Baked-In Fractions

Author: Isabel Bozada-Jones

Standards

CCSS.MATH.CONTENT.5.NF.B.7.A Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

CCSS.MATH.CONTENT.5.NF.B.7.B Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient.

CCSS.MATH.CONTENT.5.NF.B.7.C Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

Background Knowledge

Prior to this lesson, students should understand unit fractions and basic concepts in dividing fractions. This lesson gives students the opportunity to practice creating and solving problems where they have to divide fractions or divide by fractions, which can be easily differentiated based on student skill level.

Instruction

Introduce students to Bake-a-Palooza and have them play the game. The first time they play it, have them answer questions correctly. The second time they play it, have them answer questions incorrectly and watch the instructional video that plays.
- NOTE: The Bake-a-Palooza game is also available in Spanish. Hornea Hasta Que Lo Logres
Explain that to practice dividing fractions, they are going to be creating matching questions for a new version of Bake-a-Palooza. Show the questions currently in the game as an example.
For each matching questions they add to Bake-a-Palooza they should have:
1. Fractions that are divided by whole numbers or whole numbers divided by fractions.
2. Visual models for each equation
Have students create a real world problem using their fractions and visual models that could be used to create a “chapter 2” of Bake-a-Palooza.
Have students share their game ideas with others for feedback. Students can solve each other’s problems to double check their work.

Extension

Students can create videos to teach students who incorrectly answer questions in the game. If having students use their own phones to create videos, we suggest doing this activity at the end of class to minimize the number of times you need to say, “Please put your phones away.” Also, plan to have a few iPads or Android tablets available for use by students who don’t have a phone. If video editing software is available for computers or tablets, this lesson can be followed up with use of those computer applications.
Students can create multiple chapters of Bake-a-Palooza based on the three different parts of the 5th grade standard on dividing fractions.

All That Math Jazz

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Author: Isabel Bozada-Jones

Standard

STANDARD

CCSS.MATH.CONTENT.4.NF.B.3.C Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Background Knowledge

Prior to this lesson, students should understand the basic concept of fraction and how to add fractions with like-denominators. Basic knowledge of musical notation (whole notes, half notes, quarter notes, eighth notes, sixteenth notes) would be helpful, but is not necessary.

Instruction

Reflect back on students’ prior work with fractions and ask about what they have learned so far.
Explain that musical notes can be thought of like fractions and that today we are going to be working in 4/4 time signature, which is something they will learn about later, but means that a measure contains four beats and each quarter note is a beat.
Today, we are going to be starting with whole notes, which take up an entire measure, and we are going to be finding out what different rhythms are equivalent to each other.
Show students this picture of different notes.

Explain that each measure in the picture is equivalent to each other, depending on how fast the notes are, they take up different amounts of the measure, or the whole note. Show students the same picture with the equivalent fractions on it. Ask them what they notice and wonder.

Watch Using Music to Study Fractions
Show students several note combinations and have them find the least common denominator to create equivalent fractions. Demonstrate how these fractions fit into measures (equal to one whole note)
Have students play Jazz Math to practice creating equivalent fractions

Extension

Have students write addition and subtraction equations with different notes. Have them clap or play a percussion instrument to show the different parts of their equations.
Have students create their own equivalent fractions to add to the next version of Jazz Math. How would they make the game harder? How would they make it easier?

Potential Questions for Game

What notes are equivalent to this fraction?

Using Visual Models To Compare Fractions

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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.

Time

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

Start with a Game (10-20 minutes)

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.

Watch a video (2.5 minutes)

Visualize! One way of solving a problem

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.

Reflections on Ojibwe Migration

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by Janna Jensen and AnnMaria De Mars

📖 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.

CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.

D2.His.13.3-5 Use information about a historical source, including the maker, date, place of origin, intended audience, and purpose to judge the extent to which the source is useful for studying a particular topic.

⏰ Time

60 minutes

📲 Technology Required

Students need access to a computer with web browser.

📃 Summary

This lesson begins with a storyboard on the route and major events of the Ojibwe migration. Students then play the Forgotten Trail game, computing the average number of miles a character walked per day, followed by watching a video on map reading. As a group, students reflect on the challenges of the Ojibwe migration, compute the distance for just one segment and convert the distance from miles to kilometers.

📚Lesson

Storyboard on the Ojibwe Migration

Begin with this story board on the route and major events of the Ojibwe migration. We recommend having students read each section of the story as it advances. Alternatively, the teacher may read it to the class or students can read it to themselves either on devices in the classroom or at home.

