Area Model Multiplication up to ThreeDigits
Basics on the topic Area Model Multiplication up to ThreeDigits
Mr. Squeaks is trying to travel to the Stone Age by fueling his time machine with stones, clocks, and shoes. Before he does that, he needs to calculate how many he has of each. Let’s practice area model multiplication and learn to Multiply 1Digit by 3Digit Numbers.
How Do You Multiply a 3 Digit Number by a 1 Digit Number?
When multiplying 3digit by 1digit numbers, we can use an area model. An area model is a rectangular model that helps us find the product of two numbers. Let’s look at a 3 by 1 digit multiplication example.
3 Digit by 1 Digit Multiplication Example
Let's help Mr. Squeaks calculate by multiplying two hundred fortyfive times three.
The first step is to set up our area model. Start by drawing a rectangle. Next, split it into the number of parts based on how many place values are in each number. Two hundred fortyfive has three place values: hundreds, tens, and ones, so we split our rectangle in three parts. Three has one place value so we don't break the rectangle into any more parts.
[line 42 (imagined): twohundredfortyfivetimesthreerectanglesplitinthreepartsmultiplicationmultidigitnumberwith1digitnumber]
Next, label each part by writing the factors in expanded form. The top is labeled using the expanded form two hundred plus forty plus five and the three goes on the left.
[line 42 (imagined): twohundredfortyfivetimesthreerectanglesplitinthreepartstwohundredplusfortyplusfiveonthetopthreeontheleftmultiplicationmultidigitnumberwith1digitnumber]
The second step is to multiply each corresponding pair to find the partial products. Partial products are the answers we get when each pair of factors is multiplied.
In the box on the left, we multiply three times two hundred to get six hundred. Now we multiply three times forty which is one hundred twenty. Last multiply three times five to get fifteen.
[line 42 (imagined): twohundredfortyfivetimesthreerectanglesplitinthreepartsthreetimestwohundredequalssixhundredthreetimesfortyisonehundredtwentythreetimesfiveequalsfifteenmultiplicationmultidigitnumberwith1digitnumber]
After we find all the partial products, the third step is to add them. The sum of the partial products is seven hundred thirtyfive, which means two hundred fortyfive times three is seven hundred thirtyfive.
Now that we’ve practiced multiplication 3 digit by 1 digit, let’s review!
Summary
Remember, when we solve a multiplication problem using an area model, the first step is to set up the area model. The second step is to multiply each corresponding pair to find the partial products. The third step is to find the sum of the partial products.
Want some more multiplication multi digit number with 1 digit number practice? On this website you can find 3 digit by 1digit multiplication worksheets pdf along with activities and exercises.
Transcript Area Model Multiplication up to ThreeDigits
What is Mr. Squeaks doing with all those supplies? Oh... Imani needs them to fuel the time machine so they can travel to the Stone Age! Before he gives them to Imani, he needs to calculate how many stones, clocks, and shoes he has. In order to do that, we will practice "Area Model Multiplication up to ThreeDigits". An "area model is a rectangular model that helps us find the product of two numbers." Mr. Squeaks has five boxes with thirtyeight clocks in each. Let's help Mr. Squeaks calculate by multiplying thirtyeight times five. The first step is to set up our area model. Start by drawing a rectangle. Next, split it into the number of parts based on how many place values are in each number. Thirty eight has two place values...TENS and ONES, so we split our rectangle in two parts. Five has one place value so we don't break the rectangle into any more parts. Next, label each part by writing the factors in expanded form. The value of the three in the tens place is thirty and the value of the eight in the ones place is eight... so we label the TOP thirty plus eight. Then, we label the five on the LEFT SIDE. The second step is to multiply each corresponding pair to find the partial products. Partial products are the answers we get when each pair of factors is multiplied. In the box on the LEFT, we multiply five times thirty. (...) Remember, you can ignore the zeros at first to get fifteen... and then annex one zero to your answer. Five times thirty equals one hundred fifty. Now we multiply "five times eight" in the box on the RIGHT,(...) which equals forty. After we find all the partial products, the third step is to ADD them. This will give us the answer to our multiplication problem. One hundred fifty PLUS forty is one hundred ninety so (...) they have one hundred ninety clocks. Mr. Squeaks has eight boxes with seventysix shoes in each. We need to find the product of seventysix times eight. First, let's set up our area model by drawing a rectangle, (...) breaking it into parts, (...) and labeling it. When we label using expanded form, we have seventy plus six on the TOP and eight on the LEFT. The second step is to multiply each corresponding pair to find the partial products. Let's find the partial product for the box on the LEFT. What is eight times seventy? (...) Eight times seventy equals(...) five hundred sixty. Now let's find the partial product for the box on the RIGHT. Eight times six equals (...) fortyeight. Last, what is the sum of the partial products? (...) Five hundred sixty PLUS fortyeight equals(...) six hundred eight. That means Mr. Squeaks has six hundred eight shoes for the time machine. Last, Mr. Squeaks has three boxes with two hundred fortyfive stones in each. We need to find the product of two hundred fortyfive times three. The first step is to set up our area model (...) but how does this look with a threedigit number? We still label it using expanded form, (...) but now the model is broken into THREE parts since we are calculating a THREEdigit number. How do we label it? The TOP is labeled using the expanded form two hundred PLUS forty PLUS five... and the three goes on the LEFT. The second step is to multiply to find the partial products. This time, try multiplying on your own. The partial products are six hundred (...) one hundred twenty (...) and fifteen. Now, what do we do with the partial products? The last step is to find the sum of the partial products. (...) The sum of the partial products is seven hundred thirtyfive, (...) which is the number of stones Mr. Squeaks has for the time machine. Remember(...) when we solve a multiplication problem using an area model, the first step is to "set up the area model". The second step is to "multiply each corresponding pair to find the partial products". The third step is to "find the sum of the partial products". Let's see if the time machine has enough fuel. It looks like it's working...
Area Model Multiplication up to ThreeDigits exercise

