Category Archives: mathematics

Probability and fruit

📖Standards

CCSS.Math.Content.7.SP.C.5
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

CCSS.Math.Content.7.SP.C.6
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

⏰Time

30-45 minutes, depending on whether the final individual activity is performed in class or outside of class.

📲Technology Required

A projector or smart board is required to show the Google slides presentation in class. It can also be shown using any web meeting software for remote learning. The random fruit basket generator can be used by students in anything with a browser, including computers, tablets or phones. This activity is optional.

📃Summary

The Google slides presentation begins with definitions of probability, impossibility and certainty. Students are then given an example of a basket with different types of fruits and the probability of each. Students each come to the front of the class and pull a piece of fruit from the basket, writing down the probability of their selecting the type they obtained. The class data is used to create a table and compare the obtained probabilities to actual distribution of fruit in the basket. The lesson closes with students creating their own probability question.

NOTE: This lesson plan requires a basket of fruit. You could use pictures of fruit printed out or drawn on paper instead but using actual fruit from your area might be more fun. If you’d rather, though, we do have a random fruit basket generator to use with this lesson.

📚Lesson Plan

1. Presentation on Probability

Students are then given an example of a basket with different types of fruits and the probability of each.

2. Individual students compute probability

Students each come to the front of the class and pull a piece of fruit from the basket, writing down the probability of their selecting the type they obtained. The class data is used to create a table and compare the obtained probabilities to actual distribution of fruit in the basket. If students are learning at home, we have a random fruit basket generator to use with this lesson. After setting THE SAME NUMBER OF EACH FRUIT for everyone to enter, have each student click on the basket to select a random fruit and see the probability.

3. Group Activity

Complete table included in presentation as a class. Compare obtained probabilities with expected. Discuss that the expected probabilities are for a large number of trials and that it is usual to have the observe probabilities not match up exactly – or even closely – with the actual proportions when the sample size is small.

4. Probing questions

These questions are included in the presentation. Ask the class what the probability is of selecting a kiwi fruit, remembering that there are not any kiwi in the basket. If Annie’s family owns an apple orchard and her basket contains only apples, what is the probability of selecting an apple? If students need a reminder, return to the definitions of probability, impossibility and certainty at the beginning of the lesson.

5. Individual Activity

Students will create their own probability activity using household items. This activity can be performed at home, having family members draw items, or can be performed in the classroom using items in the classroom, such as different colors of pencils, or even pieces of paper with different words or pictures.

Assessment

Individual formative assessment is conducted throughout this activity by having students write the probability of the specific fruit they selected and by their performance on the individual activity creating their own probability sample and recording the results. Students can also write their answers to the in-class questions on probabilities of 0 and 1, then comparing these to the correct answer.

State Standard

Missouri Learning Standards (MLS)●7.DSP.C.5a Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Minnesota Math Standard 6.4.1.2 – Determine the probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1 inclusive. Understand that probabilities measure likelihood.

Minnesota Math Standard 6.4.1.4 – Calculate experimental probabilities from experiments; represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown.

Reading & comparing bar graphs

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📖Standards

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

CCSS.MATH.CONTENT.7.RP.A.2.B Ratios & Proportional Relationships: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

⏰Lesson Time

40- 50 minutes

📲Technology Required

Device with web-browser – Chromebook, laptop or desktop computer, iPhone or iPad

📃Summary

This lesson introduces students to reading and comparing bar graphs with proportional relationships. Students receive a slide or handout with four bar graphs and complete a set of cards with questions or complete the activity in Google slides . The lesson ends with an adventure game that includes discussion of interpreting bar graphs.

📚Lesson Plan

Related lesson plan

If you have not watched the videos on Mayan Trading and Distributions, you may want to check out this lesson plan first.

Preparing for the lesson – Options

Print out the cards if students do not have home Internet access or if you want to use the cards to do the activity in class. (Note: Business card stock may not be the best $10 I have spent as a teacher, but it’s high on the list. I don’t know what it is about cards that makes something seem like a game but I have had the greatest success with activities like this one.). Here is a PDF for the cards. If you would like to download the cards to edit and add your own questions, here is a Microsoft Word doc.

If students are learning from home, you can copy the Google slides presentation to your Google classroom and assign to students.

1. Individual Activity

Use this Google slides presentation to introduce and explain the assignment.

Print out the “Graphs” page or display it using a Smartboard, projector or in your Google classroom. Each student / group is required to complete the cards using the graphs provided.

