Author Archives: AnnMaria De Mars

Using estimation in multiplying two-digit numbers

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📖 Standards

CCSS.MATH.CONTENT.4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.

CCSS.MATH.CONTENT.4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operation … Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

⏰ Time

This lesson takes 40 minutes to an hour, depending on how long you allot your students to complete each of the 4 problem sets and whether you have students play the game.

📲 Technology Required

Computer with a projector, Smartboard or other device for your class to watch videos or videos can be shared in Google meet or other application for remote learning. Spirit Lake: The Game can be downloaded and played on Windows or Mac computers. An iPad version will be available by Fall 2021. Schools that are part of the Growing Math project or who have a 7 Generation Games site license will have access to all of these games for students to use at home or school.

Optional Recommended Resource

Use resources like the Helping Math Multiplication Worksheet Generator to make your own worksheet. Their worksheets look very much like this one on multiplication of two-digit numbers with Easter egg examples, except with many more activities in each worksheet. Note that the link will require you to register for a free download. Registration takes about 1 minute. You’ll then receive a link to download over 100 free worksheets on math topics from addition to rational numbers. Another resource we like is the Lizard Point math worksheet generator. Both will print the worksheets as well as the answer key. Note that sites using PRINT TO Google Drive may have that feature disabled after December, 2020. However, you can still from the PRINT menu select SAVE AS PDF, download a file as PDF and then upload it to your Google Drive. The Growing Math project has no affiliation with Helping Math or Lizard Point.

📃 Summary

You’ll need 20 math problems multiplying two-digit numbers. You can use math problems you already have or use one of the online worksheet generators. Based on research showing the effectiveness of distributed practice – that is, practicing a skill for more, shorter periods rather than one long session – we have students solve a few problems at a time, with videos in between. The lesson begins with a brief explanation of multiplying two digit numbers, followed by students solving 3-5 problems multiplying two-digit numbers. Students then watch a 3-minute video that works an example of multiplying a three-digit number by a two-digit number. They then solve 3-5 more problems, followed by another video, then more problems. We recommend giving a time frame – say, 7-10 minutes – to solve the problems rather than set number of problems because this allows you to begin and end each section of the lesson with all of the students at once.

📚 Lesson Plan

1. Introduction to Multiplying Two-digit Numbers

Begin with an example from Helping with Math, that gives an explanation of multiplication and a variety of types of problems. Then, have the students try to solve 3 to 5 problems. You can use those included in the Google slides linked or create your own.

2. Video : Multiplication and Estimation

Estimation is one of the most practical math skills!

There are a lot of math concepts that I use regularly when writing software or computing statistics in my day job. The one skill I use all the time is estimation. (I can tell you that the ability to accurately estimate an answer is not universal.)

Example 1: Long multiplication using “math reality checks.”

In the problem in the video above, we start out by multiplying 892 x 11, using the fact that any number multiplied by 10 is just that number with an added zero. To test our answer, we round 892 to 900 and can estimate that our answer should be near to – and less than – 9,900.

Let’s say you type the wrong number in your phone, hitting the 6 instead of the 9, since these two are pretty close and you have big fingers. Now your answer is 7,612. If you have a good grasp of estimation and multiplication, that is clearly wrong. If you’re computing how much money you need to charge a customer based on the 892 hours you expect to work at $11.00 per hour, you have just lost out on over $2,000!

3. More multiplication problems

Now that you have had a little practice and a little instruction, students solve another 3-5 problems.

4. Video : Multiplication and Estimation

This video works through a problem multiplying a 3 -digit number by a two-digit number . It also gives a strategy for solving difficult problems. That is, break the problem into smaller, easier problems.

Video 2: Use addition to solve a multiplication problem.

Here, because the last digit of one number is 7 and of the other number is 2, you know that 7 x 2 = 14. So, whatever else your answer is, it has to end in a 4.

5. Follow up to the video

As a math teacher, I heard approximately 4,897,234 times from students:

WHY do I have to do so many problems of the same type?

