math problem solving strategies lesson plan

Teaching Problem Solving in Math

• Freebies , Math , Planning

Every year my students can be fantastic at math…until they start to see math with words. For some reason, once math gets translated into reading, even my best readers start to panic. There is just something about word problems, or problem-solving, that causes children to think they don’t know how to complete them.

Every year in math, I start off by teaching my students problem-solving skills and strategies. Every year they moan and groan that they know them. Every year – paragraph one above. It was a vicious cycle. I needed something new.

I put together a problem-solving unit that would focus a bit more on strategies and steps in hopes that that would create problem-solving stars.

The Problem Solving Strategies

First, I wanted to make sure my students all learned the different strategies to solve problems, such as guess-and-check, using visuals (draw a picture, act it out, and modeling it), working backward, and organizational methods (tables, charts, and lists). In the past, I had used worksheet pages that would introduce one and provide the students with plenty of problems practicing that one strategy. I did like that because students could focus more on practicing the strategy itself, but I also wanted students to know when to use it, too, so I made sure they had both to practice.

I provided students with plenty of practice of the strategies, such as in this guess-and-check game.

There’s also this visuals strategy wheel practice.

I also provided them with paper dolls and a variety of clothing to create an organized list to determine just how many outfits their “friend” would have.

Then, as I said above, we practiced in a variety of ways to make sure we knew exactly when to use them. I really wanted to make sure they had this down!

Anyway, after I knew they had down the various strategies and when to use them, then we went into the actual problem-solving steps.

The Problem Solving Steps

I wanted students to understand that when they see a story problem, it isn’t scary. Really, it’s just the equation written out in words in a real-life situation. Then, I provided them with the “keys to success.”

S tep 1 – Understand the Problem.   To help students understand the problem, I provided them with sample problems, and together we did five important things:

• read the problem carefully
• restated the problem in our own words
• crossed out unimportant information
• circled any important information
• stated the goal or question to be solved

We did this over and over with example problems.

Once I felt the students had it down, we practiced it in a game of problem-solving relay. Students raced one another to see how quickly they could get down to the nitty-gritty of the word problems. We weren’t solving the problems – yet.

Then, we were on to Step 2 – Make a Plan . We talked about how this was where we were going to choose which strategy we were going to use. We also discussed how this was where we were going to figure out what operation to use. I taught the students Sheila Melton’s operation concept map.

We talked about how if you know the total and know if it is equal or not, that will determine what operation you are doing. So, we took an example problem, such as:

Sheldon wants to make a cupcake for each of his 28 classmates. He can make 7 cupcakes with one box of cupcake mix. How many boxes will he need to buy?

We started off by asking ourselves, “Do we know the total?” We know there are a total of 28 classmates. So, yes, we are separating. Then, we ask, “Is it equal?” Yes, he wants to make a cupcake for EACH of his classmates. So, we are dividing: 28 divided by 7 = 4. He will need to buy 4 boxes. (I actually went ahead and solved it here – which is the next step, too.)

Step 3 – Solving the problem . We talked about how solving the problem involves the following:

• taking our time
• working the problem out
• showing all our work
• estimating the answer
• using thinking strategies

We talked specifically about thinking strategies. Just like in reading, there are thinking strategies in math. I wanted students to be aware that sometimes when we are working on a problem, a particular strategy may not be working, and we may need to switch strategies. We also discussed that sometimes we may need to rethink the problem, to think of related content, or to even start over. We discussed these thinking strategies:

• switch strategies or try a different one
• rethink the problem
• think of related content
• decide if you need to make changes
• check your work
• but most important…don’t give up!

To make sure they were getting in practice utilizing these thinking strategies, I gave each group chart paper with a letter from a fellow “student” (not a real student), and they had to give advice on how to help them solve their problem using the thinking strategies above.

Finally, Step 4 – Check It.   This is the step that students often miss. I wanted to emphasize just how important it is! I went over it with them, discussing that when they check their problems, they should always look for these things:

• compare your answer to your estimate
• check for reasonableness
• check your calculations
• add the units
• restate the question in the answer
• explain how you solved the problem

Then, I gave students practice cards. I provided them with example cards of “students” who had completed their assignments already, and I wanted them to be the teacher. They needed to check the work and make sure it was completed correctly. If it wasn’t, then they needed to tell what they missed and correct it.

To demonstrate their understanding of the entire unit, we completed an adorable lap book (my first time ever putting together one or even creating one – I was surprised how well it turned out, actually). It was a great way to put everything we discussed in there.

Once we were all done, students were officially Problem Solving S.T.A.R.S. I just reminded students frequently of this acronym.

Stop – Don’t rush with any solution; just take your time and look everything over.

Think – Take your time to think about the problem and solution.

Act  – Act on a strategy and try it out.

Review – Look it over and see if you got all the parts.

Wow, you are a true trooper sticking it out in this lengthy post! To sum up the majority of what I have written here, I have some problem-solving bookmarks FREE to help you remember and to help your students!

You can grab these problem-solving bookmarks for FREE by clicking here .

You can do any of these ideas without having to purchase anything. However, if you are looking to save some time and energy, then they are all found in my Math Workshop Problem Solving Unit . The unit is for grade three, but it  may work for other grade levels. The practice problems are all for the early third-grade level.

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Problem Solving Activities: 7 Strategies

• Critical Thinking

Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough. 

I was so excited!

We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies. 

It was a proud moment for me!

Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy. 

Genius right? 

After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name. 

What a crushing blow! Just when I thought I did something special, I find out I did it all wrong. 

I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom. 

When I Finally Saw the Light

To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students. 

Problem Solving Activities

Here are seven ways to strategically reinforce problem solving skills in your classroom. 

Seasonal Problem Solving

Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!

Cooperative Problem Solving Tasks

Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.

Notice and Wonder

Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it. 

Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.

Math Starters

Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here ! 

Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.

Calculators

Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!

Three-Act Math Tasks

Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons . 

Getting the Most from Each of the Problem Solving Activities

When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next. 

Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below. 

Which of the problem solving activities will you try first? Respond in the comments below.

Shametria Routt Banks

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2 Responses

This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.

Thank you, Scott! Best wishes to you and your pre-service teachers this year!