2. Class Activity

After the students have completed the assignment, which should take around 10-15 minutes, have students share their findings to these questions with the class. Discuss and review the different questions and answers that can come from the same set of data.

3. Play Games!

Students can play the AzTech: The Story Begins to practice statistics in a history adventure game. Link available from the games page, select the device on which you want students to play. Available free for Chromebook, Android or iOS.

Assessment

AzTech Games Teacher Reports – Teachers can access standards-aligned student reports including answers to problems, number of correct answers, quiz results and pre-test/post-test results.

Students’ responses in the activities above, both individually and as a group, provide formative assessment of their ability at interpreting and extrapolating from graphical data.

State Standards

Minnesota Math Standard 7.2.2.1 – Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.

Distributions and Mayan Trading

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📖Standard

7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

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- 30 Minutes

📲Technology Required

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

📃Summary

The two videos here combine math and social studies, because, clearly, the Maya understood math. The concept of distributions is introduced in the context of trading, explaining why some objects are more valuable. Students play AzTech: Meet the Maya, which teaches measures of central tendency. The lesson concludes with a question and another video on distributions.

📚Lesson Plan

1. Watch video – Mayan Trading (1:57)

The Mayan trading video is based on an idea from one of my favorite history teachers, who says that history is more than just names and dates but also how people lived, what they used, what they did. It also has a bar chart of the relative value of objects. It explains that the Maya traded less common items for more common ones and that items that were more difficult to obtain were more valuable.

2. Play AzTech: Meet the Maya

Next, have students start the AzTech games series. They can play AzTech: Meet the Maya online or using an iPad. We recommend downloading the game onto your iPhone or iPad for better performance.

3. Question to test understanding

José tried to trade a banana for a quetzal feather and a villager threw a spear at him. Why would the villager do that? Explain using math. Extra points if you can discuss distributions in your explanation.

4. Video giving the answer to the word problem on distributions (5:15)

This five-minute video introduces distributions and variability and gives an example of computing a weighted mean from a frequency distribution.

OPTIONAL You can also copy this Google slides presentation to your own classroom if you’d rather modify the explanation for your own lecture. The slides can also be printed out and sent home with students who do not have Internet access.

ASSESSMENT

You can view your students’ progress on mastering these standards by viewing your teacher reports. The link to the teacher dashboard for AzTech: Meet the Maya student reports can be found on this page. You should have received a password during the Growing Math training.

State Standards

Minnesota State Standard 6.4.1.1 – Determine the sample space (set of possible outcomes) for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations.

Related Lesson

Distributions and Mayan Trading (Bilingual English & Spanish) – This lesson is a bilingual version of the lesson above and features resources in English and Spanish.

10 Minute Mini-Lesson: Rabbit Stew & Multiplication

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📖Standard Standards

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

⏰ Time

10 Minutes

📲 Technology Required

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

📃 Summary

Students learn about what foods the Ojibwe people ate and how their diet changed when they were forced on to the reservation. They play a multiplication tic-tac-toe to snare rabbits and spend the points earned in the game to outfit their wigwam.

📚 Lesson

1. Watch a one-minute video on rabbit stew

Narrated by Deb Gourneau, of Turtle Mountain, this video explains the importance of rabbit stew in helping people survive when food was scarce.

2. Play Rabbit Tic-Tac-Toe in Making Camp Premium

Remember, clicking on the link with the boxes in the bottom left corner will always take you to the choices page.

Click on the box with the rabbit to play a tic-tac-toe game in Making Camp. Each correct multiplication problem snares a rabbit. Incorrect problems leave an empty snare.
When you win this game, there will be an arrow to go back to the numbers page.

3. Play a Matching Game to earn more points

Click on the box with the buffalo to match multiplication problems with their answers.

4. Learn what else was part of the Ojibwe diet

Now that you have 4 more points, go back to the wigwam and if you have not already traded for these, select the fish, deer hide or parfleche to see what else the Ojibwe would eat. Click on each of these items in your wigwam to learn more about it.

Assessment

Remember that you can always see your students’ performance on the problems in Making Camp Premium by accessing the reports page. You will need to enter the password you received during training.

State Standards

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.

Minnesota Math Standard 4.1.1.1 – Demonstrate fluency with multiplication and division facts.

