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Place Value and Addition and Subtraction to 1000 1

st Nine Weeks

Investigations Unit 1 and 3 and The T-Shirt Factory by Fosnot SOL 3.1, 3.2, 3.4, 3.20 – See VDOE SOL Curriculum Framework for Details

Note: For help with setting a math community in the classroom, see the optional First Eight

Days of School in the Appendix 2, or Investigations Unit 1.

Big Ideas

The positions of digits in numbers determine what they represent

The groupings of ones, tens, and hundreds can be taken apart in different ways.

Addition and Subtraction are connected. Addition names the whole in terms of the parts, and

subtraction names a missing part.

Models can be used to solve contextual problems for all operations.

Numbers are related to each other through a variety of number relationships( i.e comparing and

ordering)

Anchor Experience

Fosnot: The T-Shirt Factory (through day 6)

Classroom Routines and Mini-lessons

Practicing Place Value

More or Less

What’s the Temperature? – every Wed.

Number strings from “Number Talks” or from “Mini-lessons for Extending Addition and

Subtraction” by Fosnot.

Calendar – smartboard calendar available at Smart Exchange – go to http://exchange.smarttech.com

and search for daily calendar, many include money, time, counting etc.

Resources

T-shirt Factory Fosnot

Based on students’ needs, use the following: Investigations: Unit 1 Inv.1 Hundreds, Tens, and Ones Inv.2 Working With 100 Investigations: Unit 3 Inv.1 Building 1,000 Inv. 2 Addition Inv. 3 Finding the Difference Inv.4 Subtraction Stories

Math Expressions : Volume 1, Unit 1, Lessons 1, 5, 6, 10, 11, 13 Volume 1, Unit 3, Lessons 1, 2, 3

Minilessons for Extending Addition and Subtraction (Fosnot)

VDOE Enhanced Scope and Sequence http://www.doe.virginia.gov/testing/sol/scope_sequence/mathematics_2009/index.php

http://exchange.smarttech.com/

http://www.doe.virginia.gov/testing/sol/scope_sequence/mathematics_2009/index.php

Comparing Numbers

Inverse Relationships

Addition and Subtraction

My Identity Is in My Pocket

Property Commute

Assessments

Example rubrics for Investigations activities are located in Appendix 2

Pre and post-assessment: Located in Appendix 1 of this document

Strategies

Models

Landmark Numbers

Splitting

Regrouping

Skip Counting

Varying adding on and removing

Constant Difference

T-Chart

Proof Drawings

Visual Representations

Vocabulary

Celsius

degree

Fahrenheit

analog/digital

difference

digit

equation

sum

number line

equivalent

greater than/less than

inverse relationship

Place Value

Expanded Form

Standard Form

Written Form

value

Online Resources/Games

VDOE Mathematics instructional video

http://www.doe.virginia.gov/instruction/mathematics/resources/videos/index.shtml

VDOE Vocabulary Word Wall Cards

http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/index.shtml

Mathwire

http://www.mathwire.com/numbersense/morepv.html

Place Value Games

http://www.free-training-tutorial.com/place-value-games.html Virtual Manipulative Kit

http://highered.mcgraw-hill.com/sites/0073519456/student_view0/virtual_manipulative_kit.html

Suffolk County Resources

http://star.spsk12.net/

Rockingham County Resource page:

http://www.rockingham.k12.va.us/resources/elementary/3math.htm#1learning

Illuminations.com

VDOE enhanced scope and sequence

ABCYA.COM (100 Number chart and many other good things)

Investigations Smartboard activities




http://www.free-training-tutorial.com/place-value-games.html




Data Analysis

1st Nine Weeks

Investigations Unit 2 and Supplemental Materials

SOL 3.17 – See VDOE SOL Curriculum Framework for Details

Big Ideas

A collection of objects with various attributes can be classified or sorted in different ways.

The same set of data can be sorted in different ways.

Data are gathered, organized, and compared in order to answer questions.

Different types of graphs provide different information about the data.

Anchor Experience

Investigations, Unit 2: Inv.1 Representing and Describing Categorical Data

Classroom Routines and Mini-lessons

More or Less

Guess My Rule

Today’s Number

What’s the Temperature? – every Wed Number strings from “Number Talks” or from “Mini-lessons for Extending Addition and

Subtraction” by Fosnot.

