3.3.3A Time

Grade: 
3
Subject:
Math
Strand:
Geometry & Measurement
Standard 3.3.3

Use time, money and temperature to solve real-world and mathematical problems.

Benchmark: 3.3.3.1 Time

Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute.

For example: Your trip began at 9:50 a.m. and ended at 3:10 p.m. How long were you traveling?

Benchmark: 3.3.3.2 Relationships Among Units of Time

Know relationships among units of time.

For example: Know the number of minutes in an hour, days in a week and months in a year.

Overview

Big Ideas and Essential Understandings 

Standard 3.3.3 Essential Understandings

Third graders tell time to the nearest minute (includes five minute intervals) on analog and digital clocks. In addition, they determine elapsed time to the nearest minute within a two hour interval. They know and understand the relationship between seconds, minutes, hours, days, weeks, months and years.

Third graders make change up to one dollar in several different ways. They are able to make change with as few coins as possible.

Third graders use analog thermometers to determine temperatures to the nearest degree in both Fahrenheit and Celsius.

Benchmark Cluster 

Benchmark Group A

3.3.3.1 Tell time to the minute using digital and analog clocks. Determine elapsed time to the minute.

3.3.3.2 Know relationships among units of time.

What students should know and be able to do [at a mastery level] related to these benchmarks:

  • tell time to the nearest five minutes
  • tell time to the nearest minute
  • determine elapsed time to the nearest minute within a two hour span
  • solve problems involving elapsed time
    • find start time given end time and elapsed time
    • find end time given start time and elapsed time
  • make the following conversions
    • minutes to hours
    • hours to minutes
    • hours to days
    • days to hours
    • days to weeks
    • weeks to days
    • months to years
    • years to months
  • make conversions involving mixed units.
  • For example, 12 days = 1 week and 5 days.

 

Work from previous grades that supports this new learning includes: 

  • Tell time to the hour, half hour and quarter hour
  • Distinguish between a.m. and p.m.
  • Use the language "quarter to," "quarter after'" "fifteen minutes after" and "fifteen minutes before."
Correlations 

NCTM Standards

Common Core State Standards

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

3.MD.1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

3.MD.2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).1 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Misconceptions

Student Misconceptions 

Students may think ....

  • the hour and minute hand on analog clocks are interchangeable.
  • the hour numeral is also the minute numeral
  • there is no difference between minutes to the hour, minutes after the hour and minutes past the hour and they can use the words interchangeably.
  • a.m. and p.m. are one and the same.

Resources

Instructional Notes 

Teacher Notes

  • Students may need support in further development of previously studied concepts and skills
  • The following conversions are part of understanding time at the third grade level:
    • minutes to hours
    • hours to minutes
    • hours to days
    • days to hours
    • days to weeks
    • weeks to days
    • months to years
    • years to months
  • Third graders need to find a conversion involving mixed units.For example, 12 days = 1 week and 5 days
  • Elapsed time must be within a two hour span.
  • Using an empty time line can aid students in finding elapsed time.

For example,

  • Good questions, and good listening, will help children make sense of the mathematics, build self-confidence and encourage mathematical thinking and communication. A good question opens up a problem and supports different ways of thinking about it. The best questions are those that cannot be answered with a "yes" or a "no."

 

Getting Started

What do you need to find out?

What do you know now? How can you get the information? Where can you begin?

What terms do you understand/not understand?

What similar problems have you solved that would help?

 

While Working

How can you organize the information?

Can you make a drawing (model) to explain your thinking? What are other possibilities?

What would happen if...?

Can you describe an approach (strategy) you can use to solve this?

What do you need to do next?

Do you see any patterns or relationships that will help you solve this?

How does this relate to...?

Why did you...?

What assumptions are you making?

 

Reflecting about the Solution

How do you know your solution (conclusion) is reasonable? How did you arrive at your answer?

How can you convince me your answer makes sense?

What did you try that did not work? Has the question been answered?

