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Lesson Plan: Word Problems: Multiplication and Division Mathematics • 3rd Grade
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to solve one- and two-step problems where one of the steps involves multiplying or dividing numbers using multiplication facts up to 10 × 10.
Students will be able to
- identify whether a word problem can be solved by using multiplication or division,
- write equations to represent word problems,
- solve one- and two-step word problems involving multiplication and division,
- use multiplication or division to check the answer to a word problem.
Prerequisites
Students should already be familiar with
- multiplication facts up to 1 0 × 1 0 ,
- addition and subtraction of two-digit numbers,
- using bar models to model word problems,
- the fact that multiplication and division are inverse operations.
Students will not cover
- using fractions or decimals,
- solving problems with more than two steps.
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Math Word Problems
Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.
There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:
- Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
- Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
- Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
- Calculate : Use your strategy to solve the problem.
- Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.
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This worksheets combine basic multiplication and division word problems. The division problems do not include remainders. These worksheets require the students to differentiate between the phrasing of a story problem that requires multiplication versus one that requires division to reach the answer.
Mixed Multiplication and Division Word Problems 1
Mixed Multiplication and Division Word Problems 2
Practicing the operations seperately is a good start for each operation, but an important word problem skill is also figuring out which math operation is needed to solve a specific question. The worksheets in this section combine both multiplication word problems and division word problems on the same worksheet, so students not only need to solve the problem but they need to figure out how to do it.
By moving into these worksheets quickly, it avoids the crutch where students learn that they always need to add or always need to subtract the two values in a problem to get the answer. This forces students to really understand the intent of the problem, not just scan the text looking for numbers.
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Lesson 6 multiplication and division in word problems
Lesson 6 multiplication and division in word problems is a mathematical tool that helps to solve math equations.
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Multiplication and Division in Word Problems
Unit 2 - Lesson #6: Multiplication as a Comparison Unit 2 - Lesson #7: Multiplication and Division in Word Problems Unit 2 - Lesson #8: Multiples and Factors.
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Lesson 6 Multiplication and Division in Word Problems. Solve. 3 Yesterday Ruth scored 2 points at the game. Today she scored 8 times as many points as she
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Multiplication and division in word problems lesson 6
Lesson 6 Multiplication and Division in Word Problems. Solve. 3 Yesterday Ruth scored 2 points at the game. Today she scored 8 times as many points as she
Lesson 6: Fractions
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In this lesson, we will learn how to solve one- and two-step problems where one of the steps involves multiplying or dividing numbers within the times
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Multiplication and Division in Word Problems
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Multiplication and Division Word Problem Types
Word problems can be such a struggle. Especially in grades 3rd and up when students have to work through all of the operations and multi-step word problems. Students often struggle to identify the operation presented, or miss part of the steps needed to solve. Explicitly teaching word problem types can help our students recognize the operations in context. The Common Core State Standards lay out the different multiplication & division word problem types that students should know. By teaching them explicitly, we help students understand multiplication and division in context to help them truly understand the operations. We connect how the math they’re learning is relevant to their real life. By focusing on the word problems and their types, we’re focusing on what makes multiplication and division what they are.
This post takes an in-depth look at each of the multiplication & division word problem types. I also give some helpful links at the bottom that discuss Cognitively Guided Instruction, or CGI problem types. They use slightly different vocabulary than the CCSS but are the same set of skills. An important note- when I talk about teaching the multiplication & division word problem types explicitly, I don’t mean that they’re only practiced during a specific unit, or that we teach specific keywords for each problem type. Students need to read the problem and understand the context. Recognizing the problem type can support that work, but it’s not focused on keywords. I also do a daily word problem outside of our focused unit work. I firmly believe in spiraling the standards in word problems so students have to focus on context to solve. For more support with problem solving, check out my Why Your Students Struggle with Word Problems, and What You Can Do About It post.
An important note before we begin-throughout our exploration of both operations, we often return back to the total . We identify in our first lesson that multiplication allows us to find the total number of objects arranged in equal groups. When we begin exploring division, we know the total number of objects we have and have to find the unknown in connection with groups. Throughout our work, with arrays, area, and equal groups, we continue to come back to the concept of total to help students identify the operation needed. It is through identifying the total as known or unknown that students will truly understand the multiplication and division operations. As you will see, that’s a focus with each of the multiplication and division word problem types.