Calendar – smartboard calendar available at Smart Exchange – go to

http://exchange.smarttech.com and search for daily calendar, many include money, time,

counting etc.

Resources

Investigations Unit 2: Inv.1

Expressions Volume 1: Unit 3 Lessons 15, 16, 17

Enhanced Scope and Sequence


o Statistics Through the Year

o Data Mania (Part1)

Assessments

Enhanced scope and sequence activities and Investigations Unit 2 have assessments.

Rubric for Investigations at the end of this document.

Strategies

Models

representing information visually

organizing data

comparing data

interpreting data

picture graph

bar graph

Vocabulary

bar graph

picture graph

fewer

more

data

organize

columns

rows

title

axes

comparing

symbol

http://exchange.smarttech.com/


less

table

classify

survey

horizontal

vertical

label

key

representation

categories

Online Resources/Games

Create a Graph http://nces.ed.gov/nceskids/createagraph/

Data Analysis in the 3rd

grade

http://www.internet4classrooms.com/skill_builders/data_analysis_math_third_3rd_grade.html

VDOE Mathematics instructional video


VDOE Vocabulary Word Wall Cards


Mathwire


Virtual Manipulative Kit


Suffolk County Resources


Rockingham County Resource page:


Illuminations.com

VDOE enhanced scope and sequence

ABCYA.COM (100 Number chart and many other good things)

Investigations Smartboard activities

http://nces.ed.gov/nceskids/createagraph/

http://www.internet4classrooms.com/skill_builders/data_analysis_math_third_3rd_grade.html







Appendix

Part 1 Assessments

Name________________ Date_______________ Pre-Assessment Place Value and Addition and Subtraction Common Assessment

1. Which number is shown below? _______________

Draw a circle around the word form that goes with the number represented above.

forty-seven four hundred seven

seven hundred four seventy-four

2. Write the numbers, in words, that come just before and just after these numbers:

Number Before Number Number After

two

thirty-three

seven hundred seven


3. Write two numbers, in words, that are less than each of the following:

twelve____________________ ________________________

one hundred_______________ ________________________

thirty___________________ ________________________

4. What number is ten more than each of the following:

57 ____________

42 ____________

317 ____________

5. Write the number that is two more than each of the following:

78 ____________

355 ____________

99 ____________

6. Draw a circle around the greatest number in each set.

448 848 884 484

216 612 261 621

359 953 539 395


7. Write these numbers in order, from smallest to largest:

34 72 27 43

_______ _______ _______ _________

smallest largest

213 241 247 413

_______ _______ _______ _______

smallest largest

8. What number is pictured below?

_____________


9. Marie has 125 buttons in a box. If she puts ten buttons in a bag, how many bags can she

fill?

__________________

Will there be buttons left over? Yes No

How many will be left over? _____________________

10. Pat had 256 baseball cards in his collection. His brother gave him some baseball cards

and now he has 521 cards. How many cards did his brother give him?

Name________________ Date_______________

1. Nora took some books to school.

She gave four books to Tom and then put two books on her desk.

Which of the following number sentences shows how many books Nora brought

to school? Circle the correct number sentence.

4 + = 2 4 - = 2

+ 2 =4 - 4 = 2

2. Which represents 745? Circle the correct answer.

700 + 40 + 5 700 + 40

70 + 45 600 + 40 + 5

3. Which represents 2,584?

2,000+500 + 80 + 4 400 + 84

300 + 80 + 4 500+ 75 + 4

4. Which number is shown here? _________________

Name________________ Date_______________

4. Match the numbers in standard and word form. Draw a line connecting the

equivalent numbers.

724 three hundred twenty-four

324 two hundred thirty-seven

473 seven hundred twenty-four

273 four hundred seventy-three

5. The Walton Toy Company received orders from 12 stores for ten games each

during the holidays.

The Speedy Delivery Company billed them for shipping 1,200 games.

Was that correct? If not, what is the correct number? How do you know?

Show your work with pictures, words, or numbers.

Walton Toy Company sent _____ games.

For the problems below: Which is greater? How do you know? Show your work in

pictures, words, or numbers.