Can the explanation be made clearer?

 

Responding (helps clarify and extend their thinking)

Tell me more.

Can you explain it in a different way?

Is there another possibility or strategy that would work?

Is there a more efficient strategy?

Help me understand this part ...

 

(Adapted from They're Counting on Us, California Mathematics Council, 1995)

Instructional Resources 

There is an interactive analog and digital clock at this link.The clock can show the current time or the time can be moved forward or back by minutes or hours. This is a tool for elapsed time.

Additional Instructional Resources

Small, M. (2009). Good questions: great ways to differentiate mathematics instruction. New York, NY: Teachers College Press.

Van de Walle, J., Karp, K., Bay-Williams, J. (2010). Elementary and middle school mathematics: Teaching developmentally. (7th ed.). Boston, MA: Allyn & Bacon.

Van de Walle, J. & Lovin, L. (2006). Teaching student-centered mathematics grades k-3. Boston, MA: Pearson Education.

Van de Walle, J. & Lovin, L. (2006). Teaching student-centered mathematics grades 3-5. Boston, MA: Pearson Education.

New Vocabulary 

New Vocabulary

"Vocabulary literally is the key tool for thinking."

Ruby Payne

a.m. - before noon

p.m. - after noon

unit - standardized quantity of measurement

Mathematics vocabulary words describe mathematical relationships and concepts and cannot be understood by simply practicing definitions.  Students need to have experiences communicating ideas using these words to explain, support, and justify their thinking.

Learning vocabulary in the mathematics classroom is contingent upon the following:

Integration:   Connecting new vocabulary to prior knowledge and previously learned vocabulary.  The brain seeks connections and ways to make meaning which occurs when accessing prior knowledge.

Repetition:    Using the word or concept many times during the learning process and connecting the word or concept with its meaning.  The role of the teacher is to provide experiences that will guarantee connections are made between mathematical concepts, relationships, and corresponding vocabulary words.

Meaningful    Multiple and varied opportunities to use the words in context.  These

Use:              opportunities occur when students explain their thinking, ask clarifying questions, write about mathematics, and think aloud when solving problems.  Teachers should be constantly probing student thinking in order to determine if students are connecting mathematics concepts and relationships with appropriate mathematics vocabulary.

Strategies for vocabulary development

Students do not learn vocabulary words by memorizing and practicing definitions. The following strategies keep vocabulary visible and accessible during instruction.

Mathematics Word Bank:  Each unit of study should have word banks visible during instruction.  Words and corresponding definitions are added to the word bank as the need arises.  Students refer to word banks when communicating mathematical ideas which leads to greater understanding and application of words in context.

Labeled pictures and charts:  Diagrams that are labeled provide opportunities for students to anchor their thinking as they develop conceptual understanding and increase opportunities for student learning.

Frayer Model: The Frayer Model connects words, definitions, examples and non-examples.

Example/Non-example Charts: This graphic organizer allows students to reason about mathematical relationships as they develop conceptual understanding of mathematics vocabulary words.  Teachers should use these during the instructional process to engage student in thinking about the meaning of words.

Vocabulary Strips:  Vocabulary strips give students a way to organize critical information about mathematics vocabulary words.

word

definition

illustration

Encouraging students to verbalize thinking by drawing, talking, and writing increases opportunities to use the mathematics vocabulary words in context.

Additional Resources for Vocabulary Development

Murray, M. (2004). Teaching mathematics vocabulary in context. Portsmouth, NH: Heinemann.

Sammons, L. (2011).  Building mathematical comprehension: Using literacy strategies to make meaning.  Huntington Beach, CA: Shell Education.

Professional Learning Communities 

Reflection - Critical Questions regarding the teaching and learning of these benchmarks

What are the key ideas related to telling time at the third grade level?  How do student misconceptions interfere with mastery of these ideas?

What experiences do students need in order to tell time to the minute successfully?

What common errors do second graders make when telling time to the minute?