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

PERIMETER OF RECTANGLES, SQUARES AND TRIANGLES

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📖Standard

CCSS.MATH.CONTENT.3.MD.D.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

CCSS.MATH.CONTENT.4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

⏰ LESSON TIME

30 minutes without gameplay, 45 minutes with gameplay

📃 SUMMARY

In this lesson plan, students will learn how to compute perimeter, apply those skills in game-based practice problems and solve perimeter problems using an interactive web-based activity with virtual manipulatives.

📲 TECHNOLOGY REQUIRED

Device with web-browser (Chromebook, laptop or desktop computer); or iOS (iPhone/iPad) with access to Google apps.

📚 Lesson Plan

1. Video: How to Find the Perimeter and Polygons

Watch this animated video that explains how to find the perimeter of different polygons, including rectangles, triangles and squares. (3:00)

2. INSTRUCTIONAL ACTIVITY WITH ASSESSMENT: Interactive perimeter problems activity

This digital activity walks students through calculating the perimeter of different shapes including a rectangle, a square and a circle in a narrative-driven context around the farm and integrates virtual manipulatives. Students are provided in-activity instruction as they are presented with and explained the formulas to use when they need to use them. Additionally, with in-activity scaffolding, students can “get a hint” on each problem.

You may elect to read and work through it during class time, giving students time to complete the problems or assign it as an individual assignment.

If your students have not used virtual manipulatives with Google slides previously, here is a 30-second introduction.

Estimated time to complete: 20-25 minutes

3. GAME: Making Camp Premium or Spirit Lake

Have students play Making Camp Premium games for 15-20 minutes (remainder of the lesson time) specifically including these icons.

Perimeter is also covered in the second half of Spirit Lake: The Game.

Assessment

In addition to the virtual manipulative activity above, remember that you can always see your students’ performance on the problems in Making Camp Premium and Spirit Lake by accessing the reports page. You will need to enter the password you received during training.

State Standards

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

Minnesota Math Standard 3.3.2.3 – Measure distances around objects.

Related Lesson

“PERIMETER OF RECTANGLES, SQUARES AND TRIANGLES (Bilingual English & Spanish)” – The Bilingual version of the lesson plan above with English and Spanish resources.

Estimation & Rounding

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📖 STANDARDS

CCSS.MATH.CONTENT.3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

CCSS.MATH.CONTENT.3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100.

⏰ LESSON TIME

30 minutes

📃 SUMMARY

In this lesson plan, students will learn about estimation as a problem solving strategy and practice rounding to the nearest 10 and 100. Including 0. The lesson will reinforce rounding up for numbers 5 and greater. Through gameplay and an interactive assessment activity that includes multi-step problem solving, students will practice rounding with an emphasis toward developing mastery.

📲 TECHNOLOGY REQUIRED

Device with web-browser (Chromebook, laptop or desktop computer); or iOS (iPhone/iPad) with access to Google apps.

📚 Lesson Plan

Watch the video– Problem Solving: Estimate (optional if playing Making Camp)

This animated movie explains how estimation and rounding can be used to solve problems that don’t require exact calculations, including multi-step word problems with an example. It also explains how rounding can be used to make numbers easier to work with and includes an example with rounding to the nearest hundreds. (3:44)

2. GAME: Making Camp Premium

Have students play Making Camp for 15-20 minutes, including this icon activity on estimation.

This activity will also reinforce visual estimation skills.

ASSESSMENT

A Day at the State Fair: Estimation is Everywhere

If your students have not previously used virtual manipulatives you may want to watch this short video.

This interactive, narrative-driven activity walks students through 6 in-context uses (multi-step word problems) of estimation and rounding to the nearest tens or hundreds, including rounding both up and down, to 0 and 100, and rounding up from 5.

You may elect to read and work through it during class time, giving students time to complete the problems or assign it as an individual assignment. Estimated time to complete: 10-15 minutes.

Also, remember that you can always see your students’ performance on the problems in Making Camp Premium by accessing the reports page. You will need to enter the password you received during training.

State Standards

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.

Minnesota Math Standard 2.1.1.4 – Round numbers up to the nearest 10 and 100 and round numbers down to the nearest 10 and 100.

Multiplying to find perimeter of polygons

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📖 STANDARDS

CCSS.MATH.CONTENT.4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

⏰ LESSON TIME

45 minutes

📃 SUMMARY

In this lesson, students will learn how to compute perimeter of different polygons using multiplication and apply those skills in game-based practice problems. They will then learn about different Indigenous traditional dwellings. The lesson ends with students contributing to and solving problems that integrate the reading on dwellings and perimeter in an online assessment.