Name________________ Date_______________

6. 20 tens or 3 hundreds

7. 12 ones or 3 tens

8. 6 thousands or 35 hundreds

9. Jessie turned over four number cards. The numbers were:

Using 4 of the numbers, what is the largest

7 3 1 9

Name________________ Date_______________

number you can make?

___________

Using 4 of the numbers, what is the smallest

number you can make?

____________

Explain your answers with pictures, words, or numbers.

10. Jordan Candy Store has 1,421 jelly beans, Taylor Candy Store has 1,241 jelly

beans, and Fisher Candy Store has 1,142 jelly beans.

List the numbers in order from least to greatest number of jelly beans.

_______________ , ______________ , _____________

Name________________ Date_______________

11. Bobby drives from Staunton to Roanoke and then to Lynchburg. He travels a

total of 125 miles. Find the distance from Staunton to Roanoke using the map

below, explain your work using pictures, words, or numbers.

46 miles

?

The distance from Staunton to Roanoke is ___________.

12. Eight plums are needed to make a pie. If Max makes seven pies, about how

many plums will he need?

Circle the correct answer:

A. Fewer than 20 plums.

B. Between 20 and 40 plums.

C. Between 40 and 60 plums.

D. More than 60 plums.

Show your work with pictures, words, or numbers.

Staunton

Roanoke

Lynchburg

Name________________ Date_______________

13. Use the map to answer the following

questions.

About how far will Joe drive from his house

to Raleigh?

____________miles

About how far is Demonte’s house from

Raleigh?

_____________ miles

Show your work below.

14. Jacob rounded his sticker collection to the nearest thousands place. He had

about 4,000 stickers. How many stickers do you think Jacob might have actually

had? Explain your answer.

15. Compare two whole numbers between 0 and 9,999 using symbols (>, <, =).

48 ________ 78 129 ________ 129

705 _______ 792 1,653 _______ 1,655

Solve the following related fact sentences.

Name________________ Date_______________

16. 5 + 3= 8, so 8-3 = ____________

17. 8+9= 17, so 17-9 =____________

Write three related basic fact sentences when given one basic fact sentence for

addition or subtraction.

18. 9 + 7 = 16 ___________________

___________________

____________________

19. 14 - 6 = 8 ___________________

___________________

Appendix 2

The First Eight Days of School

Rubrics

Getting Started: Establishing Routines & Procedures in Grade 3 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- We are all Mathematicians

Big Ideas We’re all mathematicians. Mathematicians work in an ordered environment with established routines and procedures for independent and/or cooperative math groups.

Learning

Outcomes

Students identify criteria to create a “Good Work” 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.

Anchor

Experience

for Students

Focusing the Lesson I have a problem . . . I had 18 Tuesday folders this morning. I left some in Ms. Smith’s room. Now I have 9 folders. What could I do to figure out how many I left in Ms. Smith’s room? Have students work with a partner to think about the teacher’s problem. 5 min. into students working . . . Everyone pause in their thinking . . . Guess what I’m noticing: we’re all mathematicians! Look around the room. What do you think it means to be a mathematician? Have students share different ideas. Work Time 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. Develop “Working like a Mathematician” process chart with class to which students can refer. (A good work chart should have less than 6 criteria to be effective.) Example below and on right:

• Stay on Task

• Speak/write mathematically

• Be an active listener and participant.

• Respect and organize math materials appropriately.

Activity to support

Finish task problem.

If math were an animal, what would it be? Whole class share. Were we

working like mathematicians? Let’s look back to our chart . . .

Materials Copy of task problem displayed Chart paper Markers

Teacher

Notes

Don’t worry if the kids 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

process standards to make sure the kids include these.

** On day 6 students will be sharing a collection of 100 items. You will need to

make this a homework assignment prior to Day 6.

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

Day 2-Management

Big Ideas Mathematicians use math tools to think about math and help them solve problems.

Learning

Outcomes

Students become familiar with the math tools in the classroom.

Anchor

Experience

for Students

Focusing the Lesson If you had a mathematics toolkit, what tools would you want in it to help you think about math? Have students think with a partner. Whole class share. Work Time Take a tour of mathematical tools in classroom, how they are to be used and stored. What tools might have helped us with my problem from yesterday? How and why do mathematicians use tools?

