Tag Archives: problem solving strategies

Problem-solving Two Ways (EL)

📖 Standard

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

⏰ Time

30-40 minutes

📃 Summary

Students are introduced to the various means of problem solving in a brief presentation. They watch a video on visualization, then solve a problem that asks them to visualize. After watching a video on building a model, students build and/or draw their own model of a multiplication problem or property. Lesson concludes with game play to reinforce these problem-solving strategies and learn more. This lesson assumes that students have some familiarity with multiplication of one-digit numbers and division with one-digit divisors.

📲 Technology Required

If teaching in person, the teacher will need a computer and projector or smart board to show the videos, or students can be given the links to watch on their own devices. Students will need a PC, Mac or Chromebook or tablet. Making Camp Premium, Making Camp Lakota and Making Dakota are all playable on any web browser on those devices. Spirit Lake: The Game, playable on Mac or Windows computers also teaches these same concepts. Students will also need access to the games.

📚Lesson

Watch a Video: Visualize (Visualizar in Spanish)

This video teaches you how to visualize a problem. Visualization may help you solve it more easily. If you use objects to imagine quantities of numbers in certain problems, you will be able to find the solution faster.

Short presentation and problem

After watching the video, teachers can present this short Google slides presentation or assign to students in Google classroom, giving another example of visualizing a problem. The presentation ends with asking students to visualize another problem themselves. It then leads into the next video.

Watch a video: Build a Model (Construyendo un Modelo)

If you’d rather give a presentation than show a video, here is a Google slides deck you can use as is for copy to your own Google drive and modify.

Actually Build a Model

Two possible assignment for building a model are:

  • Have students create a model using Google draw, jam board or simply drawing it on paper.
  • Build a physical model using objects in their home or school

Google slides presentation describing these assignments is given here. You can simply save to your own Google classroom and then assign to your class to include both types of problems or modify to add more explanation or delete whichever one does not apply to your class before assigning.

Play a game

Assign students to play Making Camp Premium (plays on any device) or Spirit Lake (plays on Mac and Windows computers) to practice these problem-solving strategies and more with multiplication and division. Play Making Camp Lakota to reinforce division skills and concepts.

Assessment

Two assessments are built into the lesson, on visualization and building a model. Teachers can also see which standards students have attempted and how many problems they have answered correctly in the Making Camp teacher reports.

Related: Problem-solving Two Ways

The lesson above has a companion lesson for English only learners. Problem-solving Two Ways is the same lesson from above but provides the resources, videos and Google Slides, in English.

Problem-solving with pigs: Start at the end

📖Standard

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

⏰ Time

60-75 minutes

📃 Summary

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

📲 Technology Required

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

📚 Lesson

This lesson starts with resources from National Ag in the Classroom

Virtual tour of pig farms

Virtual Field Trip to Ohio Pig Farms

Make a Pig Barn

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

  • Business-size envelopes, 4 per group
  • Paper towel, 1 per group
  • Scissors
  • Scotch tape

OPTIONAL

  • Markers
  • Toilet paper rolls, 2 per group
  • Drinking straws, 2 per group (cut into 8 equal pieces)
  • 8.5″ x 11″ white paper, 1 per group (cut in half)
  • Extra paper for making fencing, pipes, feed troughs, etc. (optional)

Instructions

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

  1. Barn: Cut an oval hole in one envelope, making a large side window for the barn. This window provides the proper ventilation for the pigs.
  2. Cut the paper towel in half and tape it onto the top of the window for the curtain.
  3. Cut another envelope in half for the ends of the barn.
  4. Tape the ends of the barn to the “sides of the barn” envelopes, one of which has the hole for the window and paper towel curtain, so that you have four sides, or a rectangle.
  5. Use the final envelope to create a roof by creasing it in half lengthwise and attaching it with tape to the top of the rectangle.
  6. Food Storage: Tape four straws, or legs, to each toilet paper roll so that the structures will stand on the legs.
  7. Use a half piece of paper, and make a cone shape by twisting and taping the ends. Tape the cone shape on the end of the toilet paper roll without the straw legs.
  8. Use the other half piece of paper to make another smaller cone shape and tape it between the straw legs on the other end of the toilet paper roll.

