1.3.2B Time
Measure the length of an object in terms of multiple copies of another object.
For example: Measure a table by placing paper clips end-to-end and counting.
Tell time to the hour and half-hour.
Identify pennies, nickels and dimes; find the value of a group of these coins, up to one dollar.
Overview
Standard 1.3.2 Essential Understandings
First grade students move beyond direct comparison as they develop an understanding of linear measurement. They measure length by laying multiple copies of a unit end to end and counting the units. For example, the pencil is eight blocks long. First graders come to understand that using a larger unit when measuring means you will use fewer units, and using a smaller unit when measuring means you will use more units. When objects are being compared they know that the units used to measure each object must be the same size.
When first graders use calendars or sequence events in stories, they are using measures of time in a real context. First graders learn to tell time to the hour and half-hour using analog and digital clocks. They relate these times to events during their day. For example, we eat lunch at 12:30 pm.
First graders identify and know the value of dimes, nickels and pennies. They are able to count groups of dimes, nickels and pennies up to a dollar.
All Standard Benchmarks
1.3.2.1 Measure the length of an object in terms of multiple copies of another object.
1.3.2.2 Tell time to the hour and half-hour.
1.3.2.3 Identify pennies, nickels and dimes; find the value of a group of these coins, up to one dollar.
Benchmark Group B
1.3.2.2 Tell time to the hour and half-hour.
What students should know and be able to do [at a mastery level] related to this benchmark:
- Tell time to the hour and half-hour.
- Use the expressions "o'clock" and "half past."
Work from previous grades that supports this new learning includes:
- Can think of time in terms of duration of an event; for example, which ball bounces longer.
- Can make comparisons of events that last different lengths of time. They can compare duration of events in their lives like brushing teeth, eating dinner, or playing during recess.
NCTM Standards
Understand measurable attributes of objects and the units, systems, and processes of measurement
PreK-2 Expectations
- Recognize the attributes of length, volume, weight, area, and time.
- Compare and order objects according to these attributes.
- Understand how to measure using nonstandard and standard units.
- Select an appropriate unit and tool for the attribute being measured.
Apply appropriate techniques, tools, and formulas to determine measurements
PreK-2 Expectations
- Measure with multiple copies of units of the same size, such as paper clips layed end to end.
- Use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meter stick.
Common Core State Standards
Measure lengths indirectly and by iterating length units.
1.MD.1. Order three objects by length; compare the lengths of two objects indirectly by using a third object.
1.MD.2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
Tell and write time.
1.MD.3. Tell and write time in hours and half-hours using analog and digital clocks.
Misconceptions
Students may think...
- the hour hand and the minute hand are interchangeable.
- the hour numerals are also the minute numerals on an analog clock.
Resources
Teacher Notes
- Students may need support in further development of previously studied concepts and skills.
- Learning about time should be taught throughout the year rather than as an isolated unit.
- Some lessons should focus on the duration of time while others focus on the mechanics of reading clocks.
- Students should identify events that occur in the morning, afternoon, evening and night.
- Students should see the calendar as a device for recording and tracking time, not just a place where patterns occur.
- Refer to the time on the clock throughout the day. This allows students to link time and events.
- Use phrases to describe time including almost _______, about _______, just before _______, just after ________, a little after ________, half past _______, between _______.
- The following is a suggested approach to help students read analog clocks, adapted from Van deWalle, J., & Lovin, L. (2006). Teaching student-centered mathematics grades k-3. Boston, MA: Pearson Education:
- Begin with a one-handed clock using language like, "It's about 6 o'clock," "It's a little past 3 o'clock," "It is halfway between 8 o'clock and 9 o'clock."
- Talk about what happens to the big hand as the little hand goes from one hour to the next. When the big hand is at 12, the hour hand is pointing exactly to a number. If the hour hand is halfway between, about where would the minute hand be?
- Use two real clocks, one with only an hour hand and one with two hands. During the day, point out the one-handed clock. Talk about the time in approximate language. Have students predict where the minute had should be when time is on the hour or half-hour.