– Almost every student I ever taught math

Explain to students that all of those facts learned, like 2 x 7 =1 4 are the basis for the commutative property of multiplication, reducing numbers to lowest terms, or solving equations by multiplying or dividing both sides by a constant, and more. You need a BASE to work from, problems that can be examples.

The fact is that the more experience you have with numbers, the more problems you solve. The more problems solved, the easier it gets.

6. Finish off by a few more math problems

Now that you’ve watched another video, it’s time for the last set of math problems.

7. Optional – Game Play

Students can Spirit Lake: The Game . Multiplying two- and three-digit numbers comes up in Level 4. We recommend allowing students to play for 15-30 minutes each session. This gives them enough time to get started but not enough time to get bored.

Assessment

Answers to the 12 -20 math problems completed by the student provide one assessment. A second assessment is in the reports for the Spirit Lake game, which show whether students answered correctly the problems in Level 4, whether they read the hint before answering the problem, and whether they were correct on the first try or had to attempt the problem more than once.

State Standards

Minnesota Math Standard 4.1.1.3 – Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.

Minnesota Math Standard 5.1.1.4 – Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.

Finding the perimeter & physical education

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📖 Standards Taught

CCSS.MATH.CONTENT.2.G.A.1

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal face

CCSS.MATH.CONTENT.3.MD.D.8 Solve real world and mathematical problems involving perimeters of polygons

⏰ Time

45 – 50 minutes depending on the time you allot to students for measuring objects and for playing the game.

📲 Technology Required

Making Camp Premium plays in any browser, so, of course, on Chromebooks. It can also be downloaded on phones or tablets and played offline by students who have limited Internet access. The teacher will need a computer, for showing to students learning from home, and a projector if showing videos in the classroom. If the classroom does not have access to a projector, the videos can be skipped. A phone or tablet with a measuring app is optional. If unavailable, students can use a ruler or tape measure instead. NOTE: The measure app comes on iPhone/ iPad by default but for an Android device you’ll need to install some type of measuring app.

Note: This is the first of three lessons using these apps, so once you have them installed, you will be set for the next two.

Measure: For iPhones or iPads

Measure app

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

Ruler app

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

Finding the perimeter activities can be fun in school or out. This is an activity recommended for children learning at home, so the instructions below target what you would send to parents, but this activity can be easily adapted for in-school use as well. Best of all, it combines math with P.E. ! Students watch a video, find the length and width of 10 objects and compute the perimeter. After the hands-on activity, students watch another video to reinforce the concept and then play the Making Camp Premium game to practice their multiplication and division.

Materials needed:

  1. A piece of paper
  2. A pen or pencil
  3. A phone or tablet – if not available, a measuring device like a ruler, measuring tape or yardstick can be used instead.
  4. Making Camp Premium (available online and for download on iOS and Android devices)

📚 Lesson Plan

Step 1: Watch the perimeter video

How to find the perimeter of polygons – 2:21

As you might guess from the title, this video explains how to find the perimeter of an object and how to determine if a shape is a polygon.

Step 2. Make a table like in the example below

OBJECTLength     Width     
Top of a box
Seat of a chair    

You can have a Google Doc you share with students with the table in the instructions. However, we recommend that students create their own table with a piece of paper because they are going to be wandering around the house or classroom and it is much easier to carry a piece of paper with you than a laptop.

For this exercise, every object should be a rectangle. Be prepared for the question,

“Is a square a rectangle?”

– every third-grader , ever

Yes. Yes it is. If you want to get technical about it, a rectangle is a quadrilateral with four 90 degree angles. Or you could just say yes, a rectangle is a shape with four sides that are not slanted and a square definitely has four sides and is not slanted.

Step 3. Introduce measurement with apps

This short Google slides presentation shows how to use the Measure app and the Ruler app.

