about which numbers will come next if the pattern continues.

Input Output Song Lyrics:

Chorus: What's happening between the in and the out?
We can always find out without any doubt.
Make an educated guess, and test it out,
'til you find out what the "rule" is all about.

When there are two sets of values, and they share
a mathematical relationship, there's a function there.
And we can use our mind - a mathematical tool -
to find and describe the relationship, called a "rule."

Learn More

This song targets TEKS (4.5B) and Common Core (4.OA.5) learning standards from 4th Grade. Look into the relevant standards here, or dig deeper into input-output tables here.

If you are interested in getting ideas on how to plan a robust standards-aligned Input/Output Tables (one step) lesson, we recommend checking out Instructure's recommendations for common core standards 4.OA.5. These pages help break down standard language, lay out the grade-appropriate level of rigor for each concept, and offer a variety of suggestions for activities (lesson seeds) that help students achieve their learning targets.

To continue browsing Numberock's math video content library, click here. To gain access to Numberock's growing library of premium content, click here.

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Input Output Tables Video | 4th Grade | NUMBEROCK

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Numberock characters throw numbers into their Input-Output machine to discover the rule that completes one-step functions.

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Splash Learn:  Multiplying 4 digit by 1 numbers

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Splash Learn:  Multiplying 4 digit by 1 numbers

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Multiply 4 digit numbers by 1 digit numbers. In 4 Digit x 1 Digit (Numbers up to 4,000) Worksheet, students make use of area models to multiply numbers. Area models are essentially visual representation of the distributive property of multiplication. For example, 3241 x 2 can be multiplied as (3000 x 2) + (200 x 2) + (40 x 2) + (1 x 2). Fluency with place value (expanded forms), distributive property of multiplication and multiplying multiples of 10 will be of great help here. This method of multiplying should acts as a precursor to the standard algorithm. It is important for the students to understand how a particular method works. The 3-digit numbers in this worksheet are restricted to those less than 4000.

Common Core Alignment

4.NBT.5Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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SplashLearn - Fun Math Practice Games for Kindergarten to 5th Grade

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Multiply 4 digit numbers by 1 digit numbers. In 4 Digit x 1 Digit (Numbers up to 4,000) Worksheet, students make use of area models to multiply numbers. Area models are essentially visual representation of the distributive property of multiplication.

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MATH4TEXAS: Representing & Solving Area Model with Multiplication

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MATH4TEXAS: Representing & Solving Area Model with Multiplication

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Third Grade / Representing & Solving One- & Two-Step Multiplication & Division Problems within 100

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3.5 Algebraic reasoning. The student applies mathematical process standards to analyze and create patterns and relationships. The student is expected to: (B) represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

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The distributive property involves addition and multiplication. So where do all the parentheses come in? Tim and Moby know.

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Fourth Grade / Representing Multi-Step Problems with Unknowns

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Daniel has a collection of baseball cards. His mom gave him a set of 48 cards for his birthday. His grandmother gave him twice as many cards as his mother did. Now he has 352 cards. How many cards did he have before his birthday?

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Fourth Grade / Representing Problems Using Input-Output Tables & Numerical Expressions

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Trey sells 50-pound bags of wood chunks to be used for smoking meat in grills. One day he sold two bags for $30, five bags for $75, seven bags for $105, and four bags for $60. Represent the situation using an input-output table and a numerical expression that could be used to find the cost for b, the number of bags sold.

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Fourth Grade / Multiplication & Division One- & Two-Step Problems

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Khan Academy: Dividing numbers: intro to remainders

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Khan Academy: Dividing numbers: intro to remainders

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Intro to remainders (video) | Remainders | Khan Academy

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Sal shows how a remainder is what’s left over in a division problem.

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Math-Drills.com includes over sixty-four thousand free math worksheets that may be used to help students learn math. Our math worksheets are available on a broad range of topics including number sense, arithmetic, pre-algebra, geometry, measurement, money concepts and much more. There are two interactive math features: the math flash cards and dots math game.

Math-Drills.com was launched in 2005 with around 400 math worksheets. Since then, tens of thousands more math worksheets have been added. The website and content continues to be improved based on feedback and suggestions from our users and our own knowledge of effective math practices.

