getting started: establishing routines & procedures in

First Days of Math for Grade 4

Getting Started: Establishing Routines & Procedures in Grade 4 The First

Days of Math in Staunton City Schools

Overview

For students, a successful experience with math begins with the basics: how to think like an active mathematician, how to speak mathematically, and how to record and share their thinking. This guide may be extended, condensed, or modified according to students’ needs. As you prepare to implement the First Days of Math during the 60 minutes of math instruction, keep in mind that it will be necessary to be flexible. These 5-15 minute lessons are to be incorporated into the daily lesson. Grade level teams may meet periodically to monitor and adjust progress. Clear statements and clear demonstrations of roles and procedures need to be established. All points and aspects need to be repeated, charts or anchors of support are to be posted and referred to again and again.

Goals

The goals of implementing the instructional strategies included in this document are to

• help students think of themselves as mathematicians who enjoy and actively participate in

math;

• establish consistent classroom roles, routines and procedures that support teaching and

learning;

• increase rigor by having students explore, express, and better understand mathematical content through NCTM process skills (communication, connections, reasoning and proof, representations, and problem solving) that are listed on the following page.

Background

Based on the idea of The First 20 days of Independent Reading by Fountas & Pinnell,

these lessons have been developed to establish the roles, routines and procedures

needed for effective mathematics instruction.

Principles of Learning are the foundation of this document. All students are told

that they are already competent learners and are able to become even better through their

persistent use of strategies and by reflecting on their efforts. Criteria for quality and

work are explicit, accessible to all students, displayed publicly, and change over time to

respond to level of rigor as learning deepens.


NCTM Process Standards

Problem Solving Instructional programs from prekindergarten through grade 12

should enable all students to—

Build new mathematical knowledge through problem solving

Solve problems that arise in mathematics and in other contexts

Apply and adapt a variety of appropriate strategies to solve problems

Monitor and reflect on the process of mathematical problem solving

Reasoning and Proof Instructional programs from prekindergarten through grade 12

should enable all students to—

Recognize reasoning and proof as fundamental aspects of mathematics

Make and investigate mathematical conjectures

Develop and evaluate mathematical arguments and proofs

Select and use various types of reasoning and methods of proof

Communication Instructional programs from prekindergarten through grade 12 should

enable all students to—

Organize and consolidate their mathematical thinking through communication

Communicate their mathematical thinking coherently and clearly to peers,

teachers, and others

Analyze and evaluate the mathematical thinking and strategies of others;

Use the language of mathematics to express mathematical ideas precisely.

Connections Instructional programs from prekindergarten through grade 12 should


Recognize and use connections among mathematical ideas

Understand how mathematical ideas interconnect and build on one another to

produce a coherent whole

Recognize and apply mathematics in contexts outside of mathematics

Representation Instructional programs from prekindergarten through grade 12 should


Create and use representations to organize, record, and communicate

mathematical ideas

Select, apply, and translate among mathematical representations to solve

problems

Use representations to model and interpret physical, social, and mathematical

phenomena


Day 1—Management 60 minutes

Big Ideas We’re all mathematicians.

Mathematicians work in an ordered environment with established routines and

procedures for independent and/or cooperative math groups.

Mathematicians use math tools to think about math and help them solve

problems.

Learning Outcomes

Students identify criteria to create a “Working as Mathematicians” chart to post.

Students understand and learn that information will be posted around the

classroom for them to use to make their work better, to support their learning and

to help them review concepts as they are learned.

Students become familiar with the math tools in the classroom.

Anchor Experience for Students

Focusing the Lesson *I’ve spent a lot of time getting this room ready in anticipation of your arrival, but one

thing that I’ve been wondering about is my room arrangement. Is there any way that I

could have arranged things so that there are an equal number of desks in each row?

