Lesson 1: Tuesday, May 7Topic: Word Problem Plan- RUMOR

I. Rationale: The purpose of this lesson is to introduce the students to a plan to guide their thinking when given a word problem. This plan will be introduced to students during this first lesson so that they are able to establish a starting point whenever given a word problem. I am using this particular approach, teaching the acronym RUMOR, because I feel it is something that the students will easily remember if practiced appropriately. Once students are able to use this plan without direction, they will have a starting point in solving problems and feel more confident in their ability to solve the problem.

II. Lesson Objectives: SWBAT list the five steps for solving a word problem (Read problem, Underline question,

Mark information, Operation/strategy, Recheck: does it make sense?) before beginning the problem.

SWBAT apply their understanding of RUMOR when solving word problems

III. Lesson Assessment: Students will be assessed on their participation while creating the anchor chart, and for their participation in solving a problem as a class using the RUMOR plan. Students will be following along and marking on their own paper as the class works through the steps together. At the end of class, students will complete an exit ticket in which they will list the five steps of RUMOR.

IV. Standards: (CCSS) 3.MP.1: Make sense of problems and persevere in solving them. (ELP) Standard 3: English language learners communicate information, ideas, and concepts

necessary for academic success in the area of mathematics.

V. Time:45 minutes

VI. Materials: Teacher Materials Student Materials

RUMOR poster papers Index cards (exit ticket) Language Objective (written on paper) Word problems (for each student) RUMOR chant on butcher paper

VII. Beginning of Lesson: Tell students to move to a desk that is next to a partner if their partner is not there. Everyone

needs to have a partner sitting next to them. Anticipatory Set: Tell students: “I heard a rumor about the 3rd graders.” Write RUMOR on

board. Ask: “What is a rumor?” Tell students: “The rumor I heard was that 3rd graders were Mathsters of Problem Solving.” Write on board. Say: “Mathsters? What does that mean?” Get student input. Explain that it is a play on words, that it sounds like ‘masters’ but has ‘math’ in it because they’re “masters of, or very good at, math problem-solving.” Ask: “What does it mean to problem solve?” Guide to: using different strategies to solve a problem.

Tell students: Today we are going to talk about the word RUMOR, and how we can use it as a plan to help us solve any math word problem. By the end of math today, you will be able to list the five very important steps in solving any word problem. (Attach language objective to board). You will be practicing these steps every day as we learn the best ways to think about different kinds of problems.

Say: “Raise your hand if you’ve looked at a word problem in math and thought, “Oh man, I have no idea where to start!” (raise hand). We are going to look at RUMOR as a way to help us think about these problems. Each one of these letters (point to RUMOR on board) stands for something we should do when we come across a word problem. What is the first thing you normally do when you come across a word problem in math? It should start with the letter R.” (wait time) Call on students who have an idea. Guide to “read the problem.” Help the students to come up with the rest of the steps for the acronym. Attach RUMOR chart to board.

Introduce RUMOR chant, have students recite chorally (they know the rhythm). Say: “Let’s read the steps together. “Read the problem, underline the question, mark the

information, operation or strategy, recheck – does my answer make sense?”

VIII. Middle of the Lesson - Central Activity: Tell students (clear explanation of tasks): We are going to work on this problem together,

using the steps in RUMOR to help us work through this problem. When I hand out this problem, we are not going to start. We are going to work through the steps of RUMOR together as a class. When you get the problem, are you going to start working on it? (no) Pencils should be down. The only materials you will need on your desk are a pencil and a highlighter.” (Hand out word problems).

Ask students: “What is the first step we should do when solving a word problem?” “Let’s all read the problem together.” Read the problem chorally.

Ask students: “What is the second step?” (underline the question). This is really similar to when you are answering questions after reading. You want to make sure you know what the question is and what information you are looking to find. Are we highlighting the question? (no) Emphasize that we are underlining the question. “What is the question in this word problem, or what are we trying to find out?” Tell students to underline only the question in the problem as you model it on the camera.

Ask students: “What is the third step?” (mark the important information). Why would it not be a good idea to underline the important information? (because we might get it confused with the question). Is there another way that we could mark the important information in the word problem?” Model highlighting the important information on the camera, have students mark theirs as demonstrated.

Ask students: “What is the fourth step in solving a word problem?” (operation or strategy). “In your head, read the problem again and think about how you would go about solving it. Give a thumbs up when you have an idea what you would do. Share with the person sitting next to you how you would solve this problem.” (give wait time). “What operation could we use to solve this problem? (get responses) Why? What are some different ideas or strategies we could use to solve this problem?”

Give students time to solve the problem independently. Tell students: “Share with your desk partner your strategy for solving the problem. Did you use similar strategies for solving the problem, or did you both do something different? Did you agree on a solution?” Have students put down their pencils while students are sharing their ideas. Ask for students to share their thinking and strategies for solving the problem. Follow along with what they are saying on the doc camera. Tell students: “There are many different strategies or ways that we

can solve a word problem, and we will start learning more about those tomorrow. I see that you are already familiar with some of them.” Name the different strategies that the students came up with to solve the problem.

Ask students: What is the last step in solving word problems?” (recheck: does it make sense?).Look at the way you solved your problem, or your process- does it make sense? Does your answer make sense? Did you answer the question being asked? Model on camera how I can recheck my process and solution.

IX. End of Lesson: Let’s review the steps we took to solve the problem together. Let’s read aloud the RUMOR

chart together. “Read the problem, Underline the question, Mark the information, Operation or strategy, Recheck for reasonableness.”

With your table partner, you will be solving a word problem using the RUMOR plan. You will put a check mark or star next to each letter of RUMOR as you complete that step. You will need to work together to make sure you both completed all the RUMOR steps. Once you have completed the problem, turn it into the basket with your name on it. After you read the problem, put a check next to the R. What will you do after you underline the question? (put a check next to the U). What will you do after you complete the word problem?

Teacher will circulate as students are working in partners to ask questions and ensure students are using all of the components of RUMOR and working cooperatively together.

End the lesson by reviewing the RUMOR chant again, chorally, in back of room.

Name:________________________

1) If all the girls in the class each wore three rings and all the boys in the class wore two rings, how many rings would there be in class today?

2) Four people are at a party. Each of them is going to give the others a gift. How many gifts will there be at the party?

3) The people in Smalltown make up their own telephone numbers. The only numerals they use are 2, 6, 7, and 8. Their telephone numbers are two digits long. This is their telephone book:

Adams 22 Crayberg 27Benson 26 Dorman 28

How many more telephone numbers can they make?

4) It is Mona’s lucky day. At the first place she stopped, she found 5 quarters in a crack of the sidewalk. At the second place, she found 9 quarters under an old barrel. At the third place, she found 13 quarters in some sand. At the fourth place, she found 17 quarters under the bleachers at the ball park. Mona kept finding quarters in the same way for the rest of the day. How many quarters did she find at the eighth place she stopped?

Lesson 2: Wednesday, May 8Topic: Identifying Problem Solving Strategies

I. Rationale: The purpose of this lesson is to introduce students to four different strategies that we will be learning about in the next three weeks. Some of the strategies students may be more familiar with, so this will also give the teacher a general understanding of which strategies the students have previously learned or used in the past, and which strategies they may be most comfortable with. This lesson will not involve practicing individual strategies, but rather be an overview of four important strategies that will be covered (drawing a diagram/picture, using/looking for a pattern, using objects, and making an organized list).

II. Lesson Objectives: SWBAT orally state the different problem-solving strategies discussed SWBAT identify differences between four different problem-solving strategies

III. Lesson Assessment: Students will be assessed formatively based on their participation in discussing the different problem-solving strategies. Students will be orally naming the different problem-solving strategies and discussing the differences between them.

IV. Standards: (CCSS) 3.MP.1: Make sense of problems and persevere in solving them. (ELP) Standard 3: English Language Learners communicate information, ideas, and

concepts necessary for academic success in the area of mathematics.

V. Time:45 minutes

VI. Materials: Teacher Student

Butcher paper/ pens Language objective poster

VII. Beginning of Lesson: Have student move to back rug, no materials needed. Countdown from ten for students to

move quickly but safely to be seated on the back rug. Review RUMOR from previous lesson. Tell students that we are going to take a closer look

at the operation and strategy section of RUMOR. Say: “We know that an operation is the +, -, x, and ÷, which is all we need to know to solve some math problems. For some other problems, though, we need to have a strategy. We can’t just add or subtract, multiply or divide. We have to think about different ways to look at and solve the problem, called strategies. Today you are going to be able to list the different strategies that we are going to be learning, and you will know the differences between them.” Hang language objective on board.

(build background) Tell students: “There are 4 strategies that we are going to really practice in the next couple of weeks. I’m curious if any of you have learned any problem-solving strategies, and if so, which ones?” (get responses). “How many of you have drawn a picture

to help you solve a problem? That is one of the strategies that we will be practicing. How many of you have used objects to help you solve a problem, like a ruler, blocks, or chips? That is another strategy we are going to be practicing. You may have used some of these strategies to solve problems, but haven’t thought of them as ‘strategies.’ We are going to make a list of the different strategies that we will be using over the next few weeks, so when you are going through your RUMOR plan, and you get to ‘operation/strategy, you will have something to choose from.”

VIII. Middle of the Lesson - Central Activity: “I mentioned that we have 4 different strategies that we will be covering in the next few

weeks, and I already gave you two of them. What was one of them?” Drawing a picture or diagram (write on butcher paper). Why would we want to draw a

picture when we are trying to solve a problem? (get responses). I’m betting that most or all of you have drawn a picture to help you solve a problem before. Could we solve 1+3 using a picture? (demonstrate on butcher paper, under drawing a picture). Many of you probably learned to add and subtract using pictures. I know that you all are MUCH further than adding and subtracting small numbers, so how could we use pictures to represent a number like 532- do we really need to draw 532 pictures of something to show that number? (get suggestions, guide to using symbols like a flat to represent each hundred). What about when you are doing fractions- what kinds of picture can you use to help you solve fraction problems? (building background) I know that you have all used many types of pictures to solve problems, and we will practice using some of those when we solve problems tomorrow.”

Look for/ Use a pattern (write on butcher paper). What is a pattern? (get student responses, guide to something that repeats itself or keeps going in a predictable way). Draw different representations for patterns on butcher paper, under look for/use a pattern. Demonstrate how count-by’s are patterns, even though they do not repeat. What are some patterns that you have noticed in math, or even seen around you outside of math? (relate to Anansi stories).

“Another strategy I mentioned earlier was using objects (write on butcher paper). I know that you have used rulers to measure, you’ve used pattern blocks to build different shapes in geometry. Think in your mind about an object you have used to solve a math problem, and how it helped you solve the problem. Quickly share with a partner sitting near you an object you have used to solve a problem and what you have used it for.” Have students share ideas. Draw some of the suggestions on the anchor chart/butcher paper under Using Objects. (ex: ruler, geoboard, calculator, clock, pattern blocks, interlocking cubes, number lines, tiles, colored chips)

Make an organized list (write on butcher paper). First, what does it mean to list something? How does having the word “organized” in front change our idea about the word “list?” What kinds of lists have you seen or made? (shopping list, to-do list, list of traits, timeline…) Draw some suggestions on butcher paper.

IX. End of Lesson: Tell students: “There are many, many different strategies that you can use to solve problems,

and these are only some of them. You can even use more than one strategy to solve a problem- maybe you start out by drawing a picture, but then you notice a pattern- you used two strategies to solve the problem. What happens if you start a problem and then realize that the strategy you were using is not working? (try a different strategy).”

“Does anyone have any questions about any of these strategies so far?” “Let’s review together the different strategies we will be practicing in the next three weeks.

(read anchor chart chorally).

Explain: I am going to pull sticks, and each person needs to be ready to read the next strategy on the list and give an example of that strategy. When I ask for an example, think about different objects you could use to help you solve a problem, or different kinds of patterns you have seen, or different lists you have seen or made, or how you could draw a picture to solve a problem, so be ready and listening!

Lesson 3: Thursday, May 9Topic: Practice: Use Objects

I. Rationale:

The purpose of this lesson is to introduce the strategy of using objects or manipulatives to solve word problems. I know that students have previously used objects to solve problems, not all have learned to think of it as a strategy to solve different kinds of problems. This lesson is meant to teach students that using objects is a strategy they may use to solve problems, even if not explicitly told to use them. This lesson will introduce several different ways that manipulatives could be used, and allows students to be creative in thinking about other objects that could be used to solve problems. In this lesson, students will also be learning to think about whether using objects would be appropriate to solve a problem.

II. Lesson Objectives: SWBAT solve a word problem by using objects or manipulatives to represent their thinking. SWBAT explain and justify their process for solving a given word problem.

III. Lesson Assessment:This lesson will be assessed formatively. First, students will be assessed based on their participation during discussion in whole-class problems and think/pair/shares. Next, while students are completing problems independently or with partners, assessment will be based on their utilizing the tools and objects available for solving the problem. Lastly, students will be assessed by their participation in explaining and justifying their process for solving the problems.

IV. Standards: (CCSS) 3.MP.2: Reason abstractly and quantitatively. (CCSS) 3.MP.3: Construct viable arguments and critique the reasoning of others. (ELP) Standard 3: English Language Learners communicate information, ideas, and

concepts necessary for academic success in the area of mathematics.

V. Time: 45 minutes

VI. Materials: Teacher Students

Language objective poster Variety of manipulatives Word Problems homework

VII. Beginning of Lesson: Tell students: Today we are going to start using the strategies we talked about yesterday to

solve problems. The first strategy we will work on is using objects to help us solve word problems. I want to first get your ideas to make a list about different types of objects we could use to help us. Tell me some of the objects you have used to help you solve problems. (get student responses, write on board).

Transition to back area, have students sit in circle. Give a 10 second countdown. (Post language objective) This is our goal for today. Let’s all read it together. (Read

chorally: I will learn how to use objects to help me think about and solve word problems.) At the end of math, we are going to look and see if we were able to meet our goal.

I have a question for you before we begin looking at different problems. Can we use any object to help us solve any problem? (get responses). Some objects work better for specific

problems, like a clock. A clock could be really useful for a question about time, but would it be very useful in a question about perimeter? Why? Before we start, I want to show you the different objects we have to work with. There are many more kinds of objects, or manipulatives, that you may see in other classrooms or schools.

Show different manipulatives available in the class, ask students what math they could be used for, and what math they wouldn’t be useful for.

VIII. Middle of the Lesson: Tell students: “Now we are going to practice using objects or manipulatives to solve

problems together. I will hang a problem up, we will read it together and use RUMOR to make our plan. Let’s first review the steps of RUMOR. (read chorally from anchor chart)

(Hang up word problem). What is the first step we are going to take when given a word problem, everyone? (read the problem). Call on random student to give next step. (underline the question). Tell students: Think in your head for just a moment, what are you trying to find out in this problem? Call on random student to share what should be underlined. (get responses, underline the question). Repeat for mark information.

The strategy we are practicing today is using objects, so that is the strategy we are going to use. There are other strategies we could use to solve problems like this, which we will talk about in the next few weeks.

Think in your mind, after reading the question, which object you would use to help you solve this problem. I’m going to call on somebody to share their idea, and we will use that object first. Give a thumbs-up when you have made a decision. (call on random student for idea).

Use object that student has suggested, and ask class: “What do I need to do next? How can I show the information that the problem has given me?” (call on students for ideas)

Continue asking for what the next steps will be until problem is complete. Ask: “Did anyone have another idea for solving this problem?” or, if not, ask “Is there another way to solve it? Could we use a different object in another way?” (have students demonstrate different ideas).

Continue to repeat with other problems, depending on amount of time.

IX. End of Lesson: (5 minutes) Tell students: “Let’s review: What different objects did we use today to help us solve

different word problems? Can a problem be solved in more than one way, or with different objects? How can objects help us to solve problems?”

Let’s all say our goal for today together (point to language objective, read chorally). Did we meet our goal? Who feels like they will be able to look at a word problem and think, “Hmm, can I use an object to help me think about and solve this problem? What kind of object will help me?”

Explain: “Tomorrow we will be practicing in small groups at different stations, or spots in the room, to use objects to solve different kinds of problems. At the end of math, we will be sharing with each other our different ideas and ways we solved the problems using objects, and then try to use objects to solve a problem on our own.”

HOMEWORK

Name: _____________________

Read the questions. Think about what strategy you could use to solve these problems. What steps would you take to solve them? You do not need to solve these questions today.

1) Marcy is making a big banner to hang on the wall. She has three red stars, three white stars, and three blue stars to put on the banner. She is going to put the stars in three rows and three columns. How can she place the stars so that each row and each column has one red star, one white star, and one blue star?

2) Place 14 blocks in three piles. The first pile should have one less than the third. The third pile should have twice as many as the second. How many blocks are there in each pile?

3) There are 32 students in a classroom. If ¼ of them wear glasses, how many students do not wear glasses?

4) Paula broke half as many balloons as Perry broke. Altogether they broke 18 balloons. How many did Perry break?

Mandy folded her t-shirts and put them into two stacks in her drawer. She put three t-shirts in each stack. She put the green shirt under the blue shirt. She put the yellow shirt on the right side of the green shirt. She put the orange shirt on top of the blue shirt. Mandy put the pink shirt between the

yellow shirt and the red shirt. Where is each t-shirt in Mandy’s drawer?Marcy is making a big banner to hang on the wall. She has three red stars, three white stars, and three blue stars to put on the banner. She is going to put the stars in 3 rows and 3 columns. How can she place the stars so

that each row and column has one red star, one white star, and one blue star?

Place 14 blocks in 3 piles. The first pile should have one less than the third. The third pile should have twice as many as the

second. How many blocks are there in each pile?

There are 32 students in a classroom. If ¼ of

them wear glasses, how many students do not wear glasses?

The caterpillar is trying to climb up the tree. It takes two minutes to

climb one foot, but it falls back six inches each time it reaches one foot. How long will it take the caterpillar to climb up the 8 foot tree?

Paula broke half as many balloons as Perry broke. Altogether they broke 18 balloons. How

many did Perry break?

Lesson 4: Friday, May 10Topic: Stations: Using Objects to Solve Word Problems

I. Rationale: The purpose of this lesson is to give students the opportunity to practice, in small groups, identifying appropriate manipulatives to help solve a word problem, using those manipulatives in solving the problem, and working cooperatively to come up with an explanation and justification for their process and solution. It also gives students an opportunity to demonstrate their understanding individually.

II. Lesson Objectives: SWBAT identify and make use of appropriate manipulatives to solve a word problem SWBAT explain and justify their process for solving a given word problem

III. Lesson Assessment: This lesson will be assessed formatively based on students’ participation in cooperatively solving a word problem using manipulatives, and their verbal explanation and justification for their process used in solving the problem. To avoid language barriers for ELL students, groups will work together to form their explanation and justification. Additionally, students will record the group’s process, solution, and explanation in their own math journal.

IV. Standards: (CCSS) 3.MP.1: Make sense of problems and persevere in solving them. (ELP) Standard 3: English Language Learners communicate information, ideas, and

concepts necessary for academic success in the area of mathematics.

V. Time: 45 minutes

VI. Materials: Teacher Students

Numbers 1-3/A-B on students desks Variety of manipulatives 3 different stations (with different

manipulatives at each) Word problems

Math reflection sheets

VII. Beginning of Lesson: Have students meet in back of room, give 10 seconds to transition. Explain: “Today we are going to do an activity where there are different stations, there will

be two groups at a station at a time. I will number you off, and you will go to the station that matches your number. What station will you go to?”

“At each station is a word problem that you will use the RUMOR plan to solve. (Review RUMOR). There will be different kinds of objects at each station, and your group will decide which objects to use to solve the problem. If your group cannot decide on one object to use, you may use different objects as long as you all are participating and working together. Our goal today is…(hang up language objective, read chorally) “I will be able to decide which objects will be most useful in solving a word problem.” “When I ring the bell, your group

needs to immediately stop working on the problem and, with a level 0 voice, begin writing down your process on your reflection sheet. On your sheet you can draw a picture or write, but I need to know how you used the objects to help you solve or work on the problem. (Write on board: How you solved the problem using objects) You could even draw a sketch if it shows the steps your group took.”

Write stem sentence on board: I solved the problem by _______. “What will you be putting on your reflection sheet?” (how you solved the problem using the

objects). When I say “switch,” your group needs to move on to the next station. If you were at station

two, you will go to three. If you were at station 3, you will move to station 1.” If you finish the problem before the bell, I challenge your group to try and come up with

another way to solve the problem. On your desks is a card with a number and a letter. The number shows which station you will

start at, and the letter shows which people are in your group. If you have a 1A, you will be working with the other people at station 1 who also have a 1A. If you have a 1B, you will be working at station 1 with the people who have a B on their card. (show where different stations are).

VIII. Middle of the Lesson - Central Activity: When I give the signal word, find your station quickly, find your group, and work through

RUMOR together. (signal word) Circulate, ask questions about why they picked the object they did, what the object

represents, how it is helping them solve the problem, etc. Assist any groups that are having difficulty.

Ring bell for reflection time, give adequate time for students to complete their explanation. Switch stations, repeat until stations are complete. Get students’ attention: “I would like to see how fast all of the objects can be picked up and

put into their containers. Stay at the station you are at, and I am going to count up from one. Once you have finished picking up all the objects, return to your seat and put both hands on your desk to show me you’re ready. Let’s see if we can get a record time!” (signal)

Once students are back at their desks, go through each problem asking students randomly (sticks) to explain which object their group used and their process for solving the problem. Ask if other groups had different ways for solving the problem, or used different objects. Clear up any misconceptions.

IX. End of Lesson: How has using objects helped you think about and solve word problems? Are some objects more useful than others? How did you decide which objects to use? Let’s all review our goal for the day: (read chorally) “I will be able to decide which objects

will be most useful in solving a word problem.” Thumbs up if you feel like we met our goal. Next week we will be learning about a couple more strategies that we can use as we solve

word problems, like drawing a picture or looking for a pattern. (If stations did not run smoothly, ask students: “Do you feel like we were able to work as a

team and make good decisions during stations? What could we have done to make this activity work better?”)

Annie and Rob were playing a board game. During the game,

they both collected white chips and red chips. Each white chip

was worth 5 points and each red chip was worth 3 points. At

the end of the game, Annie had 14 chips worth 50 points in all.

How many chips of each color did she have?

Mel, Willis, and Ashton made 20 fortune cookies for a birthday

party. Mel wrote 2/5 of the fortunes for the cookies. Willis

wrote 1/2 of the fortunes, and Ashton wrote 1/10 of the

fortunes. Who wrote the most fortunes for the cookies? Show

how you know.

Mrs. Wilberger’s third graders visited the park nature center to

see the tadpoles and

frogs. They counted 20 animals in the tank. 3/4 of the animals

had already changed to frogs. The rest were still tadpoles.

1) How many frogs were in the tank?

2) How many tadpoles were in the tank?

Explain how you know your answers are correct.

The ants are marching in the annual parade. There are 12 ants.

They must march in equal rows and each row must have more

than one ant.

1) Show all the different ways the ants can march in the parade.

2) How many different ways can they march? Explain your

answer.

HOMEWORKName: _________________

Use the RUMOR plan to answer each question. Write your answers on the record sheets. You can use the objects you were given, or use different objects to help you think about and solve the problems. (Remember: Read the problem, Underline the question, Mark the information, Operation and strategy, Recheck- does it make sense?)

The third graders are marching in the school parade. There are 20 third graders in Mrs. Long’s class. Each class must march in equal rows with no remainders. There must be more than one student in each row.Mrs. Long’s class is trying to figure out how many different ways they can march.1) Show all the different ways the class can march in the parade.2) How many different ways can the class march? Explain your answer.

Mrs. Leary’s class visited the animal shelter to see the animals that were available for adoption. They counted 24 animals in all. 1/3 of the animals were dogs. The rest were cats.1) How many dogs were at the shelter?2) How many cats were at the shelter?Explain how you know your answers are correct.

Lesson 5: Monday, May 13Topic: Practice: Draw a Picture or Diagram

I. Rationale: The purpose of this lesson is to introduce students to the strategy of drawing a picture or a diagram to help them solve word problems. This lesson will be taught in a whole-class approach, allowing students to share their ideas with each other about different types of pictures or diagrams that could be used. Because some students are still at a stage where a story problem with apples needs to be solved using nicely-drawn apples, one of my goals is to have students be able to recognize that quickly-sketched circles may also represent the same object more efficiently.

II. Lesson Objective: SWBAT solve a word problem by drawing a picture or diagram. SWBAT explain and justify their process for solving a given word problem.

III. Lesson Assessment: This lesson will be assessed formatively based on participation during whole-class discussion, and student participation during group-think times. Students will be held responsible for following along with drawing a representation on their own problem as we discuss as a class.

IV. Standard: (CCSS) 3.MP.2: Reason abstractly and quantitatively. (CCSS) 3.MP.3: Construct viable arguments and critique the reasoning of others.

V. Time: 45 minutes

VI. Materials: Teacher Students

Class problems Group problems Homework problem

VII. Beginning of Lesson: Tell students: We’ve been learning how to use RUMOR as a plan to help us understand a

word problem, and learning different strategies for helping us solve word problems. Last week we worked a bit on using objects as a strategy to help us solve problems. Today we are going to look at drawing pictures or diagrams as a strategy for solving different word problems.

Ask: Why would we even bother drawing a picture or a diagram to help us solve a problem? How could that help us?

Explain: Today we are going to work as a class and in groups to solve problems using pictures. First, we are going to look at a problem as a class. When you get the problem, think about the first steps in RUMOR that we need to complete before we begin working on the problem.

VIII. Middle of the Lesson: Once everyone has their problem, ask: What is our first step in the plan? (read the

problem). What is the second step? (underline the question). Third step? (Mark the information).

Ask: What strategy are we using today to help us solve problems? (draw a picture or diagram). Talk with your group for one minute about what you could draw to help solve this problem. I am going to pull a stick and that person is going to share what their group came up with. (after one minute, call on random student).

Demonstrate drawing what the group suggested, work with the class to solve the problem.

Once problem is solved, model how to explain what I did to solve the problem on RUMOR sheet.

Ask: Did another group have a different idea of what to draw or how to solve the problem using our strategy of drawing a picture or diagram? (demonstrate any other ideas)

Explain: You will all be getting another problem where you will work as a group to use our strategy of the day. What strategy are we using? (Draw a picture or a diagram).

Hand out problem Let’s work through the first few steps of RUMOR together. (read, underline, mark,

strategy) Explain: Think in your head for just a moment how you would draw a picture or diagram

to help you solve this problem. When I give the signal word, work with your group to decide together what you should draw and try to solve the problem.

Once you have finished the problem, each person will need to record on their record sheet how your group solved the problem. You can explain in words beside your picture, or you can just have a picture showing what you did. I will be calling on some groups to share how they solved the problem, so be ready to explain the steps your group took.

Give students adequate time to solve the problem. Call on random student to explain their group’s process and solution.

Do another group problem if time allows. At home tonight, I would like for you to use the RUMOR plan to help you understand the

problem, and then use the strategy we practiced today to solve the problem. Once you have solved the problem, explain on the record sheet how you solved it, just like we did today. (hand out homework)

When I give the signal word, meet me in the back of the room by the math area.

IX. End of Lesson: We worked today on using pictures as a strategy to help us solve word problems. Show

me on a scale of 1-5 on your fingers how comfortable you are using pictures to help you solve problems. One is ‘I don’t get it,’ three is ‘I think I kind of get it,’ and five is ‘I got this!’ How do you feel about drawing pictures to help you solve math problems?

Ask: If we have a math problem that asks us about numbers of cars, do we need to draw a car to solve the problem?

Explain: As long as we know that we are making these circles, and each circle is one car, then we do not need to draw several different little cars. We can save a lot of time when trying to solve a problem by just using a circle or square, a line or an x to show different objects in the word problems.

When you go home tonight, what plan are you going to use to help you understand the word problem? (RUMOR!) What strategy are you going to use to help you solve the problem? (draw a picture or diagram).

RUMOR chant before exiting.

Lesson 6: Tuesday, May 14Topic: Groups: Using Pictures and Objects to Solve Word Problems

I. Rationale:

The purpose of this lesson is to allow students to work cooperatively in groups to practice drawing different pictures and diagrams or use objects to solve word problems. Once students are given the chance to work in their groups, a whole-class discussion will require the students to explain and justify their process and solution for the given problem. This lesson will allow students to build off one another’s knowledge and understanding, and will require them to work together to find the most reasonable way to solve the problem at hand.

II. Lesson Objective: SWBAT use practiced strategies to solve math problems cooperatively and

independently.

III. Lesson Assessment: Students will be turning in their record sheets for the problems solved in groups, which will be assessed based on their completion. Students will also be formatively assessed based on their participation in groups.

IV. Standard: (CCSS) 3.MP.1: Make sense of problems and persevere in solving them. (CCSS) 3.MP.2: Reason abstractly and quantitatively.

V. Time: 45 minutes

VI. Materials: Teacher Students

Group questions manipulatives Homework

VII. Beginning of Lesson: Explain: Yesterday we practiced drawing different kinds of pictures and diagrams as a

strategy to help us solve problems. Today you will be working with your group to solve more problems, and you can pick one of the strategies we’ve worked on so far. What are the two strategies we’ve talked about so far? (using objects and drawing pictures).

If your group decides they want to use objects, you may get some from the back of the room to take back to your table group. If they become toys, the objects will need to be put away.

What is our plan for solving a problem? (RUMOR) At the top of your response sheet, I should be able to see that each one of you has been keeping track of each step your group does as they work through the word problem. Let’s review the 5 steps of RUMOR (chorally recite).

Once you finish the problem, I should be able to look at any person’s record sheet and be able to tell what the group did to solve the problem. It is important that you explain in words or pictures what you did to solve the problem. Is it okay to say, “I just knew?”

Show glasses problem from last week. Underline the question, mark the information, explain strategy and process for solving. When going to write on record sheet, model- I

will be looking for something like: “First, we grouped our 20 beans into 4 groups of 5. We removed 3 of the groups, or ¾ of the beans, and counted the beans that were left over. Those beans made up ¼ of the group of 20, so I know that 5 people in the class wore glasses.”

VIII. Middle of the Lesson: Say: Let’s start the first problem together. (go through read, underline, mark). When I give the signal word, you will work with your group to decide which strategy you

want to use, and work together to solve the problem using that strategy. Each person should know what is going on. For instance, if you do not understand, you should stop the group and ask for someone to explain. If you see someone who does not understand, ask if they need help. Every person in the group should be able to explain how their group solved the problem when we discuss as a class, so it is important for you to know and be able to explain. Make sure to explain or draw a picture of what your group did on your record sheet.

Have students begin, circulate as groups are working, asking questions about their process or solution. If some groups finish without giving a reasonable explanation on their record sheet, have them re-work their explanation until it is understandable. Give adequate time for groups to finish or come close.

Once most groups are finished and have an explanation for problem one, come back together as a whole-class. Call on random group to share their process and explanation.

Ask: Did any other group have a different way of solving the problem or use a different strategy? If time allows, have groups show differences on doc cam.

If explanations are sufficient, continue with another problem. If explanations need work, model an explanation on doc cam.

Pass out second problem. Remind students to work through the steps of RUMOR as they solve the problem. Give signal word to begin in groups (circulate as groups are working).

Once groups are coming to a close, call on random student to share their group’s explanation of process and solution. Ask if there were other ways of solving the problem. Have students share on doc cam.

IX. End of Lesson: Discuss group participation and teamwork: Was it effective? Did students work well

together? Give compliments to groups who worked especially well together. Ask: Thumbs-up if you felt that working in a group helped you think about different

ways to solve these problems. Think in your head for just a moment about one of the problems. If you solved it using objects, do you think you could also solve it by drawing a picture? Or if you drew a picture, could you use objects instead? Think in your mind how you would do that.

Have students share examples of how they could solve one of the problems differently. Tomorrow we are going to add another strategy to our list of options to choose from. We

are going to add ‘Look for a Pattern’ to our list of strategies. Did any of the problems we solved today have patterns that you noticed? We will look at problems that have patterns tomorrow, and we will look at how the word problems are different than the ones we’ve been working on. Do you think that you could use look for a pattern to solve any word problem? (get suggestions). We already know that some problems can be solved using

more than one strategy, but we will look tomorrow to see if we can use patterns to help us solve any kind of word problem.

For homework tonight, you need to pick one of the two strategies we’ve been working on, using objects or drawing a picture, to help you solve the problem. Make sure you are going through the RUMOR plan and checking off each step as you complete them, and give a good explanation of how you solved the problem on your record sheet.

Lesson 7: Wednesday, May 15Topic: Practice: Look for a Pattern

I. Rationale:

The purpose of this lesson is to introduce students to the strategy of looking for or using a pattern to help them solve a word problem. This lesson starts by having the teacher model on the doc cam different types of patterns that can be found when solving a word problem, and how to appropriately use the pattern to help solve the problem. This way, students will have a better understanding of how to recognize when looking for a pattern would be appropriate when given a word problem. Students will be given the opportunity to find patterns individually, and share their thinking with the rest of the class, broadening students’ understanding of different approaches to finding and utilizing a pattern to help solve a problem.

II. Lesson Objective: SWBAT recognize when finding or using a pattern to solve a word problem is

appropriate. SWBAT explain and justify their process for solving a given word problem.

III. Lesson Assessment: Students will be assessed formatively based on their participation during group discussion, as well as their recording of processes for solving different word problems.

IV. Standard: (CCSS) 3.MP.1: Make sense of problems and persevere in solving them. (CCSS) 3.MP.3: Construct viable arguments and critique the reasoning of others.

V. Time:45 minutes

VI. Materials: Teacher Students

Whole-class problems homework

VII. Beginning of Lesson: The two strategies we have used to help us solve problems are: (point to board so

everyone reads) use objects, draw a picture or diagram. Today we are going to add another strategy to our toolbox, and the strategy we are going to use today is (point to poster so everyone reads) look for and use a pattern. We talked a little bit about different patterns we might come across in math, and we talked about repeating patterns, like ABABAB, and also patterns that don’t necessarily repeat, like when you add two to a number so the pattern would be like 2, 4, 6, 8.

I saw some of you using a great way to check for patterns on another problem, which we will talk about today.

Let’s first check something, though. Do all word problems have a pattern that we can use to help us solve it? (get responses, explain how some don’t).

All of the problems we will look at today will have patterns, so as we are working on them, be thinking in the back of your head how these problems are different from other word problems you have seen.

VIII. Middle of the Lesson: I am going to give you a problem, and we are going to go through the steps of RUMOR

together as we solve the problem. We are going to use the strategy of looking for and using a pattern to help us solve the problem. When you get the problem, read it and see if you can think of a way that this problem is different than other problems we have worked on the last week. (hand out problem)

Put problem on doc cam. Ask: what is different about this problem than others we have looked at? Or what makes this look like a problem that we can look for a pattern in? (get responses, point out wording in problem)

Let’s use our plan to solve this problem. What is the first thing we do? (read the problem). Read the problem chorally.

What is the second step? (underline the question) Model on the doc cam what the students should be underlining. Third step? (mark the information) Ask: what is the important information in this word problem? (get responses, model on doc cam).

I know that I am looking for a pattern, because the problem is telling me “if the person continues in this way, how much will they have…”Think in your head how you would show that on a piece of paper, how would you find that pattern? (get responses, model on doc cam).

Have students explain as I demonstrate on doc cam how to finish solving the problem and rechecking if it makes sense.

Model another problem on doc cam, have students suggest ideas and explain their reasoning. Ask: is there another way we could solve this problem? (get suggestions)

I am going to give you another problem. I want you to solve this problem on your own, using RUMOR, and show on your paper how you figured it out, just like I was showing up here. (circulate, guide students who are stuck or off-task)

With your group, I would like you to come up with a pattern. It can even be a list of numbers or shapes, it does not need to be an entire word problem. We are going to try and solve these patterns together. I will give you two minutes to create a pattern in your group starting when I give the signal word. (hand out paper, give signal word, circulate as students are creating).

Put patterns on doc cam one at a time, have students give suggestions as to how to figure out the pattern.

IX. End of Lesson: Some word problems may have you complete a pattern, like on a quilt, others might ask

you what the missing or next numbers would be, and some others might have you look ahead, like some of the problems we did today, and find out how much there would be after a certain amount of time.

What words have you noticed were kind of like clues in word problems to show you there was going to be a pattern? (get suggestions)

Thumbs up if you feel like there are no patterns you mathsters of problem-solving can’t find?

Some are fairly tricky. Not all of them are just adding or subtracting numbers. Some patterns use more than one, like this. Write 0, 2, 1, 3, 2, 4, 3, 5, 4. (add two, subtract one). Look at this problem, think in your head, and give a thumbs-up when you have an idea of what the pattern might be. (get suggestions). Not all problems are going to be that

tricky, but that’s why it is important to really pay attention to the differences in the numbers and don’t give up if the first pattern you think of is not the one.

For homework tonight, there will be a few different patterns, and I would like you to use this strategy to help you solve the problem as you work through your steps in RUMOR.

Lesson 8: Thursday, May 16Topic: Groups: Looking for Patterns to Solve Word Problems

I. Rationale: The purpose of this lesson is to give students the opportunity to work collaboratively to find patterns and solve problems using this strategy. Students will be given questions that require them to find a pattern in different ways. Because students will be working in groups, it allows them to learn from each other and build off of each other’s understanding.

II. Lesson Objective: SWBAT solve word problems by recognizing and explaining different types of patterns

they see within the problem.

III. Lesson Assessment: This lesson will be assessed formatively as students work in groups to discuss their thinking of different patterns found and how those patterns apply to the problem being solved. Students will be assessed based on their participation in groups while solving the problems at hand, and in their participation during whole-class discussion.

IV. Standard: (CCSS) 3.MP.1: Make sense of problems and persevere in solving them. (CCSS) 3.MP.3: Construct viable arguments and critique the reasoning of others.

. V. Time: 45 minutes

VI. Materials: Teacher Student

Group questions 2 questions that do not use patterns homework

VII. Beginning of Lesson: Tell students: Yesterday we practiced finding different patterns in word problems

together as a strategy for solving different problems. What did we find in some of the word problems that were clues in telling us which strategy to use? (if ___ continues in this way…, in the same way).

We will continue seeing these clues in the questions we are going to solve in groups today. We are going to be working in our groups to solve these word problems, and what is our plan for working through our problems? (RUMOR). What else do we need besides an answer on the page? (an explanation or drawing for how we got our answer).

Each group will get a packet of problems that you will all work on together. What strategy are we practicing using today? (finding and using a pattern). There may be, just MAY be a problem or two in there that does not use a pattern. If there is, see if you can pick them out and use another method for solving it with your group.

Once you finish the problems and have each person in your group check with me, I challenge you to come up with a pattern word problem together, as a group, that I will try to solve.

When I give the signal word, what is the first thing your group is going to do together? (read the problem). (give signal word).

VIII. Middle of the Lesson - Central Activity:

Circulate as students are working in groups to find patterns in the different word problems. Make sure students are using RUMOR to work through the problems, and listing which strategy/ies they decide to use to help them solve the problem.

Take note of students who are actively participating with their groups to praise after groups.

Clarify any misconceptions about problems. Ask questions to guide students’ thinking if their group becomes stuck. Encourage groups to try a different approach if they are stuck or become frustrated.

Allow groups sufficient time to work through problems and identify patterns in several word problems.

Give signal for students to come back for whole-class discussion. Start with question one, Go through steps of RUMOR to make sure everyone reads the

problem, underlines the question, and marks the information. Ask: What strategies did your groups use to help you solve this problem. Did you use only one strategy, or a combination?

Call on groups to share one step of the problem at a time. If a group explains a process that does not work or is not correct, continue through to let students find the error and modify the process to correct it, if possible.

Once one explanation has been demonstrated, ask for another explanation, or a group who used a different strategy. Compare the approaches: is one way easier than another? Is one way faster than another? Which way is easier to understand?

Repeat for remaining questions. If time remains: Have students pull out whiteboards, give 2 minutes to draw whatever

picture they like on the board. Ask students: after two minutes, what does the whiteboard become? (math tool). Once the bell rings, we should not be drawing on the whiteboard except to answer questions. We will be playing race to erase, and seeing how speedy everyone can be at erasing their boards.

Tell students to explain what is happening in the pattern that they will see on the board on their white boards. Give example. 1, 3, 6, 10, 15, 21... Show students on white board that you will be looking for (+2, +3, +4, +5, +6….)

Write pattern on board, check students solutions on white boards, have them place white-board face-down when they have found the solution. Race to erase, write time on board.

IX. End of Lesson: Today we practiced looking for patterns in word problems. What are some clues we can

look for in word problems that make us think, “Oh! There is a pattern here!” (continues in this way, in the same way…)

Do all patterns look alike? What other strategies were helpful in solving word problems that also had patterns?

Notice that we can use more than one strategy for solving problems. What are the strategies we have practiced so far? (use objects, draw a picture or diagram,

look for a pattern). Let’s review our plan, or our checklist, for solving a word problem. Remember, RUMOR

is our checklist for things we have to do when we get a word problem. Let’s sing the chant about our checklist for solving a word problem. (draw two students to lead chant).

Tomorrow we will learn a new strategy called making an organized list. We talked a little bit about different lists you have seen inside and outside of school, like a grocery list, a numerical list, an alphabetical list, and a to-do list. When we make organized lists as a

strategy to help us solve word problems, some of those lists will be really similar to other types of lists you have seen.

Lesson 9: Friday, May 17Topic: Practice: Make an Organized List

I. Rationale: The purpose of this lesson is to introduce students to the strategy of making an organized list, which will help them to solve word problems. This lesson will be mostly taught using a whole-class instructional strategy and guided practice. This will allow students to see the teacher model

how to create different types of lists, depending on the information given in the word problem and the questions being asked. Students will be asked to think/pair/share different ideas once a few problems have been modeled. This lesson will allow students to see different representations of information given in a word problem, and help them to think about different ways that they could construct a list that is appropriate to the word problem they are attempting to solve.

II. Lesson Objective: SWBAT solve a word problem by making an organized list SWBAT explain and justify their process for solving a given word problem

III. Lesson Assessment: This lesson will be assessed formatively based on student participation during class discussion and think/pair/share times. Students will be held responsible for following along on their own worksheets as we solve the problems together as a class, thus having different examples to refer back to in the future.

IV. Standard: (CCSS) 3.MP.1: Make sense of problems and persevere in solving them. (CCSS) 3.MP.3: Construct viable arguments and critique the reasoning of others.

V. Time:45 minutes

VI. Materials: Teacher Students

Whole-class problems Group problems homework

VII. Beginning of Lesson: What are the three strategies we’ve practiced so far for solving word problems? (using

objects, drawing a picture or diagram, looking for a pattern). Like I told you yesterday, today we are going to practice using another new strategy called making an organized list. Today we are going to practice together, and we will also get some time to work in groups and talk about different ways we were able to make lists.

Let’s first think about what a list looks like. Think about the different lists we’ve talked about that we’ve seen, what were those? (grocery lists, to-do lists, numerical lists, alphabetical lists, etc). What did those look like? Organized lists in math problems are going to look really similar to those types of lists. Show different organization of lists (number line, listing in rows, listing in columns, etc.) We are going to look at problems today that will require us to make different kinds of lists.

VIII. Middle of the Lesson - Central Activity: Let’s do the first one together. (hand out problem, put model on doc cam). Go through

first steps of RUMOR. What strategy are we going to work on today? (making an organized list).

I want you to think about this problem for just a moment in your mind. What kind of list could you make to help you solve this problem? There is probably more than one way to do this, so see if you can find one or more of those ways. (give wait time)

Quickly share with your group the different ideas that you came up with, and see if anyone in your group had a different idea. I am going to pull a stick for someone to share, so make sure you have one good idea of what a list might look like to help you solve this problem. (give wait time, call on random students to share)

Model students different ideas of lists to help solve the problem on doc cam. Ask for other suggestions, model any others.

What are the differences between these lists? Do they all help us solve the problem? Which was most useful for you, and why?

Have students give ideas for how to solve the rest of the problem. Put problem 2 on doc cam, have students work individually through first steps of

RUMOR. Explain: once you get to strategy, you know which strategy we are practicing, so think of how you would make a list to help you solve the problem, and try it out. I will be walking around to see all the different lists you can come up with. Think about what information you need to have in the list, and what question you are trying to answer.

(circulate) Ask students to clarify their representations, ask questions about students’ process and clear up any misconceptions. Give adequate time for students to start and possibly finish a list)

Ask: what does your list look like? Call on students to share different types of lists they created. Ask: how did this list help you think about or solve the problem?

Use students’ lists and ideas, having them walk through solving the problem and answering the question.

If time, repeat for problem 3.

IX. End of Lesson: Today we only made organized lists to solve the problems we had. Could we have used

another strategy for solving these problems? Which one? How could it have helped us? (have students give ideas for different ways they could have solved the problems).

Remember, there is not one right way of solving a problem. Some strategies work better for different people. ___ may like to draw a picture to help him/her solve a problem, and ___ might find it easier to use objects or make a list. Can they both still come up with the same answer if they use a different strategy?

On the homework for today, I want you to practice making a list to help you solve the problem, and see how it works. If it helps, use another strategy also, to check your work and make sure your answer makes sense.

Remember, you have four different strategies to work with now, so think about what would be most helpful for you when you’re solving the word problem. What would be the easiest, what would make the most sense, and what would help you answer the question you are trying to find.

Next week we are going to mix up our problems and you are going to learn to decide which strategy works best for the problem you are trying to solve. Every one of you could use a different strategy and still get the right answer, we just have to make sure that we are using a strategy that is helpful to solve the problem. For example, looking for a pattern in a problem that does not have a pattern would not be very helpful. But you could possibly draw a picture or make a list to help you solve it.

Lessons 10, 11, and 12 Outlines:

Lesson 10: Making an organized list intro.

Whole Class:

Example 1: Give example of organized list that I have to get done today. There are 3 things I have to do after school today. I have to get groceries, go to the bank, and wash my car. What are the different orders I can do these 3 things in? --GBW, GWB, WGB, WBG, BGW, BWG

Example 2: Give example of different combos of pizza. stuffed crust, thin crust. Pepperoni, cheese. Medium, large. What are the different combos? --SPM, SPL, SCM, SCL. –TPM, TPL, TCM, TCL.

Guided Practice: Students have out white boards.

Example 1: I’m going to give you clues about a mystery number, and you will need to write an organized list of what the number could be. Here are the clues, listen carefully:

- it is a two digit number

-larger than 20

-less than 30

- an even number

Show me an organized list on your whiteboards of what numbers it could possibly be.

Example 2: Here is another practice question. John is going out to breakfast. He has 2 items on his plate. Find the different combinations that John can have if the restaurant gives a choice between: a roll or piece of toast, and fried or scrambled egg.

- roll, fried. – roll, scrambled. – toast, fried. – toast scrambled.

Example 3: What if we changed the options for John. Now her has 3 items on his plate, and can choose from roll or toast, fried or scrambled egg, and bacon or sausage. What are the different combinations?

-RFB, RFS, RSB, RSS, TFB, TFS, TSB, TSS.

Example 4: Let’s go back to numbers. A baseball team is making new jerseys for the players. They only have the numbers 2, 3, 5, and 9. They started by making 22, 23, 25, and 29. How many more combinations could they make out of those numbers?

-32, 33, 35, 39. 52, 53, 55, 59. 92, 93, 95, 99.

Independent Practice:

Example 1: A farmer is planting 4 rows of seeds in his garden. He has tomato, corn, beans, and peas. What are the different arrangements he can have for the rows of seeds?

Lesson 11 Outline: Partners- Making an Organized List

1) Go over homework

2) Warm-up: When Daryl was 11 years old and his sister Joni was 3, they watched a television show about hot air balloons. Daryl started saving his money. When Daryl was twice as old as Joni, he took her on a hot-air balloon. How old were Daryl and Joni when they rode in the balloon?

Ricky bought the new Beasts and Beetles game for 55 cents at the school store. He paid for the game with 8 coins. He only used nickels and dimes. How many of each kind did Ricky use?

3) Students in partners- work through problem 1

4) Discuss as class, check for different ways of solving

5) Students in partners- work through problem 2

6) Discuss as class- check for different ways of solving

7) if time, one more problem as whole-class

8) review RUMOR and four strategies practiced (using objects, drawing a picture, looking for a pattern, making an organized list)

Lesson 12 Outline: Mini-review (15 minutes)

Discuss: What are the five steps we take to help us think about problems, or our checklist for solving problems? Why is this so important?

Discuss: What are some different strategies we can use to help us solve problems? Are there different objects in the room we can use to help us if we need? Could we make objects?

Discuss: What should we have on our paper when we have solved a problem? Should we just have the answer? What other information do we need to include with our answers?

Warm-up: John was going to visit friends in an apartment building. He first visited Emily on the 3 rd floor. Next, he went down two floors to visit James. He then went up four floors to visit Martin. Last, he visited Amy on the highest floor of the building, three floors up from Martin. How many floors did the apartment building have?

Lesson Post-Assessment