Category Archives: mathematics

Fill in the Blank: 3 Digit Dividends

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📖 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

55 Minutes

📃 SUMMARY

This lesson plan will have students reinforce the previously presented concept of long division of 3 digit dividends by 1 digit divisors through a short review, an animated video, a fill in the blank division word problem 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 PLAN

  1. Start the lesson by having a short review on dividing 3-digit dividends by 1-digit divisors. It is suggested to review the activity that was assigned in the previous lesson, “Build Your Own Division Problem” lesson. You can find the review copy of the activity here: “Review – Build Your Own Division Problem“. (15 minutes)
  2. How to Use Division to Solve a Problem – Start with this animated video on how to use long division, with 3 digit dividends, to solve different word problems. (Time – 1:24)

3. Have students work on the activity “Fill in the Blank: 3 Digit Dividends“. The activity has students fill in the blanks to complete the division word problem, identify the problem, and solve it. (Corresponding “Fill in the Blank: 3 Digit Dividends” Activity Jamboard that’s also linked in the activity above can be used by students as space to work out their division word problems.) (20 minutes)

4. Have students play Making Camp Dakota: Past & Present using our Games Portal for Kids. The division in Making Camp Dakota will be more practice for students on problems with 3 digit dividends divided by 1 digit divisors. (15 minutes)

ASSESSMENT

The “Fill in the Blank: 3 Digit Dividends” activity is not only allowing students to continue practicing the concepts previously introduced and reviewed in this lesson, but also serves as an assessment of how well the student grasps the concept of division using 3 digit dividends and 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.  

Build Your Own Division Problem

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📖 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

50 minutes

📃 SUMMARY

This lesson plan will build upon the introduction to division with 3-digit dividends from the “Dividing 3-Digit Dividends” 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.

📲 TECHNOLOGY REQUIRED

Students will need a PC, Mac or Chromebook. Students will also need access to “Making Camp Dakota: Past & Present” using our Games Portal for Kids. “Making Camp Dakota: Past & Present” is playable on PC, Mac, and Chromebook using any browser.

📚LESSON PLAN

  1. Start the lesson by having a short review on dividing 3-digit dividends by 1-digit divisors. It is suggested to review the activity that was assigned in the previous lesson, “Dividing 3-Digit Dividends” lesson. You can find the review copy of the activity here: “Review – On Your Way Home.” (10 minutes)
  2. Students will take the information reviewed and use it to complete the “Build Your Own Division Problem” activity. In this activity, students practice division using 3-digit dividends and 1-digit divisors through using virtual manipulatives. (20 minutes)
  3. To end the lesson, students can play Making Camp Dakota: Past & Present to further practice division. Students can access the game using our Games Portal for Kids. (20 minutes)

ASSESSMENT

The “Build Your Own Division Problem” activity is not only allowing students to continue practicing the concepts previously introduced and reviewed in this lesson, but also serves as an assessment of how well the student grasps the concept of division using 3 digit dividends and 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 – Fill in the Blank: 3 Digit Dividends

The “Fill in the Blank: 3 Digit Dividends” lesson plan will have students reinforce the previously presented concept of long division of 3 digit dividends by 1 digit divisors through an animated video, a fill in the blank division word problem activity, and game play.  

Counting ropes and rational numbers

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Contributed by Lori Hieresrich

📖 Standard

CCSS.MATH.CONTENT.7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

📃 Summary

The lesson begins with a discussion of record keeping methods in Indigenous cultures. Students will watch video on Incan counting ropes. Students will create their own number line counting rope. Students watch another video on number lines. Students will use their number line to find Absolute Value of an integer. Students will demonstrate understanding of adding and subtracting integers on number line.

⏰ Time

45- 60 minutes

📲 Technology Required

The videos can be watched on any computer, phone or tablet. Not technology, but each student needs 2 yards of cord. ( As long as needed for all the knots with even spaces between.) Thicker cord is better to make it more tactile. Cord that works could be hemp, leather strips, or twine.

📚Lesson

Start with this PowerPoint presentation. Also available as a Google Slides presentation.

NOTE: If you are using it as a PowerPoint presentation, download it before making any changes. Making changes to the PowerPoint in Google Drive will delete the animations and one of the embedded videos and you don’t want to do that.

The first five slides introduce the topic of how people from different Indigenous cultures in the Americas measured time and other quantities.

2. Watch this video on Quipu accounting

3. Make a counting rope

Students make their own counting ropes using rope, string or twine. Instructions to give students are provided in the PowerPoint.

4. Use the counting rope to solve math problems

Students follow along in the presentation to solve problems using positive integers , fractions and negative integers. The concept of absolute number is introduced, as well as the fact that adding the same number but with the opposite sign will always equal zero. If students are learning at home, they can complete the problems on their own.

