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Division and English/ Language Arts

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📖 Standards

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.

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.

Using estimation in multiplying two-digit numbers

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📖 Standards

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.

CCSS.MATH.CONTENT.4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operation … Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

⏰ Time

This lesson takes 40 minutes to an hour, depending on how long you allot your students to complete each of the 4 problem sets and whether you have students play the game.

📲 Technology Required

Computer with a projector, Smartboard or other device for your class to watch videos or videos can be shared in Google meet or other application for remote learning. Spirit Lake: The Game can be downloaded and played on Windows or Mac computers. An iPad version will be available by Fall 2021. Schools that are part of the Growing Math project or who have a 7 Generation Games site license will have access to all of these games for students to use at home or school.

Optional Recommended Resource

Use resources like the Helping Math Multiplication Worksheet Generator to make your own worksheet. Their worksheets look very much like this one on multiplication of two-digit numbers with Easter egg examples, except with many more activities in each worksheet. Note that the link will require you to register for a free download. Registration takes about 1 minute. You’ll then receive a link to download over 100 free worksheets on math topics from addition to rational numbers. Another resource we like is the Lizard Point math worksheet generator. Both will print the worksheets as well as the answer key. Note that sites using PRINT TO Google Drive may have that feature disabled after December, 2020. However, you can still from the PRINT menu select SAVE AS PDF, download a file as PDF and then upload it to your Google Drive. The Growing Math project has no affiliation with Helping Math or Lizard Point.

📃 Summary

You’ll need 20 math problems multiplying two-digit numbers. You can use math problems you already have or use one of the online worksheet generators. Based on research showing the effectiveness of distributed practice – that is, practicing a skill for more, shorter periods rather than one long session – we have students solve a few problems at a time, with videos in between. The lesson begins with a brief explanation of multiplying two digit numbers, followed by students solving 3-5 problems multiplying two-digit numbers. Students then watch a 3-minute video that works an example of multiplying a three-digit number by a two-digit number. They then solve 3-5 more problems, followed by another video, then more problems. We recommend giving a time frame – say, 7-10 minutes – to solve the problems rather than set number of problems because this allows you to begin and end each section of the lesson with all of the students at once.

📚 Lesson Plan

1. Introduction to Multiplying Two-digit Numbers

Begin with an example from Helping with Math, that gives an explanation of multiplication and a variety of types of problems. Then, have the students try to solve 3 to 5 problems. You can use those included in the Google slides linked or create your own.

2. Video : Multiplication and Estimation

Estimation is one of the most practical math skills!

There are a lot of math concepts that I use regularly when writing software or computing statistics in my day job. The one skill I use all the time is estimation. (I can tell you that the ability to accurately estimate an answer is not universal.)

Example 1: Long multiplication using “math reality checks.”

In the problem in the video above, we start out by multiplying 892 x 11, using the fact that any number multiplied by 10 is just that number with an added zero. To test our answer, we round 892 to 900 and can estimate that our answer should be near to – and less than – 9,900.

Let’s say you type the wrong number in your phone, hitting the 6 instead of the 9, since these two are pretty close and you have big fingers. Now your answer is 7,612. If you have a good grasp of estimation and multiplication, that is clearly wrong. If you’re computing how much money you need to charge a customer based on the 892 hours you expect to work at $11.00 per hour, you have just lost out on over $2,000!

3. More multiplication problems

Now that you have had a little practice and a little instruction, students solve another 3-5 problems.

4. Video : Multiplication and Estimation

This video works through a problem multiplying a 3 -digit number by a two-digit number . It also gives a strategy for solving difficult problems. That is, break the problem into smaller, easier problems.

Video 2: Use addition to solve a multiplication problem.

Here, because the last digit of one number is 7 and of the other number is 2, you know that 7 x 2 = 14. So, whatever else your answer is, it has to end in a 4.

5. Follow up to the video

As a math teacher, I heard approximately 4,897,234 times from students:

WHY do I have to do so many problems of the same type?

