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

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

Minnesota State Standard – History Sub-strand 4, Standard 15 “North America was populated by indigenous nations that had developed a wide range of social structures, political systems, and economic activities, and whose expansive trade networks extended across the continent.”

Time

20 minutes

Technology required

Internet connection on a PC or Chromebook laptop, tablet, or phone.

Summary

Students watch a video on the importance of the Red River cart in expanding trade. The teacher presents (or students may read) a presentation discussing Red River carts followed by two related word problems. The lesson concludes with students playing Making Camp Premium, reinforcing multiplication facts and the Ojibwe history lesson learned.

Lesson

Watch Red River Cart history video

Presentation on Red River Carts and multiplication

Use this Google slides presentation in-class or assigned online to review a little on the Red River cart and then solve two math problems involving carts and horses. In the first activity, the students drag the correct number of wheels to show 5 groups of 3 and then 3 groups of 5, both correct answers to the question. In the second problem, students drag 4 groups of 6 horses to solve the word problem.

Play a game

Students play Making Camp Premium (instructions on which activities are included in the slides presentation).

Assessment

Making Camp Premium offers Data and Reports for teachers to access to view students playing time and the number of items answered correctly addressing each standard taught in the game.

This cross-curricular lesson includes activities and instruction in agricultural science and math. Students begin by watching a video and learning about pig farms. After making their own pig barn, they watch two short videos about solving math problems. This information is then applied to solve problems during a presentation on math around the pig farm. Students end playing one of the Making Camp games to reinforce skills and knowledge.

Technology Required

If teaching in person, the teacher will need a computer and projector or smart board to show the videos, or students can be given the links to watch on their own devices. Students will need a PC, Mac or Chromebook or tablet. Making Camp Premium, Making Camp Lakota and Making Dakota are all playable on any web browser on those devices.

Lesson

This lesson starts with resources from National Ag in the Classroom

Virtual tour of pig farms

Make a Pig Barn

This activity requires a few supplies but it is probably things you have lying around and your students will probably enjoy it.

Business-size envelopes, 4 per group

Paper towel, 1 per group

Scissors

Scotch tape

OPTIONAL

Markers

Toilet paper rolls, 2 per group

Drinking straws, 2 per group (cut into 8 equal pieces)

8.5″ x 11″ white paper, 1 per group (cut in half)

Extra paper for making fencing, pipes, feed troughs, etc. (optional)

Instructions

Use the following instructions to model for the students how to create the barn:

Barn: Cut an oval hole in one envelope, making a large side window for the barn. This window provides the proper ventilation for the pigs.

Cut the paper towel in half and tape it onto the top of the window for the curtain.

Cut another envelope in half for the ends of the barn.

Tape the ends of the barn to the “sides of the barn” envelopes, one of which has the hole for the window and paper towel curtain, so that you have four sides, or a rectangle.

Use the final envelope to create a roof by creasing it in half lengthwise and attaching it with tape to the top of the rectangle.

Food Storage: Tape four straws, or legs, to each toilet paper roll so that the structures will stand on the legs.

Use a half piece of paper, and make a cone shape by twisting and taping the ends. Tape the cone shape on the end of the toilet paper roll without the straw legs.

Use the other half piece of paper to make another smaller cone shape and tape it between the straw legs on the other end of the toilet paper roll.

If you’d like, you or your students can watch the instructions here. You can also assign this video for students learning at home to watch so they know how to make the barn. The plus is that just about every house will have every single one of these items except possibly the straws.

Optional additional science and language arts content

This link to the National Ag in the Classroom lesson has more information on pigs and pig farming, including some of the vocabulary used in the math lesson as well as a discussion of the ways farmers care for animals. I highly recommend checking it out.

Watch a video on operations key words

Trust me, this does come back to pig farming!

Students watch this video on operations keywords. This two-minute video has been watched over 14,000 times, which gives some indication of how useful students and teacher find the concept of looking at the words in a problem to decide which operation to use.

Watch a video on problem-solving – Start at the end

This 3 1/2 minute video explains that the end of the word problem is where you usually will find the question you are expected to solve. It includes one easy and one harder example, as well as a couple of useful tips.

Give a presentation

This 34-slide deck on problem-solving reinforces the information in the two math videos and gives students three problems of increasing difficulty where they have to start at the end, all centered around Laura’s pig farm.

Play a game

Now that students have been introduced to problem-solving with multiplication and division word problems, it’s time to play a game and reinforce those skills. Which game depends on what you feel your students need most. There is overlap among the games as each includes some review.

Making Camp Premium – focuses primarily on multiplication of one- and two-digit numbers. Also includes division with one-digit divisors. The content is taught in the context of Ojibwe history and culture.

Making Camp Lakota – focuses primarily on division with one-digit divisors. Also includes multiplication of one- and two-digit numbers. The content is taught in the context of Lakota history and culture.

Making Camp Dakota – focuses primarily on division of three-digit numbers with one- and two-digit divisors. Also includes multiplication of one- and two-digit numbers and division with one-digit divisors. The content is taught in the context of Lakota history and culture.

Assessment

Assessments are built into the presentation, as teachers can have students submit their answers in writing or in a Google chat prior to giving the answers during the presentation. Teachers can also see which standards students have attempted and how many problems they have answered correctly in the Making Camp teacher reports.

As the title suggests, this lesson introduces students to two other problme-solving strategies. They watch a video on visualization, then solve a problem that asks them to visualize. After watching a video on building a model, students build and/or draw their own model of a multiplication problem or property.

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.)

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.

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.

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. 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.

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.

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 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

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.

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.

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.

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!

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!

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.

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. This is the ninth in a 10-unit English/ Language Arts unit centered around a visit to their grandmother that integrates English/ Language Arts and indigenous history.

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 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

NOTE: Making Camp Dakota will be available by the end of March, 2021.

You may allow your students to just play the game, or, 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.

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.

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.

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” .

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.

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.