Activity to support

Investigations, Unit 1.1-Ten-Minute Math, pg. 26 (Note-Use Interactive

Whiteboard)

Add notes to the “Working like a Mathematician” process chart about

placing materials in their proper storage containers and location after use.

Materials Various classroom manipulatives students will have available for use during the year, including at least 50 Unifix cubes per pair of students

Interactive Whiteboard CD from Investigations “Working like a Mathematician” process chart developed on Day 1

Teacher

Notes

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.

Day 3-Problem Solving

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.

Anchor

Experience

for Students

Focusing the Lesson Did you know mathematicians use a process to think about math? Why do you think they use a process? Whole class conversation. Develop a problem solving model with your class which you’ll use throughout the year. (One example is Polya’s 4-Step Problem Solving Model.) Add your class’s process to your “Working like a Mathematician” process chart or create a separate chart you can refer to throughout the year. Work Time

We’re going to use our process to think about a problem today. Remember

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

our chart.

Students complete Problem A from Appendix.

Math Congress

Have students share how they worked like a mathematician to solve the

problem. After a student shares, have the class look back at the chart and cite

specific ways the student was working like a mathematician and/or using the

problem solving process.

Materials Problem A displayed or copied “Working like a Mathematician” process chart developed on Days 1 and 2 Problem solving model

Teacher

Notes

Post the chart on the wall in student-friendly language.

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

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

Day 4-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 the journal is a mathematical tool.

Anchor

Experience

for Students

Focusing the Lesson Today we’re going to use a mathematical tool we haven’t talked about yet: a journal. Does everyone know what a journal is? How could a math journal be a mathematical tool? Turn and talk to your partner. Whole class conversation. Develop a rubric with the class for expectations for thinking in their math journal. Work Time Let’s use your journal right now as a thinking tool.

Remind students of rubric as they respond to the following prompt: (choose

one)

Which do you like better, adding or subtracting? Why?

OR

Solve 14 – 9. Write down every step as if you were explaining how you

solved it to someone younger.

Ask a few students to share.

Activity to support

Have students work in pairs to solve Problem B from Appendix.

Select a few students to share their strategy for solving the problem.

How did thinking in your journal first help you to solve the problem? Class

debriefs. Try to highlight some of the big ideas in student responses.

Materials Problem B copied or displayed Chart paper for class rubric Student journals

Teacher

Notes

See the rubric in the Appendix.

Day 5-Vocabulary

Big Ideas Mathematicians use specialized terms to discuss mathematical ideas and build their knowledge.

Learning

Outcomes

Students understand that they will use specialized terms to discuss mathematical concepts.

Anchor

Experience

for Students

Focusing the Lesson I wonder if anyone has noticed the words which are on our word (strategy) wall. Let’s look at them for a few minutes. Does anyone recognize any of the words? Does anyone see a new word? Have a class conversation. Have you ever noticed how we use special words to talk about ideas in math? Why do you think we do that? Model how students will add new words in their journals and/or how words will be added to the classroom word wall. Work Time

Have students work in pairs to complete Problem C in Appendix. Remind

students to work as mathematicians and use a problem-solving process.

You’ll also be listening for mathematical terms from the Word Wall as they

talk together about how to solve the problem.

Select a few student groups to share how they worked through the problem-

solving process to solve the problem. After each student group shares, ask

the class if they heard any mathematical language from their classmates.

Activity to support

Materials Selected mathematical terms from vocabulary section of Unit 1 Curriculum Map posted on word wall

Problem C from Appendix, copied or displayed Student journals (to add mathematical terms in the back, if desired)

Teacher

Notes

As you introduce new vocabulary, students can record the word(s) in their journal. Have students write their definition of vocabulary word(s), make a real life connection, and draw a representation of the idea in the journal.

Introduce mathematical vocabulary, such as equation, by using terms yourself as they arise in mathematical work. If the introduction of such terms is accompanied by activities that make their meaning clear, students will begin using these terms naturally as they hear them used repeatedly in meaningful contexts.

Add terms or refresh word wall over the course of the year.

Day 6-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.

