Category Archives: fractions

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?

Unit: Word Problems for fifth-graders

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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.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.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.

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.

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

CCSS.MATH.CONTENT.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths

CCSS.MATH.CONTENT.5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Time

Approximately 2.5 hours

Unit Summary

This cross-curricular unit includes a variety of strategies and examples for solving word problems at a fifth-grade level, including division of three-digit numbers, fractions and decimals.

Buffalo Hunts and Division

This lesson begins with a video on long division (optional) or a presentation on uses of division from the playground to the buffalo hunt. Students then 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.

Watch out for blood-sucking fishes!

This 40-minute 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. Math word problems require finding half of 500 and 10 x 500.

Using Visual Models To Compare Fractions

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. (35-45 minutes)

Decimals, Epidemics & Fly Vomit – It’s science!

Learn decimals while weighing a flies and the food they eat. The lesson begins with a game on decimals and the Aztec smallpox epidemic, then moves to another disease spreader – flies. Students learn the role flies play in our ecosystem, how they eat and reproduce. (75 minutes)

Differentiation

For students who are struggling with word problems, assign these videos directly teaching strategies or watch together in class.

Word Problem Solving: Write down the numbers and what they represent. This is helpful if you have a lot of numbers and when you have to keep track of several details. A chart organizes data from the word problem. (3:17)
Problem-solving: Start at the end To make those pesky word problems easier. We’ve broken it down for you in this short video for Grades 3-5.
Duration: 3:31
Problem-solving tip: Throw it out This short video shows how to make a problem easier by throwing out information that you don’t need. Duration: 3:39

Using Visual Models To Compare Fractions

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Standards

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

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.

Better Dirt, Better Lives

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📖STANDARD

CCSS.MATH.CONTENT.4.NF.A.1
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

📲Technology Required

Students will need a Mac or Windows computer with the Fish Lake game installed. A video can be a substitute for students who do not have access to one of these devices.

⏰Time

30 minutes

📃Summary

Begin with playing the Fish Lake game. A video of the section on crop rotation may be used by schools that don’t have Fish Lake installed. Give a presentation (included) on crop rotation. Watch a video on “What is one-half” and end the lesson with a presentation (included) on whether one-half is fair.

📚Lesson

Play Fish Lake or watch video of game play

Even though you can use this lesson without playing the game, I urge you to install Fish Lake on your iPads, Mac or Windows computers. You can download it for free for computers. For iPads, email support@7generationgames.com for a discount code and we’ll get back to you the same day. Seriously, even if you normally use Chromebook, it will be a nice break and your students will love it. We recommend letting them play for 15 minutes.

Play the game Fish Lake, (available to Growing Math schools, on iPad, Windows or Mac computers). If students do not have devices to access the game, students can watch a video here.

Slide presentation on crop rotation

Use this Google slides presentation to explain crop rotation as more than just being sure each farmer did her fair share of the work or had a fair share of the fields. It was good science.

Watch a short video: What is half ?

This short (1:40) video explains that one-half is two equal parts, with examples of one-half as a distance between two points or as a shape divided into two parts.

Slide presentation on one-half as fair

Use this Google slides presentation to show two halves are equal and that 2/4 = 1/2. Multiple examples of dividing something in half are given, from six blankets to half a deer. Students can also read the presentation and manipulate the examples on their own.

Assessment

Fish Lake data reports are available for teachers to access after students have finished playing.

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.

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.