Step 4. Go measure 10 rectangles in the house

This is where the physical education comes in. Tell the student he or she has 10 minutes to complete the table with 10 items. An item can be as small as a box of candy or as big as the floor of a room. For each rectangle, write down the name of the object, the length and the width. Just put the whole number. If it says 18 1/4 or 18 1/2 just put 18. You may be tempted to tell the student to just round it but remember, he or she may not have learned fractions yet. That’s a lesson for another day.

If you don’t happen to have a ruler, yardstick or tape measure, your phone may already have a Measure app. This comes by default with an iPhone and if you don’t see it right away look in the Utilities folder. Most kids this age take any opportunity they can get to get hold of a parent’s phone. In school, you can use iPads or go old-timer and use a ruler.

To use it, point at a surface and click to select a point. Then, move the phone until you are at the end of what you want to measure.

Depending on how much exercise you want your child to get, the size of your house and how much peace you need (I won’t judge you), you may want to add a few rules like:

  • None of the objects can come from the room you are currently in.
  • They need to find rectangles in at least 3 different rooms
  • They need to find at least one rectangle in the backyard/ garage/ basement.

Once you have shown your child how to use the measure app and they have the table and a pencil, set the alarm on your phone and tell them to go. The alarm will go off when the 10 minutes are up.

Check their number of rectangles and if they are a few short give an extra 2- 5 minutes to find the rest.

Don’t have an iPhone or iPad?

The Ruler app can be downloaded free from Google Play and used to measure small objects. It only works to the size of your device but it is still easy to use and fun. There are apps in Google Play similar to the iPhone Measure app but these are not available on all Android phones.

Step 4 Watch another video on perimeter

Why? Because experience shows that students often don’t remember something if they only heard it once.

Step 5: Compute the perimeter for each object you have measured

OBJECTLength     Width     
Top of a box84
Seat of a chai r     1812

Your student does this, not you. You’ve already completed elementary school.

Step 6: Play Making Camp Premium

Making Camp Premium logo

Tell students that these videos came from Making Camp Premium and now that they have finished the rest of the assignment they have 10 minutes to play.

Assessment

This lesson includes three types of assessment, the table of measurement, the perimeter computations from those measures and the automated data collection and scoring from the Making Camp Premium reports.

Related Lesson

The next lesson in this series is Measurement and Augmented Reality .

State Standards

Minnesota Math Standard 2.3.1.1 – Describe, compare, and classify two- and three-dimensional figures according to number and shape of faces, and the number of sides, edges and vertices (corners).

Minnesota Math Standard 3.3.2.2 – Find the perimeter of a polygon by adding the lengths of the sides.

Multiplying one-digit numbers from 6 to 9

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📖 Standards

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.

CCSS.MATH.CONTENT.3.OA.A.3– Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

CCSS.MATH.CONTENT.3.OA.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, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

⏰ Time

Each lesson will require 20-30 minutes. With the four lesson plans, total time is approximately 1 1/4 to 2 hours spread over one to two weeks.

📲 Technology Required

Making Camp Premium plays in any browser, so, of course, on Chromebooks. It can also be downloaded on phones or tablets and played offline by students who have limited Internet access. The teacher will need a computer, for showing to students learning from home, and a projector if showing videos in the classroom. If the classroom does not have access to a projector, the videos can be skipped. Spirit Lake: The Game can be downloaded and played on Windows or Mac computers. Schools that are part of the Growing Math project or who have a 7 Generation Games site license will have access to all of these games for students to use at home or school.

📃 Summary

Our single-digit multiplication series is for Grade 3, although some teachers find themselves doing this in grade 4. The lesson plans with PDF links for printing and Google slide presentations are provided below. We assume you have already completed multiplication tables for 0 through 5 and for the 10s table.  While it may be tempting to do all lessons in one week, we have found it works better to spread this over a two-to three-week unit.

  • Students use visual drawings, manipulatives, and a number line to learn multiplication of one-digit numbers, coupled with their verbal explanations.
  • Students will create number sentences independently and with a partner.
  • Learning and memorizing multiplication patterns will improve later understanding of division.
  • Determine the unknown whole number in a multiplication equation relating three whole numbers.
  • Optional Brain Power activities have students write their own word problems.
  • Students play games that reinforce memory and apply multiplication in word problems.

