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UNIT: Word Problems with Multiplication and Division

Standards

CCSS.MATH.CONTENT.3.MD.D.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
CCSS.Math.Content.3.OA.B.5 Apply properties of operations as strategies to multiply and divide. 
CCSS.MATH.CONTENT.3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
CCSS.MATH.CONTENT.4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
CCSS.MATH.CONTENT.4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm

Time

Five hours

Technology Required

If teaching in person, the teacher will need a computer and projector or smart board to show the videos, or students can be given the links to watch on their own devices. Students will need a PC, Mac or Chromebook or tablet. Making Camp Premium, Making Camp Lakota and Making Dakota are all playable on any web browser on those devices. Spirit Lake: The Game, playable on Mac or Windows computers also teaches these same concepts or students can watch the videos from the game on any device with a browser.

UNIT SUMMARY

This cross-curricular unit teaches solving word problems with multiplication and division with a variety of strategies and in contexts ranging from agriculture to traditional dwellings.

Lessons

Lesson Multiplying to find perimeter of polygons

In this 45-minute lesson, students will learn how to compute perimeter of different polygons using multiplication and apply those skills in game-based practice problems. They will then learn about different Indigenous traditional dwellings. The lesson ends with students contributing to and solving problems that integrate the reading on dwellings and perimeter in an online assessment. 

Multiplication word problems

In this 40-minute integrated lesson, students learn about responsibilities of children in traditional Dakota society and discuss their responsibilities today. They learn a problem-solving strategy that can be applied to a wide range of situations, including mathematics. Students play Spirit Lake: The Game or watch videos solving multiplication problems set in the context of a story based on Dakota culture.

Travois, multiplication and 2-step problems

In this 45-minute lesson, the students will develop an understanding of the meanings of the four operations of whole numbers through activities and problems involving real life scenarios from Indigenous history. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve using the four operations problems involving single-digit factors. It includes educational videos, games and video presentations that can be used for reviews and daily practice.

Problem-solving with pigs: Start at the end

This 75-minute cross-curricular lesson includes activities and instruction in agricultural science and math. Students begin by watching a video and learning about pig farms. After making their own pig barn, they watch two short videos about solving math problems. This information is then applied to solve multiplication and division word problems during a presentation on math around the pig farm. Students end playing one of the Making Camp games to reinforce skills and knowledge.

Lesson. Problem-Solving Two ways

his 40-minute lesson assumes that students have some familiarity with multiplication of one-digit numbers and division with one-digit divisors. Students are introduced to the various means of problem solving in a brief presentation. They watch a video on visualization, then solve a problem that asks them to visualize. After watching a video on building a model, students build and/or draw their own model of a multiplication problem or property. Lesson concludes with game play to reinforce these problem-solving strategies and learn more. T

Learn 4 Math Facts at Once with Google Slides

This 60-minute lesson starts with a video as an ice breaker. Then, students read or listen to a presentation explaining how each math fact is actually four. Students complete an activity where they create their own math facts slides. A recommended video explains features of Google slides. Students complete the lesson playing Making Camp Dakota, solving word problems using division.

Learn 4 Math Facts at Once with Google Slides

Standard

CCSS.MATH.CONTENT.3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. 

CCSS.MATH.CONTENT.3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares.

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

TIME

45-60 minutes

Technology Required

Students will need access to a computer or tablet and Google slides.

Summary

Start with a video as an ice breaker. Then, students read or listen to a presentation explaining how each math fact is actually four. Students complete an activity where they create their own math facts slides. A recommended video explains features of Google slides. Students complete the lesson playing Making Camp Dakota, solving word problems using division.

LESSON

Watch a video : Four Math Facts in One

In 4 minutes, this video explains how each time you learn a math fact, you are really learning four facts

Listen to/ Read a presentation on four math facts at a time

This presentation explains how one math fact is actually four because 7 x 6 = 42 means that 42 ÷ 7 = 6 and also that 6 x 7 = 42 and 42 ÷ 6 = 7. As an added bonus, it includes some ranch vocabulary like cattle, steer, heifer and bull.

Example from presentation

After the teacher has given the first part of the presentation, students are challenged to first show how a given math fact is actually four math facts, using steers. Next, students create their own examples. The easiest way to do this is through assignment in Google classroom or other system, including email, giving students their own copies of the slides to modify.

