my homework lesson 9 multiply by a multi digit number

Curriculum  /  Math  /  4th Grade  /  Unit 2: Multi-Digit Multiplication  /  Lesson 9

Multi-Digit Multiplication

Lesson 9 of 18

Criteria for Success

Tips for teachers, anchor tasks.

Problem Set

Target Task

Additional practice.

Lesson Notes

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Multiply four-digit numbers by one-digit numbers.

Common Core Standards

Core standards.

The core standards covered in this lesson

Number and Operations in Base Ten

4.NBT.B.5 — Multiply 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.

Foundational Standards

The foundational standards covered in this lesson

3.NBT.A.3 — Multiply one-digit whole numbers by multiples of 10 in the range 10—90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

4.NBT.B.4 — Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Operations and Algebraic Thinking

3.OA.B.5 — Apply properties of operations as strategies to multiply and divide. Students need not use formal terms for these properties. Example: 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.) Example: 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.)

3.OA.C.7 — Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Multiply a four-digit whole number by a one-digit whole number using area models and the partial products algorithm. 
• Understand that partial products can be written in increasing or decreasing order when recording them vertically. 
• Estimate products by rounding factors to the largest place value. 
• Solve one-step word problems involving multiplication of four-digit by one-digit numbers (on the Problem Set and Extra Practice Problems) (MP.4).

Suggestions for teachers to help them teach this lesson

Note that the last Criteria for Success is not addressed in the Anchor Tasks below, since each problem type involving multiplication has been explored in previous lessons. However, if it seems students need additional practice with any type (particularly multiplicative compare with larger unknown), then you can use the values in Anchor Task 2 in the context of a word problem.

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

25-30 minutes

A student solved 4 × 2,387 below: 

a.   How is this different from the way we recorded partial products previously? 

b.   Did this way of recording the partial products give the correct product? Use an area model and/or the way we recorded partial products yesterday to check. 

Guiding Questions

Student response.

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Estimate the product. Then use any method to solve. 

a.     $$8 \times 5,289$$

b.     $$3,067 \times 6$$

15-20 minutes

• Problem Set Answer Key

Discussion of Problem Set

• Can you represent #3 with an area model to solve even though it’s a problem involving arrays? Why or why not? 
• Whenever there is a 0 in a factor, what does that mean about how many sections of an area model there will be? What about how many partial products there will be in the partial products algorithm? 
• In #4, can you use the expression (6 x 5,000) + (6 x 400) + (6 x 70) + (6 x 9) to solve 6 x 5,479? How is this related to the partial products algorithm? 
• I think the product in #2c is 1,490. What mistake do you think I made? What if I thought the answer was 149? 
• Did you use any strategies from Lesson 6 to solve any problems on today’s Problem Set? For example, #2c or #5c?

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

5-10 minutes

Which strategy for multiplying 5,712 and 4 should result in the correct product?

a.   Explain why the expression (4,000 + 20 + 5) × 6 can or cannot be used to find the value of 4,025 × 6.

b.   Compute 4,025 × 6.

A pencil is 7 inches long. The Empire State Building is 2,492 times as tall as a pencil. How tall, in inches, is the Empire State Building?

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

• Extra Practice Problems Answer Key

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Multiply two-, three-, and four-digit numbers by one-digit numbers and assess the reasonableness of the product.

Topic A: Multiplicative Comparison

Solve multiplicative comparison problems with a larger unknown. Distinguish multiplicative comparison from additive comparison.

4.OA.A.1 4.OA.A.2

Solve multiplicative comparison problems with a smaller unknown.

Solve multiplicative comparison problems with an unknown multiplier. Interpret a multiplication equation as a comparison.

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Topic B: Multiplication of up to Four-Digit Whole Numbers by One-Digit Whole Numbers

Multiply 10, 100, and 1,000 by one- and two-digit numbers.

Multiply multiples of 10, 100, and 1,000 by one-digit numbers. Estimate multi-digit products by rounding numbers to their largest place value.

Multiply two-, three-, and four-digit numbers by one-digit numbers using a variety of mental strategies.

Multiply two-digit numbers by one-digit numbers.