– Almost every student I ever taught math

Explain to students that all of those facts learned, like 2 x 7 =1 4 are the basis for the commutative property of multiplication, reducing numbers to lowest terms, or solving equations by multiplying or dividing both sides by a constant, and more. You need a BASE to work from, problems that can be examples.

The fact is that the more experience you have with numbers, the more problems you solve. The more problems solved, the easier it gets.

6. Finish off by a few more math problems

Now that you’ve watched another video, it’s time for the last set of math problems.

7. Optional – Game Play

Students can Spirit Lake: The Game . Multiplying two- and three-digit numbers comes up in Level 4. We recommend allowing students to play for 15-30 minutes each session. This gives them enough time to get started but not enough time to get bored.

Assessment

Answers to the 12 -20 math problems completed by the student provide one assessment. A second assessment is in the reports for the Spirit Lake game, which show whether students answered correctly the problems in Level 4, whether they read the hint before answering the problem, and whether they were correct on the first try or had to attempt the problem more than once.

State Standards

Minnesota Math Standard 4.1.1.3 – Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.

Minnesota Math Standard 5.1.1.4 – Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.

Adding fractions with like denominators

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📖 STANDARD

CCSS.MATH.CONTENT.4.NF.B.3.A Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

CCSS.MATH.CONTENT.4.NF.B.3.D Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

[For state-specific standards, click here.]

⏰ LESSON TIME

45 minutes

📃 SUMMARY

This lesson plan will explore how students can add fractions with like denominators to determine the sum of fractions. It incorporates two instructional videos, an editable presentation and educational game that can be used to practice/reinforce the concept with assessment data.    

📲 Technology Required

The teacher (or student, if learning at home) will need a computer, phone or tablet with an Internet connection to play the video. For students at home without Internet access, the teacher can print out the attached PDF or PowerPoint for students to study. The game required plays on Windows or Mac computers and on iPad. A Chromebook version will be available by April.

📚 Lesson Plan

1. VIDEO: Adding Like Fractions

Start your lesson with this one-minute video on adding fractions with like denominators.

Alternate format : POWERPOINT: Adding Fractions with Like Denominators

This presentation provides the information in the video viewed at the beginning of the lesson as a PowerPoint or PDF.

For a PDF version, go here. 

For an editable PowerPoint version, go here. 

2. Game Play

Have students play Fish Lake for 30 minutes. This lesson is most effective when introduced towards the beginning of Fish Lake gameplay since the math ties into the math in Level 3. Students who master this standard will be able to advance within the game. Students who have trouble with this standard will receive individual instruction within the game to teach and reinforce this concept. 

3. Reinforce with another video

Common denominators can help you determine what’s fair

This two-minute video gives examples of how fractions with like denominators can be used to see if everyone is doing their fair share of the work or eating a fair share of the pizza.

4. Related Lesson – Introducing Fractions

If your students are struggling with adding fractions with common denominators, they may need a review of the introduction to fractions, including defining numerator and denominator.

ASSESSMENT

You can view your students’ progress on mastering these standards by viewing your Fish Lake Teacher Reports. You can access the Fish Lake reports here. 

STATE STANDARDS

Arizona (AZ), New Mexico (NM), North Dakota (ND), South Dakota (SD), and Oregon (OR) have all adopted the math standards covered in the Common Core Standards. 

Minnesota (MN) Math Standard 

4. Number and Operation 

Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand how decimals represent quantities.4.1.2.3 – Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators.

Introducing Division

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📖 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 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.

Multiplying fractions with like denominators

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📖 STANDARD

CCSS.MATH.CONTENT.5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Click for individual state standards, or scroll to the bottom of the page.

⏰ LESSON TIME

45 minutes 

📃 SUMMARY

This lesson plan will explore how students can take what they already know about adding fractions with like denominators in order to grasp multiplying fractions with like denominators. It incorporates an instructional video, an editable presentation and an educational game that can be used to practice/reinforce the concept with assessment data. 

📲 Technology required

The game Fish Lake can be played on iPad, Mac or Windows computers. Internet is required to log in to the game with username and password. If Internet access drops, students can continue playing and their progress will be saved on the device and uploaded to the server whenever access is available. Fish Lake is available free to schools participating in the Growing Math project.