📚 Lesson Plans

Learning from home / hybrid learning tip

Several lessons include an activity, “Work with a partner.  Take turns creating your own number sentences and solving them.” This can be modified in three ways:

  • In a hybrid class, where students come in half of the days, have students leave the number sentences to be solved by the other half the following day. Of course, students can also do the activity with other students in their class that day.
  • If students are learning from home using Zoom or Google Meet, they can post their number sentences in the chat for other students to solve.
  • Students at home can include their number sentences in homework they return either in packets or electronically and receive number sentences submitted by other students returned in the same format (homework packets, email, etc.)

If students have unreliable Internet access, the Spirit Lake Demo can be downloaded on Mac or Windows computers and played off line. Installers are available for Windows and macOS.

Lesson 6 – Multiplying by 6

Tell students that this week they are going to learn how to multiply numbers from 6 to 9. Now that they know most of their multiplication tables from 0-5, they are ready to play Making Camp at the end of the lesson. Start with this Google slides presentation that introduces multiplication and arrays. Feel free to modify the slides to provide more explanation as needed by your students.

Teaching students at home and need to print out the slides? Click here for a PDF.

End the lesson by playing Making Camp Premium or Spirit Lake for 15-30 minutes.

Lesson 7 – Multiplying by 7

Depending on your students’ progress and interest, you may want to hold off on this lesson for another day or jump right into it after the six tables. Personally, I find it works much better if these lessons are spread out across at least one day each. Today’s lesson starts with a Google Slides presentation that practices multiplying by 7.

Teaching students at home and need to print out the slides? Click here for a PDF.

End the lesson by playing Making Camp Premium or Spirit Lake for 15-30 minutes.

Lesson 8 – Multiplying by 8

Almost there! For a little variety, start the lesson with a game, either Making Camp Premium or Spirit Lake. After playing the games, for even more variety, this Google slides presentation shows students how to insert images in Google doc or slides files so they can create their own illustration of concept like 8 x 6 = 48 .

Teaching students at home and need to print out the slides? Click here for a PDF.

8 x 6 = 48 pigs

Lesson 9 : Multiplying by 9

Hurray! We did it! Today’s lesson covers multiplying by 9, with skip counting, a brief review of arrays, students creating their own number sentences and a little variety with students finding objects around their class or home to show 9 x 9 = 81 or other number sentences you assign/ they create. You may want to modify the Google slides presentation for today to emphasize any area where your students struggled or you think they need a refresher.

9 x 9 = 81 dots

After the presentation, students should play Making Camp for 15-30 minutes. If you would like stickers, pencils or other incentives to give your students to congratulate them for learning their multiplication tables to 100, just email support@7generationgames.com and we’ll be happy to send you a teacher gift pack.

End the lesson by playing Making Camp Premium or Spirit Lake for 15-30 minutes.

Teaching students at home and need to print out the slides? Click here for a PDF.

Assessment

Each lesson includes multiple assessment:

  1. Students complete the multiplication tables – these can be shown with a projector (in class), on a screen, if teaching remotely, and on paper for students learning at home.
  2. Students write their own number sentences using the multiplication learned each lesson.
  3. Students complete the problems written by their classmates.
  4. Optionally, students write word problems.
  5. Optionally, student complete word problems written by their classmates.
  6. Making Camp Premium and Spirit Lake both have teacher reports showing the number of multiplication problems attempted and answered correctly.

State Standards

Minnesota State Standard 3.1.2.3 – Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division.

Minnesota State Standard 3.1.2.4 – Solve real-world and mathematical problems involving multiplication and division, including both “how many in each group” and “how many groups” division problems.

Minnesota Math Standard 3.2.2.2 – Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true.

Multiplying one-digit numbers: 0 to 5

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📖 Standards

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.