Recommended Video: Math Facts with Google Slides

If your students are unsure how to copy and paste, how to select multiple elements at a time, rotate objects or insert a duplicate slide, it is all in this video. Why not watch the video first? Because students often pay more attention once they realize they have questions that can be assigned by the assigned video.

How do you copy 84 chickens?

Play Making Camp Dakota

Making Camp Dakota
Making Camp Dakota teaches division of two- and three-digit dividends

Play Making Camp Dakota: Past and Present to learn about Dakota history and culture and solve division problems, such as dividing the people on the buffalo hunt. Students can be assigned to go directly to the game here or to access it by selection in the games portal for kids.

Assessment

Two types of assessment are included in this lesson:

  1. Students create their own math facts slides, and in-game assessment.
  2. Problems are scored automatically in Making Camp Dakota and data are available through the teacher reports.

Differentiated Instruction

Many students with learning disabilities have stronger achievement in one area than another, for example their grade level in reading is higher than in mathematics. For these students in higher grades, an assignment to learn to use presentation software such as Google slides is age appropriate and intrinsically interesting and at the same time increases their knowledge of basic math facts.

Fill in the Blank: 3 Digit Dividends

📖 STANDARD

CCSS.MATH.CONTENT.4.NBT.B.6

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

⏰ LESSON TIME

55 Minutes

📃 SUMMARY

This lesson plan will have students reinforce the previously presented concept of long division of 3 digit dividends by 1 digit divisors through a short review, an animated video, a fill in the blank division word problem activity, and game play.  

📲 TECHNOLOGY REQUIRED

Students will need a PC, Mac or Chromebook or tablet. Making Camp Premium and Dakota are both playable on any web browser on those devices. Students will also need access to the games.

📚LESSON PLAN

  1. Start the lesson by having a short review on dividing 3-digit dividends by 1-digit divisors. It is suggested to review the activity that was assigned in the previous lesson, “Build Your Own Division Problem” lesson. You can find the review copy of the activity here: “Review – Build Your Own Division Problem“. (15 minutes)
  2. How to Use Division to Solve a Problem – Start with this animated video on how to use long division, with 3 digit dividends, to solve different word problems. (Time – 1:24)

3. Have students work on the activity “Fill in the Blank: 3 Digit Dividends“. The activity has students fill in the blanks to complete the division word problem, identify the problem, and solve it. (Corresponding “Fill in the Blank: 3 Digit Dividends” Activity Jamboard that’s also linked in the activity above can be used by students as space to work out their division word problems.) (20 minutes)

4. Have students play Making Camp Dakota: Past & Present using our Games Portal for Kids. The division in Making Camp Dakota will be more practice for students on problems with 3 digit dividends divided by 1 digit divisors. (15 minutes)

ASSESSMENT

The “Fill in the Blank: 3 Digit Dividends” activity is not only allowing students to continue practicing the concepts previously introduced and reviewed in this lesson, but also serves as an assessment of how well the student grasps the concept of division using 3 digit dividends and 1 digit divisors.

Making Camp Dakota Teacher Reports

You can view your students’ progress on mastering these standards by viewing your Making Camp Dakota teacher reports. You can access the Making Camp Dakota reports here.

STATE STANDARDS

Minnesota State Standards

4.1.1.6 – Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction.  

5.1.1.1 – Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal.  

Build Your Own Division Problem

📖 STANDARD

CCSS.MATH.CONTENT.4.NBT.B.6 

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

⏰ LESSON TIME

50 minutes

📃 SUMMARY

This lesson plan will build upon the introduction to division with 3-digit dividends from the “Dividing 3-Digit Dividends” lesson. Students will be able to continue practicing dividing 3-digit dividends by 1-digit divisors through a short review, an activity where students build their own division problems, and game play.

📲 TECHNOLOGY REQUIRED

Students will need a PC, Mac or Chromebook. Students will also need access to “Making Camp Dakota: Past & Present” using our Games Portal for Kids. “Making Camp Dakota: Past & Present” is playable on PC, Mac, and Chromebook using any browser.