Assessment

In addition to the problems completed as a class in the presentation, students complete this worksheet with problems on using a number line with positive and negative integers and absolute value. Only print the first page. The second page is the answer key.

Number line and absolute value – word doc

Number line and absolute value – pdf

Differentiated instruction (optional)

Knots on a counting rope video or the children’s book by the same name give other examples of using a rope to count. This would be appropriate for younger children or those in the class who are at a lower grade level in reading proficiency.

Recommended Related Lesson

The Codex in Latin American history and math

Mean, Median and Mode

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by Dr. Craig Waddell

📖 Standard

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context

⏰ Time

30-40 Minutes 

📲 Technology Required

Device with web-browser – Chromebook, laptop or desktop computer, phone or tablet

📃 Summary

Students play a game teaching basic statistics and history. Next, they are given a presentation with problems students solve finding mean, median, mode, range and outliers.

📚Lesson

Play a game teaching basic statistics and Latin American history

Meet the jaguars in AzTech: Meet the Maya

Play AzTech: The story begins. Students who have finished this game can continue on in the series in AzTech: Meet the Maya. Allow students 15-20 minutes to play.

Students can click on a button in the left of their screen to choose the language and play the games in either Spanish or English.

Assess knowledge of Mean, Median and Mode as a class

Use this Google slides presentation to present sets of numbers to the class to use for finding mean, median, mode and range. This is also available as a PowerPoint presentation.

This presentation can also be assigned for students to complete at home, if learning remotely. Slides with answers can be deleted, or left in for students to check their work.

Review as Necessary

If students need a review, they can watch this video on how to find the mean.

Finding the Average video

ASSESSMENT

You can view your students’ progress on mastering these standards by viewing your teacher reports. AzTech: The Story Begins and AzTech: Meet the Maya links can be found on this reports page. You should have received a password during the Growing Math training.

A second form of assessment is available through this the questions in the presentation.

Related lesson/ Differentiated Instruction

If your students need instruction on computing the mean, try this lesson, Understanding the mean, with skunks. This review can be done with the entire class or assigned to individual students as needed.

Mean, Median and Mode (Bilingual English and Spanish) – The bilingual version of this lesson plan that includes English and Spanish resources.

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

Map from Forgotten Trail

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.

Buffalo Hunts and Division

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📖 Standard

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

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.

NOTE: Teachers who have not yet covered decimals in their class have an option within the lesson to only teach the first standard.

⏰ Time

25- 30 minutes

📲 Technology Required

Computer or mobile device

📃 Summary

Begin with a video on long division (optional) or a presentation on uses of division from the playground to the buffalo hunt. 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.

📚Lesson

Video: Optional for Review

If your students need a review of the steps in long division, we recommend this six-minute video that uses the acronym HMS ↓ to teach students to :

  • Ask How Many
  • Multiply
  • Subtract
  • Bring down

Presentation on Division and Buffalo Hunts

This Google slides presentation gives common factors in buffalo hunts across different tribes and explains how whether it is computing the number of hides a horse can carry or how long each group gets to play at recess, division is always useful.

NOTE: This presentation includes two slides that reference converting a fraction to a decimal. If you have not yet introduced this concept, those slides can be deleted.

Video: Long Division by Guessing

For those students who don’t know where to start with long division – guess!

Play a Game – Making Camp Dakota

Select the Buffalo Icon (top left corner) in the first MATH screen to practice long division.

Math Screen #1 from Making Camp Dakota

Related Lessons

For more instruction on division check out these two lessons:

Related videos

These two videos, each about 1 minute in length, give more information on traditional Dakota buffalo hunts.

Becoming a buffalo hunter

Dakota deer and buffalo hunting

Ratio, Proportion and Animal Identification

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📖 Standard

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

⏰ Time

60-70 minutes

📲 Technology Required

A computer, phone or tablet with Internet connection is required to watch the video and play Making Camp Navajo. If these are not available, the assignment can be printed out and distributed to students or shown in the classroom on a projector with computer.

📃 Summary

Students hear or read a presentation on ratio, percentage decrease, rate and proportion. They watch a short video on ratio. Students collect data either outdoors or using images provided. They then compute ratio, rate, increase and proportion using the data.

📚Lesson

Review the concepts and introduce the assignment

Begin with this presentation that explains ratio, rate, percentage increase/ decrease and proportion. The presentation also introduces the assignment students will complete. There is a video included in the presentation on ratio. If you have difficulty playing the video Atlantean Dodgeball, in the presentation, here is the direct link.

Students complete data collection, ratio, rate and proportion assignment

There are four options for completing this assignment, depending on your environment. Ideally, students would collect data outside, but if you are in the middle of the city or it is winter and there are no animals around, you may want to select one of the other options. Allow students to choose one of the four options or delete whichever does not fit your situation.