CCSS.MATH.CONTENT.3.OA.A.3– Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

CCSS.MATH.CONTENT.3.OA.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, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

⏰ Time

Each lesson will require 20-30 minutes. With the five lesson plans, total time is approximately 2 to 2 1/2 hours spread over one to two weeks.

📲 Technology Required

Making Camp Premium plays in any browser, so, of course, on Chromebooks. It can also be downloaded on phones or tablets and played offline by students who have limited Internet access. The teacher will need a computer, for showing to students learning from home, and a projector if showing videos in the classroom. If the classroom does not have access to a projector, the videos can be skipped.

📃 Summary

Our single-digit multiplication series is for Grade 3. The lesson plans with PDF links for printing and Google slide presentations are provided below. If you need to go back to basics, visit ‘Multiplication as Repeated Addition.’  While it may be tempting to do all lessons in one week, we have found it works better to spread this over a two-to three-week unit.

  • Students use visual drawings, manipulatives, and a number line to learn multiplication of one-digit numbers, coupled with their verbal explanations.
  • Students will create number sentences independently and with a partner.
  • Learning and memorizing multiplication patterns will improve later understanding of division.
  • Determine the unknown whole number in a multiplication equation relating three whole numbers.
  • Optional Brain Power activities have students write their own word problems.
  • Students play games that reinforce memory and apply multiplication in word problems.

📚 Lesson Plans

Learning from home / hybrid learning tip

Several lessons include an activity, “Work with a partner.  Take turns creating your own number sentences and solving them.” This can be modified in three ways:

  • In a hybrid class, where students come in half of the days, have students leave the number sentences to be solved by the other half the following day. Of course, students can also do the activity with other students in their class that day.
  • If students are learning from home using Zoom or Google Meet, they can post their number sentences in the chat for other students to solve.
  • Students at home can include their number sentences in homework they return either in packets or electronically and receive number sentences submitted by other students returned in the same format (homework packets, email, etc.)

Lesson 1 – Multiplying by 0 or 1

Tell students that this week they are going to learn how to multiply numbers from 0 to 5. On Friday, they will be able to play games that use multiplication. They can watch the video below to see what’s coming up. It is deliberately a quick view to get students curious and motivated to get to the games coming up.

Students learn the meaning of a number times zero, or zero times a number, both as regards to equal-size groups and number line jumps. Today’s lesson starts with a Google Slides presentation that shows how multiplication of 0 and 1 works. Feel free to modify the slides to provide more explanation as needed by your students.

Teaching students at home and need to print out the slides? Click here for a PDF.

Lesson 2 – Multiplying by 2

Depending on your students’ progress and interest, you may want to hold off on this lesson for another day or jump right into it after lesson 1. Students learn the meaning of a number times two, or two times a number, both as regards to equal-size groups and number line jumps. Today’s lesson starts with a Google Slides presentation that shows how multiplication of 2 works. This is begun by talking about skip counting.

Teaching students at home and need to print out the slides? Click here for a PDF.

Lesson 3 – Multiplying by 3

Tell students that two more lessons and then, let the games begin! Here is another 30-second video to spark their interest.

It’s time for learning multiplication by 3s. After watching the video, here is another Google slides presentation. While each of these is somewhat similar, we find that can be attractive to students in that they feel it’s not too challenging, they are getting this multiplication idea. We do not recommend doing more than one of these lessons per day when students are first learning their multiplication tables. Practice 3 tables and then go on to another topic for the rest of the day.

Teaching students at home and need to print out the slides? Click here for a PDF.

Lesson 4 – Multiplying by 4

On lesson 4, we are mixing it up just a little. We introduce the idea that 4 x 5 = 5 x 4, so, really, you only have to learn half your multiplication tables. We also move past looking at just shapes and circles and look at multiplying fish, because, why not?

4 x 3 = 12 fish

Start with the Google slides presentation. Tell students today they will be learning a secret that makes multiplication easier.

Teaching students at home and need to print out the slides? Click here for a PDF.

