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I can use expanded and short multiplication to multiply 2-digit by 1-digit numbers.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

Use times tables and place value to estimate the product of a 2-digit by a 1-digit multiplication.
Use expanded short multiplication to multiply a 2-digit by a 1-digit number.
Use short multiplication to multiply a 2-digit by a 1-digit number.

Common misconception

Pupils may find it difficult to identify the multiples of 10 a number is between when estimating.

Provide a number line and continue to use stem sentences to support pupils in their thinking.

Keywords

Estimation - To find a value that is close enough to the right answer, usually with some thought or calculation involved is known as estimation.

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Hello, I'm Miss Miah, and I'm so excited to be a part of your learning journey today.

I hope you enjoy this lesson as much as I do.

By the end of this lesson, you'll be able to use expanded and short multiplication to multiply two-digit by one-digit numbers.

Your keywords for today are estimation, or estimate.

To find a value that is close enough to the right answer, usually with some thought or calculation involved, is known as estimation.

So, our lesson outline is estimate and multiply a two-digit by a one-digit number, using expanded and short multiplication.

The first part of our lesson is to do with estimating to check solutions.

In this lesson, you'll meet Sophia and Alex.

You may have seen these methods of representing multiplication.

So, we've got here expanded multiplication, short multiplication, informal, and the grid model.

You will be exploring which method you find most efficient for different questions.

Don't forget, you can also use mental strategies.

Sophia and Alex are calculating 4 multiplied by 75.

Sophia's got 208 as her answer.

What advice would you give to support her before she calculates the answer? I'll give you a moment to think.

Before you calculate the total, it is a good idea to estimate.

This will help us find a number that is close enough to the right answer.

So, before you calculate the total, it is a good idea to estimate, and I'm going to talk you through how you would do this.

So, our equation here is 4 multiplied by 75.

75 is in between 70 and 80.

4 multiplied by 70.

Hmm.

Now, you can use your table facts to help you if you're not quite sure about this question.

So, you know that 4 multiplied by 7 is 28.

So, 4 multiplied by 7 tens is 28 tens, which is equivalent to 280.

You then multiply 4 by 80.

So, 4 multiplied by 8 is 32, so 4 multiplied by 8 tens is 32 tens.

This is 320.

So, 4 multiplied by 75 must be between 280 and 320.

Over to you.

Fill in the missing numbers to complete this estimation.

48 multiplied by 6.

48 is between 40 and 50.

40 multiplied by 6 is.

50 multiplied by 6 is.

So, 48 multiplied by 6 is between.

and.

You can pause the video here.

How did you do? So, let's go through the answers.

48 is between 40 and 50.

40 multiplied by 6 is 240.

50 multiplied by 6 is 300.

So, the answer for 48 multiplied by 6 must be between 240 and 300.

Alex finds the product and records his calculation.

So, 75 multiplied by 4.

You can see that Alex has partitioned 75 into 70 and 5.

4 multiplied by 70 is 280.

4 multiplied by 5 is 20.

280 add 20 is 300.

So, Alex says, \"I know my answer must be between 280 and 320 because I estimated.\" Alex has probably calculated correctly, because 300 falls between 280 and 320.

Back to you.

Select an appropriate estimation equation for 52 multiplied by 3.

You've got 3 options here: 55 multiplied by 3; 50 multiplied by 3; and 60 multiplied by 3.

You can pause the video here to have a think.

How did you do? If you've got 50 multiplied by 3, so option B, you are correct, and this is because 52 is closer to 50.

Moving on.

81 multiplied by 5.

Sophia used short multiplication, and this is her calculation.

Using estimation, do you think Sophia is correct? I want you to explain your thinking to your partner.

So, let's see what's happened.

Sophia went back to check her estimated answer.

81 is in between 80 and 90.

5 multiplied by 80 is 400.

5 multiplied by 90 is 450.

So, 81 multiplied by 5 must be between 400 and 450.

Sophia went back to check her estimation.

She got 45 as her product.

45 is not between 400 and 450.

Her answer should have been between 400 and 450.

This is why it is super useful to estimate.

Now, Alex is calculating 35 multiplied by 6.

He estimates his answer to be 240.

\"35 is close to 40.

Then I multiplied 40 by 6.

This is 240.\" 35 multiplied by 6.

Let's see.

So, 35 is in between 30 and 40.

And if you're not sure what 6 multiplied by 30 is, you can use your table facts to help you.

You know that 6 multiplied by 3 is 18.

So, 6 multiplied by 3 tens is 18 tens, which is equivalent to 180.

