Category Archives: mathematics

Dividing 3-Digit Dividends

📖STANDARD

CCSS.MATH.CONTENT.4.NBT.B.6

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

⏰ LESSON TIME

30-45 minutes

📃 SUMMARY

This lesson will build upon the already introduced concepts and vocabulary of division in our “Introducing Division” lesson. Students will learn and be able to practice dividing 3 digit dividends by 1 digit divisors through a short review, activity, and game play.

📲TECHNOLOGY REQUIRED

Students will need a PC, Mac or Chromebook or tablet. Making Camp Premium and Dakota are both playable on any web browser on those devices. Students will also need access to the games.

📚 LESSON

Start the lesson by reviewing the important division basics. This Division Review Google Slides reviews “what we know.” The presentation goes over the definition of division, key terms, division symbols, and examples.

Have students work through the On Your Way Home division activity where they take what they know and practice dividing 3 digit dividends by 1 digit divisors. The activity takes division problems and puts them into real-world context, visiting stores on your way home from the park.

Have students play Making Camp Premium and/or Making Camp Dakota using our Games Portal for Kids. The division magnets game in Making Camp Premium can be used as review before moving on to Making Camp Dakota. The division in Making Camp Dakota will be more practice for problems with 3 digit dividends divided by 1 digit divisors.

ASSESSMENT

Assessment is built into the “On Your Way Home” activity through the creation of their own division problem after repeated practice of 3 digit dividends divided by 1 digit divisors.

Making Camp Dakota Teacher Reports

You can view your students’ progress on mastering these standards by viewing your Making Camp Dakota teacher reports. You can access the Making Camp Dakota reports here.

STATE STANDARDS

Minnesota State Standards

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.

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.

Related Lesson: Build Your Own Division Problem

The “Build Your Own Division Problem” lesson plan will build upon the introduction to division with 3-digit dividends from this lesson. Students will be able to continue practicing dividing 3-digit dividends by 1-digit divisors through a short review, an activity where students build their own division problems, and game play.

Multiplication Terms

📖Standard

CCSS.Math.Content.3.OA.B.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.)

CCSS.MATH.CONTENT.3.OA.A.1
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

⏰ TIME

40 minutes

📲TECHNOLOGY REQUIRED

In class:

Printer to print cards. Computer with projector in classroom to watch video. Access to computers or tablets to play games.Students can also play on phones.

Link for flash cards if you don’t have two-sided printing. Students cut and fold the cards.

Link for flash cards if you DO have two-sided printing. Just print out one sheet and have students cut out the cards.
Hint: If using this as a center activity or for multiple classes, teachers may wish to make a few sets of cards and laminate them.

Remote:

Computer with Internet access to view flash cards, watch video and play games.

📃 SUMMARY

Students watch a video on multiplication terms then review terms with flash cards. Students quiz each other with flash cards. The lesson closes with practicing multiplication and division by playing Making Camp Premium.

📚 Lesson

Watch video

Learn Multiplication Terms with Ms. Sancjhez

Perhaps you know the definition of a product and a factor, but what about the distributive property of multiplication? Have you ever thought about the Identity Property as a mirror or the Zero Property of Multiplication occurring because zero is a number that won’t share the spotlight? Learn these and more with Ms. Sanchez.

Make the Cards

I strongly recommend having students make their own cards. It saves work for the teacher, it is one more opportunity for students to see the material and some students learn better when physically engaged.

If you will be using printed flash cards, there are two downloadable PDFs.

If you can print two-sided, you can just print out these sheets. They can cut the cards out with scissors, with the term on the front and the definition on the back.

If your printer doesn’t print two-sided, you’ll find it easier to use these sheets because the definition of each term is next to it. The student can cut between cards and then bend in the middle of the paper to have term on the front and definition on the back.

Present multiplication terms to students (Optional)

Teachers may wish to present multiplication terms using this Google slides deck. Copy to your own Google drive and edit to add additional cards or explanation.

Review multiplication terms flash cards

Students review math cards individually.

Students can review using printed cards or review cards in a Google slides presentation shared with students . This activity should take 5-10 minutes.

Students review with classmates

After reviewing individually, students take 5 minutes to pair up and quiz their classmates. Students should take turns giving a term and asking for the definition. Students learning remotely can pair up with a classmate and take turns using the Google slides presentation to quiz one another.

Play a game

Students play the Making Camp Premium game to practice multiplication and division.

Assessment

Making Camp Premium offers Data and Reports for teachers to access after students are finished playing. If you are remote teaching students experiencing low internet connectivity students can play offline but the data will not be transmitted to show their progress.