Watch a video on how to find the mean

Warning: bad singing ahead. This short video tells how to find the mean – in song. You may skip this video if you have already used it in a previous lesson.

Play the Forgotten Trail Game

Students should play the game at least through the first level. The game begins with a middle school class learning about the Ojibwe migration. Students will solve math problems related to the average number of miles walked per day and fraction of distance covered.

Watch a video on using scales in maps

This video is 7 minutes and covers what is a scale, how to use one and that different maps have different scales. If you feel your students are already familiar with this information, you may skip this video. In the days of Google maps and GPS we have found students often are not as familiar with this information as you might assume.

Presentation on Reflections on the Ojibwe Migration

In this Google slides presentation, students are asked to reflect on the Ojibwe migration. What would it have taken to survive such a journey? They use their map skills to estimate the distance of one leg of the journey, in both kilometers and miles.

Presentation is also available as a PowerPoint.

Synonyms Video

Now that students have seen synonyms as words for the same thing and miles and kilometers as measures for the same distance, finish up with this short (less than 2 minutes) video on synonyms.

Assessment

Slides 14, 18 and 21 can be printed out for students to answer individually, or can be answered as a group in class. Data are available on activities completed and math problems answered in the Forgotten Trail reports. For more information, check out our reports page.

Converting fractions to decimals

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📖 Standard

CCSS.MATH.CONTENT.7.NS.A.2.D Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

⏰ Time

30-40 minutes

📲 Technology Required

A projector or smart board is required to show the Google slides presentation in class. It can also be shown using any web meeting software for remote learning. The random candy generator can be used by students in anything with a browser, including computers, tablets or phones. This activity is optional. It’s actually more fun with fun-size bags of candy like Skittles or M & M’s.

📃 Summary

Students watch a video or hear a presentation explaining using long division to convert fractions to decimals. A second method of using place value is discussed when the denominator is tenths, hundredths or thousandths. Students then play a game that teaches converting fractions to decimals and end with an activity finding the decimal representing each color in a bag of candy. A simulator is included if no bags of candy are available!

📚 Lesson

EITHER watch the video below

This is a 7-minute video that gives the steps in converting fractions to decimals, with multiple examples, using both long division and place value.

OR Use this Google Slides Presentation

The Google slides presentation covers the same material as the video with the same examples. The steps in the long division problems are animated in the presentation. If you prefer a PowerPoint presentation you can find that here. Both can be viewed from these links or you can copy into your own Google drive or download to modify for your class.

The presentation and video both include two sample problems to work as a class.

NOTE: The presentation includes an activity converting fractions to decimals using candy or a random sample application.

Play a Game

On mobile devices

Play the Empiric Empire game for 10 minutes. This game teaches fractions and decimals in the context of concepts from epidemiology such as prevalence, incidence and mortality rate. This game is available for iPad, iPhone or Android.

On Chromebook

Don’t have any of those devices? Play the Minnesota Turtles game for five minutes. After the game (it’s short), assign these problems:

The game says that 5/9 = 56% – prove it using long division. Is this a repeating or terminating decimal? HINT: Remember that 56% = .56
The game says that 4/9 = 44% – prove it using long division. Is this a repeating or terminating decimal?

Convert fractions with Candy

The Google Slides/ Powerpoint ends with an activity where students use a pack of candy to find fractions, convert those fractions to decimals and graph the result. If you don’t have time / forgot to buy bags of candy, you can use a simulator here. Random fact: The average fun-size bag contains 12 pieces of candy. There is a link for plain graph paper in the slides. If you’d prefer graph paper with fractions and decimals already entered, this page is divided into sixteenths.

Assessment

This lesson includes three types of assessment. There are the problems completed together in class, included within the presentation or video. There are the problems completed within the Empiric Empire game which you can see in the teacher reports. Alternatively, there are the two problems assigned after the Minnesota Turtles game. There is also an assessment at the end of the slides using different colors of candy to convert fractions to decimals and chart the results.

Individualization

Assign this problem to more advanced students:

Think back to what we learned in the previous lesson about fractions, decimals and percentages being three different ways of looking at the same number. You answered the two questions below. What is a different way to prove that 4/9 = 44%/

The game says that 5/9 = 56% – prove it using long division. Is this a repeating or terminating decimal? HINT: Remember that 56% = .56
The game says that 4/9 = 44% – prove it using long division. Is this a repeating or terminating decimal?

Google Slides and Math

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📖Standards

CCSS.MATH.CONTENT.6.SP.B.5.C Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

CCSS.ELA-LITERACY.RH.6-8.7 Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts.