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

Optional additional science and language arts content

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

Watch a video on operations key words

Trust me, this does come back to pig farming!

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

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

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

Start at the End
piglets

Give a presentation

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

Play a game

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

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

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

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

Assessment

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

Related lesson : Problem-solving Two ways

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

Problem-solving Two Ways

📖Standard

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

⏰ Time

30-40 minutes

📃 Summary

Students are introduced to the various means of problem solving in a brief presentation. They watch a video on visualization, then solve a problem that asks them to visualize. After watching a video on building a model, students build and/or draw their own model of a multiplication problem or property. Lesson concludes with game play to reinforce these problem-solving strategies and learn more. This lesson assumes that students have some familiarity with multiplication of one-digit numbers and division with one-digit divisors.

📲Technology Required

If teaching in person, the teacher will need a computer and projector or smart board to show the videos, or students can be given the links to watch on their own devices. Students will need a PC, Mac or Chromebook or tablet. Making Camp Premium, Making Camp Lakota and Making Dakota are all playable on any web browser on those devices. Spirit Lake: The Game, playable on Mac or Windows computers also teaches these same concepts. Students will also need access to the games.

📚 Lesson

Watch a Video: Visualize

This video teaches you how to visualize a problem. Visualization may help you solve it more easily. If you use objects to imagine quantities of numbers in certain problems, you will be able to find the solution faster.

Short presentation and problem

After watching the video, teachers can present this short Google slides presentation or assign to students in Google classroom, giving another example of visualizing a problem. The presentation ends with asking students to visualize another problem themselves. It then leads into the next video.

Watch a video: Build a Model

If you’d rather give a presentation than show a video, here is a Google slides deck you can use as is for copy to your own Google drive and modify.

Actually Build a Model

Two possible assignment for building a model are:

  • Have students create a model using Google draw, jam board or simply drawing it on paper.
  • Build a physical model using objects in their home or school

Google slides presentation describing these assignments is given here. You can simply save to your own Google classroom and then assign to your class to include both types of problems or modify to add more explanation or delete whichever one does not apply to your class before assigning.

Play a game

Assign students to play Making Camp Premium (plays on any device) or Spirit Lake (plays on Mac and Windows computers) to practice these problem-solving strategies and more with multiplication and division. Play Making Camp Lakota to reinforce division skills and concepts.

Assessment

Two assessments are built into the lesson, on visualization and building a model. Teachers can also see which standards students have attempted and how many problems they have answered correctly in the Making Camp teacher reports.

Related: Problem-solving Two Ways (EL)

The lesson above has a companion lesson for English Learners. Problem-solving Two Ways (EL) is the same lesson from above but provides the resources, videos and Google Slides, in Spanish.

Two-Digit Multiplication and Estimation

📖Standard

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.

⏰Time

35- 45 minutes

📲Technology Required

Computer with a projector, Smartboard or other device for your class to watch videos

NOTE: You’ll also need 20 math problems: 3-digit numbers multiplied by a 2-digit number. You can use what you already have, use the worksheet provided or use the Multiplication Worksheet Generator to make your own worksheet.

📃Lesson Summary

Students practice multiplication for a few problems, watch a video on using estimation to solve problems, hear a brief presentation from their teacher, solve more practice problems, watch a second video and practice more problems. They end the lesson with a game and a discussion of which strategies proved most useful.

📚Lesson Plan

Start with multiplication problems

Have the students solve 3 to 5 problems.

NOTE: This lesson requires a total of 9 to 15 multiplication problems. This worksheet has 24 problems multiplying a three-digit numbers by a two-digit number. Teachers can assign any selection of these problems or use their own. We give the students a worksheet of 24 problems and tell them to pick any ones they want to solve. Of course, teachers should do whatever works for them.

A PDF of the answers to the multiplication problems can be found here.

Watch a video

This 3-minute video explains multiplication of 2-digit and 3-digit numbers

This video explains steps in long multiplication, with examples and a reality check.

Discuss the video

Use this Google slides presentation for a short discussion of the video and how to apply the information learned about estimation and long multiplication.