Multiply three-digit numbers by one-digit numbers.

Topic C: Multiplication of Two-Digit Whole Numbers by Two-Digit Whole Numbers

Multiply two-digit multiples of 10 by two-digit multiples of 10. Estimate multi-digit products by rounding numbers to their largest place value.

Multiply two-digit multiples of 10 by two-digit numbers.

Multiply two-digit numbers by two-digit numbers using a variety of mental strategies.

Multiply two-digit by two-digit numbers using four partial products.

Multiply two-digit by two-digit numbers using two partial products and assess the reasonableness of the product.

Topic D: Multi-Step Word Problems

Abstract the formulas for the area and perimeter of a rectangle and apply those formulas in real-world and mathematical problems involving multiplication, addition, and subtraction.

4.MD.A.3 4.OA.A.3

Solve two-step word problems involving multiplication, addition, and subtraction.

4.OA.A.2 4.OA.A.3

Solve multi-step word problems involving multiplication, addition, and subtraction.

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Strategies for Teaching Multi-Digit Multiplication

• Freebies , Math , Planning , Strategies

Common Core requires that we teach students strategies before we introduce them to the traditional algorithms. When it comes to teaching multi-digit multiplication, it’s common for teachers to focus solely on the partial products method and forget about the rest. Instead, I like to scaffold my students’ learning first so that they are ready for both partial products and the traditional algorithm with more concrete methods.

It’s important that we are teaching students in the way that they learn best. One method of scaffolding is to start all concepts in a concrete manner and then work toward a more abstract manner. I talk about this in my post, Teaching Math so Students Get It . In this case of teaching my students how to multiply multi-digit numbers, I first start with the area model, then work up to the box model, introduce the distributive property, and then move into the partial products method. Depending on your grade level and standards, then you may teach the traditional algorithm after. This allows for scaffolding, instead of rescuing students later on.

The Area Model as a Multi-Digit Multiplication Strategy

When I introduce my students to the area model, I first remind them of what this model looks like with basic multiplication numbers, such as 7 x 8. I provide students with base-ten blocks and have them create an array. Then I ask them to “just try” creating one with a larger number such as 27 x 4. Then, depending on how that goes, we will create the model. I will either model it or guide them. I remind students of place value and together we first create the sides of our array. For instance, in the problem 27 x 4, we create the two tens and the seven ones using our base ten blocks on one side and create the four ones on the other.

Next, we have to fill in the space to create an array. I express that we could do this with actual one base ten blocks, but it would take us a long time. Instead, it would be best to use the larger ones that would fit. This is an important step because later they will need this when they get to double digits and with understanding division. Once everything is filled in, we now count our total blocks for that section and add them up to get our final answer. You can see this in the anchor charts below, found in my fourth grade multi-digit multiplication math workshop unit (or found on TpT here ).

Using the area model with 2-digit numbers by 2-digit numbers is essentially the same, except the area model is just a bit larger. (I don’t recommend moving into the 2-digit by 2-digit model until after you have had plenty of practice with all of the multi-digit numbers by 1 digit. This post is to assist all multi-digit multiplication needs.) This area model typically involves more tens and hundreds.

The Box Model as a Multi-Digit Multiplication Strategy

The box model follows the area model perfectly!

As seen in the image below, I typically create an area model first and then draw boxes around it to show my students the relationship between the two. Instead of actually usually manipulatives (concrete), we are now moving into drawing our models. In fact, in my math workshop and in my class, I often have my students draw symbols of the base-ten blocks after they have created the area model, so the transition is even nicer.

Now students are in the semi-concrete or representational stage. They are drawing the boxes and placing the numbers outside the box so that they can determine the answers for each box through multiplication.

The box model is really no different except that now they are not physically manipulating any base-ten blocks. This is a great time to mention decomposing, because that will be something you’ll be mentioning a lot during both the distributive property and later in other concepts, such as area.

When I talk about decomposing, I like to remind my students that this is really no different than what they did when they broke numbers up into the expanded form.

When students work on the 2-digit numbers by 2-digit numbers, they are now working with a 4-square box. Just as before, they are only multiplying the boxes in a grid-like way and then adding them up. See the charts below for a more detailed explanation.