Anchor

Experience

for Students

Focusing the Lesson Yesterday after you solved the problem, some students shared how they worked through the problem-solving process. Why do you think mathematicians share? Sometimes it’s hard to know how to explain our thinking. What can we say when we’re not sure? When mathematicians are sharing, do the rest of us mathematicians have a job? What if we don’t completely understand the strategy that someone is sharing? What should we do then? I want to show you an aide to help us talk as mathematicians . . . (Appendix-bubble sheet)http://central.spps.org/information/staff/files/AccTalkV3.pdf One more thing . . . all mathematicians won’t share their thinking every day (why teacher won’t call on everyone). We’ve talked about a lot of different ideas related to sharing as mathematicians. What should we add to our chart? Work Time

Make a collection of 100. Your collection can be anything—pictures,

toothpicks, pebbles, and so on. How will you know you have exactly 100?

Scaffolding question to ask students who might be counting objects

individually- Is there a way you can group them to help you know?

Math Congress

Now it’s time to share. Look again at the bubble sheet and expectations

from “Working as a mathematician” chart.

Ask 3 or 4 students to share how they thought about counting their

collection of 100 items. Try to select students who might have used

different groupings, looking especially for a student who grouped by 10.

Point out skip counting as a strategy if a student demonstrates.

Debrief at the end of math congress what you noticed during the math

congress:

I noticed the way ___________________ was specific about explaining her

thinking. As mathematical listeners, could we have done anything

differently?

Materials Copy of task problem displayed “Working as a mathematician” chart Bubble sheet from appendix Items for students to collect and group

http://central.spps.org/information/staff/files/AccTalkV3.pdf

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.

Day 7- 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.

Anchor

Experience

for Students

Focusing the Lesson 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. Students share ideas. Establish rules for group work and add to chart. Work Time

Now you’ll have the chance to put those expectations into practice.

Introduce and engage students in the game Capture 5 (Investigations, Unit

1.5)

Journal

Have students reflect in their math journals about Capture 5 using the

following prompt:

Reflect on your participation in class today and complete the following

statements:

-I learned that I . . .

-I was surprised that I . . .

-I noticed that . . .

Materials Journal prompt displayed “Working as a mathematician” chart Student math journals

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.

Day 8- 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.

Anchor

Experience

for Students

Focusing the Lesson If I have 2 pencils and John has 2 pencils, how many pencils would we have together? Let’s figure it out. Turn and talk to your partner. Teacher “works” the problem on the board by writing 2 + 2 = 5. When a student says it’s wrong, be adamant that it’s correct. Why? “Because I just know 2 + 2 = 5 . . . I just know it!” 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. Have 3 or 4 groups share. Point out different ways groups are providing proof, like a proof drawing or other kind of representation or actual manipulatives. Have a class conversation: Does it matter whether mathematicians have proof? Why or why not? How does proving your thinking help mathematicians to understand their work? What’s the different between proving your thinking and writing a number sentence? Do we need to add any ideas to our chart about how mathematicians prove their thinking? Work Time

Now you’ll have the chance to put those expectations into practice.

What might the missing numbers be?

_____ _____ + _____ = 32

Complete task problem independently in math journal. Remind students to

give proof in their journal entry.

Have 3 or 4 students share proof for their thinking, using the document

camera.

In summary

Let’s evaluate how we’re doing as mathematicians. Teacher reads over

“Working as a mathematician” 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 get

better at during the next few weeks of math class?

Materials Task problem displayed “Working as a mathematician” chart Student math journals

Rubric Grades K-3

As a Mathematician, I can…..

Level

Understand the Math

Use a Strategy

and Reasoning

Communicate My

Thinking

4 (S+)

Superior

Work.

WOW

☺

I understand the problem very

well and have a complete plan to

solve it.

I complete all of the math in the

problem very well.

I get a complete and correct

answer.

I can use quite a few

strategies to get an answer.

I use good reasoning.

I can tell if my answer

makes sense.

I can think of how this

problem is like another

problem.

I can clearly explain my

answer and all of the steps.

I can record my thinking

very well on paper with

words, drawings and math

symbols.

I use the right words,

drawings and math symbols

all of the time.

3 (S)

Good work.

Got it

I understand the problem and

have a plan to solve it.