📚LESSON PLAN

  1. Start the lesson by having a short review on dividing 3-digit dividends by 1-digit divisors. It is suggested to review the activity that was assigned in the previous lesson, “Dividing 3-Digit Dividends” lesson. You can find the review copy of the activity here: “Review – On Your Way Home.” (10 minutes)
  2. Students will take the information reviewed and use it to complete the “Build Your Own Division Problem” activity. In this activity, students practice division using 3-digit dividends and 1-digit divisors through using virtual manipulatives. (20 minutes)
  3. To end the lesson, students can play Making Camp Dakota: Past & Present to further practice division. Students can access the game using our Games Portal for Kids. (20 minutes)

ASSESSMENT

The “Build Your Own Division Problem” activity is not only allowing students to continue practicing the concepts previously introduced and reviewed in this lesson, but also serves as an assessment of how well the student grasps the concept of division using 3 digit dividends and 1 digit divisors.

Making Camp Dakota Teacher Reports

You can view your students’ progress on mastering these standards by viewing your Making Camp Dakota teacher reports. You can access the Making Camp Dakota reports here.

STATE STANDARDS

Minnesota State Standards

4.1.1.6 – Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction.  
5.1.1.1 Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. 

Related Lesson – Fill in the Blank: 3 Digit Dividends

The “Fill in the Blank: 3 Digit Dividends” lesson plan will have students reinforce the previously presented concept of long division of 3 digit dividends by 1 digit divisors through an animated video, a fill in the blank division word problem activity, and game play.  

Buffalo Hunts and Division

📖 Standard

CCSS.MATH.CONTENT.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

CCSS.MATH.CONTENT.5.NBT.A.3.A Read and write decimals to thousandths

CCSS.MATH.CONTENT.5.NBT.A.4 Use place value understanding to round decimals to any place.

NOTE: Teachers who have not yet covered decimals in their class have an option within the lesson to only teach the first standard.

⏰ Time

25- 30 minutes

📲 Technology Required

Computer or mobile device

📃 Summary

Begin with a video on long division (optional) or a presentation on uses of division from the playground to the buffalo hunt. Watch a short video working long division problems. Finish with practicing long division in Making Camp Dakota. Short videos on Dakota buffalo hunt traditions and related math lessons are also linked.

📚Lesson

Video: Optional for Review

If your students need a review of the steps in long division, we recommend this six-minute video that uses the acronym HMS ↓ to teach students to :

  • Ask How Many
  • Multiply
  • Subtract
  • Bring down

Presentation on Division and Buffalo Hunts

This Google slides presentation gives common factors in buffalo hunts across different tribes and explains how whether it is computing the number of hides a horse can carry or how long each group gets to play at recess, division is always useful.

NOTE: This presentation includes two slides that reference converting a fraction to a decimal. If you have not yet introduced this concept, those slides can be deleted.

Video: Long Division by Guessing

For those students who don’t know where to start with long division – guess!

Play a Game – Making Camp Dakota

Select the Buffalo Icon (top left corner) in the first MATH screen to practice long division.

Math Screen #1 from Making Camp Dakota

Related Lessons

For more instruction on division check out these two lessons:

Related videos

These two videos, each about 1 minute in length, give more information on traditional Dakota buffalo hunts.

Becoming a buffalo hunter

Dakota deer and buffalo hunting

Breaking Down Division with Remainders

Lesson by James Gumela

📖 STANDARD

CCSS.MATH.CONTENT.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

LESSON TIME

30-45 minutes 

📃 SUMMARY

This lesson plan will explore how students interpret remainders in the context of a problem. They will learn how to divide and have a number leftover. Students will be using the concept of division and remainders. An instructional video will be presented as well as a PowerPoint presentation and an educational game that can be used to reinforce the concept of remainders with assessment data.

📲 TECHNOLOGY REQUIRED

 Device with web-browser (Chromebook, laptop or desktop computer); or iOS (iPhone/iPad) with access to Google apps. 

📚 Lesson

Watch Video

In division, remainders occur when a number can’t be evenly divided. This video will help the students understand the concept of remainders.

Also available in spanish:

Break Down Long Division in a Presentation

This Google slides presentation: Division with remainders reviews the parts of a division problem; quotient, division and divisor, then works a sample problem step by step. The presentation ends with a practical question in a word problem- when you have a remainder, what do you do with the amount that remains?