📲 TECHNOLOGY REQUIRED

Device with web-browser (Chromebook, laptop or desktop computer); or iOS (iPhone/iPad) with Google Drive apps.

📚 Lesson

1. Play GAME: Making Camp Premium

For 15 minutes, have students play the game Making Camp Premium.

Instruct them to specifically play the mini-game with this icon

If they need a refresher in how to compute perimeter, they should click this icon to watch a video

ALTERNATIVE: Perimeter is also covered in the second half of Spirit Lake: The Game, which is currently available for Windows and Mac computers.

2.READ: Home, Sweet Home: Tipis, Hogans, Wigwams and More

Read this short post about traditional dwellings of Native American tribes from different parts of the United States. It can be read aloud as a group or individually. (Estimated time: 7-10 minutes)

3. Discuss how to Compute Perimeter

This Google slides presentation reviews the definition of a polygon and perimeter and provides the formulas for finding the perimeter of a rectangle, square and triangle with examples for each. You can review it together in class or online, copy to Google classroom to assign to students or print out to send home for students without Internet access. (Estimated time: 5-10 minutes)

4. Testing understanding : Perimeter in Action

This activity draws from the “Home, Sweet Home” reading and lessons on perimeter to have students apply their understanding of how to compute the perimeter of rectangles, triangles and hexagons using multiplication. Get the Google slides presentation here. Students contribute numbers to create multiple problem options.

(Estimated time: 10 minutes)

ASSESSMENT

You can view your students’ progress on mastering these standards by viewing your teacher reports. Both Making Camp Premium and Spirit Lake Report links can be found on this reports page. You should have received a password during the Growing Math training. If you need the password, email growingmath@7generationgames.com from your school email account and we’ll get the password to you right away.

State Standards

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

Minnesota Math Standard 4.3.2.4 – Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements.

Division and English/ Language Arts

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📖 Standards

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.

CCSS.ELA-LITERACY.W.4.3
Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.

⏰ Time

40-45 minutes

📲 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. Schools that are part of the Growing Math project or who have a 7 Generation Games site license have access to the game for students to use at home or school.

📃 Summary

This is a fun lesson where students practice division, combined with Ojibwe history and then complete a creative writing assignment.

📚 Lesson Plan

1. Game Play with Making Camp

Open Making Camp. Go to the main choices screen by clicking on the small green icon with boxes at the lower left of the screen.
Click NUMBERS.
Click the box with the numbers to practice division.

Click the numbers box for division practice.

Refrigerator magnets on a beige background. Button at the top says GET PROBLEM — Each correct quotient earns a fridge magnet to decorate the fridge!

Students should play until they earn at least 15 points.

2. Spend the points earned and learn about Ojibwe history

One of the best teachers we know said, “History is more than names and dates. It’s how people lived. It’s the things they used.” When trading for a wigwam, students will watch videos on how to build a wigwam and on trading. They’ll learn that tribes traded with one another for hundreds of years.

3. Short story writing prompt

So how did we get from a refrigerator to a wigwam? You can use this Google slides presentation to tie in Native American history with Sam’s life in the twenty-first century. This presentation can also be added to your Google classroom as an assignment for students. Here is the introduction for Sam and his account:

This is Sam. He’s also Ojibwe but he’s not from a long time ago. He’s 16 years old. He lives on a reservation in the northern United States. You’ve probably heard of it. He doesn’t live in a wigwam. He lives in a white house with a grey roof. That’s the refrigerator in his house. The magnets have been there ever since he was in second grade.

4. Writing assignment

Read about Sam and write a story about him. What do you think happened to him in second grade? Why does everyone except for his cousin, Angie, think he’s not smart? Do you think he and Angie can really walk to Maine?

Assessment

Math problems in Making Camp Premium are scored automatically. You can see how many students attempted and the number correct in the data reports. All Growing Math teachers and all schools with 7 Generation Game licenses receive access to these reports. Writing assignments can be assessed according to the teacher’s own rubric.

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.

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.

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

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

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:

A piece of paper
A pen or pencil
A phone or tablet – if not available, a measuring device like a ruler, measuring tape or yardstick can be used instead.
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

OBJECT	Length	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

OBJECT	Length	Width
Top of a box	8	4
Seat of a chai r	18	12

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

Step 6: Play Making Camp Premium

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.