Most Math-Drills users are classroom teachers or parents. Classroom teachers use our math worksheets to assess student mastery of basic math facts, to give students extra math practice, to teach new math strategies, and to save precious planning time. Parents use our math worksheets to give their children extra math practice over school breaks and to enhance their math education. Home schools use our math worksheets in their programs to develop and strengthen math skills in their children.

Most Popular Free Math Worksheets this Week

Supporting Student Learning with Free Math Worksheets by Math-Drills

Math-Drills believes that education should be accessible to all children despite their socioeconomic situation or any other factors. Since it began in 2005, all the math worksheets on Math-Drills have been free-to-use with students learning math. The Math-Drills website works well on any device and worksheets can be printed or used on a screen.

Math-Drills worksheets are also used in special education, adult education, tutoring, colleges, high schools, prisons and a variety of other situations. Special education teachers especially like that we break down math skills and provide large-print options. Adult learners appreciate the simple uncluttered format that our worksheets offer. Tutors use our math worksheets to reduce their costs and focus on student learning. High school, college and university educators sometimes need remedial resources for students to allow them to continue with more advanced topics.

Students who practice their math skills with our math worksheets over school breaks keep their math skills sharp for upcoming school terms. Because we provide answer keys, students are able to self-assess and use the immediate feedback provided by an answer key to analyze and correct errors in their work. Our interactive (fillable) math worksheets allow them to fill in their answers on the screen and save or print the results.
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Join our newsletter to find out about new math worksheets and other information related to the website.

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Math-Drills includes over 58 thousand free math worksheets for students in elementary and middle school. Our easy to print math worksheets are free to use in your school or home.

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MATH4TEXAS: Math4Texas showcases the Math TEKS by grade level with tips, examples, digital tools, and videos to help parents understand the math concepts and skills that their children are learning.

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MATH4TEXAS: Math4Texas showcases the Math TEKS by grade level with tips, examples, digital tools, and videos to help parents understand the math concepts and skills that their children are learning.

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Education.com: Various online games, printable worksheets, guided lessons, engaging activities, among other teacher-created sources, cover the wide scope of the fourth grade math curriculum, from simplification to statistics.

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Education.com: Various online games, printable worksheets, guided lessons, engaging activities, among other teacher-created sources, cover the wide scope of the fourth grade math curriculum, from simplification to statistics.

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Free Online 4th Grade Math Games | Education.com

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Award winning educational materials like worksheets, games, lesson plans and activities designed to help kids succeed. Start for free now!

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Math World: An interactive program that covers all Math learning goals for grades K-6. 

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Math World: An interactive program that covers all Math learning goals for grades K-6. 

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Khan Academy: Setting up 2- Step Word Problems

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Khan Academy: Setting up 2- Step Word Problems

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If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

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Setting up 2-step word problems (video) | Khan Academy

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If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

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Splash Learn: A highly engaging interactive website. 

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Splash Learn: A highly engaging interactive website. 

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Q1: What is distributive property of multiplication?
Ans: Distributive property of multiplication over addition simplifies multiplication of large numbers using the smaller known facts. One such example is: 40 x 105 which can be written as 40 x (100 + 5) = 40 x 100 + 40 x 5 which can be now solved mentally very quickly as 4000+200= 4200.
Q2: How do we multiply numbers by 1-digit numbers?
Ans: We can easily multiply 2, 3 or 4-digit numbers by 1-digit numbers using column method. We can write the digits in column as per their palce values and multiply them. We can also use area model or box model to multiply them.
Q3: How can we use area model for multiplication?
Ans: We can write both the numbers to be multiplied in expanded form and arrange them along length and the width of a rectangles. Then, we find the area of each rectangle using the formula: length x width. The sum of all the areas of rectangles is equal to the product of numbers.
Q4: How do we multiply 2-digit numbers by 2-digit numbers?
Ans: We can multiply 2-digit numbers by 2-digit numbers using column method, area model or lattice method. To practice multiplication, there are ample of games in SplashLearn website. You just need to find math games in the home page and find 'multiplication games' in the tab 'Math Games by Topic' to practice this concept.
Q5: How do we multiply numbers?
Ans: We can multiply numbers using column method, area model, or lattice method. To practice multiplication, there are ample of games in SplashLearn web page. To play fun games on multiplication, visit SplashLearn page and select your grade or find "multiplication games" in the tab "Math Games by Topics"; then your are ready to have fun while applying your knowledge.
Q6: How to multiply numbers by expanding them?
Ans: We can write both the numbers to be multiplied in expanded form and arrange them along length and the width of a rectangles. Then, we find the area of each rectangle using the formula: length x width. The sum of all the areas of rectangles is equal to the product of numbers.