Equal Groups as Multiplication & Division
In my Introducing Multiplication and an Working with Division posts I walk through my hands-on, engaging lessons I use to introduce each operation. When introducing both operations, we focus on equal group arrangements. It’s crucial for students to understand that multiplication and division works with equal groups so it makes sense to begin here. When we first start working with multiplication and division word problems, I ask students to identify the items that are arranged in groups, and identify what that group looks like. For example, the group might be a box or a bag. Those objects could also just be objects in other scenarios. So, identifying that an object is grouped within something helps students to understand the word problem and that an equal group scenario is present.
MULTIPLICATION – Total Unknown
These are the word problems we typically think of with multiplication. It’s an arrangement of items into equal groups to find the total number of items. Identifying that the number of groups and the number of items into each group are known, while the total is unknown, helps students solve these word problems.
QUOTATIVE DIVISION – # of Groups Unknown
When the number of groups are unknown, it is a quotative division problem. Let me clear, I don’t teach my students the term quotative . Rather, I teach them that there are two types of division. When students are able to identify that the total number of objects is known, but the number of groups is unknown, they then know that they are dividing. It’s important that students have lots of practice with both types of division.
PARTITIVE DIVISION – # in each Group Unknown
When a word problem identifies the total number of items and how the items are arranged, but doesn’t give the number in each group, these are partitive division. Think of it as partitioning . The number of groups is known so the partitions are known. Again, I don’t teach this term with my students, but it’s important that students know that division is presented in two ways.
Once both operations have been introduced and practiced separately, I like to use my Multiplication & Division Scenario Tables Task Cards to practice writing equations and understanding group arrangements in context. I find that removing all of the components of the word problem, and working through just the total and group information, helps students truly understand the operations in connection with equal groups. This helps them then apply their learning within word problems. Students get practice with different ways items can be grouped, which helps them look for and identify grouping relationships in word problems later.
Arrays as Multiplication & Division
In conjunction with teaching equal group arrangements described above, arrays should also be included. Arrays are how students are first introduced to multiplication in 2nd grade. Students should have background knowledge with rows and columns vocabulary. Arrays are how I connect what we’re learning now, with what they learned before. Therefore, I teach arrays at the same time that I teach equal group arrangements. I correlate rows and the number of groups. I always emphasize that the columns are the same as the number in each row (or the group).
It’s important to note that the CCSS lay out two rigors of array word problems: ones where the items in rows are presented, and those that give the word problem in rows and columns. Through continued exposure and practice, students understand that these are interchangeable. Array word problems are not very common, but are definitely a problem type that students should have exposure and practice with. They also lay the foundation for students to work with our next word problem type: area
Area as Multiplication and Division
Area is a critical component of our multiplication and division work. It’s a major part of 3rd grade math instruction and it’s important that students work with many word problems where they have to recognize area in context and solve. This is especially important to learn how to differentiate between area and perimeter by making connections between arrays and what is known about multiplication and division. Area should be introduced with arrays and connected to an area model. This concrete, visual example helps students connect what they already know (arrays) with their new learning (area). Unit squares are written in the standards to be this bridge. Area models continue on as you work with more the more complex rectilinear figures, and to help students understand the distributive property of multiplication . The CCSS don’t list area problems as their own line, rather, they’re included with arrays. While this certainly makes sense since arrays can be created inside the rectangle, and that’s how area should be introduced, most area word problems don’t use rows or columns when providing side lengths. I think it’s an important distinction to look at area word problems separate from arrays.
MULTIPLICATION
Solving area problems again connects back to total and known/unknown values. When students are trying to identify the total area of the shape, and are given both side lengths, students need to multiply to find the area.
When students are given the total area of the shape, but need to find a missing side length, they must divide.
Ultimately, if students have a solid understanding of multiplication and division word problems and their connection to total , they will likely be successful with area word problems.
Comparison Word Problems
The most complex multiplication and division word problem types are comparison word problems, in my opinion. Just as they are in addition & subtraction , the way these problems are structured, cause them to be more complex than the others. For these, it’s important to look at each of the different problem types and digest what’s being given. I use a 3 Reads Routine when working through word problems, and these problems always bring the greatest discussion as students grapple with the information that’s presented.
The multiplication and partitive division (constant unknown) examples have very similar wording since they both have the comparison statement: “6 times as much”. This is a description of the relationship between two groups-the total, and the comparison group. The quotative (comparison) example is worded differently since the unknown is the comparison relationship: “How many times as much does”
The key to understanding multiplicative comparison problems is that the comparison is the repeating groups, whereas the constant is the group size.
In a multiplication word problem , you are told the amount in the comparison group, 6, and the constant, 4. Each bag of apples is $4, so if it’s 6 times as much, it’s the same as having 6 of the bags. Thus, 4 x 6.