The Distributive Model as a Multi-Digit Multiplication Strategy

For some reason, teachers don’t like to tackle the distributive property and/or the students fear it. But, if you have worked your way up using the previous methods, this strategy isn’t as scary as it appears.

Since we just talked about decomposing numbers in the last strategy, students should now know they can take the larger number and break it up into smaller numbers. I give them the freedom to choose how they break it up. Then I provide them with boxes to break it up and multiply away!

Down at the bottom of this distributive property chart (above), you can see that I have turned the box sideways and have used colored pens. I did this intentionally before I moved into partial products. I wanted to make sure students are seeing what each box is made up of. For instance, the first box (in red) is 100 x 6, the second box (in yellow-orange) is 20 x 6, and the third box is 3 x 6. Then I showed them how it’s written out and added up. I did this for two reasons. First, because they will see this again when we get to partial products (next), and second because they will see it when they learn to use the distributive property in algebra (FOIL) later.

Partial Products as a Multi-Digit Multiplication Strategy

Most teachers are likely aware of the Partial Products method. In case you are not, it’s really just taking the larger number and breaking it out into expanded form and then having the other factor multiply each of the expanded form factors. Then they are added up to get the final product. (See chart below.)

You’ll notice that my colors are back. Whenever possible, I use colors to help differentiate each step. I remind students that we are using the distributive property (which is not scary now!) and decompose our larger number into the expanded form. Then we multiply each new factor one at a time. I always write each new product with the multiplication problem next to it so students can see where I got it from. Then, after we have found all the products to each of those, we add them up to find our final product. This strategy also helps later when introducing the “placeholder” in the traditional algorithm.

When we get to double digits, it is the same thing, but I like to introduce a method called the “bow tie method.” Just as before, students would decompose both factors into an expanded form. Then they multiply in a bow tie method. If you look at the illustration below, you can see this method through the use of the colors. I actually have my students draw it on their papers to help them so they don’t miss a factor as they are multiplying. As they work through the bow tie method, they record the products for each one. Once finished, they add the products together to get the final product.

Understandably, if you prefer to have your students begin preparing for the traditional algorithm, you could have them do the “bow tie” method in the traditional algorithm motions, like in the chart below. Overall, the point of the “bow tie” method is to make sure no factors are missed or hit twice.

For students to truly be ready for multi-digit multiplication with the traditional algorithm, they must first go through the strategies that Common Core requires. This requires us to also teach in the way that students learn best. If you want your students to do well with multi-digit multiplication, you will need to scaffold the concepts by first starting with the concrete method of using an area model, working to a semi-concrete, representational model of the box method, and then into both the distributive property and the partial products method.

Using just one method will not cut it. Students need this gradual release with multi-digit multiplication before they’ll be ready or they just won’t fully understand the concept and be successful.

Grab the FREEBIE!

To help your students practice these strategies, I have a freebie to get you started! Click here to download the freebie!

Then check out my multi-digit multiplication lesson plans, games, and activities that go along with these anchor charts so that you can save time lesson planning today. Purchase the 4th grade Large Numbers Multiplication Math Workshop Unit here on my website or found on TpT by clicking here .

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• → Curriculum
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Multiply Multi-Digit Whole Numbers Lesson Plan

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Multi Digit Multiplication Whole Numbers Guided Notes with Doodles Sketch Notes

Ever wondered how to teach multi-digit multiplication of whole numbers in an engaging way to your 5th-grade students?

In this lesson plan, students will learn about multiplying multi-digit whole numbers using the standard algorithm and their real-life applications. Through artistic, interactive guided notes, check for understanding, practice activities like a doodle & color by number activity, and a maze worksheet, students will gain a comprehensive understanding of multi-digit multiplication.

The lesson ends with a real-life example that explores how multi-digit multiplication of whole numbers is used in practical, everyday situations such as order purchases, merchandise organization. Then, they reflect on their learning and mastery of this topic through self assessments and short prompts.