Measurement and Augmented Reality

1 Reply

📖STANDARDS

CCSS.MATH.CONTENT.3.MD.B.4: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

CCSS.MATH.CONTENT.2.MD.A.2: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

⏰ TIME

40-50 minutes

📲TECHNOLOGY REQUIRED

The teacher will need a computer with projector or smart board to show the presentation. Students will need a tablet or phone to do the activity and a measurement app installed. They will also need a ruler or tape measure.

This is the second of three lessons that use Augmented Reality apps. If you did the first lesson on perimeter, you already have one of the measurement apps installed.

You’ll need a measurement app installed.

Measure: For iPhones or iPads

If using an iPhone, the Measure app should already be installed. On iPads, it may not be. Before starting this lesson, we recommend you check and, if not, parents or teachers can download the app for free here.

For Android Devices

Android devices do not come with a measure app. I tried several free AR measurement apps and all were difficult to use. I can’t honestly recommend any. Not an augmented reality app, but students can use the Ruler app by NixGame. It is simply a ruler on a phone and you can only use it to measure items the length of the phone/ tablet. We tried a lot of ruler and measure apps on Google Play and this is the one we recommend as the easiest for elementary school students to use and with the least annoying ads.

📃 Summary

Students learn that augmented reality is a type of computer application that adds to (augments) the reality we see. They learn that the measure apps on phones and tablets are a type of augmented reality. Students use an app to measure items, then use a ruler or tape measure to measure again. They plot their measurements on line plots and compare the two measures.

📚 LESSON

Short Presentation on Augmented reality.

Use this Google slides presentation to explain what is augmented reality, with examples. It also includes the video below.

Watch a video of an augmented reality app

This one-minute video is also in the Google slides but it is included here just in case, since we know media doesn’t always play in presentations, even when it should! (You can also check out some AR math apps here.)

Introduce apps your students will be using for measurement

Use this short presentation to explain how to use apps to measure, well, anything. If you already completed the first lesson on measuring perimeter and used this presentation, you may want to show it again to remind them and also to make the point that they were using augmented reality already and didn’t know it!

Measure Using Augmented Reality and Reality

Students find 10 items to measure using both the app and a ruler or tape measure. For each item, they complete the attached worksheet. Here is the same worksheet as a Google doc if are going to have them complete it online.

We strongly encourage the teacher to do one item with the class as an example. If your class has not yet mastered fractions, you may wish to tell them to just enter the whole number part of the measurement, as in this example.

Create two line plots

Optional: Watch this video on creating a line plot

If your students are not familiar with line plots, you may want to have them watch this seven-minute video which explains line plots step by step.

Now that students have watched the video and collected the data, their final task is to create two line plots of their results. Feel free to copy and paste the text below into your Google classroom or other assignment.

Line Plot Assignment

OPTIONAL: If students are learning online, they can use Jamboard to create a line plot, as shown in the video below.

You are going to make TWO line plots.

First, make a line plot of the ten measurements you did with the APP.
Second, make a line plot of the ten measurements you did with the RULER or TAPE MEASURE.

Now that you have your line plots, answer these questions.

Compare the two line plots. Do they look the same?
Compare your line plots with other students in the class.

Assessment

You can assess student’s progress through the assignment completed which shows both their measurement skills and ability to create and interpret line plots.

Individualizing Instruction

For students who are more advanced, you may wish to have them measure items and complete line plots using fractions or mixed numbers rather than just whole numbers.

Related lesson

The lesson Finding the perimeter and physical education is the first in the unit of augmented reality lessons.

Watch out for blood-sucking fishes!

📖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.

Ratio, rate and proportion

📖Standard

CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

📲Technology Required

⏰TIME

45 minutes

📃SUMMARY

In this lesson students are given definitions of ratio and rate and examples of computing rate and distance. Students complete a short assignment using animals observed outdoors as the data for computing ratio, rate and proportion. An alternative assignment is given for students learning at home or otherwise requiring modification. The lesson concludes with game play.

📚LESSON

Mini-lecture

Begin with this Google slides presentation defining ratio and rate and including examples of rate and distance problems. Students learning at home can read the presentation and do the activities and problems on their own.

OPTIONAL VIDEO

If your students are having difficulty understanding the problems, this video may help.

An example of solving time, rate and distance problems

Compute rate, ratio and proportion

In this short assignment, also linked in the Google slides presentation, using animals observed outdoors as the data for computing ratio, rate and proportion.

Everyone needs to get a partner. You and your partner will go outside and each count as many different species of animals as you can. Do this for exactly 5 minutes. Two of the exact same kind of animal only count as one species.
After 5 minutes is up, find the ratio of your animals compared to your partner’s list of animals.
Next, find the rate. How many animals did you see per minute?
Lastly, your group shall compare your ratio to another group. Are they proportional or non-proportional?

An alternative assignment is given for students learning at home or otherwise unable to work outside with a partner, where students find animals in two slides.