- Students may need support in further development of previously studied concepts and skills.
- 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)
This lesson provides an introduction to and practice with the concept of time. The activities focus students' attention on the attributes of time and enables students at varying levels to develop knowledge and skills in using time.
Instructional Activities
Create a deck of cards like the example below. Each student will need a card. Any extra cards will need to be distributed as the cards will circle back to the beginning card. (If the first card is I have 5:00, who has 1:30, the last card will be who has 5:00?) This game is a great way to practice telling time. For more information, visit.
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.
New Vocabulary
"Vocabulary literally is the key tool for thinking."
Ruby Payne
hour: unit of time, equal to 60 minutes; 24 hours make 1 day
half hour: unit of time, equal to 30 minutes
half-past: unit of time, equal to 30 minutes
minute: unit of time, equal to 60 seconds; 60 minutes make 1 hour
before:
after:
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.
|
This is a _________. |
This is not a ________. |
|
|
|
Vocabulary Strips: Vocabulary strips give students a way to organize critical information about mathematics vocabulary words.
|
word |
definition |
illustration
|
|
word
analog clock
|
definition
a clock that uses the numerals 1 to 12 plus rotating hands to show the time
|
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.
Reflection - Critical Questions regarding the teaching and learning of these benchmarks.
What are the key ideas related to telling time at the first grade level? How do student misconceptions interfere with mastery of these ideas?
What experiences do students need in order to tell time to the hour and half hour successfully?
What common errors do first graders make when telling time?
When checking for student understanding of telling time at the first 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.
How can teachers assess student learning related to these benchmarks?
How are these benchmarks related to other benchmarks at the first 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.
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.
Sammons, L., (2011). Building mathematical comprehension: Using literacy strategies to make meaning. Huntington Beach, CA: Shell Education.
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.
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.
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., Kharas, K., & Burns, M. (2002). Grades 3-5 lessons for algebraic thinking. Sausalito, CA: Math Solutions Publications.
Assessment
Performance assessment:
- Show students various times on the hour and half-hour and ask them to read the time.
Solution: Student correctly reads the time shown on the clock.
Benchmark: 1.3.2.2
- Write the time shown on these clocks:
Solution: Student correctly reads the time shown on the clock.
Benchmark: 1.3.2.2
Differentiation
One handed clocks. Helps students focus on just the hour hand, and can be used to highlight the concept of half past the hour.
Concrete - Representational - Abstract Instructional Approach
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.
Adapted from The Access Center: Improving Access for All K-8 Students.
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 k-2. 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.
- Language for telling time can be especially confusing. Words like half-past, half-hour, or 30 minutes will need to be explained and illustrated during instruction. Students will need to use clocks with movable hands as they construct the concept of telling time.
- Word banks need to be part of the student learning environment in every mathematics unit of study. Refer to these throughout instruction.
- Use vocabulary graphic organizers such as the Frayer model (see below) to emphasize vocabulary words such as clock, time, hour, half hour and minute.
- Sentence Frames
Math sentence frames provide support 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:
|
It's about ________________ o' clock. |
|
It's almost ________________. |
|
It is just before _______________. |
|
It's between __________and ____________. |
|
It's just after ______________________. |
- 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 Resources
Bresser, R., Melanese, K., & Sphar, C. (2008). Supporting English language learners in math class, grades k-2. Sausalito, CA: Math Solutions Publications.
Students can extend their learning to the quarter hour before and after the hour. Children can demonstrate the relationship between analog and digital clocks, by writing the times they read on analog clocks.
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 k-2. 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
|
Students are ... |
Teachers are ... |
|
reading the time on analog and digital clocks. |
providing opportunities to read a clock throughout the school day. |
|
showing a given time on a clock. |
using the language of time: half past, thirty minutes past, etc. |
|
understanding the meanings of half-past or thirty minutes past and connecting time notation to these ideas. |
connecting multiple representations of time. |
Additional Resources
For Mathematics Coaches
Chapin, S. and Johnson, A. (2006). Math matters: Understanding the math you teach: Grades k-8. (2nd ed.). 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.
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.