When checking for student understanding of telling time at the third grade level, what should teachers

  • listen for in student conversations?
  • look for in student work?
  • ask during classroom discussions?

Examine student work related to a task involving telling time. What evidence do you need to say a student is proficient? Using three pieces of student work, determine what student understanding is observed through the work.

What are the key ideas related to determining elapsed time to the minute?  How do student misconceptions interfere with mastery of these ideas?

What experiences do students need in order to determine elapsed time to the minute?

What common errors do third graders make when determining elapsed time to the minute?

When checking for student understanding when determining elapsed time to the minute, what should teachers

  • listen for in student conversations?
  • look for in student work?
  • ask during classroom discussions?

Examine student work related to a task involving determining elapsed time to the minute. What evidence do you need to say a student is proficient? Using three pieces of student work, determine what student understanding is observed through the work.

How can teachers assess student learning related to these benchmarks?

How are these benchmarks related to other benchmarks at the third grade level?

Professional Learning Community Resources

Bamberger, H., Oberdorf, C., & Schultz-Ferrell, K. (2010). Math misconceptions prek-grade 5: From misunderstanding to deep understanding. Portsmouth, NH: Heinemann.

Chapin, S., and Johnson, A. (2006). Math matters: Understanding the math you teach, grades K-8. (2nd ed.). Sausalito, CA: Math Solutions Press.

Chapin, S., O'Connor, C., & Canavan Anderson, N. (2009). Classroom discussions: Using math talk to help students learn (Grades K-6). Sausalito, CA: Math Solutions.

Fosnot, C., & Dolk, M. (2002). Young mathematicians at work: Multiplication and division. Portsmouth, NH: Heinemann.

Hyde, Arthur. (2006). Comprehending math adapting reading strategies to teach mathematics, K-6. Portsmouth, NH: Heinemann.

Lester, F. (2010). Teaching and learning mathematics: Transforming research for elementary school teachers. Reston, VA: National Council of Teachers of Mathematics.

Otto, A., Caldwell, J., Wallus Hancock, S., & Zbiek, R.(2011). Developing essential understanding of multiplication and division for teaching mathematics in grades 3 - 5. Reston, VA.: National Council of Teachers of Mathematics.

Parrish, S. (2010). Number talks: Helping children build mental math and computation strategies grades K-5. Sausalito. CA: Math Solutions.

Sammons, L., (2011). Building mathematical comprehension: Using literacy strategies to make meaning. Huntington Beach, CA: Shell Education.

Schielack, J. (2009). Focus in grade 3, teaching with curriculum focal points. Reston, VA: National Council of Teachers of Mathematics.

References 

Bamberger, H., Oberdorf, C., & Schultz-Ferrell, K. (2010). Math misconceptions prek-grade 5: From misunderstanding to deep understanding.  Portsmouth, NH: Heinemann.

Bender, W. (2009). Differentiating math instruction: Strategies that work for k-8 classrooms! Thousand Oaks, CA: Corwin Press.

Bresser, R., Melanese, K., & Sphar, C. (2008).  Supporting English language learners in math class, grades k-2. Sausalito, CA: Math Solutions Publications.

Burns, Marilyn. (2007). About teaching mathematics:  A k-8 resource (3rd ed.). Sausalito, CA: Math Solutions Publications.

Burns, M. (Ed). (1998). Leading the way: Principals and superintendents look at math instruction. Sausalito, CA:  Math Solutions.

Caldera, C. (2005). Houghton Mifflin math and English language learners. Boston, MA:  Houghton Mifflin Company.

Carpenter, T., Fennema, E., Franke, M., Levi, L., & Empson, S. (1999). Children's mathematics cognitively guided instruction. Portsmouth, NH: Heinemann.     

Cavanagh, M. (2006). Math to learn: A mathematics handbook. Wilmington, MA:  Great Source Education Group, Inc.

Chapin, S., & Johnson, A. (2006). Math matters: Understanding the math you teach, grades K-8. (2nd ed.). Sausalito, CA: Math Solutions Press.