In a ( partitive) division word problem , you are given the total number (the cost of the box of apples). Once you partition, or divide, that cost into 6 equal groups, you are able to identify the cost of one of those groups, which is the same as the cost of the small bag of apples, and that is the same as the number of ducks.
In a ( quotative) division word problem, you are given the constant, the cost of the small bag, along with the cost of the box of apples. The unknown is the relationship between them. With these word problems, the wording of the question can often throw students off.
Once students are able to decompose the word problem to identify the total, and the comparison, they’re able to connect that to what they already know about multiplication and division to help them when solving. Teaching students to closely read the word problem is key. To read more about my 3 Reads Routine you can click the image below.
Looking for additional resources? You can download my Multiplication & Division Word Problem Types reference sheet and use it to help identify and write the different word problem types for classroom practice.
Want additional multiplication & division word problem practice? I have a FREE Multiplication & Division Word Problem Task Cards set. Each of the multiplication & division word problem types discussed here are practiced during the 24 task card set. This is great practice for later in the year to ensure students have ample practice with each type. It would even be a great tool to help students discuss the different problem types and how they’re presented. To download the Multiplication & Division Word Problem Type Task Cards, just fill out the form below and they’ll be sent straight to your email.
Sign up to receive your free Multiplication & Division Word Problem Types Task Cards! After confirming your email, you’ll receive the file and be signed up for my weekly newsletter.
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You might also find the following links helpful.
Partitive & Quotative Division from SFUSD
CGI Resources from LAUSD
Multiplication & Division Word Problems from ND Counts
Two Ways of Thinking of Division from Langford Math
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Multiplication & Division Word Problems Practice
This fun word problem worksheet will surely challenge your young mathematicians! They will look for the key words in each problem to help determine which math operation to use. Once they have finished this resource, they will be ready for more!
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Multiplication and division in word problems lesson 6
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Lesson 6 Multiplication and Division in Word Problems. Solve. 3 Yesterday Ruth scored 2 points at the game. Today she scored 8 times as many points as she
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Multiplication and Division Word Problem Types - Printable or Google Classroom
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Multiplication and Division Numberless Word Problems
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One and two step word problems for multiplication, division with or w/o QR codes
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Multiplicative Comparison Word Problems (Multiply or Divide) - CCSS 4.OA.A.2
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Multiplication and Division Word Problems - Digital and Print - Equal Groups
Also included in: Word Problems - Addition, Subtraction, Multiplication, Division - Digital Print
Multiplication & Division Word Problems Task Cards
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Multiplication and Division Word Problems
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Multiplication Word Problems for Grade 3
Simple multiplication.
These worksheets contain simple multiplication word problems. Students should derive a multiplication equation from the word problem, solve the equation by mental multiplication and express the answer in appropriate units. Students should understand the meaning of multiplication before attempting these worksheets.
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- 4th grade (U.S.): Multiplication and division
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Multiplication and division word problems
The Multiplication and division word problems exercise appears under the 4th grade (U.S.) Math Mission , Arithmetic essentials Math Mission and Mathematics I Math Mission . This exercise introduces word problems involving one-step multiplication and division situations.
Types of Problems
There are two types of problems in this exercise:
Find right equation
Solve equation
This exercise is easy to get accuracy badges because the problems all become one-step equations. Speed badges are easy also because the problems recycle at a pretty fast rate.
- The exercise description says that there may be remainders, but research has not found any with remainders.
- Until you cycle through all problems, it is important to read carefully as sometimes the division versus multiplication can be subtle without a careful read.
Real-life Applications
- Choreographers need to be able to divide the piece they want to perform, into smaller pieces so that everyone will be able to do and give their best, whether they dance or choreograph an orchestra. In the end of the day they need to flow together in harmony and they will use division to accomplish that.
- Multiplication is needed and used by mechanics for repairing cars by multiplying when they overhaul the engine, measure the pistons or just to put in a new gearbox or engine.
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In this video we will be working through mathematical word problems or word sums that would apply what we learned in the previous videos on multiplication (t...
Multiplication: place value and area models Learn Using area model and properties to multiply Multiplying with distributive property Multiplying with area model: 6 x 7981 Multiplying with area model: 78 x 65 Lattice multiplication Why lattice multiplication works Practice Multiply 2-digits by 1-digit with distributive property 4 questions Practice
Multiplication and division word problems (within 100) CCSS.Math: 3.OA.A.3 Google Classroom A roller coaster has 4 4 different cars. Each car holds 10 10 people. How many people are on the roller coaster when all the cars are full? people Stuck? Review related articles/videos or use a hint. Report a problem 7 4 1 x x y y \theta θ \pi π 8 5 2 0 9 6
solve one- and two-step word problems involving multiplication and division, use multiplication or division to check the answer to a word problem. Prerequisites Students should already be familiar with multiplication facts up to 1 0 × 1 0, addition and subtraction of two-digit numbers, using bar models to model word problems,
Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics.