If observing animals outside is not an option, here are two images your students can use to identify animals. Click the link for an image you can save in your Google classroom.

Scene 1- Animals in the savanna

Yes, all these animals can be found in the African savanna

Key for scene 1 – Image with animals labeled

Names of the 23 animals in scene 1

If students don’t have a partner, they can use Scene 2, Animals in unexpected places, for their second data collection.

Key for scene 2 – Image with animals labeled

Names of the 24 animals in scene 2

Play Making Camp Navajo

Play the Making Camp Navajo game to learn more about ratio and equivalent ratio.

(Available Fall, 2021). If you’d like access to the beta version, please email us at growingmath@7generationgames.com We’d be happy to provide it to you.

Differentiated instruction (optional)

The presentation discusses the animal kingdom and the six kingdoms many biologists use for classification of living organisms. For students who are particularly interested in this topic, the post, “Are insects animals?” can be provided as supplemental reading or teachers may wish to print this out for students who do not have home Internet access.

RELATED LESSONS

These two lessons are recommended for students prior to this assignment.

What is a statistical question?

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📖 Standard

CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts
for it in the answers

📲 Technology Required

Computer with projector, for students learning in class. For students learning at home, materials can be accessed on any device with a browser and application to read PDF files or can be printed out and sent home with students.

⏰ Time Required

2 hours (We recommend doing this over two class periods)

📃 Summary

Teachers begin the lesson with a Google slides presentation explaining the requirements for a statistical question. Students complete an assignment identifying whether or not a question qualifies as a statistical question. After class discussion, students complete a second assignment using a small data set shown on a map. In Part 3, students write and answer their own statistical questions using a data set provided, giving an explanation for their answers. Optionally, students can complete a more challenging assignment drawing conclusions from a graph and/or play a game and identify statistical questions.

📚 Lesson

Before you begin, you should have printed out or added to your Google classroom and shared with students the STUDENT handout from the U.S. Census Bureau, “What is a statistical question?” The student version is 11 pages. If you are short on printer paper, you can skip printing page 1. Also, pages 7 and 8 are an optional activity.

You should also print or download the TEACHER version of the Census Bureau handout, “What is a statistical question?” which includes answers to questions in the first two assignments and explanations why each answer was or was not a statistical question.

Introduce students to definition of a statistical question

Begin with the Google Slides presentation, “What is a statistical question?” which breaks down the two components of a statistical question – it must be answered by data and the data must vary.

Students complete assignment on identifying a statistical question

Have students complete Part 1 of the handout “What is a statistical question?” After all students have answered the questions in Part 1, discuss their answers in small groups or as a class.

Students complete Part 2, assignment on identifying a statistical question using real data

Have students complete Part 2 of the handout “What is a statistical question?” After all students have answered the questions in Part 1, discuss their answers in small groups or as a class.

Then, continue with the Google slides presentation and have students complete Part 2 of the student handout from the U.S. Census Bureau (linked above). Have students discuss their answers with one another.

Either correct the answers as a class or collect these to correct yourself. Remember, the teacher handout, linked above, has the correct answers.

We recommend you end the first day’s lesson here and begin the next lesson after students have had the assignments from Part 1 and Part 2 corrected.

Students complete part 3, creating their own statistical questions from data.

Students complete Part 3 of the handout on “What is a statistical question?”

Discuss students’ answers in class. Provide feedback on whether a question really is a statistical question and whether students’ answers to their questions are correct. Allow students time to explain their conclusions.

Optional: Students Complete Part 4

First, use the Google slides presentation, starting on Slide 24, to explain how to read an area chart.

Next, have students complete Part 4 from the student handout, “Drawing conclusions from a graph.”

AzTech: Empiric Empire

Optional: Play Empiric Empire

After students have completed Parts 1 to 3 of the student handout (and, optionally, Part 4), have them play the game Empiric Empire. As an additional optional assignment, ask students to identify statistical questions asked and answered during the game.

If students do not have phones but have Chromebooks, they can play Disaster Deduction Detectives instead – available June, 2022.

Assessment

For assignments in Parts 1 and 2 the teacher version of the handout has correct answers and explanations. For assignments in Parts 3 and 4 of the student handout, examples of correct responses are given but these will vary as students provide their own statistical questions.

For the Empiric Empire game, the teacher reports show student responses to questions. It should be noted that this game does begin with fractions and decimals, which are a prerequisite to statistics.

Teach Ratio with Math Snacks

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📖 Standard

CCSS.Math.Content.6.RP.A.1 Understand ratio concepts and use ratio reasoning to solve problems.

📲 Technology Required

Computer with projector, for in-class use. Computer or tablet with Internet access for home use.