Chapin, S., O'Connor, C., & Canavan Anderson, N. (2009). Classroom discussions: Using math talk to help students learn (Grades K-6). Sausalito, CA: Math Solutions.

Dacey, L., & Salemi, R. (2007). Math for all: Differentiating instruction k-2. Sausalito, CA: Math Solutions.

Donovan, S., & Bradford, J. (Eds). (2005). How students learn: Mathematics in the classroom. Washington, DC: National Academies Press.

Dougherty, B., Flores, A., Louis, E., & Sophian, C. (2010). Developing essential understanding of number & numeration pre-k-grade 2. Reston, VA: National Council of Teachers of Mathematics.

Felux, C., & Snowdy, P. (Eds.). ( 2006). The math coach field guide: Charting your course. Sausalito, CA: Math Solutions.

Fuson, K., Clements, D., & Beckmann, S. (2009). Focus in grade 2 teaching with curriculum focal points. Reston, VA: National Council of Teachers of Mathematics.

Hyde, Arthur. (2006). Comprehending math adapting reading strategies to teach mathematics, K-6. Portsmouth, NH: Heinemann.

Kilpatrick, J., & Swafford, J. (Eds). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.

Leinwand, S. (2000). Sensible mathematics: A guide for school leaders. Portsmouth, NH:  Heinemann.

Lester, F. (2010). Teaching and learning mathematics: Transforming research for elementary school teachers. Reston, VA: National Council of Teachers of Mathematics.

Murray, M. (2004). Teaching mathematics vocabulary in context. Portsmouth, NH: Heinemann.

Murray, M., & Jorgensen, J. (2007). The differentiated math classroom: A guide for teachers k-8. Portsmouth, NH: Heinemann.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

O'Connell, S., & SanGiovanni, J. (2011). Mastering the basic math facts multiplication and division strategies, activities & interventions to move students beyond memorization. Portsmouth, NH: Heinemann

Parrish, S. (2010). Number talks: Helping children build mental math and computation strategies grades K-5. Sausalito. CA: Math Solutions.

Sammons, L. (2011). Building mathematical comprehension: Using literacy strategies to make meaning. Huntington Beach, CA: Shell Education.

Schielack, J., Charles, R., Clements, D., Duckett, P., Fennell, F., Lewandowski, S., ... & Zbiek, R. M. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence. Reston, VA: NCTM.

Seeley, C. (2009). Faster isn't smarter: Messages about math teaching and learning in the 21st century. Sausalito, CA: Math Solutions.

Small, M. (2009). Good questions: Great ways to differentiate mathematics instruction.  New York, NY: Teachers College Press.

Uittenbogaard, W., & Fosnot, C. (2008). Mini-lessons for early multiplication and division, Grades 3-4. Portsmouth, NH: Heinemann.

Van de Walle, J., Karp, K., Bay-Williams, J. (2010). Elementary and middle school mathematics: Teaching developmentally. (7th ed.). Boston, MA: Allyn & Bacon.

Van de Walle, J. A., & Lovin, L. H. (2006). Teaching student-centered mathematics grades K-3. Boston, MA: Pearson Education.

West, L., & Staub, F. (2003). Content focused coaching: Transforming mathematics lessons. Portsmouth, NH: Heinemann.

Wickett, M., Ohanian, S., &  Burns, M. (2002). Teaching arithmetic: Lessons for introducing  division, Grades 3-4. Sausalito, CA: Math Solutions.

Willoughby, S. S. (1997). Functions from kindergarten through sixth grade. Teaching Children Mathematics, Feb., 314-18.

Yeatts, K., Battista, M., Mayberry, S., Thompson, D., & Zawojewski, J. (2004). Navigating through problem solving and reasoning in grade 3. Reston, VA: National Council of Teachers of Mathematics.

Zemelman, S., Daniels, H., & Hyde, A. (2005). Best practices: Today's standards for teaching and learning in America's schools. Portsmouth, NH: Heinemann.    