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Maneuvering the Middle

Student-Centered Math Lessons

Math Problem Solving Strategies

How many times have you been teaching a concept that students are feeling confident in, only for them to completely shut down when faced with a word problem?  For me, the answer is too many to count.  Word problems require problem solving strategies. And more than anything, word problems require decoding, eliminating extra information, and opportunities for students to solve for something that the question is not asking for .  There are so many places for students to make errors! Let’s talk about some problem solving strategies that can help guide and encourage students!

1. C.U.B.E.S.

C.U.B.E.S stands for circle the important numbers, underline the question, box the words that are keywords, eliminate extra information, and solve by showing work.  

• Why I like it: Gives students a very specific ‘what to do.’
• Why I don’t like it: With all of the annotating of the problem, I’m not sure that students are actually reading the problem.  None of the steps emphasize reading the problem but maybe that is a given.

2. R.U.N.S.

R.U.N.S. stands for read the problem, underline the question, name the problem type, and write a strategy sentence. 

• Why I like it: Students are forced to think about what type of problem it is (factoring, division, etc) and then come up with a plan to solve it using a strategy sentence.  This is a great strategy to teach when you are tackling various types of problems.
• Why I don’t like it: Though I love the opportunity for students to write in math, writing a strategy statement for every problem can eat up a lot of time.

3. U.P.S. CHECK

U.P.S. Check stands for understand, plan, solve, and check.

• Why I like it: I love that there is a check step in this problem solving strategy.  Students having to defend the reasonableness of their answer is essential for students’ number sense.
• Why I don’t like it: It can be a little vague and doesn’t give concrete ‘what to dos.’ Checking that students completed the ‘understand’ step can be hard to see.

4. Maneuvering the Middle Strategy AKA K.N.O.W.S.

Here is the strategy that I adopted a few years ago.  It doesn’t have a name yet nor an acronym, (so can it even be considered a strategy…?)

UPDATE: IT DOES HAVE A NAME! Thanks to our lovely readers, Wendi and Natalie!

• Know: This will help students find the important information.
• Need to Know: This will force students to reread the question and write down what they are trying to solve for.
• Organize:   I think this would be a great place for teachers to emphasize drawing a model or picture.
• Work: Students show their calculations here.
• Solution: This is where students will ask themselves if the answer is reasonable and whether it answered the question.

Ideas for Promoting Showing Your Work

• White boards are a helpful resource that make (extra) writing engaging!
• Celebrating when students show their work. Create a bulletin board that says ***I showed my work*** with student exemplars.
• Take a picture that shows your expectation for how work should look and post it on the board like Marissa did here.

Show Work Digitally

Many teachers are facing how to have students show their work or their problem solving strategy when tasked with submitting work online. Platforms like Kami make this possible. Go Formative has a feature where students can use their mouse to “draw” their work. 

If you want to spend your energy teaching student problem solving instead of writing and finding math problems, look no further than our All Access membership . Click the button to learn more. 

Students who plan succeed at a higher rate than students who do not plan.   Do you have a go to problem solving strategy that you teach your students? 

Editor’s Note: Maneuvering the Middle has been publishing blog posts for nearly 8 years! This post was originally published in September of 2017. It has been revamped for relevancy and accuracy.

Problem Solving Posters (Represent It! Bulletin Board)

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Reader Interactions

18 comments.

October 4, 2017 at 7:55 pm

As a reading specialist, I love your strategy. It’s flexible, “portable” for any problem, and DOES get kids to read and understand the problem by 1) summarizing what they know and 2) asking a question for what they don’t yet know — two key comprehension strategies! How about: “Make a Plan for the Problem”? That’s the core of your rationale for using it, and I bet you’re already saying this all the time in class. Kids will get it even more because it’s a statement, not an acronym to remember. This is coming to my reading class tomorrow with word problems — thank you!

October 4, 2017 at 8:59 pm

Hi Nora! I have never thought about this as a reading strategy, genius! Please let me know how it goes. I would love to hear more!

December 15, 2017 at 7:57 am

Hi! I am a middle school teacher in New York state and my district is “gung ho” on CUBES. I completely agree with you that kids are not really reading the problem when using CUBES and only circling and boxing stuff then “doing something” with it without regard for whether or not they are doing the right thing (just a shot in the dark!). I have adopted what I call a “no fear word problems” procedure because several of my students told me they are scared of word problems and I thought, “let’s take the scary out of it then by figuring out how to dissect it and attack it! Our class strategy is nearly identical to your strategy:

1. Pre-Read the problem (do so at your normal reading speed just so you basically know what it says) 2. Active Read: Make a short list of: DK (what I Definitely Know), TK (what I Think I Know and should do), and WK (what I Want to Know– what is the question?) 3. Draw and Solve 4. State the answer in a complete sentence.

This procedure keep kids for “surfacely” reading and just trying something that doesn’t make sense with the context and implications of the word problem. I adapted some of it from Harvey Silver strategies (from Strategic Teacher) and incorporated the “Read-Draw-Write” component of the Eureka Math program. One thing that Harvey Silver says is, “Unlike other problems in math, word problems combine quantitative problem solving with inferential reading, and this combination can bring out the impulsive side in students.” (The Strategic Teacher, page 90, Silver, et al.; 2007). I found that CUBES perpetuates the impulsive side of middle school students, especially when the math seems particularly difficult. Math word problems are packed full of words and every word means something to about the intent and the mathematics in the problem, especially in middle school and high school. Reading has to be done both at the literal and inferential levels to actually correctly determine what needs to be done and execute the proper mathematics. So far this method is going really well with my students and they are experiencing higher levels of confidence and greater success in solving.

October 5, 2017 at 6:27 am

Hi! Another teacher and I came up with a strategy we call RUBY a few years ago. We modeled this very closely after close reading strategies that are language arts department was using, but tailored it to math. R-Read the problem (I tell kids to do this without a pencil in hand otherwise they are tempted to start underlining and circling before they read) U-Underline key words and circle important numbers B-Box the questions (I always have student’s box their answer so we figured this was a way for them to relate the question and answer) Y-You ask yourself: Did you answer the question? Does your answer make sense (mathematically)

I have anchor charts that we have made for classrooms and interactive notebooks if you would like them let me me know….

October 5, 2017 at 9:46 am

Great idea! Thanks so much for sharing with our readers!

October 8, 2017 at 6:51 pm

LOVE this idea! Will definitely use it this year! Thank you!

December 18, 2019 at 7:48 am

I would love an anchor chart for RUBY

October 15, 2017 at 11:05 am

I will definitely use this concept in my Pre-Algebra classes this year; I especially like the graphic organizer to help students organize their thought process in solving the problems too.