📚 Lesson Plan

1. VIDEO: Adding and Multiplying Fractions with Like Denominators

Start your lesson with this video on adding and multiplying fractions with like denominators.

Adding and multiplying fractions: Definitions and examples 3:33

This three-minute video begins with adding fractions with a common denominator. It explains that denominator is more than the number on the bottom, it is the number of parts the whole is divided into. Multiplying fractions with like denominators is shown, with examples, to be the same thing as adding the fraction multiple times.

Teaching Options

The video above is also available as editable PowerPoint presentation and as Google slides. Teachers may prefer to use these as part of a mini-lecture

2. GAME: Fish Lake

Have students play Fish Lake for 30 minutes. This game can be played on Mac, Windows and iPad. You can find the link on our games page. This lesson is most effective when introduced towards the beginning of Fish Lake gameplay since the math ties into the math in Level 3. Students who master this standard will be able to advance within the game. Students who have trouble with this standard will receive individual instruction within the game to teach and reinforce this concept.

ASSESSMENT

You can view your students’ progress on mastering these standards by viewing your Fish Lake Teacher Reports. You can access the Fish Lake reports here. 

STATE STANDARDS 

Arizona (AZ), New Mexico (NM), North Dakota (ND), South Dakota (SD), and Oregon (OR) have all adopted the math standards covered in the Common Core Standards. 

Minnesota (MN) Math Standard 

6. Number & Operation

Multiply and divide decimals, fractions and mixed numbers; solve real-world and mathematical problems using arithmetic with positive rational numbers. 

6.1.3.1 – Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms.

Subtracting Fractions: Like denominators

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📖 Standards

CCSS.Math.Content.5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

📃 Summary

After this lesson, students will know how to solve multi–step word problems using addition and subtraction of fractions with like (common) denominators. After watching the video, students will login to “Aztech: The Story Begins” on a device with the website or application. Students will be faced with a fractions problem in Level 1 which uses a calendar to find the fraction of days students did homework. The game character points out that 16/31 may not be “all the time” but it is still more than half. Throughout the game, students will be presented with AzTech history.

⏰ Time required

30 -45 minutes, including individual assessment

📲 Technology required

The game in this lesson plan can be played on the web on any Chromebook, Mac or Windows computer with reliable Internet access. If students do not have high-speed Internet at home, the game can be pre-loaded on to iPads and played offline with no Internet required.

📚 Lesson Plan

1. Video: Adding Like Fractions

Adding fractions with common denominators 1:10

“Like fractions” are those with the same denominator. This is also called a common denominator. How do you add like fractions? This quick video from the game Fish Lake has simple examples of comparing fractions and fraction addition.

2. Presentation or video: When is a fraction the same as 1 ?

Understanding that N/N = 1 for any number 3:32

If the numerator and denominator are the same, then this fraction equals 1. N/N = 1 How can you apply your knowledge of fractions to help you figure out how far you’ve gone on your trip and how much further you have to go? Teachers can either have students watch the video or use this 27-slide presentation in both Google slides format and PowerPoint. Both include examples of fractions of 8/8 , 3/3 and 4/4 all equaling one. Examples include distance, money and a bowl of stew.

3. Game: Play AzTech – The Story Begins

Students will login to “Aztech: The Story Begins” on a device with the website or application. Students using Chromebook, Mac or Windows computers can play on the web here. Students using an iPad can download the app here. Throughout the game, students will be presented with Aztech history. Students will be faced with fraction and statistic examples, leading to similar problems that need to be solved.

Estimated time for this portion: 10 minutes.

Assessment

Individual Assessment

Use this template to have students create their own fraction equation.

It includes a calendar template and these instructions:

Use this template to show what you did most in the last month when you weren’t in school.  

  • First, make a copy in your own Google Drive.
  • Second, put a 1 in the calendar for the first day of this month and continue until all days of the month are filled. 
  • Third, make a picture or write what you did each day in each of the boxes. 
  • Fourth, write your own fraction equation like this:
    • On 11/31 of the days, I played games on the computer.
    • On  7/31 of the days I worked planting my garden
    • On 13/31 of the days I was doing homework.