Then we can move on to 6 multiplied by 40.

You know that 6 multiplied by 4 is 24, so 6 multiplied by 4 tens is 24 tens, which is equivalent to 240.

So, 35 multiplied by 6 must be between 180 and 240.

Alex used the grid model and short multiplication, however, got two very different answers, and you can see that there.

The estimated answer is between 180 and 240.

Now, I want you to take a moment to think about which is more likely to be right.

So, what did you think? The grid model is more likely to be correct because the answer is in between 180 and 240.

Over to you.

Select an appropriate estimation for 83 multiplied by 6.

You can pause the video here.

So, how did you do? If you got B, you are correct, and this is because I did 80 multiplied by 6, because 83 is closer to 80.

Onto the tasks.

For question one, you're going to be writing an estimation for the following multiplication equations: A: 16 multiplied by 4; B: 42 multiplied by 6; and C: 55 multiplied by 7.

Then use an efficient strategy to calculate.

Don't forget, there are various strategies you can use, such as the informal written method, grid model, expanded multiplication, short multiplication, and even mental strategies.

Using the short multiplication and grid model below, find the multiplication needed, write an estimate, and fill in the gaps.

You can pause the video here.

Off you go.

So, how did you do? Let's work through our calculations.

16 multiplied by 4.

We know that 16 is in between 10 and 20.

We multiply both by 4, which gives us a range of 40 to 80.

So, our answer must be between 40 and 80.

For the second question, we know that 42 is between 40 and 50, so we multiply both by 6.

So, our answer must be between 240 and 300.

And lastly, for question 3, 55 is in between 50 and 60.

We multiply both by 7.

So, our answer must be between 350 and 420.

If you've got all 3 of those correct, well done.

Right, onto question two.

You were to use short multiplication and the grid method below to first find the multiplication needed, and then you were to write an estimate, and then fill in the gaps.

So, your estimates should have ranged between 240 and 300, because 40 multiplied by 6 is 240, and 50 multiplied by 6 is 300.

Whilst filling in the gaps, this is what you should have got for both methods.

If you got both correct, really good job.

Well done.

Onto the second part of our lesson.

So, this time, you'll be using expanded and short multiplication to solve problems. Let's go.

Now, short and expanded multiplication are useful if there are more instances of regrouping.

It is important for you to know when you may have to regroup in the ones or tens column.

So, look at the equation on the screen now.

You've got 31 multiplied by 4.

The ones will not need to be regrouped because we've got 4 multiplied by one 1, which is 4 ones.

The tens, however, will need to be regrouped, because 4 multiplied by 3 tens is 12 tens, which is greater than 10 tens.

We must regroup.

Imagine having a bag filled with so many strategies.

You can pick and choose the strategy that you would like to use for each problem.

Try and pick the most efficient one.

Sometimes you may choose a strategy because there's no regrouping involved.

Another time, you may choose a strategy from your multiplication kit because there is regrouping involved.

So, think carefully about the method that you pick.

Let's begin.

In week 1, 31 cups of lemonade are sold.

The following week, 4 times as many are sold.

How many cups of lemonade were sold that month? I want you to think about what is known, what is unknown, and what multiplication equation is needed.

What will your estimate be? So, this is Alex's estimate: 4 multiplied by 31.

He knows that 31 is in between 30 and 40.

He's multiplied both by 4, which means that 4 multiplied by 31 must be between 120 and 160.

Alex used the expanded method to show his calculation, and you can see that's on the screen there.

And Sophia's used short to show her calculation.

Are they both correct? Have a think.

Do they both match their estimate? Well, both of their answers match their estimate, and they are both correct.

In this case, Sophia's recording is more efficient.

Over to you.

Use estimation to decide which has a suitable answer for this multiplication, 47 multiplied by 3.

Is it A or is it B? If you've got A, you are correct.

A matches the estimation as it is in between 120 and 150.

And how did we get that range? Well, 47 is in between 40 and 50.

We multiply both numbers by 3.

So, 40 multiplied by 3 is 120, and 50 multiplied by 3 is 150.

And we can see here that, in the expanded method, our product is 141.

And 141 is in between 120 and 150.

So, A is correct.

Let's move on.

3 multiplied by 67 is our equation.

Sophia has used short multiplication this time.

Alex has used expanded.

We can see that they've estimated.

So, 3 multiplied by 60 is 180.

3 multiplied by 70 is 210.

The answer must be between 180 and 210.

Now, looking at both answers, we can see that both are between that range.

However, in this case, Izzy may have made a mistake.

Where do you think she made her mistake? You can pause the video here to have a think.