April 20, 2018 at 7:36 am

I love the process you’ve come up with, and think it definitely balances the benefits of simplicity and thoroughness. At the risk of sounding nitpicky, I want to point out that the examples you provide are all ‘processes’ rather than strategies. For the most part, they are all based on the Polya’s, the Hungarian mathematician, 4-step approach to problem solving (Understand/Plan/Solve/Reflect). It’s a process because it defines the steps we take to approach any word problem without getting into the specific mathematical ‘strategy’ we will use to solve it. Step 2 of the process is where they choose the best strategy (guess and check, draw a picture, make a table, etc) for the given problem. We should start by teaching the strategies one at a time by choosing problems that fit that strategy. Eventually, once they have added multiple strategies to their toolkit, we can present them with problems and let them choose the right strategy.

June 22, 2018 at 12:19 pm

That’s brilliant! Thank you for sharing!

May 31, 2018 at 12:15 pm

Mrs. Brack is setting up her second Christmas tree. Her tree consists of 30% red and 70% gold ornaments. If there are 40 red ornaments, then how many ornaments are on the tree? What is the answer to this question?

June 22, 2018 at 10:46 am

Whoops! I guess the answer would not result in a whole number (133.333…) Thanks for catching that error.

July 28, 2018 at 6:53 pm

I used to teach elementary math and now I run my own learning center, and we teach a lot of middle school math. The strategy you outlined sounds a little like the strategy I use, called KFCS (like the fast-food restaurant). K stands for “What do I know,” F stands for “What do I need to Find,” C stands for “Come up with a plan” [which includes 2 parts: the operation (+, -, x, and /) and the problem-solving strategy], and lastly, the S stands for “solve the problem” (which includes all the work that is involved in solving the problem and the answer statement). I find the same struggles with being consistent with modeling clearly all of the parts of the strategy as well, but I’ve found that the more the student practices the strategy, the more intrinsic it becomes for them; of course, it takes a lot more for those students who struggle with understanding word problems. I did create a worksheet to make it easier for the students to follow the steps as well. If you’d like a copy, please let me know, and I will be glad to send it.

February 3, 2019 at 3:56 pm

This is a supportive and encouraging site. Several of the comments and post are spot on! Especially, the “What I like/don’t like” comparisons.

March 7, 2019 at 6:59 am

Have you named your unnamed strategy yet? I’ve been using this strategy for years. I think you should call it K.N.O.W.S. K – Know N – Need OW – (Organise) Plan and Work S – Solution

September 2, 2019 at 11:18 am

Going off of your idea, Natalie, how about the following?

K now N eed to find out O rganize (a plan – may involve a picture, a graphic organizer…) W ork S ee if you’re right (does it make sense, is the math done correctly…)

I love the K & N steps…so much more tangible than just “Read” or even “Understand,” as I’ve been seeing is most common in the processes I’ve been researching. I like separating the “Work” and “See” steps. I feel like just “Solve” May lead to forgetting the checking step.

March 16, 2020 at 4:44 pm

I’m doing this one. Love it. Thank you!!

September 17, 2019 at 7:14 am

Hi, I wanted to tell you how amazing and kind you are to share with all of us. I especially like your word problem graphic organizer that you created yourself! I am adopting it this week. We have a meeting with all administrators to discuss algebra. I am going to share with all the people at the meeting.

I had filled out the paperwork for the number line. Is it supposed to go to my email address? Thank you again. I am going to read everything you ahve given to us. Have a wonderful Tuesday!

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1.6: Problem Solving Strategies

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• Michelle Manes
• University of Hawaii

Think back to the first problem in this chapter, the ABC Problem. What did you do to solve it? Even if you did not figure it out completely by yourself, you probably worked towards a solution and figured out some things that did not work.

Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solve them), you learn strategies and techniques that can be useful. But no single strategy works every time.

How to Solve It

George Pólya was a great champion in the field of teaching  effective problem solving skills. He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities). He wrote many mathematical papers along with three books, most famously, How to Solve it . Pólya died at the age 98 in 1985. [1]

George Pólya, circa 1973

• Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY 2.0 ( http://creativecommons.org/licenses/by/2.0 )], via Wikimedia Commons ↵

In 1945, Pólya published the short book How to Solve It , which gave a four-step method for solving mathematical problems:

• First, you have to understand the problem.
• After understanding, then make a plan.
• Carry out the plan.
• Look back on your work. How could it be better?

This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.

Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!

We have already seen one problem solving strategy, which we call “Wishful Thinking.” Do not be afraid to change the problem! Ask yourself “what if” questions:

• What if the picture was different?
• What if the numbers were simpler?
• What if I just made up some numbers?

You need to be sure to go back to the original problem at the end, but wishful thinking can be a powerful strategy for getting started.

This brings us to the most important problem solving strategy of all:

A Problem Solving Strategy: Try Something!

If you are really trying to solve a problem, the whole point is that you do not know what to do right out of the starting gate. You need to just try something! Put pencil to paper (or stylus to screen or chalk to board or whatever!) and try something. This is often an important step in understanding the problem; just mess around with it a bit to understand the situation and figure out what is going on.

Note that being "good at mathematics" is not about doing things right the first time. It is about figuring things out. Practice being okay with having done something incorrectly. Try to avoid using an eraser and just lightly cross out incorrect work (do not black out the entire thing). This way if it turns out that you did something useful, you still have that work to reference! If what you tried first does not work, try something else! Play around with the problem until you have a feel for what is going on.

Last week, Alex borrowed money from several of his friends. He finally got paid at work, so he brought cash to school to pay back his debts. First he saw Brianna, and he gave her 1/4 of the money he had brought to school. Then Alex saw Chris and gave him 1/3 of what was left after paying Brianna. Finally, Alex saw David and gave him 1/2 of the remaining money. Who got the most money from Alex?

Think/Pair/Share

After you have worked on the problem on your own for a while, talk through your ideas with a partner if possible (even if you have not solved it). What did you try? What did you figure out about the problem? This problem lends itself to two particular strategies. Did you try either of these as you worked on the problem? If not, read about the strategy and then try it out before watching the solution.

A Problem Solving Strategy: Draw a Picture

Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric, like this one, thinking visually can help! Can you represent something in the situation by a picture?

Draw a square to represent all of Alex’s money. Then shade 1/4 of the square — that’s what he gave away to Brianna. How can the picture help you finish the problem?

After you have worked on the problem yourself using this strategy (or if you are completely stuck), you can watch someone else’s solution.

A Problem Solving Strategy: Make Up Numbers

Part of what makes this problem difficult is that it is about money, but there are no numbers given. That means the numbers must not be important. So just make them up!

Try this: Assume (that is, pretend) Alex had some specific amount of money when he showed up at school, say $100. Then figure out how much he gives to each person.

Or try working backward: suppose Alex has some specific amount left at the end, say $10. Since he gave David half of what he had before seeing David, that means he had $20 before running into David. Now, work backwards and figure out how much each person got.

Watch the solution only after you tried this strategy for yourself.

If you use the “Make Up Numbers” strategy, it is really important to remember what the original problem was asking! You do not want to answer something like “Everyone got $10.” That is not true in the original problem; that is an artifact of the numbers you made up. So after you work everything out, be sure to re-read the problem and answer what was asked!

(Squares on a Chess Board)

How many squares, of any possible size, are on a 8 × 8 chess board? (The answer is not 64... It’s a lot bigger!)

Remember Pólya’s first step is to understand the problem. If you are not sure what is being asked, or why the answer is not just 64, be sure to ask someone!

Think / Pair / Share

After you have worked on the problem on your own for a while, talk through your ideas with a partner if possible (even if you have not solved it). What did you try? What did you figure out about the problem, even if you have not solved it completely?

Most people want to draw a picture for this problem, but even with the picture it can be hard to know if you have found the correct answer. The numbers get big, and it can be hard to keep track of your work. Your goal at the end is to be absolutely positive that you found the right answer. Instead of asking the teacher, “Is this right?”, you should be ready to justify it and say, “Here’s my answer, and here is how I got it.”

A Problem Solving Strategy: Try a Simpler Problem

Pólya suggested this strategy: “If you can’t solve a problem, then there is an easier problem you can solve: find it.” He also said, “If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?” In this case, an 8 × 8 chess board is pretty big. Can you solve the problem for smaller boards? Like 1 × 1? 2 × 2? 3 × 3?

The ultimate goal is to solve the original problem. But working with smaller boards might give you some insight and help you devise your plan (that is Pólya’s step (2)).

A Problem Solving Strategy: Work Systematically

If you are working on simpler problems, it is useful to keep track of what you have figured out and what changes as the problem gets more complicated.

For example, in this problem you might keep track of how many 1 × 1 squares are on each board, how many 2 × 2 squares on are each board, how many 3 × 3 squares are on each board, and so on. You could keep track of the information in a table:

A Problem Solving Strategy: Use Manipulatives to Help You Investigate

Sometimes even drawing a picture may not be enough to help you investigate a problem. Having actual materials that you move around can sometimes help a lot!

For example, in this problem it can be difficult to keep track of which squares you have already counted. You might want to cut out 1 × 1 squares, 2 × 2 squares, 3 × 3 squares, and so on. You can actually move the smaller squares across the chess board in a systematic way, making sure that you count everything once and do not count anything twice.

A Problem Solving Strategy: Look for and Explain Patterns

Sometimes the numbers in a problem are so big, there is no way you will actually count everything up by hand. For example, if the problem in this section were about a 100 × 100 chess board, you would not want to go through counting all the squares by hand! It would be much more appealing to find a pattern in the smaller boards and then extend that pattern to solve the problem for a 100 × 100 chess board just with a calculation.

If you have not done so already, extend the table above all the way to an 8 × 8 chess board, filling in all the rows and columns. Use your table to find the total number of squares in an 8 × 8 chess board. Then:

• Describe all of the patterns you see in the table. If possible, actually describe these to a friend.
• Explain and justify any of the patterns you see (if possible, actually do this with a friend). If you don't have a partner to work with, imagine they asked you, "How can you be sure the patterns will continue?"
• Expand this to find what calculation(s) you would perform to find the total number of squares on a 100 × 100 chess board.

(We will come back to this question soon. So if you are not sure right now how to explain and justify the patterns you found, that is OK.)

(Broken Clock)

This clock has been broken into three pieces. If you add the numbers in each piece, the sums are consecutive numbers. ( Consecutive numbers are whole numbers that appear one after the other, such as 1, 2, 3, 4 or 13, 14, 15.)

Can you break another clock into a different number of pieces so that the sums are consecutive numbers? Assume that each piece has at least two numbers and that no number is damaged (e.g. 12 isn’t split into two digits 1 and 2).

Remember that your first step is to understand the problem. Work out what is going on here. What are the sums of the numbers on each piece? Are they consecutive?

After you have worked on the problem on your own for a while, talk through your ideas with a partner if possible (even if you have not solved it). What did you try? What progress have you made?

A Problem Solving Strategy: Find the Math, Remove the Context

Sometimes the problem has a lot of details in it that are unimportant, or at least unimportant for getting started. The goal is to find the underlying math problem, then come back to the original question and see if you can solve it using the math.

In this case, worrying about the clock and exactly how the pieces break is less important than worrying about finding consecutive numbers that sum to the correct total. Ask yourself:

• What is the sum of all the numbers on the clock’s face?
• Can I find two consecutive numbers that give the correct sum? Or four consecutive numbers? Or some other amount?
• How do I know when I am done? When should I stop looking?

Of course, solving the question about consecutive numbers is not the same as solving the original problem. You have to go back and see if the clock can actually break apart so that each piece gives you one of those consecutive numbers. Maybe you can solve the math problem, but it does not translate into solving the clock problem.

A Problem Solving Strategy: Check Your Assumptions

When solving problems, it is easy to limit your thinking by adding extra assumptions that are not in the problem. Be sure you ask yourself: Am I constraining my thinking too much?

In the clock problem, because the first solution has the clock broken radially (all three pieces meet at the center, so it looks like slicing a pie), many people assume that is how the clock must break. But the problem does not require the clock to break radially. It might break into pieces like this:

Were you assuming the clock would break in a specific way? Try to solve the problem now, if you have not already.

Problem-Solving Strategies

There are many different ways to solve a math problem, and equipping students with problem-solving strategies is just as important as teaching computation and algorithms. Problem-solving strategies help students visualize the problem or present the given information in a way that can lead them to the solution. Solving word problems using strategies works great as a number talks activity and helps to revise many skills.

Problem-solving strategies

1. create a diagram/picture, 2. guess and check., 3. make a table or a list., 4. logical reasoning., 5. find a pattern, 6. work backward, 1. create a diagram/draw a picture.

Creating a diagram helps students visualize the problem and reach the solution. A diagram can be a picture with labels, or a representation of the problem with objects that can be manipulated. Role-playing and acting out the problem like a story can help get to the solution.

Alice spent 3/4 of her babysitting money on comic books. She is left with $6. How much money did she make from babysitting?

2. Guess and check

Teach students the same strategy research mathematicians use.

With this strategy, students solve problems by making a reasonable guess depending on the information given. Then they check to see if the answer is correct and they improve it accordingly.  By repeating this process, a student can arrive at a correct answer that has been checked. It is recommended that the students keep a record of their guesses by making a chart, a table or a list. This is a flexible strategy that works for many types of problems. When students are stuck, guessing and checking helps them start and explore the problem. However, there is a trap. Exactly because it is such a simple strategy to use, some students find it difficult to consider other strategies. As problems get more complicated, other strategies become more important and more effective.

Find two numbers that have sum 11 and product 24.

Try/guess  5 and 6  the product is 30 too high

  adjust  to 4 and 7 with product 28 still high

  adjust  again 3 and 8 product 24

3. Make a table or a list

Carefully organize the information on a table or list according to the problem information. It might be a table of numbers, a table with ticks and crosses to solve a logic problem or a list of possible answers. Seeing the given information sorted out on a table or a list will help find patterns and lead to the correct solution.

To make sure you are listing all the information correctly read the problem carefully.

Find the common factors of 24, 30 and 18

Logical reasoning is the process of using logical, systemic steps to arrive at a conclusion based on given facts and mathematic principles. Read and understand the problem. Then find the information that helps you start solving the problem. Continue with each piece of information and write possible answers.

Thomas, Helen, Bill, and Mary have cats that are black, brown, white, or gray. The cats’ names are Buddy, Lucky, Fifi, and Moo. Buddy is brown. Thoma’s cat, Lucky, is not gray. Helen’s cat is white but is not named Moo. The gray cat belongs to Bill. Which cat belongs to each student, and what is its color?

A table or list is useful in solving logic problems.

Since Lucky is not gray it can be black or brown. However, Buddy is brown so Lucky has to be black.

Buddy is brown so it cannot be Helen’s cat. Helen’s cat cannot be Moo, Buddy or Lucky, so it is Fifi.

Therefore, Moo is Bill’s cat and Buddy is Mary’s cat.

5. Find a pattern.

Finding a pattern is a strategy in which students look for patterns in the given information in order to solve the problem. When the problem consists of data like numbers or events that are repeated then it can be solved using the “find a pattern” problem-solving strategy. Data can be organized in a table or a list to reveal the pattern and help discover the “rule” of the pattern.

 The “rule” can then be used to find the answer to the question and complete the table/list.

Shannon’s Pizzeria made 5 pizzas on Sunday, 10 pizzas on Monday, 20 pizzas on Tuesday, and 40 pizzas on Wednesday. If this pattern continues, how many pizzas will the pizzeria make on Saturday?

6. Working backward

Problems that can be solved with this strategy are the ones that  list a series of events or a sequence of steps .

In this strategy, the students must start with the solution and work back to the beginning. Each operation must be reversed to get back to the beginning. So if working forwards requires addition, when students work backward they will need to subtract. And if they multiply working forwards, they must divide when working backward.

Mom bought a box of candy. Mary took 5 of them, Nick took 4 of them and 31 were given out on Halloween night. The next morning they found 8 pieces of candy in the box. How many candy pieces were in the box when mom bought it.

For this problem, we know that the final number of candy was 8, so if we work backward to “put back” the candy that was taken from the box we can reach the number of candy pieces that were in the box, to begin with.

The candy was taken away so we will normally subtract them. However, to get back to the original number of candy we need to work backward and do the opposite, which is to add them.

8 candy pieces were left + the 31 given out + plus the ones Mary took + the ones Nick took

8+31+5+4= 48   Answer: The box came with 48 pieces of candy.

Selecting the best strategy for a problem comes with practice and often problems will require the use of more than one strategies.

Print and digital activities

I have created a collection of print and digital activity cards and worksheets with word problems (print and google slides) to solve using the strategies above. The collection includes 70 problems (5 challenge ones) and their solution s and explanations.

sample below

How to use the activity cards

Allow the students to use manipulatives to solve the problems. (counters, shapes, lego blocks, Cuisenaire blocks, base 10 blocks, clocks) They can use manipulatives to create a picture and visualize the problem. They can use counters for the guess and check strategy. Discuss which strategy/strategies are better for solving each problem. Discuss the different ways. Use the activities as warm-ups, number talks, initiate discussions, group work, challenge, escape rooms, and more.

Ask your students to write their own problems using the problems in this resource, and more, as examples. Start with a simple type. Students learn a lot when trying to compose a problem. They can share the problem with their partner or the whole class. Make a collection of problems to share with another class.

For the google slides the students can use text boxes to explain their thinking with words, add shapes and lines to create diagrams, and add (insert) tables and diagrams.

Many of the problems can be solved faster by using algebraic expressions. However, since I created this resource for grades 4 and up I chose to show simple conceptual ways of solving the problems using the strategies above. You can suggest different ways of solving the problems based on the grade level.

Find the free and premium versions of the resource below. The premium version includes 70 problems (challenge problems included) and their solutions

There are 2 versions of the resource

70 google slides with explanations + 70 printable task cards

70 google slides with explanations + 11 worksheets

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Problem-Based Tasks in Math

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Providing students with opportunities to grapple with math has led to amazing things happening in my class. Students are totally excited and are driven to figure out not just how to solve a problem but why it works.

– Jessica Proffitt, Fifth-Grade Teacher at Two Rivers

Watch two rivers’s teachers and students at work on problem-based tasks in math.

Problem-Based Tasks Require Students to Apply Their Knowledge in New Contexts

Problem-based tasks are math lessons built around a single, compelling problem. The problems are truly “problematic” for students — that is, they do not offer an immediate solution.

The problems provide an opportunity for students to build conceptual understanding. Problem-based tasks require students to apply their current understanding and skills to new contexts that highlight core math concepts. For example, when students solve a problem that could be solved with multiplication before they have formally been taught what multiplication is and how it works, they build an understanding that multiplication is repeated addition.

Well-designed problem-based tasks provide multiple entry points for students to engage in problem solving, ensuring that all students have access to the same concepts. When students solve the problems in different ways—including drawing pictures, acting out the problem, writing algorithms, and using manipulatives—they make connections between the variety of models that all accurately illustrate the underlying mathematics.

Problem-Based Tasks in Math Resources

Math Interventions

Introduction.

• Subitizing Interventions
• Counting Interventions: Whole Numbers Less Than 30
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• Math Rules and Concepts Lesson Plans

You can use either  Explicit Instruction  or Self-Regulated Strategy Development when you intervene to support your student's problem solving skills. The following lesson plan targets a specific problem-solving skill using explicit instruction. As you read this plan, consider: 

How does this plan support objective mastery?

Problem Solving Intervention Plan

Art, E. (2017). Problem solving intervention packet. New York, NY: Relay Graduate School of Education.

This lesson plan supports objective mastery because the teacher employs Principles of Specialized instruction to help the student visualize Part/Part/Whole (Part Unknown) problems to identify what she is supposed to figure out. In this lesson plan, she isolates the skill (identifying what the problem is), and uses explicit instruction to teach the student how to identify two what is happening in the story and what she is trying to figure out. After she explains the process she'll take, she uses metacognition and shows the student how she asks these two questions as she is reading. Finally, she builds in multiple at-bats so that the student has the opportunity to practice this strategy over and over so that she can reach her objective.

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Solving Word Problems (Grades 1-2)

Our Solving Word Problems lesson plan provides students with strategies to help them solve word problems, such as using illustrations or drawings. Students practice solving example word problems using the given strategies.

Description

Additional information.

Our Solving Word Problems lesson plan develops math problem-solving strategies for young students. This interactive lesson equips students to identify and define keywords and use pictures or diagrams for math problem solving (addition and subtraction). Students are asked to work collaboratively, in pairs, to compose word problems that incorporate pictures or diagrams and exchange problems with other groups to solve. Students are also asked to individually complete practice problems in order to demonstrate their understanding of the lesson.

At the end of the lesson, students will be able to identify and define keywords and use pictures or diagrams for math problem solving (addition and subtraction).

State Educational Standards: LB.Math.Content.1.OA.A.2, LB.Math.Content.2.OA.A.1

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Solving Word Problems

This concept is hard for students. Thanks for explicit lesson on solving word problems.

We recently began homeschooling my son, after learning that he has not been being taught many subjects due to being in self-contained unit at school because of his behavioral issues. After explaining a few things to him, the material really helped to guide him on to the next part in our efforts to get him caught up. Thank you.

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Math Problem Solving Strategies (Intermediate) - Lesson Plan & Templates

Grade Level: Intermediate (3-6) | Academic Subject: STEM | VariQuest Tools: Design Center Software | VariQuest Tools: Perfecta 2400 | VariQuest Tools: Poster Maker 3600 | Featured Topics: Common Core | Featured Topics: Lessons and Activities | Academic Subject: Mathematics | Featured Topics: Templates for FREE download

We are excited to announce our partnership with two super creative educators from  The Curriculum Corner ! You can expect to see more blog posts containing free Common Core aligned lesson ideas, teacher resources and templates you can easily print with your VariQuest® Perfecta® Poster Design System - just be sure you have the latest version of the VariQuest Software ! 

Lesson:  introduction to problem solving strategies (two-day lesson) , level:  intermediate , objectives & ccss alignment:  students will increase independence in using various strategies to solve different types of word problems., *note: ccss has problem solving strategies spread throughout the domains for math.  this lesson focuses on giving them a review of each of the various strategies.  it is suggested that teachers follow up this review with a more in-depth lesson in each of the strategies as they fit naturally into the curriculum or as there is student need. , materials & visuals: , anchor chart – problem solving strategies, math notes for problem solving, click on each image to download the pdf and print to a poster.

Preparation: 

Think through a sample problem for each of the strategies listed on the anchor chart.  these will be shown to the students as examples., prepare “problem solving” anchor chart for mini-lesson., copy the “math notes for problem solving” page for each child in the classroom.  you may choose to three-hole-punch this page for use in a math notes binder/folder to be kept by students and referred to throughout the year., mini-lesson:, ask students what a “strategy” is.  accept several answers and then lead the class to the conclusion that a strategy is a plan to reach a goal.  next, ask the students how strategies might apply in math., display the anchor chart titled “problem solving strategies” for the students.  review the strategies and remind students that these are some ways that they can use to solve all kinds of different math problems., pass out “math notes for problem solving” to each student and explain that this page is a place for them to write down some notes that will help them to remember what each strategy is and how to use it.  they will keep this in their math binder/folder and can pull it out as a reminder when needed., *note: the boxes of this resource have been left blank so that the teacher can decide the level of support needed to fill it out.  students may need to draw or write exactly what the teacher shares for each strategy or they may be allowed to draw or write whatever they feel will help them to remember the strategy., briefly explain a few of the eight strategies and guide students as to how you would like for them to take their notes (copying the teacher notes or creating their own depending on grade or skill level).  introduce however many strategies that time allows for in this first lesson, and then complete the note-taking for the final strategies the following day., have students place their math notes into an organized binder or folder that will be kept and used throughout the year..

ECS401 Assessment Plan Demonstration

Disclaimer:  i did not do my 3-week block this term. however, i did my 8-week, once-a-week, block in which i taught 5 individual lessons. so, i will be demonstrating my assessments in those 5 lessons. , azimuth and altitude lesson (lesson 9), outcome(s) and indicator(s).

EU9.4 Analyze human capabilities for exploring and understanding the universe, including technologies and programs that support such exploration.

g. Describe and apply techniques for determining the position of objects in space using horizontal (e.g. azimuth and altitude) and equatorial coordinate systems (e.g., declination and right ascension).

Lesson Description

Students are learning azimuth and altitude for the first time. This lesson is their first introduction. With this lesson, students will understand the context of Azimuth and Altitude and find their measurements either using estimation or a protactor. They will also learn new definitions such as the Azimuth, Altitude, and Zenith. This also taps into their previous knowledge about angles.

Assessment Strategies

Guided Notes: Student Guided Notes

Reasoning: Some students are unable to write full sentences. So, my cooperating teacher searched for a visual guided notes package that fully aligns with what she intends to teach the students about space. This notes package is visually appealing which could engage students to read the notes.

What Kind of Assessment (as, for, of)?

Formative Assessment: Assessment as Learning – Students are responsible for filling up the notes and adding their notes whenever necessary for them. They could add more notes if the teacher has said something important or helpful that was not included in the notes.

Worksheet: Student Worksheet

Reasoning: This is part of the notes package. This worksheet is intended to further practice students’ newly acquired knowledge which is finding the azimuth and altitude in the given domes in the worksheet. If students are struggling to find the measurements just by looking at the visuals, we provide them with two protractors and attach them. This way, it becomes a circle where students can physically measure the azimuth. This method is for adaptation since some students would like to see the measurements in real-time. It could be difficult because some of the measurements are in 3D, meaning they must estimate their measurements. By using two protractors and laying them flat on the table, students can estimate more accurately.

Aside from practicing their azimuth and altitude measurements, students are given four thinking questions to extend their understanding of the topic.

Formative Assessment: Assessment for Learning – student checks their understanding by doing the activity and the four extending questions. This worksheet also informs the teacher of the student’s understanding of measurements and the overall concept of azimuth and altitude (with zenith).

Formative Assessment: Assessment as Learning – Students reflect on their understanding by doing the activity. They could also ask for help from us teachers whenever they need it. So, they are being responsible for their learning as they do the worksheet.

Bloom’s Taxonomy Category

Remembering – They were to remember what azimuth, altitude, and zenith are. They are to remember how to measure azimuth and altitude and the measurement of zenith.

Understanding – They are to understand the measurements and what they represent. They are to understand why the zenith does not need an azimuth measurement.

Applying – They apply their newly acquired knowledge and apply them in different scenarios. For example, Azimuth and Altitude are used heavily in battle royale video games to determine coordinates in the map. This is implied during the lecture.

Easy: Guided Notes, First Section of the worksheet

Medium: Extended questions of the worksheet (2nd part)

8.2 Solving Equations Lesson (Math 9)

P9.2 Model and Solve situational questions using linear equations of the form:

• x/a + b = c, a ≠ 0

where a, b, and c are rational numbers.

a. Explain why the equation a/x = b, cannot have a solution of x = 0.

c. Write a linear equation to represent a particular situation.

g. Explain how the preservation of equality is involved in the solving of linear equations.

i. Solve a linear equation symbolically.

j. Analyze the given solution for a linear equation that has resulted in an incorrect solution, and identify and explain the error(s) made.

Students will be extending their prior knowledge of solving equations from using integers to using rational numbers. Students will tackle different ways of isolating the variable.

Guided Notes: 8.2 Student Notes

Reasoning: Same with the first lesson. Also, it is easier if the students are following along rather than just looking at how I demonstrate solving the questions. I also make sure to keep asking students what to do next (like they are the ones teaching me how to solve it) so they are fully involved in solving it.

Activity: Figure Out the Error: Figure Out the error Activity

Reasoning: One of the indicators states, “Analyze the given solution for a linear equation that has resulted in an incorrect solution, and identify and explain the error(s) made.” This activity assesses their ability to see the error, why is it an error, and how to fix the error.

Formative Assessment: Assessment as Learning – Students assess their ability to solve equations to be able to answer this problem.

Formative Assessment: Assessment for Learning: It also helps me as a teacher to see their level of understanding to inform my teaching practices.

Exit Slips: Exit Slip

Reasoning: Students will be able to think of different ways of solving equations involving fractions. They could even try to show me a demonstration on the exit slip. It is also an adaptation if some students are struggling to put their thinking into words. The second question is simple, yet could become complex because there are no numbers involved, only variables. My cooperating teacher told me that students are struggling whenever the x is in the denominator since they have to do a bunch of operations to fully isolate it. So, I would like to see how students will tackle this question before I proceed with new things. This is not for marks.

Formative Assessment: Assessment for Learning – It informs me on where the student’s understanding is in terms of solving the variable without the use of numbers as well as their order of operations and fractions.

Remembering – remembering their order of operations, the importance of equality, etc.

Understanding – Understanding concepts of isolating the variable and what they understand when they are asked to “solve for x”

Analyzing – The figure out the error activity encourages students to take the given information apart and look for errors and ways to solve and correct the calculation.

Easy: Guided notes, exit slips

Medium: Figure out the error activity

8.1 & 8.2 Solving Equations Review Activity (Math 9)

• x/a = b, a ≠ 0
• a/x = b, x ≠ 0

d. Observe and describe a situation relevant to self, family, or community which could be represented by a linear equation.

h. Verify, by substitution, whether or not a given rational number is a solution to a given linear equation.

This is a review day for students. However, instead of just reviewing using textbook questions, I have prepared 3+ activities for them to review 8.1 and 8.2 Solving equations. Some adaptations are giving equations with just integers as numbers instead of rational numbers to tone down the difficulty. Additional activities include colouring, solving the maze, and fixing the puzzle to reach different cognitive demands.

Solving Equation Puzzle: Solving One-Step Equations Puzzle Page 3-16

Reasoning: This puzzle is cut into pieces and I encouraged the students to work on the floor or use a masking tape to put the appropriate pieces together. It is a fun way to do math while doing puzzles. I found that students liked working with the puzzles like a mystery being solved.

Equation Maze: Writing Two-step Equations Maze Page 2

Reasoning: Another fun way to exercise their understanding of creating equations from the given word problems.

Colour by Number Worksheet (Rational Numbers): Solving Two Step Equations Coloring Activity 2 (KEY: Solving Two Step Equations Coloring Activity 2 key )

Reasoning: I am proud of myself because I created this activity. This is a colour-by-number activity. It is like a fun alternative to multiple choice because students would want to produce a great image of the fish taco. This is another fun way of exercising their ability to solve equations while having a relaxed nature of colouring at the same time.

Colour by Number Worksheet (Integers – for adaptation): Two-step equation Coloring activity on pages 3 and 5 (KEY: Two-step equation Coloring activity Page 3 and 5 key )

Reasoning: This is for backup for adaptation. Same colour by number questions but the numbers used are integers instead of rational.

Formative Assessment: Assessment for Learning – it informs me as a teacher where they are before their summative assessment.

Remember – Students remember the things they learned about in previous classes.

Understand – Students understand what they learned to be able to do the activities.

Easy: All activities. It is meant to be a fun review day before their exam from my cooperating teacher.

8.4 Equations with Variables on Both Sides (Math 9)

• ax = b + cx
• ax + b = cx + d
• a(bx + c) = d(ex + f)

Where a, b, c, d, e, and f are rational numbers.

j. Analyze a given solution for a linear equation that has resulted in an incorrect solution, and identify and explain the error(s) made.

This is the continuation of the Linear Equations unit. Now, students are learning to solve equations when the variables are on both sides. They have learned this before with integers, but now they are learning this unit with rational numbers.

Guided Notes: Student Notes pages 11-12

Reasoning: Same as the previous lessons.

Scavenger Hunt: Scavenger Hunt Cards (Student Worksheet: Solving Equations Scavenger Hunt Student Worksheet )

Reasoning: I am always trying to find ways to make math engaging for students. Scavenger hunt is another idea that I found and applied in my math class. I scattered the cards around the area and had students answer the questions and find the cards with their answers on them. I also made it a competition which even engaged them more. The team with the most cards solved will get a treat next week. I did collect the papers and marked them but they were not for marks. With marking, I made sure to add comments and point out where students stumbled while solving the equation, so they would know for next time. A student also drew an image on their sheets and gave them an extra mark for it!

Worksheet with same questions on Scavenger Hunt activity: Worksheets Not Scavenger Hunt – Copy (KEY: Worksheets Not Scavenger Hunt )

Reasoning: This is for students who do not want to participate in walking around the class and finding cards. it consists of the same questions in the scavenger hunt activity. It is also an adaptation for students with mobility issues. In my case, I do not have students with mobility issues, but if I were to use this activity again in the future, then I would be ready for certain circumstances.

Formative Assessment: Assessment for Learning – Since students are submitting their work, even if they just worked on 1-3 questions, I could infer their level of understanding. This also informs me of where they are at in terms of increasing difficulty in solving equations with rational numbers.

Formative Assessment: Assessment as Learning: Students take notes so they take accountability for their understanding of the topic. They are also allowed to have partners in the scavenger hunt activity, so they look at each other’s calculations and infer whether they got the correct answer.

Remembering – Students are remembering and/or tapping into their previous knowledge to be able to do the activity.

Understanding – Understanding the topic will allow students to do the activity.

Easy: They are just using their knowledge from previous classes and applying it in the activity.

9.1 Representing Inequalities

P9.3 Demonstrate understanding of single variable linear inequalities with rational coefficients including:

• solving inequalities

a. Observe and describe situations relevant to self, family, or community, including First Nations and Métis communities, that involve inequalities and classify the inequality as being less than, greater than, less than or equal to, or greater than or equal to.

i. Graph the solution of a linear inequality on a number line.

j. Explain why there is more than one solution to a linear inequality.

Students will re-ignite their prior knowledge about inequality symbols and will apply them with word problem scenarios. They will also tackle abstract thoughts such as the infinite possibilities of an answer for an inequality.

Guided Notes : Student Notes 4-5

Exit Slips: Exit Slip 9.1

Reasoning: The questions in the exit slips intend to review what they just learned about the closed and open circles. They can state the difference between them and their meaning. Then the rest of the questions are extended question which focuses on the student’s understanding of reverse statements of inequalities. The last question is intended to be a thinking task in which students will think of all the possible values that prove the inequality. My cooperating teacher told me that some students have still yet to cover the idea of infinity. So, I created the question to see if students would mention infinity and spark that idea within them. This is not for marks even though there are total marks indicated in the slips.

Formative Assessment: Assessment as Learning – Students assess themselves using the guided notes as well as my comments from their exit slips. My comments in the exit slips are for students to assess their understanding of the topic taught in today’s class as well as the previous classes.

Formative Assessment: Assessment for Learning – This exit slip will guide me with individual students’ understanding of inequality. This is a type of evidence that I take from my students to inform me about my teaching (if they understood) and their learning.

Remembering – Students are recalling information from previous classes or the previous school year.

Understanding – Students summarize their knowledge through the exit slip.

Applying – Students apply their understanding in a complex setting.

Easy: Guided Notes and first question of the exit slip

Medium: 2nd and 3rd questions of the exit slip because it requires more thinking and analysis.

Personal Growth

During those 8 weeks, I found that it is quite hard to come up with assessments when you have a bunch of students with different needs. Throughout my pre-internship, I tried my hardest to always have backup activities just in case something did not work out the way I intended to. I always thought that I always have to grade all the things that I do with my students. This made me realize that I am not giving them a chance to improve their learning or to fully understand the concept first before I evaluate it.

One of my goals is to enhance my skill in giving descriptive feedback. I think I achieved this when I was making comments on a student’s exit slips. I gave them feedback and suggestions on how to improve their thinking and answer the questions. and if their answer is right, I added some notes to consider going forward. It felt nice giving feedback and I hope that the students have read it so could self-assess as well.

I am looking forward to my 3-week pre-internship because I will have more authority on how to teach certain things and put my instruction into it.  I will probably be able to achieve one of my goals which is to implement different types of assessment in the classroom. Although I have done a variety, most of them are just different types of “check your understanding” activities. I would like to tackle more on assessments where students have created the criteria and can show their understanding in different ways.

ALL RIGHTS RESERVE TO THE OWNERS OF SOME OF THE TASKS I HAVE IMPLEMENTED IN MY CLASSROOM. 

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Mastering the "Take from 10" Subtraction Strategy - Lesson Plan

In this interactive math lesson, students will explore the 'take from 10' strategy for subtraction. through engaging tasks and visual aids, they will learn how to subtract a single-digit number from a two-digit number within 20. the lesson includes warm-up exercises, guided practice, independent practice, and problem-solving activities..

Know more about Mastering the "Take from 10" Subtraction Strategy - Lesson Plan

The 'Take from 10' strategy is a visual approach to subtraction where students break down the minuend into tens and ones, subtract the subtrahend from ten, and then add back any remaining ones.

The 'Take from 10' strategy helps students visualize subtraction by breaking down numbers into tens and ones. It allows them to mentally manipulate numbers and make subtraction easier.

While the focus of this lesson is on subtracting single-digit numbers from two-digit numbers within 20, the 'Take from 10' strategy can be extended to larger numbers as well. It provides a foundation for understanding subtraction with regrouping.

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