Van de Walle, J. & Lovin, L.  (2006). Teaching student-centered mathematics grades k-3. Boston, MA: Pearson Education.

Van de Walle, J. & Lovin, L.  (2006). Teaching student-centered mathematics grades 3-5. Boston, MA: Pearson Education.

West, L., & Staub, F. (2003). Content focused coaching: transforming mathematics lessons Portsmouth, NH: Heinemann.

Assessment

  • The first time Ms. Anderson's class visited the science display, they left the classroom at the time shown on this clock. 

They returned to the classroom 55 minutes later. What time did they return to the classroom?

Solution:  2:10

Benchmark: 3.3.3.2

Source: Trends in International Mathematics and Science Study(1999, Item N15).

NCTM. (2005).  Grades 3-5 Mathematics Assessment Sampler. Reston, VA: NCTM.

MCAIII Item Sampler Questions:

  • Mai Ka starts reading a book at the time shown on the clock.

She stops reading 1 hour and 12 minutes later. What time does Mai Ka stop reading?

A.     4:08

B.     4:44

C.     5:05

D.     5:08

Solution: C 5:05

Benchmark: 3.3.3.2

MCA III Item Sampler

  • A movie is 2 hours and 28 minutes long. How many minutes long is the movie?

A.    88 minutes

B.    120 minutes

C.    148 minutes

D.    228 minutes

Solution: C 148 minutes

Benchmark: 3.3.3.2

MCA III Item Sampler

  • The clocks show the times at which George began and finished baseball practice. How long did baseball practice last?

A. 15 minutes

B. 2 hours

C. 2 hours and 15 minutes

D. 20 minutes

Solution:

Benchmark: 3.3.3.1

MCA III Item Sampler

  • John left home at 6:35. He walked for 25 minutes to get to school. What other information do you need to know to determine whether or not John arrived at school on time?

A.  how long school lasts

B.  how fast John walks

C.  the distance to school

D.  the time school begins

Solution: D the time school begins

Benchmark: 3.3.3.2, 3.3.3.2

MCA III Item Sampler

Differentiation

Struggling Learners 

Struggling Learners

Using an empty time line can aid students in finding elapsed time.

For example,

Concrete - Representational - Abstract Instructional Approach

(Adapted from The Access Center: Improving Access for All K-8 Students)

The Concrete-Representational-Abstract Instructional Approach (CRA) is a research-based instructional strategy that has proven effective in enhancing the mathematics performance of students who struggle with mathematics.

The CRA approach is based on three stages during the learning process:

Concrete         -           Representational       -           Abstract

The Concrete Stage is the doing stage. The concrete stage is the most critical in terms of developing conceptual understanding of mathematical skills and concepts.  At this stage, teachers use manipulatives to model mathematical concepts. The physical act of touching and moving manipulatives enables students to experience the mathematical concept at a concrete level.  Research shows that students who use concrete materials develop more precise and comprehensive mental representations, understand and apply mathematical concepts, and are more motivated and on-task.   Manipulatives must be selected based upon connections to the mathematical concept and the students' developmental level.

The Representational Stage is the drawing stage.  Mathematical concepts are represented using pictures or drawings of the manipulatives previously used at the Concrete Stage. Students move to this level after they have successfully used concrete materials to demonstrate conceptual understanding and solve problems.  They are moving from a concrete level of understanding toward an abstract level of understanding when drawing or using pictures to represent their thinking.  Students continue exploring the mathematical concept at this level while teachers are asking questions to elicit student thinking and understanding.

The Abstract Stage is the symbolic stage.  Teachers model mathematical concepts using numbers and mathematical symbols.  Operation symbols are used to represent addition, subtraction, multiplication and division.  Some students may not make a clean transfer to this level. They will work with some symbols and some pictures as they build abstract understanding.  Moving to the abstract level too quickly causes many student errors.   Practice at the abstract level will not lead to increased understanding unless students have a foundation based upon concrete and pictorial representations. 