Lesson 5 : Multiplying by 5 and 10

Begin with reinforcing students on how much they have learned already. After today’s lesson you’ll be half-way to having learned your times tables for all the numbers from 0 to 100. Hurray! Let them know that at the end of today’s lesson they will be getting to play Making Camp. Also, today they will be learning TWO tables and a new trick. Start with this Google slide presentation.

After the presentation, students should play Making Camp for 15-30 minutes. If you would like stickers, pencils or other incentives to give your high scoring students, just email support@7generationgames.com and we’ll be happy to send you a teacher gift pack.

Teaching students at home and need to print out the slides? Click here for a PDF.

Assessment

Each lesson includes multiple assessment:

  1. Students complete the multiplication tables – these can be shown with a projector (in class), on a screen, if teaching remotely, and on paper for students learning at home.
  2. Students write their own number sentences using the multiplication learned each lesson.
  3. Students complete the problems written by their classmates.
  4. Optionally, students write word problems.
  5. Optionally, student complete word problems written by their classmates.

In addition, at the end of lesson 5, students begin playing Making Camp, which has teacher reports showing the number of multiplication problems attempted and answered correctly.

State Standards

Minnesota State Standard 3.1.2.3 – Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division.

Minnesota State Standard 3.1.2.4 – Solve real-world and mathematical problems involving multiplication and division, including both “how many in each group” and “how many groups” division problems.

Minnesota Math Standard 3.2.2.2 – Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true.

Science, language arts and math with wildflowers

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📖 STANDARDS

English/ Language Arts

CCSS.ELA-LITERACY.RI.6.7 Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue.

CCSS.ELA-LITERACY.RI.6.4 Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.

Next Generation Science Standard

MS-LS2-1 Ecosystems: Interactions, Energy, and Dynamics: Analyze and interpret data to provide evidence for the effects of resource availability on organisms and populations of organisms in an ecosystem.

Mathematics Standard

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.

📲 Technology required

Optionally, the teacher will have access to a printer to print pages 2-3 of the book and selected pages to color. Since choke cherry and Simpson’s Ball Cactus are mentioned in the problems, it is recommended that, at a minimum, these pages should be printed. Alternatively, the link can be shared to students who are learning from home to read material on their computer.

📃 Summary

This is a true STREAM lesson. Combining science, reading, art and mathematics. Students read a description of the pine forest ecosystem and life zones. They define any new words in their personal dictionary. Students then use information on plant life to identify life zones and locate these zones in terms of altitude. Students who complete the activity before the allotted class time play a game that teaches fractions and basic statistics.

⏰ Time Required

50 minutes

📚 Lesson Plan

Read pages two and three of Wildflowers of Ponderosa Pine Forests Coloring Book – These pages explain the pine forest ecosystem, including an illustration of Life Zones.

Complete word journal

Some teachers call it a personal dictionary, to others it’s a word journal. Regardless, the goal is the same, for students to record new words, give a dictionary definition and “make the word their own”. This can be done by rewriting the definition in their own words, using the word in a sentence or including an illustration of the word.

Two dictionary sites to recommend for definitions are below. An added bonus to mention to students is that they can hear words pronounced.

Since students often ask for an example, here is an example you can link in your lesson.

The personal dictionary assignment, with all links, can be found here. Feel free to copy and paste into your Google classroom or other site, or print out for your class.

Use Life Zones to Solve Problems

Angie and Sam are on their way to Michigan but they have gotten so, so lost! They are somewhere in Colorado. Sam has sent Angie this text:

Hey, Angie! I can’t see you anywhere. All I can see are trees, a whole lot of trees, and if I look up the mountain, I see even more trees, closer together. I recognize this plant with red berries. Grandma called it choke cherry. Where are you? How can I meet you? Should I go up or down?

Angie texts him back,

There aren’t that many trees around me, but there are some of these round cactus plants. We are definitely not in Michigan!

Use the information on life zones to answer these questions. (Hint: You may have to look on the plant pages as well.)