• Standard : CCSS 5.NBT.B.5
• Topic : Factors, Multiples & Divisibility
• Grade : 5th Grade
• Type : Lesson Plans

Learning Objectives

After this lesson, students will be able to use the standard algorithm to:

Multiply two-digit numbers by one-digit numbers

Multiply two-digit numbers by two-digit numbers

Multiply three-digit numbers by one-digit numbers

Multiply three-digit numbers by two-digit numbers

Prerequisites

Before this lesson, students should be familiar with:

Basic understanding of regrouping or carrying over in addition and subtraction

Colored pencils or markers

Multi Digit Multiplication Whole Numbers Guided Notes with Doodles

Key Vocabulary

Multi-Digit

Whole Numbers

Introduction

As a hook, ask students why knowing how to multiply multi-digit whole numbers is important in everyday life. Refer to the last page of the guided notes as well as the FAQs below for ideas.

Use the first page of the guided notes to introduce multiplying 2-digit numbers by 1-digit numbers. Walk through the steps involved in this multiplication process while students fill in the blanks on their guided notes (pg. 1), emphasizingƒsetting up the problem by stacking the numbers to the right. Model the first two or three examples on the page so they see how to use the steps. Students will then see how to multiple 3-digit numbers by 2-digit numbers. Model the multiplication process using examples and emphasize the significance of placing zeroes when moving to the next place value.

Use the second page of the guided notes to allow students to practice how to use the standard algorithm to multiple whole numbers. There are 3 levels of practice that increases in difficulty. Level 1 contains multiplication of 2-digit by 1-digit numbers. Level 2 contains multiplication of 2-digit by 2-digit numbers. Level 3 contains multiplication multiplication of 3-digit by 2-digit numbers.

Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.

Continue with the third page of the guided notes for a fun maze activity ! Students will solve multi-digit multiplication problems to escape the maze. Walk around to answer student questions.

Then, use the fourth page of the guided notes for a fun color by number activity . Students solve math problems to unlock colors to fill in an image. Fast finishers can also be assigned this activity for extra practice. Alternatively, you can assign it as homework for the remainder of the class.

Real-Life Application

Use the last page of the guided notes, called real life applications, to bring the class back together, and introduce the concept of using multidigit multiplication in real-world scenarios. Students read about how it can be used in calculating the total cost of purchasing multiple items at a store, determining the area of a rectangular garden, or organizing merchandise in a factory. Then, they reflect on their learning and confidence about this math topic.

Additional Self-Checking Digital Practice

If you’re looking for digital practice for multiplying whole numbers, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.

Here’s 1 activity to explore:

Multiplying Multi-Digit Whole Numbers Pixel Art | Products | Google Sheets

Additional Print Practice

A fun, no-prep way to practice multiplying whole numbers is Doodle Math — they’re a fresh take on color by number or color by code. It includes multiple levels of practice, perfect for a review day or sub plan.

Here are 1 activity to try:

Multidigit Multiplication Doodle Math Twist on Color by Number | Product

What are multi-digit whole numbers? Open

Multi-digit whole numbers are numbers that consist of two or more digits, without any decimal or fraction parts.

How can I multiply multi-digit whole numbers? Open

To multiply multi-digit whole numbers, follow these steps:

Place the numbers so that one number is above the other, and stacked to the right.

Multiply each digit of the bottom number by each digit of the top number, starting from the rightmost place value.

Carry over, if needed.

Repeat with the next digit on the bottom. Place zeroes in the appropriate spot, if needed.

Add the partial products together to get the final product.

Why is it important to learn how to multiply multi-digit whole numbers? Open

Learning to multiply multi-digit whole numbers is important because:

It helps in solving real-world problems involving large quantities.

It builds a strong foundation for more advanced math concepts.

It improves mental math skills and overall math proficiency.

Can you provide examples of practice problems for multiplying multi-digit whole numbers that are similar to the ones in the guided notes? Open

Sure! Here are a few examples:

What strategies can I use to solve multi-digit multiplication problems? Open

Some helpful strategies for solving multi-digit multiplication problems include:

Partial products method

Lattice method

Standard algorithm method

*In this guided notes, only the standard algorithm is used.