Additional Resources

Bender, W. (2009). Differentiating math instruction: Strategies that work for k-8 classrooms! Thousand Oaks, CA: Corwin Press.

Dacey, L., & Lynch, J. (2007). Math for all: Differentiating instruction grades 3-5. Sausalito, CA: Math Solutions.

Murray, M. & Jorgensen, J. (2007). The differentiated math classroom: A guide for teachers k-8. Portsmouth, NH: Heinemann.

Small, M. (2009). Good questions: Great ways to differentiate mathematics instruction. New York, NY: Teachers College Press.

Van de Walle, J., Karp, K., & Bay-Williams, J. (2010). Elementary and middle school mathematics: teaching developmentally. (7th ed.) Boston, MA: Allyn & Bacon.

Van de Walle, J. & Lovin, L. (2006). Teaching student-centered mathematics grades k-3. Boston, MA: Pearson Education.

Van de Walle, J. & Lovin, L. (2006). Teaching student-centered mathematics grades 3-5. Boston, MA: Pearson Education.

English Language Learners 
  • Using an empty time line can aid students in finding elapsed time.

For example,

  • Word banks need to be part of the student learning environment in every mathematics unit of study. Refer to these throughout instruction.
  • Word Use vocabulary graphic organizers such as the Frayer model (see below) to emphasize vocabulary words count, first, second, third, etc.

  • Sentence Frames

Math sentence frames provide support that English Language Learners need in order to fully participate in math discussions.  Sentence frames provide appropriate sentence structure models, increase the likelihood of responses using content vocabulary, help students to conceptualize words and build confidence in English Language Learners.

Sample sentence frames related to these benchmarks:

Elapsed time means ________________________________________.

  • When assessing the math skills of an ELL student it is important to determine if the student has difficulty with the math concept or with the language used to describe the concept and conceptual understanding. 

Additional ELL Resource

Bresser, R., Melanese, K., & Sphar, C. (2008). Supporting English language learners in math class, grades k-2. Sausalito, CA: Math Solutions Publications.

Extending the Learning 

Additional Resources

Bender, W. (2009). Differentiating math instruction-strategies that work for k-8 classrooms! Thousand Oaks, CA. Corwin Press.

Dacey, L., & Lynch, J. (2007). Math for all: Differentiating instruction grades 3-5. Sausalito, CA: Math Solutions.

Murray, M. & Jorgensen, J. (2007). The differentiated math classroom: A guide for teachers k-8. Portsmouth, NH: Heinemann.

Small, M. (2009). Good questions: Great ways to differentiate mathematics instruction.  New York, NY: Teachers College Press.

Parents/Admin

Classroom Observation 

Administrative/Peer Classroom Observation

Students are ...

Teachers are ...

telling time to the minute using analog and digital clocks.

providing clock models for student use.

Connecting an Empty Number Line to the process of finding elapsed time.

finding elapsed time within a two hour span.

providing real-life contexts for students to calculate elapsed time.

determining elapsed time in problem solving situations.

providing contexts involving

  • find start time given end time and elapsed time
  • find end time given start time and elapsed time.

 

converting units of time

  • minutes to hours
  • hours to minutes
  • hours to days
  • days to hours
  • days to weeks
  • weeks to days
  • months to years
  • years to months.

 

providing contexts for converting between units of time. Connecting student skills in addition, subtraction and multiplication to converting between units of time.

What should I look for in the mathematics classroom?

(Adapted from SciMathMN,1997)

What are students doing?

  • Working in groups to make conjectures and solve problems.
  • Solving real-world problems, not just practicing a collection of isolated skills.
  • Representing mathematical ideas using concrete materials, pictures and symbols. Students know how and when to use tools such as blocks, scales, calculators, and computers.
  • Communicating mathematical ideas to one another through examples, demonstrations, models, drawing, and logical arguments.
  • Recognizing and connecting mathematical ideas.
  • Justifying their thinking and explaining different ways to solve a problem.