  1. In which of the five life zones is Sam right now? How do you know?
  2. In which of the five life zones is Angie right now? How do you know?
  3. Should Sam go up the mountain or down the mountain to meet up with Angie? Why?

Click here for the life zone assignment as a Google doc.

BONUS 1: Game Play

You might recognize Sam and Angie from the game, Forgotten Trail, where they try to retrace their ancestors’ journey across the U.S. and Canada. If you finish this assignment and your personal dictionary before class time is over, play Forgotten Trail here.

BONUS 2: Art

As an alternate bonus activity, students may color the pictures in the book according to the legend included. This would require that the teacher print pages for students. Since choke cherry and Simpson’s Ball Cactus are mentioned in the problems, it is recommended that, at a minimum, these pages should be printed.

Assessment

Recommended rubric for the Personal Dictionary is as follows:

This assignment is worth 100 points. A minimum of ten words is required. You can include up to two extra  words for an additional 20 points.

Each word is worth 10 points.

  • Dictionary definition – 3 points
  • Definition in your own words – 5 points
  • Use in a sentence or draw a picture – 2 points

Recommended rubric for Life Zone Questions

Each question is worth 25 points.

Sam is in the Montane zone (5 points). We know this because he sees a lot of trees and the Montane zone is a forested area. He said that there are even more trees up ahead so we know he is not in the subalpine area because above that are no trees (10 points). He also saw choke cherry plants and these are at elevation from 7,000 – 9,000 feet. The Montane zone starts at 8,000 feet. (10 points)

Angie is in the Foothills (5 points). We know this because she says there are not many trees (10 points) and she sees the Simpson’s Ball Cactus which is common in the Foothills (10 points).

Sam should go down the mountain to meet Angie (5 points) because Sam is in the Montane zone, which is at 8,000 to 10,000 feet (10 points) and she is in the Foothills which is at (6,000 to 8,000 feet) so he needs to go down in altitude to meet her (10 points).

Assessment for Forgotten Trail math problems

Problems are scored automatically within the game. Teachers who are part of the Growing Math project or with 7 Generation Games site license can access student data from the Reports page.

Introducing Division

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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

30 minutes 

📃 SUMMARY

This lesson plan introduces the concepts and vocabulary of division and provides students the opportunities to practice both recognition and recall of division facts. Math literacy activities are recommended to help students remember and understand math terms. Students can play the Making Camp Premium game, with division with one-digit divisors or Making Camp Lakota which includes one- and two-digit divisors.

📲 Technology required

The games, Making Camp Premium and Making Camp Lakota can be played on any web browser – Chrome, Firefox, Bing, etc or downloaded on iOS or Android devices. The Making Camp Premium game can be played with or without an Internet connection. Internet is required to log in to the Making Camp Lakota game with username and password. Both games are available at no extra charge to schools with a 7 Generation Games site license or who are part of the Growing Math Project.

📚 Lesson Plan

1. Introductory mini-lecture

5-7 minutes

  1. Explain why division is important. When we want to share something, whether it is the hours spent doing chores or a birthday cake, we divide it.
  2. Tell students they will be taking notes on the videos, writing down key words that appear in the video (e.g. quotient, dividend) and their definitions for review at the end of the session. (Math literacy helps with identifying math terms; textbooks will start to make sense.)

2. Watch Videos

7 minutes

Division Terms

What’s division? How do we use division every day? 3:31 minutes

The Division terms video is included in Making Camp Lakota, a game teaching division and Lakota history. It is also in the Making Camp Premium game. Before starting the video remind students to be ready to take notes.

Division (Multiplication in Reverse)

Why is learning multiplication important for learning division? 2:41 Minutes

3. Game Play

15 minutes

Play Making Camp Premium for multiplication and division.

Making Camp Premium can be played online on any computer (Windows, Mac, Chrome), or you can download it for your phone or tablet (iOS and Android). This game is part of the 7 Generation Games school license and also available as part of the Growing Math project.