Introduction

Multiplication and division should be introduced in its most basic form at the earliest opportunity so that children can begin to familiarize themselves with these key operations. According to a study, successive research has shown that: children as young as preschoolers solve many multiplication and division word problems by connecting modeling with counting and grouping skills and with various strategies involving addition and subtraction. Hence it is very important to grasp the concepts of multiplication well because multiplication forms the building block for other mathematical concepts. A lot of sums can be solved with confidence just by learning multiplication tables. For example, knowing that 3 x 3 = 9 will help children understand that 30 x 30 = 900, and 300 x 300 = 90000. Being versed with multiplication properties and multiplication facts too helps in calculations. Also, Multiplication definition can be the inverse function of the division. Multiplication knowledge can come handy in verifying the division sums using the inverse. For example, 28 ÷ 4 = 7 is correct because 7 x 4 = 28.

Mathematical Representations of Multiplication

First Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Then, multiply to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Let children begin by investigating the formulas for area and perimeter. They use their understanding of the area and perimeter formulas to solve multiplication problems including the language of times as much with a focus on math problems using area and perimeter as a context (e.g., "A field is 9 feet wide. It is 4 times as long as it is wide. What is the perimeter of the field?"). Let kids create diagrams to represent these problems as well as write equations with symbols for the unknown quantities. For example, the width of a tent is 5ft and the length is twice the width. The rectangular air mattress measures 3ft by 6ft. If the mattress is put in the tent, how many squares feet of floor space will be available for the rest of the things?

In 4th grade math, the multiplicative comparison is crucial as it helps in understanding multiplication as scaling in Grade 5 and sets the stage for proportional reasoning in Grade 6. Introducing multiplication with area and perimeter allows for new and interesting multiplication word problems as children learn to calculate with larger numbers and interpret more complex problems.

First, let kids see perimeter as the sum of all four sides but a faster way is to double the sum of the length and width. Hence the formula as P = 2 × (l + w). Now let kids use the formula 2 × (l + w) to solve for perimeter and to find an unknown side length.

Kids can similarly find the area by counting the number of squares in the rectangle or counting number of squares in one row and then skip count that number for all the rows which are just multiplying the number of rows by the number in each row. Hence, a quicker way is to multiply the length times the width. Nine rows of 3 units each is like a multiplication array. We can just multiply 9 × 3. Total squares in the multiplication grid give the area of the rectangle.

This can be extended by exploring multiplication arrays to word problems. Let kids Solve multiplicative comparison mathematics problems by applying the area and perimeter formulas.

Multiplication by Single-Digit Numbers

Common core multiplication standards emphasize on reasoning, looking for and making use of multiplication table chart and various mathematical strategies that can help children understand better. Hence, for this purpose, SplashLearn has put together multiple strategies on how to teach multiplication that can be explored by parents to practice with their kids.

For teaching multiplication of multi-digit numbers by a single-digit kid should initiate by decomposing numbers into base ten units. Provide kids with sufficient multiplication practice of area models, the standard algorithm, and in the context of word problems, including multiplicative comparison problems, multiplication drills and multiplication and division worksheets. Multiplication charts and manipulatives like place value disks to represent multiplication also helps kids visualize the process. Once comfortable with the above methods kids can be progressed to the abstract level as they learn how to multiply three- and four-digit numbers by one-digit numbers. Finally, kids learn how to do double-digit multiplication by the partial products, the standard algorithm, and the area model via the distributive property of multiplication.

Place Value Disk Method

Let's try to solve 2 digit multiplication with a single number using disks.

For example: 2 × 23

First, draw disks to represent 23 on the place value chart.