Have students work with a partner to think about the teacher’s problem. [Every class will be different due to varying class sizes. If you have a class of 17, 19 or 23, then your class will have the unique opportunity to deal with remainders. Obviously if you’ve already arranged the class in equal rows, you might want to rethink that for the first day so that this activity is possible.] 5 minutes into students working . . . *Everyone, pause in your thinking . . . Guess what

I’m noticing: we’re all mathematicians! Look around the room. This year we’re all

going to be mathematicians as we learn and do math together. Mathematicians work

in an ordered environment so we need to decide together what that will mean for us.

What do you think it means to be a mathematician? Students share different ideas.

Begin to develop “Working as Mathematicians” chart with class for future reference. You will add to this chart each day of this unit, so it does not have to be completed today. Solicit student suggestions. Refer to the process standards for wording if you get stuck. Write everything in a positive tone about what mathematicians “do,” not a list of “don’ts.”

Examples below and on right:

• Stay on Task

• Speak/write mathematically

• Be an active listener and participant.

• Respect and organize math materials appropriately.

*Let’s look at our seating chart problem. What are some of the solutions you and your

partner found? Have students share with the group. Talk about whether all of their

solutions would be practical for your room. (Example: 11 rows of 2 desks each)

*Italics denote “teacher talk”

http://www.nctm.org/standards/content.aspx?id=322


*As mathematicians, we often use mathematical tools to help us solve problems. How

and why do mathematicians use tools?

*If you had a mathematics toolkit, what tools would you want in it to help you solve

problems? Have students think with a partner. Whole class shares.

Take a “tour” of mathematical tools in classroom. Be specific about your expectations of how they are to be used and stored. *Is there anything about mathematical tools that we can add to our chart? Add notes to the “Working as Mathematicians” chart about appropriate use and replacing materials to their proper storage containers after use. Work Time *Can tools help us solve the desk arrangement problem more easily? Pretend the

baggie I am giving you represents a classroom of desks. Find ways to arrange

them so that there are an equal number of desks in each row.

Give each pair of students a baggie containing 24 counters or Unifix cubes, but don’t tell them how many they have. Some students might count them and others might just start dividing them up without counting them. Note who does what. Those who count and use their multiplication facts to help them are not on the same level as those who just start arranging them. This is a time for you to circulate, observe, and eavesdrop. Ask questions that encourage and challenge students to find more solutions. Take notes of your observations.

After a reasonable amount of time ask everyone to stop on one last arrangement. Have students leave them on their desks.

*Sometimes mathematicians learn from each other’s solutions. Now we are

going to take a gallery walk. Where have you heard of a “gallery” before? What

does one do in a gallery?

A gallery walk in class is when we walk around the room and check out everyone

else’s solutions. Look to see everyone’s interesting solutions. I expect you to walk

in an orderly manner. All talk must be about the math that you are observing.

(Here, add any other instructions that pertain to your particular room

arrangement/flow.)

After the gallery walk. . .* Did you see solutions that you did not have? How did

using math tools help you find your solutions? How many possible solutions were

there? Let’s list them on the board.

Activity to support

*How were we working like mathematicians? Let’s look back to our chart and check.

Is there anything you’d like to add?


Materials Chart paper Markers Various classroom manipulatives students will have available for use during the year, including baggies with 24 counters or Unifix cubes per pair of students

Teacher Notes Don’t worry if the students only come up with a few ideas at first. It’s better if the ideas are generated slowly and meaningfully by the students. Refer to the chart frequently over the first weeks of class. Use the chart to point out positive mathematical behaviors which you’re seeing in individual students. Use the chart to give the class specific ways which they can improve their mathematical behaviors. Add ideas as you recognize new ways the class is working as mathematicians or as specific issues arise in the class. Note that the seating chart problem is provided with the upcoming Fosnot’s Muffles’ Truffles study of arrays in mind. Note how students use the array and who uses multiplication facts to help solve quickly.


Day 2—Problem Solving 60 minutes

Big Ideas Mathematicians use a process to think about and solve problems.

Learning Outcomes

Students understand the importance of problem-solving every day.

Students learn that there is a process involved when solving problem.


Focusing the Lesson

*What do you think of when you hear the phrase “going through the process” of

something? Can you give me an example? What does the word “process” mean?

*Did you know mathematicians use a process to think about math? Why do you think

they do that? Whole class conversation.

Prior to today’s lesson, develop a problem solving model for your class which you’ll use throughout the year. Perhaps you have a favorite one already. You may change the words if you think it will work better for your students.

[One example is Polya’s 4-Step Problem Solving Model. See illustration here and the sample at the end of Day 2’s lesson plan.]

Add your class’s process to your “Working as Mathematicians” chart or create a separate poster or bulletin board you can refer to throughout the year. [You might also want to print copies of the steps for students to glue into the front of their math journals on Day 4.]

Work Time *We’re going to use our problem solving process to think about some problems today.

Remember, we’re working like mathematicians, so keep in mind what we’ve written on

our chart. Let’s try out our new 4-step problem solving model to see how it works.

Project large print copies included with this lesson or write problems on the board for

students to read.

Problem 1: *Mrs. Baker was stacking the tissue boxes her students brought to class.

On the first shelf she placed 7. On the second shelf she squeezed in 8. On the third

shelf she put 6. How many tissue boxes did she have?

*First, let’s look at our 4 Steps to Problem Solving chart and ask ourselves some

questions… Walk students through the process in a “think aloud” manner and ask them

the questions. Encourage students to share their thinking on how to approach this

problem. Someone might even realize that they can model it with the tissue boxes

students have brought to school. Record their thinking on chart paper or the board for

all to see. Does everyone see how you came to a solution?

For problem 2, have them go through the process steps with a partner. Have them

show their solutions on their own paper.


http://teacher.scholastic.com/lessonrepro/lessonplans/steppro.htm

http://teacher.scholastic.com/lessonrepro/lessonplans/steppro.htm


Problem 2: *Zack read 14 books over the summer. Grace read 9. They each watched 7

DVD’s. How many more books did Zack read than Grace?

Circulate around the room and make observations. Be sure to comment to students who are working as mathematicians. Take notes on what you observe and hear as students work. Who are your early finishers? How can you keep them busy while others are finishing up? After students have had time to work. . . *How was the second problem different from the first problem? Accept reasonable answers. *What did you discover when you took the time to go through the steps? How was the problem solving process helpful? Allow time for pairs to share solutions and to discuss how the process worked for them. If no one noticed, be sure to point out that problem 2 has some unnecessary info. Pre-assessment

Administer Part 1 of Grade 4 Pretest. If students do not get to the STOP sign today, they may pick up where they left off tomorrow. Note who is struggling, who is taking time to work thoroughly, and who the fast finishers are.

Materials “Working as Mathematicians” chart developed on Day 1, markers 4 Step Problem Solving model poster (your choice which model) Students need paper and a pen Copies of Part 1 of Grade 4 Pretest Consider having students do math in pen so that they cannot erase their initial thinking! You’ll be surprised what you will learn when they can’t erase.

Teacher Notes Leave the problem solving poster up in the room for the coming weeks until it becomes a habit.

Problem 1: Mrs. Baker was stacking the tissue boxes her students brought to class. On the first shelf she placed 7. On the second shelf she squeezed in 8. On the third shelf she put 6. How many tissue boxes did she have?

Problem 2: Zack read 14 books over the summer. Grace read 9. They each watched 7 DVDs. How many more books did Zack read than Grace?


#1 UNDERSTANDING

the PROBLEM

Can you state the problem in your own

words?

What are you trying to find or do?

What information do you know from

the problem?

What are the unknowns?

What information, if any, is missing or

not needed?

#2 DEVISING a PLAN

Look for a pattern.

Look at similar problems, and decide if the

same approach can be applied in this

problem.

Try a simpler example of the problem to

understanding the solution of the original

problem.

Make a table or a diagram

Write an equation.

Use guess and check.

Work backwards.

Model the problem using manipulatives.

#3 CARRYING OUT the

PLAN

Use the strategy or strategies in step 2

and perform any necessary actions or

computations.

Check each step of the plan as you

proceed.

Show your work to prove your thinking.

#4 LOOKING BACK

Check the results with the original problem.

Does your answer make sense? Is it

reasonable?

Is there another way to find a solution?

Based on the problem-solving steps first

outlined by George Polya in 1945.


Day 3—Representation 60 minutes

Big Ideas Mathematicians use multiple ways to represent ideas

Learning Outcomes

Students understand that in math there are multiple ways to represent mathematical ideas in solving problems

Students understand that some of these ways might include using manipulatives to represent their thinking, drawing pictures, using numbers and words, or a combination of these ways.

Students understand that to be most effective, they must use representations to organize, record, and communicate their mathematical ideas.


Focusing the Lesson

*Let’s take a little survey of the class. I will ask you some questions and give you four

choices from which to choose. You will raise your hand when you hear the one that

best applies to you. (If you want to read them first and then have a show of hands on a

second reading, it is up to you, but that takes away the surprise of choice four.)

1. *Which of these choices best describes you regarding pencil sharpening?

-- I usually hold the pencil still while I turn the handle.

--I usually twist the pencil as I turn the handle.

-- I prefer to use my own handheld pencil sharpener for the best results.

--I just chew my pencils to a point.

Hopefully there will be a variety of answers and it is OK for there to be a little silliness. Emphasize the fact that no matter how you do it, your pencil ends up with a sharp point.

2. *Which of these choices best describes you regarding eating dinner?

--I usually eat my favorite food first, then I work down to my least favorite.

--I usually go around my plate and eat some of everything until I’m full.

--I mix my food together and then eat it.

--I usually feed it to the dog under the table.

Emphasize the point that no matter how you do it, your dinner gets eaten.

3. *Which of these choices best describes you regarding personal cleanliness?

--I usually prefer to take a bath.

--I usually prefer to take a shower.

--I wash off at the sink.

--I just run through the sprinkler.

Emphasize the point that no matter how you do it, you get clean.



*So, why do I ask you these silly questions during a math lesson? How can this possibly apply to working as a mathematician? Hopefully, students will come up with some great connections. Bottom line, the point is that we may approach math from different entry points. We might go about solving problems in different ways, show our thinking in different ways, and communicate our understanding in different ways, but in the end, we are solving the same problem. Work Time

*Let’s demonstrate these ideas with a math task. I will give each pair a slip of paper telling you exactly what I want you to do. You have 5 minutes to work. Then we will share our results. Give each pair a plain sheet of white paper and a task slip. [See next page for slips. Note that they are differentiated by level of difficulty. Be mindful as you hand them out. ]

Circulate around the room and make observations. Be sure to comment to students who are working as mathematicians. Take notes on what you observe and hear as students work. Who are your early finishers? How can you keep them busy while others are finishing up? After students have had time to work, ask students to take another gallery walk to see the many ways that the same idea was represented. Then have them return to their seats. *What did you discover on your gallery walk? What did everyone’s task have in common? What can we write on our Mathematicians chart about representation? Collect and display papers to serve as a reminder that mathematicians use multiple ways to represent ideas. Pre-assessment

Administer Part 2 of Grade 4 Pretest . If there are some who did not finish Part 1, they may begin where they left off.

Materials Plain copy paper

Task slips already printed and cut apart Coin manipulatives “Working as Mathematicians” chart Grade 4 Pretest

Teacher Notes We want to get students away from the mindset that there is only one “right way” to solve a problem and to represent our thinking. Some ways are more efficient than others, but students will realize that when they are ready. The understanding needs to be nurtured first. Don’t be too quick to jump in and tell them how to solve problems. That is not our role in a student centered math class.


1. Represent $1.00 by using

manipulative coins on your desktop.

2. 1. Represent $1.00 by using manipulative coins on your desktop.

3. Represent $1.00 by using manipulative coins on your desktop. You must have at least one of each coin. 4. Represent $1.00 by drawing coins on

your paper.

5. Represent $1.00 by drawing coins on your paper.

6. Represent $1.00 by drawing coins on your paper. You must have at least one of each coin. 7. Represent $1.00 by writing an

addition problem with a sum of $1.00.


8. Represent $1.00 by writing an

addition problem with a sum of $1.00.

9. Represent $1.00 by writing a

subtraction problem that equals $1.00.


subtraction problem that equals $1.00.


multiplication problem that equals

$1.00.

12. Represent $1.00 by writing a word

problem that equals $1.00. Use all

words and no numbers.

13. Represent $1.00 by writing a word

problem that equals $1.00. Use all

words and no numbers.


PRE-ASSESSMENT PART 1

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PRE-ASSESSMENT PART 2

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18 Flower Problem

19 Gum/Candy

Problem

20 6x6=9x4 Proof


Day 4—Working Together

Big Ideas Mathematicians work collaboratively developing good work ethics and being responsible to other mathematicians

Learning Outcomes

Students learn that they can work with others to share information and to learn new information.


Focusing the Lesson Prior to the lesson, decide how you will want students to partner up for this unit. It is best that they are already sitting next to each other. This will save transition time. *Mathematicians work together a lot. We’ll work together as a whole class but we’ll

also work with partners and small groups.

*Why do you think mathematicians work together? Can we learn more when we’re

working with someone else? Why or why not?

*If I’m a mathematician working with another mathematician, what responsibilities do

I have to my partner?

*Turn and talk to your partner about 3 ways you’re going to be responsible to each

other.

Keep this part moving because you will need the time for the unit introduction. Students share ideas. Establish rules for group work and add to Mathematicians chart. Work Time Today begins Day One of the Fosnot unit Muffles’ Truffles [page 13]. Please be sure you have read the teacher’s manual from start to finish so that you know where the unit is headed. Follow the plan as closely as possible. Circulate among the pairs and ask questions. Note the kinds of questions the teacher in the book asks, the strategies to look for, and the support offered in the example script.

Closure

*On your Report Card exit ticket give yourself a grade on the kind of math partner you’ve been today. Explain why you think you deserve that grade. Next, give your partner a grade and explain why you think so.

Materials “Working as Mathematicians” chart See complete list of materials on page 13 of Muffles’ Truffles Report Card exit ticket copies for every one

Teacher Notes Although these lessons are pretty well spelled out, you will still need to study them, think about your expectations, focus on the routines you are hoping to establish, and assess how individual students are responding. It will take time for this to become a routine for you as well as the students! Remember that you are part of a greater team—a PLC of mathematicians! Collaborate with other teachers in your grade level, your math coach or differentiation specialist. If we want the students to work together, then we must set the example.



Working Together Report Card

My Name: Partner’s Name:

Grade I give myself ________ Grade I give my partner _____

Comments:

Comments:

Working Together Report Card Prepared by __________________

My Name: Partner’s Name:

Grade I give myself ________ Grade I give my partner _____

Comments: Comments:


Day 5—Sharing

Big Ideas Mathematicians share their thinking strategies, listen to other mathematicians, ask questions, and make conjectures about their findings.

Learning Outcomes

Students understand that sharing and learning from other mathematicians is an important part of working as a mathematician.


Focusing the Lesson

*Since the first day of math, we have been sharing our thinking with each other. Why do you think mathematicians share? I want to show you an aide to help us talk as mathematicians. It will be useful when you’re not sure what to say. [Show the “Talk Bubbles” poster; discuss how it can be helpful.]

*One way we have shared is with a gallery walk. We took a gallery walk the day we walked around and looked at everyone’s arrangements of the 24 counters. Sometimes we will take gallery walks to look at each other’s work. How is a gallery walk helpful?

*Today we will also share our thinking with a math congress. What do you think of when you hear the word “congress?” I looked it up, and one definition says “a society or organization of people with common interests and concerns.” How does that definition apply to us as mathematicians?

*When a mathematician is sharing, what is the job of the rest of us mathematicians? If we don’t completely understand the strategy that someone is sharing, what should we do?

*One more thing . . . every mathematician will not be called to share his or her thinking with the group every day. [Explain that you will call on a variety of strategies so we all can learn different ways to approach a problem. Everyone called to share may not have a 100% correct solution, but everyone will be thinking like a mathematician.]

*We’ve talked about a lot of different ideas related to sharing as mathematicians. What should we add to our chart?

Sharing Time

Today continues with Day Two of the Fosnot unit Muffles’ Truffles [page 20]. There will first be a gallery walk to give students a chance to review and comment on each other’s posters. You might consider hanging these posters in the hallway for ease of movement and so that students from the other classes can look at them as well. This will be followed by a math congress where a few posters you’ve carefully selected will be shared and discussed more fully. Use the questions modeled in the teacher’s manual to guide you until this feels natural.

Materials “Working as Mathematicians” chart See complete list of materials on page 20 of Muffles’ Truffles Students’ posters from Day One of Muffles’ Truffles

Teacher Notes Students must develop the habit of communicating their thinking in complete sentences using mathematical terms correctly—it doesn’t happen automatically. As teachers we must ask for and acknowledge when they successfully communicate their thinking. Wouldn’t it be wonderful to encourage this habit in all subjects? Perhaps if they speak in complete sentences they will write in complete sentences? Can’t hurt!



Day 6—Writing/Representations in Math

Big Ideas Mathematicians use and record mathematical representations to interpret and model everyday life activities.

Learning Outcomes

Students understand that they are expected to write about their mathematical thinking on a daily basis.

Students understand that writing about their thinking is a way to represent mathematical concepts.

Students understand that their math journal is a mathematical tool for recording the problem-solving process.


Focusing the Lesson *Today we’re going to use a mathematical tool we haven’t talked about yet: a journal.

Does everyone have a journal? How could a math journal be a mathematical tool?

Turn and talk to your partner.

Whole class conversation. Talk to the students about how they will use their math journals this year. Depending on your expectations, some suggestions for your consideration might include:

Glue in a copy of the 4 Steps for Problem Solving

Glue in a copy of the Talk Bubbles Have students date all their entries Will you have students copy problems into their

journals or will you provide copies to glue in? Have students solve problems in them and

show their work, drawings, etc. Have students write to explain their strategies

or thinking Have students use their journals as an archive of

past problems to review strategies, show growth, etc.

Create a glossary or vocab section in the back Use journals as a formative assessment

Some generic prompts and question stems are included following this lesson plan for later use. Eventually, you might want to develop a rubric for assessing math journals. A search online will result in samples you can adapt.

Today, continue with Day Three of the Fosnot unit Muffles’ Truffles [page 23]. Begin with the minilesson “Around the Circle.” Then introduce the context with Muffles’ latest predicament. Circulate around the room as students work on their latest task. Listen to students’ conversations. Watch for opportunities to introduce vocabulary words congruent, equivalent, halving, doubling, and the commutative, associative, and distributive properties.

Closure

*In your math journal, explain how you calculated the price of each box. Did you

have to count each square? What’s another way that you could figure out the price?

Did you use any shortcuts? Explain in complete sentences how you knew what to

do. Project copy of this prompt (included) on document camera for all to see.



Materials “Working as Mathematicians” chart 4 Step Problem Solving model poster Talk Bubbles Poster Student journals Copies of 4 Steps of Problem Solving Copies of the Talk Bubbles Glue sticks See complete list of materials on page 23 of Muffles’ Truffles

Teacher Notes Add anything meaningful that was discussed today to the “Working as Mathematicians” chart. Again, students must develop the habit of communicating their thinking in complete sentences using mathematical terms correctly—it doesn’t happen automatically. As teachers we must ask for and acknowledge when they successfully communicate their thinking. Be sure you are comfortable with your math journal expectations. Be consistent in how you expect students to organize their work, or they will tend to slack off. Emphasize the value of the journal as another mathematical tool.

RESPOND to the FOLLOWING WRITING PROMPT

in your MATH JOURNAL:

Explain how you calculated

the price of each box. Think…

Did you have to count each square?

What’s another way that you could figure out

the price? Did you use any shortcuts?

Explain in complete sentences how you knew

what to do.


Some questions to guide students’ writing:

Suggestions for a weekly math prompt:

a. This week in math I learned ________________

What I know about ___________ so far is _____________ .

What I'm still not sure about __________ is _____________________.

b. I want to learn more about__________________________.

c. My favorite part of math this week was _______________________.

d. The hardest part of math this week was __________________________.

e. I need more help understanding __________________________.

Other generic prompts you might like to use:

What is the most significant thing I learned this week?

What are the steps needed to solve this type of problem?

How is this problem similar to others I already know how to solve?

What makes this problem different from other ones?

What vocabulary words can I use to help me explain this procedure?


Day 7—Proof for your thinking

Big Ideas Mathematicians give proof for their thinking.

Mathematicians push each other for accurate proof, including references to ideas shared in previous classes, to deepen their understanding of a mathematical idea.

Learning Outcomes

Students understand that they must prove their thinking. Simply writing the answer is not enough.


Focusing the Lesson *I was looking at some of your sample boxes from yesterday, and I wondered which ones I could buy if I had a $20 bill. I decided that I could buy one 4x3 box and one 2x5 box for that price. Mathematically, it would look like this: (4x3) + (2x5)= $20 worth

When a student says it’s wrong, be adamant that it’s correct. Why? If no one notices, keep at it until someone realizes it is incorrect.

*If you’re so sure I’m wrong, is there a way to prove it to me? Record a way to prove this to me in your math journal.

Allow a couple of minutes for students to do this. Have 2 or 3 students share. Point out different ways they are providing proof, like a proof drawing or other kind of representation or actual use of blueprints.

Have a class conversation: *Does it matter whether mathematicians have proof? Why or why not? How does proving one’s thinking help other mathematicians to understand their work? What’s the difference between proving your thinking and writing a number sentence?

What do we need to add to our chart about how mathematicians prove their thinking?

Work Time Today continues with Day Four of the Fosnot unit Muffles’ Truffles [page 28]. Students will complete their designs and make posters for math congress. As math congress progresses today, start using the open array and partial products as you record student ideas. The graph paper blueprints will be proof that an open array is correct.

In summary

*Let’s evaluate how we’re doing as mathematicians. Teacher reads over entire “Working as Mathematicians” chart.

*What do we do really well as a class of mathematicians?

What are some areas that are hard for us/things we can focus on to improve during the next few weeks of math class?

Is there anything that you think we need to add to our chart?

Materials Task problem displayed “Working as Mathematicians” chart Student math journals See complete list of materials on page 28 of Muffles’ Truffles

Teacher Notes Keep charts posted for “Working as Mathematicians,” 4 Steps of Problem Solving, Journal Rubrics, etc. and refer to them often. It is quite likely that you are also doing the First 20 Days of Reading simultaneously. Compare and contrast expectations between the subjects. What do the students notice?



This ends the First Days of Math for grade four. Practice the routines and

thinking set forth in these first seven lessons. Point out whenever students

are “working like mathematicians.” Add to the chart whenever a new idea

surfaces. Keep charts up for easy reference until routines are well-established,

and revisit them throughout the year.

Please refer to the Grade 4 Mathematics Curriculum Map #1 for the next few

weeks of Multiplication and Division with the Array. Continue with the order

of Muffles’ Truffles. You will notice that the days are not spelled out beyond

that. You will use your own judgment to supplement with Investigations and

other resources. This is not the time for “drill and kill” worksheets and timed

tests. Help students realize that they can multiply by using what they already

know with the strategies presented in this unit.

Giving students multiplication charts, especially those stuck on their desks, is

strongly discouraged and is in opposition to the mission of these lessons.

Should you wish to give homework, feel free to copy pages from the Student

Activity Book that came with Investigations.

Keep student observation notes to use as formative assessments to guide your

instruction. Feel free to pull a small group to the back table whenever you

think it would be beneficial. On the other hand, be prepared to challenge

those who are fast finishers and ready for more.

As you go through these plans, please make note of what worked and what

needs to be changed. These plans will be revised as needed after this year’s

trial run. Your feedback is crucial to the whole process.

getting started: establishing routines & procedures in

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