Can you solve the multiplication problem?
HintsHave you multiplied each side of the area model?
After you have multiplied each side, your area model should look like this.
Have you added the partial products together?
Don't forget any zeros!
SolutionFirst of all, solve the equation on the left:
 4 x 30 = 120
 4 x 9 = 36
 120 + 36 = 156

Can you complete the area model and solve the problem?
HintsMultiply each part separately. In this example 20 is being multiplied by 4, then 2 is being multiplied by 4.
At the bottom we need to add the partial products, and then complete the original multiplication problem.
SolutionMr. Squeaks had 5 boxes with 68 pencils in each. This is how the area model looks when it is completed.
 We multiply 5 by 60 to get 300.
 Then we multiply 5 by 8 to get 40.
 We then add 300 and 40 to get 340.
 68 x 5 = 340.

Can you spot the mistakes in the area model?
HintsThink about how we partition a three digit number, has it been done correctly here? What should 248 be partitioned into?
What should the first digit in each of the three area model equations be?
Have the zeros been included on if necessary?
SolutionThe image above shows the mistakes highlighted.
 When partitioning a three digit number we need only the hundreds in the first box, so this should have been 200, both above the box and in the first box.
 4 x 40 is 160, not 16. We can multiply 4 x 4 first to make it easier, but the 0 needs adding onto the end again.
 In the third box the first number should have been 4, as that is what we are multiplying 248 by.
 The final answer at the end is incorrect because of the mistakes in the area model. 248 x 4 = 992.

Can you find the correct answers to the multiplication problems?
HintsHave you partitioned the two or three digit number?
This example shows how we could set up 32 x 3 using an area model.
SolutionThe grid above has been filled in for the problem 42 x 7. 42 has been partitioned into tens and ones to give 40 and 2.
To solve:
 First of all we multiply 7 by 40 to get 280.
 We then multiply 7 by 2 to get 14.
 Now we need to add 280 and 14 to get 294.
 Therefore 42 x 7 = 294.
 83 x 3 = 249
 113 x 4 = 452
 207 x 2 = 414
 325 x 3 = 975

Can you complete the area model and find the answer?
HintsRemember to multiply 3 by the tens and the ones of the two digit number.
Add up your products to find the answer to the multiplication problem.
SolutionHere is the completed area model:
 3 x 30 = 90
 3 x 5 = 15
 We then add 90 and 15 to get 105.
 So, 35 x 3 = 105.

Can you solve the multiplication problems?
HintsRemember to partition your two or three digit number.
Add the partial products to find the answer.
SolutionFor the first problem:
 We need to partition 39 into 30 and 9.
 We then multiply 8 by 30 to get 240, and 8 by 9 to get 72.
 Next, add 240 and 72 to get 312.
 Therefore, 39 x 8 = 312
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For the second problem:
 Partition 76 into 70 and 6.
 Multiply 4 by 70 to get 280, and 4 by 6 to get 24.
 Add 280 and 24 to get 304.
 Partition 122 into 100, 20 and 2.
 Multiply 6 by 100 to get 600, 6 by 20 to get 120, and 6 by 2 to get 12.
 Add 600, 120 and 12 to get 732.
 Partition 341 into 300, 40 and 1.
 Multiply 7 by 300 to get 2,100, 7 by 40 to get 280, and 7 by 1 to get 7.
 Add 2,100, 280 and 7 to get 2,387.