⏰ Time

120 – 180 minutes (You may wish to use 2-3 class periods)

📲 Technology Required

The games used here require a Chromebook, Windows or Mac computers or iPads.

📃 Summary

Students play three games that teach fractions and statistics. Students learn enhanced features of Google slides. They then create a Google slides presentation stating which is their favorite game and why.

📚 Lesson

0. Optional: Google Slides Basics

If students are not familiar with Google Slides, begin with the Google Slides Basics lessons. If students know how to create slides document, select a theme, add text, images, transitions and animations, you can skip this step.

1. Introduce the assignment

Explain to students that they will be playing three different educational games and making a recommendation for future classes. If there is only time to play one of these games, which should the teacher choose. A copy of the assignment is here with both Chromebook and iPad games included. Save to your Google classroom or other system and delete whichever device is not available to your students. If your students have access to both devices, no editing is required. Since their presentation will be made with Google Slides and they want it to be as convincing as possible, they should include images and video to support their points.

2. Play AzTech: The Story Begins

This game teaches fractions and basic statistics, integrated with social studies terms and Latin American history.

Allow students 10 -15 minutes to play the game.

3. Learn about Google Slides Advanced Features

This presentation has links to six videos beyond Google slides basics.

Click on the links on the left side of the screen to learn about:

Modifying the theme
Inserting video
Adding effects to text and images

Allow 10-15 minutes to watch videos and start on their presentations.

4. Play Forgotten Trail or Fish Lake Adventure

Students play Fish Lake Adventure (iPad) a game that teaches fractions or Forgotten Trail (Chromebook), a game that teaches fractions and statistics.

Allow 10-15 minutes to watch videos and continue their presentations.

5. More Google Slides Advanced Features

Continue with more Google slides basics. Watch three videos on the right side of the screen on :

Customizing with Word Art
Publishing to the web
Presentation notes

Allow 10-15 minutes to watch videos and continue their presentations.

6. Play AzTech: Meet the Maya

Allow students the option of playing AzTech: Meet the Maya or continuing one of the two previous games. Meet the Maya continues the game series that teaches fractions and basic statistics, integrated with social studies terms and Latin American history.

Allow 10-15 minutes to play and continue their presentations.

7. Finish !

It’s decision time. Students will select one game to finish for their presentation. Students who finish ahead of the class may play the other games.

Allow 30 minutes to finish the game they have chosen and continue their presentations.

8. Optional (extra credit) Present or publish

Depending on your class and your own objectives, you may want to end this lesson with students either publishing their presentations to the web or presenting in class and trying to convince their classmates that the game they have chosen is the one students should be using to learn next year.

Allow 30 minutes to finish the game they have chosen and continue their presentations.

Fractions Equal to 1

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📖STANDARD

CCSS.MATH.CONTENT.3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

CCSS.MATH.CONTENT.3.NF.A.2.A Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

CCSS.MATH.CONTENT.3.NF.A.2.B Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

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.

⏰ LESSON TIME

45 minutes

📃 SUMMARY

This lesson plan will build upon the already introduced concepts and key terms of fractions in our “Introducing Fractions” lesson plan. Students will learn that a fraction N/N =1 and be able to solve problems with fractions equal to 1 in various contexts, including number lines, time and pizza.

📲TECHNOLOGY REQUIRED

Students will need a PC, Mac or iPad. Fish Lake is playable on PC and Mac through an online download and installation as well as on iPad through an App Store download. Students will also need access to the games.

📚 LESSON

Start the lesson by having your students watch the “Fractions Equivalent to 1” video. In this video, students are introduced to the concept of when fractions equal 1 and shown different examples. (This video is 3 minutes and 32 seconds.)

Fractions Equivalent to 1

Students will take the information from the video and use it to complete the “A Fraction Can Equal 1” activity in this Google slides deck. In this activity, students practice grasping the concept of a fraction, N/N, equaling 1 through different real-world situations. (20 minutes)
To end the lesson, students can play Fish Lake to further practice fractions. (20 minutes)

ASSESSMENT

Assessment is built into the conclusion of the activity where students break apart the number line into N parts, label the number line, and state what fraction equals 1. The last activity problem will show if students have understood the concept of N/N = 1. Fish Lake data reports are also available for teachers to access after students have finished playing.

STATE STANDARDS

Minnesota State Standards

3.1.3.1 – Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line.

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

Watch out for blood-sucking fishes!

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📖STANDARD

CCSS.ELA-LITERACY.RI.5.4 Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5 topic or subject area.