23 is: 2 tens 3 ones.

Draw 1 more group of 23 on the chart.

Now the value of the ones is 2 × 3 ones = 6 ones.

The value of the tens is 2 × 2 tens = 4 tens.

Add up the partial products. The final sum is 46.

Hence 2 X 23 = 46

Similarly, solve one digit by two digit multiplication of 4 × 54

First, draw disks to represent 54 on the place value chart. 54 is: 5 tens 4 ones.

Draw 3 more groups of 54 on the chart.

Now the value of the ones is 4 × 4 ones = 16 ones.

The value of the tens is 4 × 5 tens = 20 tens.

Add up the partial products. The final sum is 216.

Hence 4 X 54 = 216

Now extend the use of place value disks to represent one-digit by multi digit multiplication

Partial Products Drawing Method

Example: Solve 3 × 851 using a partial product drawing on the place value chart.

This time, rather than recording 3 groups of 851 to begin, record the partial products as we multiply each unit. Begin with ones place: 3 × 1 one is 3 ones. Record that in the pace value chart.

In tens, we get: 3 times 5 tens which are 15 tens. Record this in the place value chart as 1 hundred 5 tens a bit lower than the ones so you can see the separate partial product.

Then do the hundreds. 3 times 8 hundreds is 24 hundreds. Record that in the place value chart as 2 thousands 4 hundreds. Now sum all the partial products to get the final answer. Hence, 3 x 851 = 2553

Standard Algorithm Method

Let us take a look at the sample problem in order to understand how to do multiplication through standard algorithm:

Problem: Solve 6 × 162.

First, represent 6 × 162 on the multiplication chart using the repeated addition way.

In this, we have, 6 hundreds, 36 tens, and 12 ones.

10 ones can be regrouped for 1 ten and 30 tens for 3 hundreds. The answer becomes 9 hundreds, 7 tens, and 2 ones. Standard algorithm is an efficient way of doing fast math.

Observe the ones column of the place value chart:

6 times 2 ones is equal to 12 ones.

Regrouping 10 ones for 1 ten leaves 2 ones.

Next record the number of regrouped tens on the line under the tens column. Record the number of ones in the ones place.

Now observe the tens column of the place value chart. 6 times 6 tens are same as 36 tens.

Exchange 30 tens for 3 hundreds leaving 6 tens. But 1 ten was regrouped from the ones, so 36 tens plus the 1 ten makes 37 tens. So, we have 3 hundreds and 7 tens after we regroup. Now record the number of hundreds on the line in the hundreds column.

Record the number of tens in the tens place.

Cross out the line in the tens place, as it has already been counted.

Now, observe the hundreds place. 6 × 1 hundred = 6 hundreds.

6 hundreds plus the 3 hundreds we regrouped equals 9 hundreds.

Write it at the hundreds place and cross out the 3 hundreds that have been used. Hence the answer becomes: 972

Connect Area Model and Partial Products Method

Let us look at 234 X 8 using the area model.

First, draw a rectangle with the length of 8 and the width of 200.

Multiply 8 times 200. That equals 1,600.

Draw two more rectangles both with the length of 8 and widths of 30 and 4 respectively. Multiply 8 times 30 (=240) and 8 times 4 (=32). Then combine all three rectangles and find the area of all three rectangles put together. Total Area = 1872

Comparing the partial products to the rectangular area model you will observe that the area inside each smaller rectangle is the same as each of the partial products. The distributive property allows breaking apart the large multiplication problem into three smaller ones. Add the areas individually which sums to 1872. Hence, the area model is another way to represent the partial products in multiplication.

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Multiplication Games for 4th Grade Kids Online - SplashLearn

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Q1: What is distributive property of multiplication? Ans: Distributive property of multiplication over addition simplifies multiplication of large numbers using the smaller known facts. One such example is: 40 x 105 which can be written as 40 x (100 + 5) = 40 x 100 + 40 x 5 which can be now solved mentally very quickly as 4000+200= 4200.

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Numberock’s Rounding Song | Rounding Numbers Rap Video + Lyrics

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You’re watching about to watch a really fun Rounding Song by Numberock.. This song rounds whole numbers to the nearest 10th and 100th.