So, Izzy did not include the regrouped tens.

Now, this is very important because sometimes, even when we estimate, we may get a number that is within the range.

So, in this case, it helps to double check the answer.

And when it comes to regrouping, we can see that she did not regroup her 2 tens because 3 multiplied by 7 is 21 ones.

So, she should have placed the 2 underneath in the tens column.

Back to you.

Which method would you use for the following question? 73 multiplied by 8.

I would like you to explain your reason to your partner.

You can pause the video here.

How was that discussion? So, you or your partner may have said something like this.

When using short multiplication, you may find it easier to regroup using this method, and that you may also find that it's a quicker process.

With the expanded multiplication, you may find that it helps you to align your partial products, and you may also find that you just find that method easier to record.

So, back to you.

Choose the correct multiplication for this word problem.

In one month, 78 apples are harvested.

In the following month, 3 times as much is harvested.

How many apples were harvested that month? Is it, A: 3 multiplied by 78; B: 73 multiplied by 8; or, C: 37 multiplied by 8? Pause the video now to have a think.

How did you do? If you got A, you are correct, and that is because our knowns are 78 apples and that there's three times as much, which means we're multiplying by 3.

Our unknown is the product.

Right, onto our final two tasks.

For this task, you are going to be completing the following questions, using expanded or short multiplication.

You'll write the multiplication needed, and then you're going to estimate the answer.

So, 1-A: In one month, 37 cups of lemonade are sold.

The following month, 5 times as many are sold.

How many cups of lemonade were sold that month? 1-B: In one week, 79 cups of lemonade are sold.

The following week, 8 times as many are sold.

How many cups of lemonade were sold that month? Question two: In the third month, 204 lemons are sold in different batches.

Example: two batches of 102.

How many other possible solutions could there be? You can pause the video now.

Off you go.

How did you do? So, for question one, the multiplication equation that you were solving was 37 multiplied by 5, and we know that 37 is close to 40.

40 multiplied by 5 is 200.

When multiplying 37 by 5, your answer should've been 185.

Personally, I would've used short multiplication to answer this question.

For question B, the multiplication equation that you were calculating was 79 multiplied by 8.

Now, 79 is close to 80, so you would've multiplied 80 by 8, which would've given you 640.

So, the answer should be near 640.

When multiplying 8 by 79, your product should've been 632.

So, 632 cups were sold that month.

If you got that question right, well done.

Now, for question two, we were calculating the different possible batches that the 204 lemons could've been sold in.

So, the first example that was given to us were 2 batches of 102.

Here are the other solutions that you could've also had: Three batches of 68; four batches of 51; six batches of 34; and 12 batches of 17.

I wonder, after this lesson, which method you found more efficient, and which method you felt more confident in using.

My favourite is short multiplication, but I also do love using the grid model as well.

Let's summarise our learning.

Today, we estimated and multiplied a two-digit by a one-digit number, using expanded and short multiplication.

You can use times tables facts and place value to estimate the product of a two-digit by a one-digit multiplication.

You can use expanded and short multiplication to multiply a two-digit by a one-digit number.

I hope you enjoyed this lesson as much as I did, and I hope that you remember to estimate before you go into solving any multiplication equations, as this will give you an advantage of knowing whether your answer is close to being accurate or not.

Thank you for joining me.