CCSS.MATH.CONTENT.5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

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

⏰TIME

40 minutes

📲TECHNOLOGY REQUIRED

Either a project or smart board connected to the computer will be required to view presentation and videos in class or students will need a computer to watch during a web meeting. The game can be played on any computer or tablet.

📃SUMMARY

This lesson introduces new science vocabulary words, teaches about indigenous and invasive species and includes a couple of math problems showing how quickly invasive species multiply. It concludes with students playing the Making Camp Dakota: Past and Present game.

📚LESSON

Watch the Mouths to Feed Video

Invasive Species Giant Insect!

This one-minute video is a little silly with a giant insect but it is a good starter for the lesson to spark student interest.

Give a presentation on indigenous and invasive species

This Google slides presentation introduces the concepts of indigenous and invasive species. It also provides geography information on the Great Plains and Great Lakes as well as a couple of math problems computing how quickly one fly can turn into 5,000.

This content can be assigned to students as reading, but we recommend the teacher present as a mini-lecture first, if possible, and include the reading for students to review.

Watch video Seven Ways to Leave Hungry Pests Behind

We recommend assigning students to write down any words in the video that they don’t recognize.

Play Making Camp Dakota: Past and Present

Have students access the Games Portal for Kids to play Making Camp Dakota: Past and Present. If you want sections specific to this lesson in indigenous plants and animals, have them select the two icons below.

In the LIFE section of Making Camp Dakota: Past and Present, select this icon to learn about how indigenous people used herbs.

In the NUMBERS section, select this icon to learn about buffalo hunting.

As an added bonus, the buffalo section ends with a question on division of three digit numbers.

Buffalo hunt long division problem from Making Camp Dakota — Buffalo Hunt Division – from Making Camp Dakota

Optional: Lesson challenges and extension

National Ag in the Classroom has four, related lessons at the sixth to eighth-grade level on invasive species. Some of the readings may be above the grade level, but they recommend “jigsaw reading” where each student in a group takes a piece of a reading, then explains that paragraph or two to the rest of the class.

If your students are interested in invasive species, or you want some students to have more of a challenge, we recommend checking out this resource.

Assessment

In-class formative assessment occurs when asking students to answer math problems during the lesson. Students learning remotely can post answers in chat. Students in a classroom can hold up a piece of paper with their answer, allowing the teacher to check understanding at a glance.

Completion and accuracy of the responses in Making Camp Dakota can be checked in the data reports.

Rates, Ratios and Proportions with Fractions

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📖STANDARDS

CCSS.MATH.CONTENT.7.RP.A.1 Compute unit rates, including those that involve complex fractions, with like or different units.

CCSS.MATH.CONTENT.7.RP.A.2.C. Represent proportional relationships by equations

⏰Time Required

30-45 minutes

📲Technology Required

Projector and computer required to watch video in class. Alternatively, students can be assigned to watch on computer, phone or tablet at home. Google apps or PowerPoint required for slide presentation.

📃Lesson Summary

Students watch a 4-minute video giving examples of finding unit rates by simplifying fractions. They solve a problem together as a class and are given a short lecture on solving rate problems with complex fractions. Problems provided can be worked by students individually or done together in class.

📚Lesson Plan

This lesson plan assumes that your students understand simplifying complex fractions. They should know how to divide a fraction by an integer or by another fraction.

1. Watch video explaining unit rates

2. Solve a problem as a class

Using this Google slides presentation, students solve a problem together as a class. They are reminded the meaning of “reciprocal” and that in dividing one fraction by another, you multiply by the reciprocal of the fraction in the denominator. Additional slides give students instruction and tips on solving rates problems that include complex fractions.

3. Solve a variety of problems involving rates and complex fractions

The problem set is found here and the answer key with problems solved step–by-step is here. You know your class best. If you have already covered complex fractions and rate problems, these can be used as formative assessment or review. Alternatively, you may wish to either:

Assign the problems, have the students give these a try and then correct together as a class.
Select some of the problems to review together and assign the remainder as homework.
Assign the problems for students to complete individually, as either in-class work or homework and grade using the answer key provided.

4. Watch a video of a student applying ratio and proportion

At this point, many students will still need further clarification. In this video, Eva shows how she uses ratio and proportion to reduce a recipe for 4 dozen cookies to one for 2 dozen cookies.

Assessment

Students will be assessed based on performance on the problems provided.

State Standards

Missouri Learning Standard 7.RP.A.1

Minnesota Math Standard 7.2.2.1 – Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.

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.