The division magnets game practices division of one-digit numbers into two digit numbers, like 35 ÷ 5.

There are also games for multiplication and a lot of videos and games on history and English/ language arts. Making Camp Premium also teaches about Ojibwe history and culture.

For more division, play Making Camp Lakota.

In mathematics content, Making Camp Lakota focuses only on division, combined with, of course, Lakota history and culture. With development funded by the Thunder Valley Community Development Corp. this game is free to play on the web or downloadable for iPad or Android tablets.

ASSESSMENT

This lesson plan includes two types of assessment.

  1. You can view your students’ progress on mastering these standards by viewing your Making Camp Premium Teacher Reports. See an example below.
Student data by standard from Making Camp Premium
Sample Student Report

2. To assess student understanding of math vocabulary, review their notes written while viewing the division terms video.

Related Content

We have a YouTube division playlist! The videos above are part of a five-video series clues students in on everything from dividends to long division with remainders. (And they are short, ranging from one and a half to three and a half minutes each.) These videos can be played on any device in class or at home.

State Standards

Minnesota Math Standard 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.

Minnesota Math Standard 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.

Time Rate Distance Problems

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📖 Standards

CCSS.Math.Content.7.EE.B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

CCSS.Math.Content.4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. (Common Core Standards)

📃 Summary

Time-rate-distance problems are word problems that involve the distance an object will travel at a certain average rate for a given period of time. Because we have found many students struggle with this type of problem, we find it so helpful to have multiple examples through videos, slides, and through a video game. In all of these problems, students solve for distance. Video, game and presentation resources are available in both English and Spanish.

The formula for distance problems is: 

distance = rate × time or d = r × t

📲 Technology required

The game AzTech: The Story Begins can be played for free on iOS (iPad and iPhone) and in a web browser on any computer. The game can be installed in an iPad and played off-line by students who do not have reliable Internet access.

⏰ Time required

15-25 minutes – time varies depending upon discussion of questions and length of game play allowed.

📚 Lesson Plan

Watch video introducing students to Time-Rate-Distance problems

Introducing time-rate-distance problems 3:04

This brief video uses number bonds as one means of finding the total number of hours, then multiplies hours by rate to find the total distance. We work step by step through an example to find how far Spanish troops needed to ride to attack the Aztecs.

2. Video or Presentation of time-rate-distance example

How many miles did Grandma drive? 1:24

Teaching Options

Students can watch another video solving for distance. If it takes 2 1/2 days to get to Honduras from Iowa, and Grandma drives 60 miles per hour without stopping, what is the distance from Iowa to Honduras? This video solves the problem step by step, beginning with converting 2.5 days to hours.

Alternatively, teachers can use this presentation as PowerPoint or in Google slides to present the same material either in class or in a web meeting. These presentations are also available in Spanish as PowerPoint and in Spanish as Google slides.

3. Video or Presentation of a second time-rate-distance example

How far is Iowa from Texas? 1:19

Teaching Options

Students can watch another video solving for distance. If it takes Grandpa one day to get from Iowa to Texas and he drives 55 miles per hour, what is the distance from Iowa to Texas? This video shows, step by step, how to solve this problem.

Alternatively, teachers can use this presentation as PowerPoint or in Google slides to present the same material either in class or in a web meeting. These presentations are also available in Spanish as PowerPoint and in Spanish as Google slides.

Assessment

Bonus question in level 1 of AzTech: The Story Begins

Play AzTech: The Story Begins. Not only will students have fun and be exposed to educational content on Latin American history, but they will also have to answer mathematics questions to progress. Instruct students to be sure to answer the first bonus question, shown above. Remind them that the icon at the bottom of the screen can be used to pull up a calculator. (There is no arrow on the screen in the game. It is merely shown above for emphasis.) 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” .

State Standards

Minnesota Math Standard 6.2.3.2 – Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results.

Minnesota Math Standard 7.1.2.1 – Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents.

Minnesota Math Standard 4.1.1.3 – Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, 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.