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What comes next?" }, "questionType": "Multiple choice", "correct": [ { "text": "42" } ], "choices": [ { "text": "40" }, { "text": "41" }, { "text": "42" }, { "text": "43" } ], "id": "a59e33a2-9f96-4e53-432a-f6002d40f255", "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f" }, { "type": "Question", "question": { "text": "Izzy is chanting her 7 times tables in descending order: ... 77, 70, 63, ______ . What comes next?" }, "questionType": "Short answer", "correct": [ { "text": "56" }, { "text": "fifty-six" }, { "text": "Fifty-six" }, { "text": "Fifty six" } ], "id": "341d5847-1c09-ba96-0df8-37838870a0a1", "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f" }, { "type": "Question", "question": { "text": "Use short multiplication to calculate this question: 56 × 3 = ______" }, "questionType": "Short answer", "correct": [ { "text": "168" }, { "text": "one hundred and sixty eight" }, { "text": "One hundred and sixty eight" } ], "id": "1b5d187f-143c-f0ed-cda3-1b4b5939bec1", "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f" }, { "type": "Question", "question": { "text": "Use expanded multiplication to calculate this question: 74 × 5= ______" }, "questionType": "Short answer", "correct": [ { "text": "370" }, { "text": "Three hundred and seventy" }, { "text": "three hundred and seventy" } ], "id": "66e06a12-f229-47c2-fb9e-a128356f3686", "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f" }, { "type": "Question", "question": { "text": "Sam has 71 shiny cards, Izzy has 213 shiny cards. Izzy has ______ times as many." }, "questionType": "Short answer", "correct": [ { "text": "3" }, { "text": "three" }, { "text": "Three" } ], "id": "eec4e8b7-6312-99df-672e-02d0cba4ba07", "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f" } ], "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 5", "topic": null, "unit": "Multiplication by partitioning leading to short multiplication (2 by 1-digit)", "lessonCount": "10", "age": [ 9, 10 ], "gradeId": "age_9_10", "gradeStage": "Key Stage 2", "lesson": "Estimate and multiply a 2-digit by a 1-digit number using expanded and short multiplication" } }, { "id": "935fb19e-c2fb-dd01-fc19-3657baf2153d", "type": "Resource", "resourceType": "Quiz", "title": "Estimate and multiply a 2-digit by a 1-digit number using expanded and short multiplication", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "To estimate for the calculation: 4 × 72, 72 is between __________." }, "questionType": "Multiple choice", "correct": [ { "text": "70 and 80" } ], "choices": [ { "text": "60 and 70" }, { "text": "70 and 80" }, { "text": "65 and 70" } ], "id": "c38ad507-21e5-7edb-07cd-9136cccdc84e", "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f" }, { "type": "Question", "question": { "text": "Select the correct number to complete the estimation.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137204%2Fukbq2ueo0wrivouxbmpz.png&w=640&q=75", "imageKey": "935fb19e-c2fb-dd01-fc19-3657baf2153d/question/394da359590b1e0bf95cc31d12bf5a76.png" }, "questionType": "Multiple choice", "correct": [ { "text": "280" } ], "choices": [ { "text": "28" }, { "text": "74" }, { "text": "208" }, { "text": "280" } ], "id": "981da355-5802-6a12-5902-3f07783956db", "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f" }, { "type": "Question", "question": { "text": "Write the correct number to complete the estimation.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137224%2Fjfuvsv9jxzrucsrqqewv.png&w=640&q=75", "imageKey": "935fb19e-c2fb-dd01-fc19-3657baf2153d/question/c061ae545ca866640c5af45f8ac455dd.png" }, "questionType": "Short answer", "correct": [ { "text": "360" }, { "text": "Three hundred and sixty" }, { "text": "three hundred and sixty" } ], "id": "1ba8a9f3-2cb8-20fd-0866-d60d25e89232", "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f" }, { "type": "Question", "question": { "text": "Select an appropriate estimation for 63 × 3" }, "questionType": "Multiple choice", "correct": [ { "text": "60 × 3" } ], "choices": [ { "text": "65 × 3" }, { "text": "60 × 3" }, { "text": "70 × 3" }, { "text": "6 × 3" } ], "id": "6826cdd2-558e-95a5-18b0-2aefba393037", "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f" }, { "type": "Question", "question": { "text": "Use estimation to decide which has a suitable answer for this multiplication: 46 × 3", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137209%2Fuffmzxihamj8vnblmvrr.png&w=640&q=75", "imageKey": "935fb19e-c2fb-dd01-fc19-3657baf2153d/question/e30044156016d4b43abbb683404a3cc5.png" }, "questionType": "Multiple choice", "correct": [ { "text": "A" } ], "choices": [ { "text": "A" }, { "text": "B" } ], "id": "ef8140bc-9597-3a08-4ebc-0e95af0a905d", "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f" }, { "type": "Question", "question": { "text": "Solve the worded problem using short multiplication: In one month 34 cups of lemonade are sold. The following month, six times as many are sold. How many cups of lemonade were sold that month?" }, "questionType": "Short answer", "correct": [ { "text": "204" }, { "text": "204 cups" }, { "text": "Two hundred and four" }, { "text": "Two hundred and four cups" }, { "text": "two hundred and four cups" } ], "id": "4bb59598-4bfe-5532-c902-548b82169f4f", "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f" } ], "lessonId": "688f3284-ddc2-c562-0f93-ef537800e11f", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 5", "topic": null, "unit": "Multiplication by partitioning leading to short multiplication (2 by 1-digit)", "lessonCount": "10", "age": [ 9, 10 ], "gradeId": "age_9_10", "gradeStage": "Key Stage 2", "lesson": "Estimate and multiply a 2-digit by a 1-digit number using expanded and short multiplication" } } ] }