Play a Game – Making Camp Dakota

Making Camp Dakota follows a family at a pow-wow as the children learn about Dakota culture through stories from their elders and apply their long division skills along the way.

Differentiated Instruction

GAME: Making Camp Premium

Have students play Making Camp Premium using these icons. Students who struggle with this standard will receive individual instruction within the game to teach and reinforce this concept. 

Menu from Making Camp Premium
Man standing in front of trees, a game icon

ASSESSMENT: Making Camp Premium Reports

You can view your students’ progress on mastering these standards by viewing your Making Camp Dakota and Making Camp Premium teacher reports. You can access the teacher reports here.

STATE STANDARDS:

Minnesota Math Standard 5.1.1.2 Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 

Dividing 3-Digit Dividends

📖STANDARD

CCSS.MATH.CONTENT.4.NBT.B.6

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

LESSON TIME

30-45 minutes

📃 SUMMARY

This lesson will build upon the already introduced concepts and vocabulary of division in our “Introducing Division” lesson. Students will learn and be able to practice dividing 3 digit dividends by 1 digit divisors through a short review, activity, and game play.  

📲TECHNOLOGY REQUIRED

Students will need a PC, Mac or Chromebook or tablet. Making Camp Premium and Dakota are both playable on any web browser on those devices. Students will also need access to the games.

📚 LESSON

Begin by reviewing division.
  1. Start the lesson by reviewing the important division basics. This Division Review Google Slides reviews “what we know.” The presentation goes over the definition of division, key terms, division symbols, and examples. 
  1. Have students work through the On Your Way Home division activity where they take what they know and practice dividing 3 digit dividends by 1 digit divisors. The activity takes division problems and puts them into real-world context, visiting stores on your way home from the park. 
  1. Have students play Making Camp Premium and/or Making Camp Dakota using our Games Portal for Kids. The division magnets game in Making Camp Premium can be used as review before moving on to Making Camp Dakota. The division in Making Camp Dakota will be more practice for problems with 3 digit dividends divided by 1 digit divisors.    

ASSESSMENT

Assessment is built into the “On Your Way Home” activity through the creation of their own division problem after repeated practice of 3 digit dividends divided by 1 digit divisors.

Making Camp Dakota Teacher Reports

You can view your students’ progress on mastering these standards by viewing your Making Camp Dakota teacher reports. You can access the Making Camp Dakota reports here.

STATE STANDARDS  

Minnesota State Standards

4.1.1.6 – Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction.  

5.1.1.1 – Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal.  

Related Lesson: Build Your Own Division Problem

The “Build Your Own Division Problem” lesson plan will build upon the introduction to division with 3-digit dividends from this lesson. Students will be able to continue practicing dividing 3-digit dividends by 1-digit divisors through a short review, an activity where students build their own division problems, and game play.  

Division and English/ Language Arts

📖 Standards

CCSS Standard:
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

CCSS.ELA-LITERACY.W.4.3
Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.

Time

40-45 minutes

📲 Technology Required

Making Camp Premium plays in any browser, so, of course, on Chromebooks. It can also be downloaded on phones or tablets and played offline by students who have limited Internet access. Schools that are part of the Growing Math project or who have a 7 Generation Games site license have access to the game for students to use at home or school.

📃 Summary

This is a fun lesson where students practice division, combined with Ojibwe history and then complete a creative writing assignment.

📚 Lesson Plan

1. Game Play with Making Camp

  1. Open Making Camp. Go to the main choices screen by clicking on the small green icon with boxes at the lower left of the screen.
  2. Click NUMBERS.
  3. Click the box with the numbers to practice division.
Click the numbers box for division practice.
Each correct quotient earns a fridge magnet to decorate the fridge!

Students should play until they earn at least 15 points.

2. Spend the points earned and learn about Ojibwe history

One of the best teachers we know said, “History is more than names and dates. It’s how people lived. It’s the things they used.” When trading for a wigwam, students will watch videos on how to build a wigwam and on trading. They’ll learn that tribes traded with one another for hundreds of years.