11/31 + 7/31 + 13/31  =   31/31

Of course, if there are 28 or 30 days in the month, your denominator will be different.

Group Assessment

Use the video below to solve the problem from Level 1 in AzTech: The Story Begins as a group. This video shows the problem from level 1 on finding the fraction of days Xitlali did homework and gives a hint on how to solve it. Ask the students why Xitlali said that 16/31 was more than half. How did she know? Introduce the concept of equivalent fractions.

Fraction problem using a calendar

State Standards

Minnesota State Standard 4.1.2.3 – Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators.

Introducing Fractions

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📖 Standards

CCSS.Math.Content.3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts

CCSS.MATH.CONTENT.4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

📃 Summary

The student will learn the definition of fraction, parts of fractions and how fractions have been used in past and present. This lesson begins with a video example of how fractions could be used by Native Americans to keep track of time. Next, a presentation is used to give a definition of fraction, numerator and denominator. Both the presentation and the second video use one-half as an example of a fraction. Other videos and presentation in the lesson divide a whole into fourths. The entire lesson takes 30-40 minutes.

📚 Lesson Plan

1. Video: An example of how our ancestors used fractions

How Native Americans used fractions 1:21

This video explains how a whole area, such as a lake, could be broken into equal parts and how that knowledge could be applied to tell time, thereby avoiding the danger of going home in the dark.

2. Presentation: Definitions of fractions, numerator and denominator

This presentation, with 25 slides, defines a fraction and each of its parts. One-half is used as an example of a fraction. You can access this presentation as Google Slides or PowerPoint. We estimate it takes about 7 minutes, with pauses for student input.

3. Video: Is one-half fair?

When something is divided into two equal parts, that is one-half 1:22

How many times have you heard kids insist something wasn’t fair? This video uses fractions and the concept of one-half to determine if two people are doing the their fair share of the work, getting their fair share of a pile of blankets.

4. Video: What is half

What is one half? 1:40


In this example of meeting between two camps, students will learn the definition of one-half and how to apply this knowledge to determine if the distribution of effort is fair. The video provides both examples of one-half – a whole divided into two equal parts – and non-examples, when a whole is divided into two unequal parts.

5. Presentation: Using fractions

This presentation, with 13 slides, gives an example of dividing a trail into four equal parts, fourths, or quarters. Zoongey Giniw sets his snares at four spots, equal distances apart on the trail. The presentation is available in PowerPoint or Google Slides. We estimate it takes about 5 minutes.

6. Video: Why Snare Rabbits?

Why Turtle Mountain has a Jackrabbit Road :58

Why is Zoongey Giniw snaring rabbits? As Turtle Mountain elder, Deb Gourneau explains in this video, when the Ojibwe people on the Turtle Mountain reservation did not have deer to eat and could not leave the reservation, they escaped starvation by snaring rabbits.

7. Game Play: Fish Lake

Students can play Fish Lake on Mac or Windows computers or iPad. Fish Lake covers fractions a long list of fractions standards. Recommended time: 15 minutes. Teachers in the Growing Math program receive licenses for Fish Lake for all of their students. If you need a license, please email info@7generationgames.com

8. Game Play: Forgotten Trail

Learn Fractions and statistics: Playable on Chromebook

If your students don’t have access to iPads, Mac or Windows computers and are using Chromebooks, they can play Forgotten Trail, which teaches this fraction standard, as well as standards for measurement and data. You can see the full list here. Recommended time: 15 minutes. Teachers in the Growing Math program receive licenses for Forgotten Trail for all of their students. If you need a license, please email info@7generationgames.com

9. Next lesson: Adding fractions with like denominators

Once you have introduced fractions, the next step we recommend is adding and comparing fractions with a common denominator.

Assessment

Assessment is built into the presentation as students are asked how they would write Long Foot’s portion of the buffalo as a fraction. There is a test of all of the fractions standards taught in Fish Lake here. It can be used as a pre- and post-test to show growth or at the end of a unit on fractions.

State Standards

Minnesota Math Standard 3.1.3.2 – Understand that the size of a fractional part is relative to the size of the whole.