I complete all of the math in the

problem.

I get a complete and correct

answer

I can use one strategy to

get an answer.

I use some reasoning.

Sometimes I can tell if my

answer makes sense.

Sometimes I can think of

how this problem is like

another problem.

I can explain my answer

and most of the steps.

I can record my thinking on

paper most of the time.

I use the right words,

drawings and math symbols

most of the time.

Level

Understand the Math

Use a Strategy

and Reasoning

Communicate My

Thinking

2 (S-)

Incomplete

work.

I need some

help.

Not Quite

I understand only some of the

problem and I may not have a

plan to solve it.

I complete only some of the

math in the problem.

I get a wrong answer.

I might not have a strategy

or it is the wrong one.

My reasoning is not always

complete or helpful.

I try, but I do not know

how this is like another

problem.

I explain a little bit of my

answer but not the steps.

I record my thinking on

paper very little.

I use very few simple

words, drawings and math

symbols.

1 (N)

Beginner work.

I need a lot of

help.

I need help.

I am confused by the problem

and need help to solve it.

I do not complete all of the math

in the problem.

I get a wrong answer.

I don’t use any strategies to

get an answer.

I do not use reasoning.

I can’t tell if my answer

makes sense.

I can’t think of a similar

problem.

I do not explain my answer

at all.

I do not record my answer

or it is very confusing.

I get confused about which

math symbols to use.

Rubric for Assessing Student Understanding of Mathematical Concepts Grades K-2

Level Understanding Strategies and Reasoning Communication

4 (S+)

Superior

performance,

independence

Shows a superior understanding of the problem

including the ability to identify the appropriate

mathematical concepts and the information necessary

for its solution

Completely addresses all mathematical components

presented in the task

Puts to use the underlying mathematical concepts

upon which the task is designed

Solution must be complete and correct.

Uses a very efficient and sophisticated

strategy leading directly to a solution

Employs refined and complex reasoning

Evaluates the reasonableness of the solution

Makes mathematically relevant

observations and/or connections

Clear, effective explanation detailing how

the problem is solved; all of the steps are

included so that the reader does not need to

infer how and why decisions were made

Mathematical representation effectively used

Precise and effective use of mathematical

terminology and notation

3 (S)

Adequate

performance and

mastery

Shows an adequate understanding of the problem and

the major concepts necessary for its solution

Addresses all of the components presented in the

task

Solution must be complete and correct.

Uses a strategy that leads to a solution of

the problem

Uses effective mathematical reasoning

All parts are correct and a correct answer is

achieved

Clear explanation given

Appropriate use of accurate mathematical

representation

Appropriate use of mathematical

terminology and notation

2 (S-)

Meets competency

with assistance,

needs support and

practice

Shows a partial understanding of the problem and the

major concepts necessary for its solution

Addresses some, but not all, of the mathematical

components presented in the task

Incomplete solution, indicating that parts of the

problem are not understood

Uses a strategy that is partially useful,

leading some way toward a solution, but not

to a full solution of the problem

Some evidence of mathematical reasoning

Some parts may be correct, but a correct

answer is not achieved

Incomplete explanation; may not be clearly

presented

Some use of appropriate mathematical

representation

Some use of mathematical terminology and

notation appropriate to the problem

1 (N)

Has difficulty, even

with support

Shows limited understanding of the problem and the

major concepts necessary for its solution

Inappropriate concepts are applied and/or

inappropriate procedures are used

May address some of the mathematical components

presented in the task

Little or no evidence of a strategy or

procedure or uses a strategy that does not

help solve the problem

Little or no evidence of mathematical

reasoning

So many mathematical errors that the

problem could not be resolved

No explanation of the solution, the

explanation cannot be understood or it is

unrelated to the problem

No use, or mostly inappropriate use, of

mathematical terminology and notation

I DON’T KNOW WHAT TO SAY . . . I WANT TO

JOIN THE CONVERSATION

THINK MORE DEEPLY

Could you explain your answer?

I have a different opinion because . . .

What is your proof?

Say more about that . . .

Where do you see that?

I’d like to add to what _______ said.

Why do you think that?

I have a different opinion because . . .

Something else I noticed was . . .

I agree with what _____ said because .

. .

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