3. Short story writing prompt

So how did we get from a refrigerator to a wigwam? You can use this Google slides presentation to tie in Native American history with Sam’s life in the twenty-first century. This presentation can also be added to your Google classroom as an assignment for students. Here is the introduction for Sam and his account:

This is Sam. He’s also Ojibwe but he’s not from a long time ago. He’s 16 years old. He lives on a reservation in the northern United States. You’ve probably heard of it. He doesn’t live in a wigwam. He lives in a white house with a grey roof. That’s the refrigerator in his house. The magnets have been there ever since he was in second grade.

Read the passage about Sam.

4. Writing assignment

Read about Sam and write a story about him. What do you think happened to him in second grade? Why does everyone except for his cousin, Angie, think he’s not smart? Do you think he and Angie can really walk to Maine?

Assessment

Math problems in Making Camp Premium are scored automatically. You can see how many students attempted and the number correct in the data reports. All Growing Math teachers and all schools with 7 Generation Game licenses receive access to these reports. Writing assignments can be assessed according to the teacher’s own rubric.

State Standards

Minnesota Math Standard 4.1.1.6 – Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction.

Minnesota Math Standard 5.1.1.1 – Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal.

Introducing Division

📖 Standard

CCSS Standard:
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

LESSON TIME

30 minutes 

📃 SUMMARY

This lesson plan introduces the concepts and vocabulary of division and provides students the opportunities to practice both recognition and recall of division facts. Math literacy activities are recommended to help students remember and understand math terms. Students can play the Making Camp Premium game, with division with one-digit divisors or Making Camp Lakota which includes one- and two-digit divisors.

📲 Technology required

The games, Making Camp Premium and Making Camp Lakota can be played on any web browser – Chrome, Firefox, Bing, etc or downloaded on iOS or Android devices. The Making Camp Premium game can be played with or without an Internet connection. Internet is required to log in to the Making Camp Lakota game with username and password. Both games are available at no extra charge to schools with a 7 Generation Games site license or who are part of the Growing Math Project.

📚 Lesson Plan

1. Introductory mini-lecture

5-7 minutes

  1. Explain why division is important. When we want to share something, whether it is the hours spent doing chores or a birthday cake, we divide it.
  2. Tell students they will be taking notes on the videos, writing down key words that appear in the video (e.g. quotient, dividend) and their definitions for review at the end of the session. (Math literacy helps with identifying math terms; textbooks will start to make sense.)

2. Watch Videos

7 minutes

Division Terms

What’s division? How do we use division every day? 3:31 minutes

The Division terms video is included in Making Camp Lakota, a game teaching division and Lakota history. It is also in the Making Camp Premium game. Before starting the video remind students to be ready to take notes.

Division (Multiplication in Reverse)

Why is learning multiplication important for learning division? 2:41 Minutes

3. Game Play

15 minutes

Play Making Camp Premium for multiplication and division.

Making Camp Premium can be played online on any computer (Windows, Mac, Chrome), or you can download it for your phone or tablet (iOS and Android). This game is part of the 7 Generation Games school license and also available as part of the Growing Math project.

The division magnets game practices division of one-digit numbers into two digit numbers, like 35 ÷ 5.

There are also games for multiplication and a lot of videos and games on history and English/ language arts. Making Camp Premium also teaches about Ojibwe history and culture.

For more division, play Making Camp Lakota.

In mathematics content, Making Camp Lakota focuses only on division, combined with, of course, Lakota history and culture. With development funded by the Thunder Valley Community Development Corp. this game is free to play on the web or downloadable for iPad or Android tablets.

ASSESSMENT

This lesson plan includes two types of assessment.

  1. You can view your students’ progress on mastering these standards by viewing your Making Camp Premium Teacher Reports. See an example below.
Student data by standard from Making Camp Premium
Sample Student Report

2. To assess student understanding of math vocabulary, review their notes written while viewing the division terms video.

Related Content

We have a YouTube division playlist! The videos above are part of a five-video series clues students in on everything from dividends to long division with remainders. (And they are short, ranging from one and a half to three and a half minutes each.) These videos can be played on any device in class or at home.

State Standards

Minnesota Math Standard 4.1.1.6 – Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction.

Minnesota Math Standard 5.1.1.1 – Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal.