Visually Thinking

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SWBAT determine the operation needed to problem solve.

Big Idea

Seeing is believing! Students will discuss various ways word problems can be solved to determine the operation needed to problem solve.

Warm up!

20 minutes

 By the end of third grade students who are proficient in this particular standard are able to determine the operation needed to solve given word problems.  Students often rely on visual representations to assist them in their learning.  All of my students love to shop! The picture was an amazing way for them to understand what it means to visually  assess a problem.  I ask students what do you think will happened to the girl if she continues to walk with the boxes in her hand.  Students quickly said she is going to fall!  Ok!. Think of a way to help her solve this problem because we don't want her to fall. MP1

Student's responses:

Get a larger bag.

Take some of the things back.

Give me some of the boxes.

I did not anticipate our investigation would have lead us to these responses, but a teacher can hardly predict where students thinking may be. Their responses are hilarious! I tell students well guess what you all thought of a way to solve the problem with the information given.  What was the problem? (too many boxes) Right! you guys came up with some pretty good solutions.  Well today we are going to look at problem solving from a different perspective.  We are going to analyze word problems to determine the operation needed to solve the problem!  Are you guys ready?



Materials: paper, pencils

  I want to use something familiar and engaging to connect students to the lesson. Ok! Can someone give me an active count of the students here today? (30)


Since there are 30 students, We have 30 desks in the classroom.  Use your paper to illustrate how the desks would look if we put 5 desks in each row.  How many rows are there?  What does the illustration remind you of? (arrays) Explain? There are 6 rows and five desks in each row.  Can students see the operation being used here? Can anyone think of how we have used arrays before? (multiplication)

Ok, let's look at the given problem from another angle. 

We have 30 desks in the classroom. how many rows would there be if we divided the desks into rows of 5? 

What do we need to know?

How many desk are there?

How many rows?

What operation did you use to solve your problem?

Are there additional ways this problem can be solved?

What happens if five students withdraw from school? What operation did you use?

What happens if ten students enrolled in school?  What operation did you use?

  My focus here was to have my students discuss various strategies used to solve word problems.  This allows them to reason within range, and focus on the best methods for them to solve multi-step word problems.

Now Let's learn how to Buck our problem

20 minutes

I invite students to the carpet to watch a brief video on how to solve word problems.  It is a great illustration on how to break word problems down to make them easier to  for students to solve. Fantastic for giving students the additional support they need when problem solving on their own.  Students are given index cards to write the problem solving steps. I tell them we are going to use it later on in the lesson to us them solve problems.MP1MP2

B-box the question

U-underline key detail

C-circle your vocabulary

K- Knock out information you do not need

S- solve the problem

Working Together

20 minutes


Materials: dry erase boards, and dry erase markers

To begin, I post a word problem on the board.  I ask students to read the word problem with me aloud. I usually have students to read the problem aloud at least twice to make sure they understand.  It is good for them to re-check the wording of the problem because this can be kind of tricky for most students. I give them about five minutes or so to assess the problem. Don't forget to use the BUCK problem solving steps to assist you in solving.


There are 24 children at John's party. If John gives each child 6 pieces of candy, how many does each child get? 

What does the problem tell us?

B- How many does each child get?

U- 24 children get 6 pieces of candy.

C- how many does each

K- John's party,  If John

I ask student volunteers to share their work.  I want to see if students came up with different ways to illustrate their work, noticed any repeated patterns, or estimated within reason.


I want students to refocus on the main idea of the lesson. (how to determine the operation needed to solve the problem.)  Sometimes students need additional time to analyze word problems to see if their estimation strategies will arrive at a reasonable answer. MP2 

Small group discussion: 

arranging an array by putting 6 desks in each row. This is an array model. 

Have the student count the number of rows, and columns.  6 X 4=24

Another way this task can also be solved by drawing pictures of equal groups. 

4 groups of 6 equals 24 objects

A student can also reason through the problem mentally or verbally, “I know 6 and 6 are 12. 12 and 12 are 24.

Therefore, there are 4 groups of 6 giving a total of 24 desks in the classroom.”


Independent Task

20 minutes

For the independent task, I ask students to return to their assigned seats. 

Students will perform an independent task on their own. 

Problem solving skill: BUCK

I tell students you guys have been working really hard today.  I saw some great visual representations, and I heard some good quality thinking going on.  I think you guys are some awesome visual thinkers!

Now, I want you guys to show me what you know! To do this, I want you to think of a time you  shared something with your friends. Then, create your own word problem. Be sure to draw a mathematical representation that can accurately represent your problem.  As you guys are drawing think of the math operation that can be connected to the picture.  Don't forget that there is more than one way to solve a problems.  If you feel like you can only come up with one way, or if you have trouble composing your word problem, turn and ask your neighbor for help.  Turn and talk creates an opportunity for students to compare ........ This allows me to focus more on students who seem to be struggling.


  Because some students need extra support, I get them started by telling them about my 16th birthday party.

I can remember when I turned 16.  I invited 8 of my friends to a sleep-over.  I wanted to make sure that each of my friends received 6 party favors. Can you guys think of how I can write this in a word problem?

Word Problem Format:

Carol invited 6 friends to a sleep over.  She want each of her friends to receive 6 party favors.  How many party favors does Carol need in all?


What do we know so far?      Carol has six friends

What does Carol want to do for each of her friends?  Give them 6 party favors.

After that, students are given about 20 minutes or so to perform their task.  I circle the room to check for understanding.  

Student Work-Sample