How can I check my answers when multiplying multi-digit whole numbers? Open

You can check your answers by:

Estimating the product and comparing it to the actual answer.

Using a calculator to verify the multiplication.

Reversing the operation (division) to see if you get back the original numbers.

Are there any real-life applications of multiplying multi-digit whole numbers? Open

Yes, multiplying multi-digit whole numbers is used in various real-life situations such as:

Calculating total costs when buying multiple items

Determining area and perimeter of objects

Solving problems related to time, distance, and speed

Want more ideas and freebies?

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Number & Operations in Base Ten – 4th Grade

Use place value understanding and properties of operations to perform multi-digit arithmetic..

CCSS.Math.Content.4.NBT.B.5 Multiply 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.

Teacher Notes The teacher needs to understand how place value helps students find the product in multi-digit multiplication problem.  It is important to use multi-digit multiplication problems to reenforce place value. Example: "Four tens times three tens is twelve tens.  Regroup and put one in the hundreds and two in the tens." Students who develop flexibility in breaking numbers apart have a better understanding of the importance of place value and the distributive property in multi-digit multiplication.

Student Knowledge Goals

Vocabulary area model Commutative Property of Multiplication Distributive Property of Multiplication over Addition equal groups equation factor Identity Property of Multiplication partial product place value product rectangular array strategy

Lessons Engage NY Module 3 B-4 – Interpret and represent patterns when multiplying by 10, 100, and 1,000 in arrays and numerically. Engage NY Module 3 B-5 – Multiply multiples of 10, 100, and 1,000 by single digits, recognizing patterns. Engage NY Module 3 B-6 – Multiply two-digit multiples of 10 by two-digit multiples of 10 with the area model. Engage NY Module 3 C-7 – Multiplication of up to Four Digits by Single-Digit:  Use place value disks to represent two-digit by one-digit multiplication. Engage NY Module 3 C-8 – Extend the use of place value disks to represent three- and four-digit by one-digit multiplication. Engage NY Module 3 C-9 – Multiply three- and four-digit numbers by one-digit numbers applying the standard algorithm. Engage NY Module 3 C-10 – Multiply three- and four-digit numbers by one-digit numbers applying the standard algorithm. Engage NY Module 3 C-11 – Multiply three- and four-digit numbers by one-digit numbers applying the standard algorithm.

Student Video Lessons Learn Zillion - Multiply Multi-Digit Whole Numbers Learn Zillion - Solve multiplication problems Study Jams – Distributive Property Virtual Nerd – Multiplication

Online Problems, Games, and Assessments Khan Academy – Questions and Video Lessons Multiply 1-digit numbers by 2-digit numbers Multiply 1-digit numbers by 3-digit or 4-digit numbers Multiplication patterns over increasing place values Properties of multiplication Distributive property: find the missing factor Multiply using the distributive property Multiply a 2-digit number by a 2-digit number: complete the missing steps Multiply a 2-digit number by a 2-digit number Multiply numbers ending in zeroes

Printables Multiplication – Single & Multi-Digit 4.NBT.B.5 - 60 pages of PDF worksheets

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5.4 Wrapping Up Multiplication and Division with Multi-Digit Numbers

• Students use the standard algorithm to multiply multi-digit whole numbers. They divide whole numbers up to four-digits by two-digits divisors using strategies based on place value and properties of operations.

Section A Goals

• Multiply multi-digit whole numbers using the standard algorithm.

Section B Goals

• Divide multi-digit whole numbers using strategies based on place value, properties of operations, and the relationship between multiplication and division.

Section C Goals

• Multiply and divide to solve real-world and mathematical problems involving area and volume.

Section A: Multi-digit Multiplication Using the Standard Algorithm

Estimate and find products, partial products in diagrams, partial products in algorithms, standard algorithm: one-digit and multi-digit numbers with composing, standard algorithm: multi-digit numbers without composing, standard algorithm: multi-digit numbers with composing.