⏰ Time

90 minutes

📃 Summary

Students watch a video from Math Snacks in which Isabella uses the ratio of words she speaks to her date to determine if it was a good or bad day. The video has a companion teacher guide with questions to stimulate students’ thinking about ratios and test their understanding. Students play a game where they brew potions with given ratios to defeat an opponent. Students then complete a learner’s guide assessing and reinforcing their knowledge of ratios.

📚 Lesson

Read the Bad Date Teacher Guide

The Teacher Guide, available from Math Snacks, will give you an overview of the lesson. This guide includes several discussion questions for use with students.

Watch the Bad Date Video

This three- and-a-half-minute humorous video uses the ratio of words in a conversation to show a couple of bad dates and one good one.

Have a class discussion

Use the discussion questions in the Teacher Guide from Math Snacks to check students’ understanding. Note that this will require you to restart and show the video again, stopping at specific points.

If you have not yet introduced equivalent ratios to your class, you may want to skip some of these questions and come back later.

Play the Game Ratio Rumble

The Ratio Rumble game can be played online here at the Math Snacks website or downloaded free for iPads. The first game level begins with 1:1 ratios and gets more complex in higher levels.

Students complete the learner guide

It’s called a learner guide, not a worksheet, so that makes it cool! Seriously, the Bad Date Learner Guide, available here from Math Snacks, has two pages of review and assessment items that test understanding. Students are asked to draw a picture of a ratio, complete “what-if” scenarios and give some examples of other situations in which 1:1 ratios would or would not be desirable.

Related lesson

For another introduction of ratio, see the lesson Introduction to Ratio and Proportion.

Scrambled states: Ag in math

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📖 Standard

NGSS 4-LS1-1:  Construct an argument that plants and animals have internal and external structures that function to support survival, growth, behavior, and reproduction.

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,

⏰ Time

3-4 hours over 4-5 sessions. The data collection will need to be completed at least two weeks after the seeds are planted.

📲 Technology Required

No technology is required. Students may use Jamboard for line plots and Google docs for word journals, but both of these activities can also be done on paper.

📃 Summary

Teachers read an age appropriate book about plants and record new vocabulary in their personal dictionary. The teacher or student selects an agriculture activity from the booklet More Scrambled States of Agriculture. Garden in a glove is one recommended activity. Students collect and record data on the number of days until germination, showing the results in one more more line plots.

📚 Lesson

It is recommended that this lesson follow the Scrambled States: Ag in Language Arts unit.

Read an age appropriate book about plants.

Both the lesson plan for Garden in a Glove and More Scrambled States of Agriculture booklet have several recommendations for age appropriate books on plants in general or specific plants, like wheat. Teachers may wish to read the book aloud to the class, have students take turns reading aloud, either in groups or as a whole class, or assign to students to read on their own. I recommend 2-3 sessions of 15 minutes of read aloud or 20 minutes of independent reading.

Update Word Journals

Students should update their word journals, what some teachers refer to as a “personal dictionary”, with any new words from the book. If this is your students’ first experience using a word journal, you may wish to give them this Google doc to read or read it together as a class, “Creating your personal dictionary.“

Select an Agriculture Activity (1 hour)

Garden in a glove lesson plan, found here, is my favorite and it could relate to almost any book on the list. You need:

  • Food prep gloves – 1 for each student – that you can probably get from your school cafeteria,
  • A bag of cotton balls
  • 5 different packs of seeds
  • A marker

Soak the cotton balls in water, put 3-5 seeds in each one and put five cotton balls, each with different seeds, in the five fingers of the glove. Don’t forget to write on each finger what is in it. Create a chart of the germination time for each type of seed. Read the lesson plan for more detail.

If Garden in a Glove doesn’t suit your needs, check More Scrambled States of Agriculture for ideas you might like better.

Ask students to generate hypotheses about how long it will take for the seeds to germinate, whether all the seeds will take the same amount of time (assuming you did Garden in a Glove).

Record your measurements

Students create either :

  • Create 5 line plot showing the number of seeds that germinated for each number of days, one plot for each type of seed, OR
  • Create one line plot with a different color used for each type of seed.

Ask the students whether their hypotheses were supported.

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.

Assessment

Three forms of assessment are included in this assignment.

  • In the personal dictionary or word journal, students are required to include a minimum of five words with definitions for 50 points. Each word, spelled correctly is 2 points and a correct definition is another 8 points. I deduct a point for grammar or spelling errors in the definition, but only one.
  • For the agriculture activity, this is simply pass/ fail marked as completed or not.
  • The line plots are scored based on accuracy. I give 10 points for each plot/ type of seed for a total of 50 points possible and another 10 points each for stating a hypothesis and answering whether or not it has been supported.