End with a game

Students play AzTech games for 15 minutes to end the lesson. Time-rate-distance problems are included as a bonus question in AzTech: The Story Begins and are required to win the game in AzTech: Meet the Maya.

Assessment

Once students have played the game, you can look in the AzTech teacher reports to see an individual students response. You will need to know your students’ usernames. To see an example of a report, enter the username “ddtester” .

Related lesson

Introduction to ratio and proportion is a recommended lesson prior to this discussion of rate, ratio and proportion

Rational numbers, adding and subtracting decimals

2 Replies

📖STANDARD

CCSS.MATH.CONTENT.7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers

CCSS.MATH.CONTENT.7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers

⏰TIME

30-45 minutes

📲TECHNOLOGY REQUIRED

A projector and computer in class or a computer, phone or tablet at home is required to watch the videos and see the Google slides. Slides can also be printed and sent home with students.

📃LESSON SUMMARY

Students watch two videos explaining decimal and fraction equivalence. They are then presented with a brief reminder of natural, integer and rational numbers. A slide presentation discusses adding and subtracting decimals. The lesson ends with teacher and student-generated practice problems.

📚LESSON

Since the previous lesson discussed rational numbers and fractions, we introduce this lesson with two videos explaining the equivalence of fractions and decimals.

Video Introducing Decimals

This three minute video discusses fractions, decimals and percents as three ways of expressing the same number.

This second video shows examples of fractions and decimals as equivalent.

Presentation and Practice Problems

Use this Google slides presentation to reinforce the understanding of rational numbers introduced in the previous lesson. Students can answer two formative assessment questions during a presentation or these can be done on their own with students learning at home. The lesson ends with students writing and sharing their own decimal addition and subtraction problems with classmates.

Enrichment Option

To provide motivated or advanced students more information on types of numbers, assign this optional two-page reading on types of numbers.

ASSESSMENT

Formative assessment problems are given in the presentation. Students also write their own problems and answers. AzTech: Empiric Empire teacher reports are available for assessing student answers in Data an d Reports.

STATE STANDARD

Missouri Learning Standards (MLS) 7.NS.A.1.a

Ratios as fractions

3 Replies

📖Standard

CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

⏰Time Required

10 minutes

📲Technology Required

Projector or smart board for in–class or access to computer or tablet for web meeting for remote learning.

📃Lesson Summary

Students are presented with definitions of ratio and proportion along with multiple examples and ways to solve these problems.

📚Lesson

Watch the video Ratios and Rates below, which discusses ratios and fractions.

Yes, this lesson plan is just a video. We watched LOTS of boring videos on ratios and rates to find this one!

This video can be used before or after the lesson on Introduction to Ratio and Proportion, either as an introduction for students who need more preparation or a second look for students who could benefit from having the material presented in a different way.

Assessment

Use assessment from Introduction to Ratio and Proportion lesson.

Understanding averages using skunks

3 Replies

📖STANDARDS

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context, such as by:

CCSS.MATH.CONTENT.6.SP.B.5.A Reporting the number of observations.
CCSS.MATH.CONTENT.6.SP.B.5.B Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

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.

⏰LESSON TIME

30 minutes

📃SUMMARY

In this lesson plan, students will learn how to find the mean and calculate the average and practice finding the average in a game environment. They will learn about skunks and skunk farming through primary source material. Then analyzing historical data, students will calculate the average.

📲TECHNOLOGY REQUIRED

Device with web-browser (Chromebook, laptop or desktop computer)

📚LESSON

Introduce the Assignment

Students can read the assignment, Going on a Skunk Hunt , on their own or teachers can read it to the class and ask any questions (5 minutes)

Through the next three activities – video, reading and assessment – students will gather clues to unlock the “secret password” for the Skunk Hunt and get to play a short online game. Individual links to the video, reading and assessment components are included below for your reference, but are all included in the Skunk Hunt activity as well for ease of student access.

The answer to the Skunk Hunt/secret password is: 3harvestnewyork1911

VIDEO

Watch this animated video explaining how to find the average. The video includes an example problem walking through the process, introduces the formula to find the average and also includes vocabulary to explain that mean and average the same thing. (2:00)

READING

Read this short post, Skunks for Fur and Farming , about the intersection of skunks and agriculture, incorporating information from primary sources and historical data. (5-10 minutes)

ASSESSMENT

In this assessment activity, Playing the Skunk Market ,students will use a table with historical data to solve two to four problems asking students to find the average. Two problems require solving for the average and two problems require solving for the average or estimating the average. (10-15 minutes)

ANSWER KEY AVAILABLE HERE.