Practice multiplying 2-digit and 3-digit numbers again

Now that students have had a chance to watch and discuss the video showing long multiplication, step by step, it’s time for them to practice again. They have 10 minutes to complete another 3 to 5 math problems.

Watch another video to review the steps

Now that students have watched one video and practiced their skills with a few problems they watch a second video to reinforce those steps.

Practice multiplying 2-digit and 3-digit numbers again

Now that students have had a chance to watch and discuss the video showing long multiplication, step by step, it’s time for them to practice again. They have 10 minutes to complete another 3 to 5 math problems.

Peer-grading (optional)

You may wish to share the answer key with students and have them grade their own or their peer’s problems.

Discussion

As a class, discuss strategies for solving problems, including doing a reality check, estimation and breaking problems into smaller problems. Ask students which strategies worked best for them.

Play a Game

Both Spirit Lake: The Game and Making Camp Dakota (released in February, 2021) teach multiplication of two- and three-digit numbers.

Assessment

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

Estimation & Rounding

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.

Multiplication word problems

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. (Common Core Standards)

H.3-5.3     Describe the North Dakota Native American Essential Understandings. (US State – ND – Social Studies 2019 Standards)

Summary

In this integrated lesson, students learn about responsibilities of children in traditional Dakota society and discuss their responsibilities today. They learn a problem-solving strategy that can be applied to a wide range of situations, including mathematics. Students play Spirit Lake: The Game or watch videos solving multiplication problems set in the context of a story based on Dakota culture. Students can complete a written assessment in class and on-line classes can complete these problems in Google doc or other preferred method .

Technology required

The game in this lesson plan, Spirit Lake, can be played on Mac or Windows computers. Once students have logged in, they can continue playing, even if the Internet drops. The program should be installed on devices before the lesson. Students will create a username and password the first time they play the game. If students need to play offline, they can play Spirit Lake Beginnings – Lakota . If students do not have access to a Mac or Windows computer they can watch similar content in the linked videos.

Time Required

30-40 minutes

Lesson Plan

1. Presentation on responsibilities and problem-solving

Begin with the PowerPoint presentation discussing student responsibilities. Also available as Google slides. Discuss with students the responsibilities they have at home. Explain that whether students are baking a cake or solving a multiplication problem they can take the same four steps to solve their problems. You’ll also use this presentation for practice during the lesson and assessment at the end of the lesson.

Time: 5-10 minutes depending on length of student discussion.

2. Practice

Complete multiplication table on page 11 of Google slides presentation independently 2-3 minutes

3. Game Play

Play the Spirit Lake game, In levels 1 and 2 of the game, players solve multiplication problems set in the context of a story based on the history and culture of the Dakota people. They learn a problem-solving strategy that can be applied to a wide range of situations, including mathematics. .After this lesson, students will be able to solve word problems using multiplication of one-digit numbers and understand the general application of problem-solving steps. (10-15 minutes)

Option for students without access to Mac/ Windows computers

3a. Game Play Video

For schools that want the game play and multiplication problems from Spirit Lake: The Game but now your students are at home, without a computer, what do you do? You can have them watch this four-minute preview up to the multiplication word problem. Your students will learn a few words in Dakota, see the game and be set for your lesson on multiplying one-digit numbers.

3b Instructional Video

In this six-minute video, students learn four steps in solving a problem: understand what’s required, select a strategy, do it, and test it. Multiplication word problems are used as examples, but these scaffolding strategies for Grades 3-5 can be applied to any problem in math.

Assessment

Individual Assessment

Have students work independently to solve the problem in the PowerPoint or Google slides linked above. Have students present their solutions. Show one recommended solution that is in the presentation.

If students will be completing the assignment in class, print out pages 11,12 and 14 for assessment. On-line classes can complete these problems in Google doc or other method used by the teacher for assignments.

Estimated time: 5 minutes

A second assessment is in the reports for the Spirit Lake game, which show whether students answered correctly the problems in Levels 1 and 2, 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. Note that these reports are NOT available for Spirit Lake Beginnings, which is played offline.

Group Assessment

Continue with the PowerPoint presentation or Google slides. Students will work in groups to solve 4 multiplication problems. Estimated time: 5 minutes

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.