# Using Visual Models To Compare Fractions

## Standards

CCSS.MATH.CONTENT.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2

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.

## Technology Required

Students will need a Mac or Windows computer or an iPad to play the Fish Lake game. Alternatively, students can play Forgotten Trail on the web using Chromebooks or any computer with a web browser.

35-45 minutes

## Lesson Summary

Students play 2-3 levels of a game that teaches and assesses adding and comparing fractions with different numerators and denominators, with the context of a story from Ojibwe history. They create their own problems using visual models to compare fractions. Students discuss classmates’ problems. The lesson culminates with a video on visualization as a problem-solving strategy.

## Lesson

Students play the Fish Lake game through level 2. This requires installing the game on an iPad or a Mac or Windows computer. If only Chromebooks are available, students can play the Forgotten Trail Game instead. We do recommend Fish Lake if iPads are available. Although mathematics and social studies standards taught in both games overlap, the change from using Chromebooks in most lessons to a more console-level game can improve student engagement.

### Students create their own problems (10 minutes)

Use slides 1-4 of this Slides presentation to explain the assignment. Optionally, for students learning at home or for homework, it can be assigned to students in Google classroom or similar system.

### Discuss math problems students created (10 minutes)

Because students very often ask, “What do you mean?” or “Give me an example?” slides 5-11 of the presentation give an example.

## Assessment

This lesson includes three types of assessment. In the games, students are presented with math word problems that relate to the game narrative. Their answers are scored and data can be accessed for each student from the teacher reports. Students submit math problems they have written for teacher feedback. Also, teacher can use whole class discussion of student problems as a gauge for understanding or have students in pairs or small groups submit written discussion of their peers’ math problems.

# Ojibwe Clans and Migration (Bilingual English & Spanish)

### 📖STANDARDS

NCSS theme – The study of people, places, and environments enables us to understand the relationship between human populations and the physical world.

Minnesota State Standard – History Sub-strand 4, Standard 15 “North America was populated by indigenous nations that had developed a wide range of social structures, political systems, and economic activities, and whose expansive trade networks extended across the continent.”

40 minutes

### 📲 Technology needed

Internet connection on a PC or Chromebook laptop, tablet, or phone.

### 📃 Summary

This Ojibwe clan lesson for Grade 3 is focused on Ojibwe culture. Students learn where people and places are located and why they are there. They will become familiar with the causes, patterns and effects of Ojibwe settlement and migration. They will learn of the different population centers in Ojibwe society and investigate the impact of human activities on the environment.

## 📚 Lesson

The downloadable Google Slides presentation is available here. This has a digestible summary of the Ojibwe migration, and why and how it happened. The Ojibwe clans are introduced as well as the new lifestyles that the Ojibwe adopted after they migrated to the Great Lakes area and Ontario, Canada.

## Game

Making Camp Bilingual can reinforce clans and culture studies using the Life section.

1. Select the LIFE button from the main choice screen.
2. From the LIFE choices, click on the box in the middle of the bottom row, the one with the four people, and watch the video about Ojibwe social structure. Answer the questions that follow the video.
3. Next, select the box on the bottom right. Watch the overview video on clans and totems. Answer the questions.
4. Students can also click on each individual clan totem icon to learn more about each Ojibwe clan and answer a question about each of them to earn points.

Students can use the language button to switch between English and Spanish while watching the videos.

Alternatively, students may also play Forgotten Trail, which is an adventure game that homes in on the Ojibwe migration. Two kids in the game retrace the Ojibwe migration on their own and learn more about Ojibwe history along the way.

### Assessment

Teachers will be able to view student reports for Making Camp Bilingual to view how many modules students completed in the LIFE section and their scores for each one.

### Related Lesson

“Ojibwe Clans and Migration” – The English Only version of the lesson plan above featuring Making Camp Premium.

# Ojibwe Clans and Migration

### 📖STANDARDS

NCSS theme – The study of people, places, and environments enables us to understand the relationship between human populations and the physical world.

Minnesota State Standard – History Sub-strand 4, Standard 15 “North America was populated by indigenous nations that had developed a wide range of social structures, political systems, and economic activities, and whose expansive trade networks extended across the continent.”

40 minutes

### 📲 Technology needed

Internet connection on a PC or Chromebook laptop, tablet, or phone.

### 📃 Summary

This Ojibwe clan lesson for Grade 3 is focused on Ojibwe culture. Students learn where people and places are located and why they are there. They will become familiar with the causes, patterns and effects of Ojibwe settlement and migration. They will learn of the different population centers in Ojibwe society and investigate the impact of human activities on the environment.

## 📚 Lesson

The downloadable Google Slides presentation is available here. This has a digestible summary of the Ojibwe migration, and why and how it happened. The Ojibwe clans are introduced as well as the new lifestyles that the Ojibwe adopted after they migrated to the Great Lakes area and Ontario, Canada.

## Game

Making Camp Premium can reinforce clans and culture studies using the Life section.

1. Select the LIFE button from the main choice screen.
2. From the LIFE choices, click on the box in the middle of the bottom row, the one with the four people, and watch the video about Ojibwe social structure. Answer the questions that follow the video.
3. Next, select the box on the bottom right. Watch the overview video on clans and totems. Answer the questions.
4. Students can also click on each individual clan totem icon to learn more about each Ojibwe clan and answer a question about each of them to earn points.

Alternatively, students may also play Forgotten Trail, which is an adventure game that homes in on the Ojibwe migration. Two kids in the game retrace the Ojibwe migration on their own and learn more about Ojibwe history along the way.

### Assessment

Teachers will be able to view student reports for Making Camp Premium to view how many modules students completed in the LIFE section and their scores for each one.

### Related Lesson

“Ojibwe Clans and Migration (Bilingual English & Spanish)” – The Bilingual version of the lesson plan above featuring Making Camp Bilingual.

# 📖 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.

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.

## 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.

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.

### 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.

# 📖 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

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?

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

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 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

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.