RELATED: This lesson plan corresponds with the math standards covered in and refers to content included in Forgotten Trail. Forgotten Trail is recommended as a supplemental resource for this activity. The image at the top of this post is from that game. You can view your students’ progress on mastering these standards by viewing your teacher reports. You can access the Forgotten Trail reports here.

10-Minute Multiplication Practice with Ojibwe History

1 Reply

📖Standards

CCSS. Math 3OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

CCSS.MATH.CONTENT.3.OA.C.7– Fluently multiply and divide within 100

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

⏰Time Required

10 minutes

📲Technology Required

Computer/tablet with internet access for reporting student assessment data from Making Camp.

📃Summary

Ojibwe History Integrated with Math If your students are like most people, you’re having a hard time getting them to focus. Each of these three activities only takes a few minutes and teaches Native American history or multiplication. These 10-minute lessons can be done as stand-alone activities at the beginning or end of a class to raise student engagement, or the three in this unit can be combined for a single 30-45 minute lesson.

📚Lesson

Activity 1

Matching Multiplication

Step 1: Have students open Making Camp Premium. If you need more detailed instructions on how to access Making Camp Premium, student usernames and logging in, please go to this lesson plan.

Step 2: If students are playing the game for the very first time, they will watch the two introductory videos that talk about Native Americans and how to play the game (5 minutes). Then you will see the Making Camp choice screen.

Step 3: Have students click the NUMBERS box to view the six math challenges. You can press the round, green button at the bottom left with white squares to return to the choice screen at any time.

Step 4: Have students click on the top left box (with cards) to play a memory game. In this game, you match multiplication problems with their answers. You may assign this activity for 5 minutes of multiplication drills.

Activity 2

The Multiplication Dog

Step 1: Have students click on the icon with the dog.

This lesson opens with a paragraph explaining that some tribes used dogs to haul heavy loads, using a type of sled called a travois. The player then has the opportunity to earn a dog and items for their dog in the game by answering multiplication problems. The game resets when it is finished, and also takes about 5 minutes.

Activity 3

Reaping the Rewards of Math Practice at the Wigwam

The player should now have enough points to get a wigwam and at least two items to supply their wigwam.

Step 1: Click on the wigwam icon on the bottom left. This will play a video on how a wigwam was built, followed by a second video that briefly discusses that trading existed between and within tribes long before the settlers came.

Step 2: The player then has an option to trade points for items for their wigwam.

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Clicking on the wigwam in the lower left corner will bring the player to their wigwam. Purchased items appear here for decoration and interaction.

Clicking on an item brings up a text box with information on how that item was used or obtained by the Ojibwe people.

Some items also perform actions when clicked. For example, the parfleche opens to show pemmican inside; when clicked, the dog walks across the wigwam.

This image has an empty alt attribute; its file name is mv-206x300.jpg

Assessment

Making Camp Premium offers Data and Reports for teachers to access after students are finished playing.

State Standards

Minnesota History Substrand 2, Standard 3. Historical events have multiple causes and can lead to varied and unintended outcomes.

Related: 10-Minute Multiplication Practice with Ojibwe History (Bilingual English & Spanish)

The lesson above has a companion lesson for English Learners. 10-Minute Multiplication Practice with Ojibwe History (Bilingual English & Spanish) is the same lesson from above but provides the resources in English and Spanish, featuring Making Camp Bilingual.

Introduction to ratio and proportion

5 Replies

📖Standard

CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

⏰Time Required

30 minutes

📲Technology Required

Projector or smart board for in–class or access to computer or tablet for web meeting for remote learning. Presentation could be printed for students at home without computer access.

📃Lesson Summary

Students are presented with definitions of ratio and proportion along with multiple examples and ways to solve these problems.

📚Lesson

Introduce ratios and proportions

Use the Google slides presentation for definition of ratio and proportion and some practice problems.

NOTE TO TEACHER: This presentation includes multiple explanations for multiple levels of understanding. There is a solution using algebra, with cross-multiplication and an explanation of why cross-multiplication works. There is also an explanation using equivalent fractions. If you are teaching an algebra class, use the first explanation and delete the second. For a more basic math class, delete the first explanation and just use equivalent fractions.

Use ratio and proportion in real life

The end of the presentation gives a recipe for biscuits. You can delete the answer in slide 29 if you want to test their knowledge or you can leave it in for students to check themselves.

Here are three ways you can use this:

Have students actually bake using their recipe solution.
Have students simply answer the question (easiest)
Select one or more incorrect answers as well as the correct answer and bake yourself. Then bring the results in and have students taste them. This takes more work from the teacher but can be pretty hilarious if you feel in a baking mood or can get a volunteer to do it.

Assessment

Assessment can be done as a group, having students answer the questions posed in the presentation or students can submit answers individually.

Related lesson

Ratios as fractions is a nine-minute video that can be used to preview this material or for re-teaching for those students who are still struggling.