Tag Archives: fractions

Fractions Equal to 1

📖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.

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.