What are teachers doing?

  • Making student thinking the cornerstone of the learning process. This involves helping students organize, record, represent, and communicate their thinking.
  • Challenging students to think deeply about problems and encouraging a variety of approaches to a solution.
  • Connecting new mathematical concepts to previously learned ideas.
  • Providing a safe classroom environment where ideas are freely shared, discussed and analyzed.
  • Selecting appropriate activities and materials to support the learning of every student.
  • Working with other teachers to make connections between disciplines to show how math is related to other subjects.
  • Using assessments to uncover student thinking in order to guide instruction and assess understanding.

For Mathematics Coaches

Chapin, S. and Johnson, A. (2006).  Math matters: Understanding the math you teach: Grades k-8, 2nd edition.  Sausalito, CA: Math Solutions.

Donovan, S., & Bradford, J. (Eds). (2005). How students learn: Mathematics in the classroom. Washington, DC: National Academies Press.

Felux, C., & Snowdy, P. (Eds.). ( 2006). The math coach field guide: Charting your course. Sausalito, CA: Math Solutions.

Sammons, L., (2011).  Building mathematical comprehension: Using literacy strategies to make meaning.  Huntington Beach, CA: Shell Education.

West, L., & Staub, F. (2003). Content focused coaching: Transforming mathematics lessons. Portsmouth, NH: Heinemann.

For Administrators

Burns, M. (Ed). (1998).  Leading the way: Principals and superintendents look at math instruction. Sausalito, CA:  Math Solutions.

Kilpatrick, J., & Swafford, J. (Eds). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.

Leinwand, S. (2000). Sensible mathematics: A guide for school leaders. Portsmouth, NH:  Heinemann.

Lester, F. (2010). Teaching and learning mathematics: Transforming research for school administrators. Reston, VA:  National Council of Teachers of Mathematics.

Seeley, C. (2009). Faster isn't smarter: Messages about math teaching and learning in the 21st century. Sausalito, CA: Math Solutions.

Parents 

Parent Resources

Mathematics handbooks to be used as home references:

Cavanagh, M. (2004). Math to Know: A mathematics handbook. Wilmington, MA:  Great Source Education Group, Inc.

Cavanagh, M. (2006). Math to learn: A mathematics handbook. Wilmington, MA:  Great Source Education Group, Inc.

Helping your child learn mathematics

Provides activities for children in preschool through grade 5

What should I look for in the mathematics program in my child's school? A Guide for Parents developed by SciMathMN

Help Your Children Make Sense of Math

Ask the right questions

In helping children learn, one goal is to assist children in becoming critical and independent thinkers. You can help by asking questions that guide, without telling them what to do.

Good questions, and good listening, will help children make sense of the mathematics, build self-confidence and encourage mathematical thinking and communication. A good question opens up a problem and supports different ways of thinking about it. The best questions are those that cannot be answered with a "yes" or a "no."

Getting Started

What do you need to find out?

What do you know now? How can you get the information? Where can you begin?

What terms do you understand/not understand?

What similar problems have you solved that would help?

While Working

How can you organize the information?

Can you make a drawing (model) to explain your thinking? What are other possibilities?

What would happen if . . . ?

Can you describe an approach (strategy) you can use to solve this?

What do you need to do next?

Do you see any patterns or relationships that will help you solve this?

How does this relate to ...?

Can you make a prediction?

Why did you...?

What assumptions are you making?

Reflecting about the Solution

How do you know your solution (conclusion) is reasonable? How did you arrive at your answer?

How can you convince me your answer makes sense?

What did you try that did not work?

Has the question been answered?

Can the explanation be made clearer?

Responding (helps clarify and extend their thinking)

Tell me more.

Can you explain it in a different way?

Is there another possibility or strategy that would work?

Is there a more efficient strategy?

Help me understand this part...

Adapted from They're counting on us, California Mathematics Council, 1995