PLC Activity

Build Multiplication Fluency

Multiplication fluency, section b: multi-digit division using partial quotients, world’s record folk dance, different partial quotients, an algorithm using partial quotients, divide using partial quotients, practice an algorithm using partial quotients, find missing side lengths, world’s record noodle soup, fractions as partial quotients (optional), section c: let’s put it to work, lots of milk, shipping trash, food waste journal (optional).

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McGraw Hill My Math Grade 5 Chapter 2 Lesson 10 Answer Key Multiply by Two-Digit Numbers

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 2 Lesson 10 Multiply by Two-Digit Numbers  will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 2 Lesson 10 Multiply by Two-Digit Numbers

Find 44 × 12. Estimate 44 × 10 = ____

Helpful Hint By estimating first, you can determine if your answer is reasonable.

Guided Practice

Independent Practice

Estimate. Then multiply. Use your estimate to check your answer.

Question 8. 21 × 42 = ____ Answer: 882

Question 9. 69 × 14 = ____ Answer: 996

Question 10. 83 × 367 = ____ Answer: 30461

Problem Solving

Question 14. Marshall’s mother buys 2 boxes of granola bars each week. Each box contains 8 granola bars. If she continues buying 2 boxes each week, how many granola bars will she buy in a year (1 year = 52 weeks)? Answer: 832 granola bars.

Explanation: If Marshall’s mother continues to buy two boxes each week Marshall’s mother will have 832.

Question 15. Mathematical PRACTICE 5 Use Math Tools A delivery truck travels 278 miles each day. How far does it travel in 25 days? Answer: 6950

Explanation: Given, Speed = 278 miles Time = 25 days Distance = Speed × time = 278 × 25 = 6950

Question 16. A cow can eat 25 pounds of hay a day. At that rate, how many pounds of hay can a cow eat in 31 days? Answer: 775 pounds

Explanation: The cow eats 25 pounds of hay a day. Can a cow eat in 31 days? 25 × 31 = 775 So the cow eats 775 pounds of hay in 31 days.

Hot Problems

Question 17. Mathematical PRACTICE 2 Use Number Sense Find 235 × 124. Use the same strategy that you used for multiplying by a two-digit number except include multiplying by the hundreds place. Answer: 29140

Explanation: 235 × 124 = 29140

Question 18. ? Building on the Essential Question How do you multiply by two-digit numbers? Answer: Step 1: Estimate the product using the nearest ‘tens‘ to verify the answer. Step 2: Multiply any one of the numbers by the ‘ones’ digit of the second number. Step 3: Multiply the number by the tens digit of the number. Step 4: Finally, add the two partial products to get the final product and verify it with the estimated product.

McGraw Hill My Math Grade 5 Chapter 2 Lesson 10 My Homework Answer Key

Question 3. 470 × 56 = ____ Answer: 26320

Question 4. Ms. Jenkins was arranging chairs for a school awards assembly. Each row contained 15 chairs. If there were 21 rows, how many chairs had to be arranged? Answer: 315 chairs had to be arranged.

Explanation: Jenkins was arranging chairs for a school awards assembly No of chairs in each row = 15 Then multiply the number of chairs in 21 rows 15 × 21 = 315

Question 5. Leon earns $14 an hour. How much does he earn in 4 weeks if he works 12 hours each week? Answer: $672

Explanation: He worked a total of 12 × 4 = 48 Then multiply that by 14 × 28 =672 $672

Question 6. Mathematical PRACTICE 5 Use Math Tools Without actually calculating, how much greater is the product of 98 × 50 than the product of 97 × 50? Answer: (98 – 97) × 50 = 1 × 50 = 50 98 × 50 is greater than 97 × 50 by 50.

Explanation: (5 × 12 + 8 × 14)  × 12 (60 + 112) × 12 172 × 12 $2064 The buckets indicate the money earned each week.

Test Practice

Question 8. Each day there are 12 tours at the glass factory. Twenty-eight people can go on a tour. How many people can tour the glass factory each day? A. 236 people B. 280 people C. 336 people D. 436 people Answer: 336 people

Explanation: Each day there are 12 tours at the glass factory, and on each tour 28 people can assist, in order to know how many people can tour the glass factory 12 × 28 = X 336 = X

Fluency Practice Mathematical practice 6

Fluency Practice

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