This worksheets combine basic multiplication and division word problems. The division problems do not include remainders. These worksheets require the students to differentiate between the phrasing of a story problem that requires multiplication versus one that requires division to reach the answer. Mixed Multiplication and Division Word Problems 1
Lesson 6: Fractions Lesson 6 Multiplication and Division in Word Problems. Solve. 3 Yesterday Ruth scored 2 points at the game. Today she scored 8 times as many points as she 500+ Math Specialists 6 Years in business
Word problem worksheets: Mixed multiplication & division. Below are six versions of our grade 4 math worksheet with mixed multiplication and division word problems. All numbers are whole numbers with 1 to 4 digits. Division questions may have remainders which need to be interpreted (e.g. "how many left over").
Lesson 6 multiplication and division in word problems answer key - This lesson focuses on solving real-world problems using multiplication and the Multiply or. ... Invite your child to share what he or she knows about multiplication and division in word problems by doing the following activity together.
Math Unit 2 Lesson 6: Multiplication and Division in Word. In this lesson, we will learn how to solve one- and two-step problems where one of the steps involves multiplying or dividing numbers within the times
Try the Deciphering Division Word Problems pre-lesson. Learning Objectives Students will be able to identify key division terms in word problems to help solve long division problems with one-digit divisors. EL adjustments On Introduction (5 minutes)
The multiplication and partitive division (constant unknown) examples have very similar wording since they both have the comparison statement: "6 times as much". This is a description of the relationship between two groups-the total, and the comparison group.
Multiplication & Division Word Problems Practice. This fun word problem worksheet will surely challenge your young mathematicians! They will look for the key words in each problem to help determine which math operation to use. Once they have finished this resource, they will be ready for more!
Unit 2 - Lesson #6: Multiplication as a Comparison Unit 2 - Lesson #7: Multiplication and Division in Word Problems Unit 2 - Lesson #8: Multiples and Factors. 9th maths algebra exercise 3.4 Annual compound interest calculator By using date of birth numerology Decimal hundredths worksheets Differential equation photomath Equation of a parallel ...
The lesson:lists 6 multiplication words and 6 division wordsprovides interactive examples of each in which students identify the key word and decide whether to multiply or divide includes a printer friendly study guide of the key words to keep in student binders and access to a FREE printable practice worksheet.
This will be completed in class and requires students to translate real-world problems into multiplication and division number sentences and solve them. E: Students will be evaluated based on the accuracy of their responses on the Zero and Eight worksheet. Students will also be evaluated based on their performance on the Lesson 1 Exit Ticket.
Students work to determine whether they would use addition, subtraction, multiplication, or division to solve each of 12 word problems cards. Kids love to get up and move around, so they are sure to enjoy this game! This can be used as a whole class review game, scoot style, or in centers.
Lesson 6: Fractions—Multiplication and Division D. Legault, Minnesota Literacy Council, 2014 1 Mathematical Reasoning LESSON 6: Fractions—Multiplication and Division Lesson Summary: First, students will solve a word problem involving fractions. In Activity 1, ... 1 1/3 x 5 = 4/3 x 5/1 = 20/3 = 6 2/3 inches. Lesson 6 Extra Problem about Food ...
These worksheets contain simple multiplication word problems. Students should derive a multiplication equation from the word problem, solve the equation by mental multiplication and express the answer in appropriate units. Students should understand the meaning of multiplication before attempting these worksheets. Worksheet #1 Worksheet #2 ...
This differentiated set of math worksheets includes 3 levels of multiplication and division word problems of varying difficulty. These worksheets are ideal for years 3, 4, 5 and 6 classes and are a perfect resource for mixed-ability classes. Help students practise their multiplication and division skills with these word problems. Differentiated resources like these multiplication and ...
15. hr. min. sec. SmartScore. out of 100. IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)!
The Multiplication and division word problems exercise appears under the 4th grade (U.S.) Math Mission, Arithmetic essentials Math Mission and Mathematics I Math Mission. This exercise introduces word problems involving one-step multiplication and division situations. There are two types of problems in this exercise: Find right equation: This problem describes a word problem and has a multiple ...
hr. min. sec. SmartScore. out of 100. IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)!