All the resources on this page come from the GADOE Framework 1st Grade Unit 4 Overview. Reviewing this information before or during planning can help ensure your instruction is aligned with the standards and is at the depth expected.

Unit 4 Overview

In this unit students will:

• Develop an understanding of linear measurement.

• Measure lengths as iterating length units.

• Tell and write time to the hour and half hour.

• Represent and interpret data.

The measure of an attribute is a count of how many units are needed to fill, cover, or match the attribute of the object being measured. Students need to understand what a unit of measure is and how it is used to find a measurement. They need to predict the measurement, find the measurement, and then discuss the estimates, errors, and the measuring process. It is important for students to measure the same object with differently sized units.

Students need to make their own measuring tools. For instance, they can place inch cubes end to end along a piece of cardboard, make marks at the endpoints of the clips and color in the spaces. Students can now see that the spaces represent the unit of measure, not the marks or numbers on a ruler. Eventually they write numbers in the center of the spaces. Students should know that the numbers on the ruler represent units of measurement. Learning to use a ruler accurately and with understanding requires becoming comfortable with the meaning of the units on the ruler. Compare and discuss two measurements of the same distance, one found by using a ruler and one found by aligning the actual units end to end, as in a chain of inch cubes. Students should also measure lengths that are longer than a ruler. The units of measure used, such as paper clips, should correspond with a standard unit of measure (Ex. Each paper clip is 1-inch-long) and this correspondence should be stated to the students explicitly by the teacher. Further info: Investigating Measurement Knowledge, Jenni K. McCool and Carol Holland May 2012, Volume 18, Issue 9, Page 542 See more at: http://www.nctm.org/publications/article.aspx?id=33156#sthash.o6B8Bisy.dpuf

Have students use reasoning to compare measurements indirectly. To order the lengths of Objects A, B and C, examine, then compare the lengths of Object A and Object B and the lengths of Object B and Object C. The results of these two comparisons allow students to use reasoning to determine how the length of Object A compares to the length of Object C. For example, to order three objects by their lengths, reason that if Object A is smaller than Object B and Object B is smaller than Object C, then Object A has to be smaller than Object C. The order of objects by their length, from smallest to largest, would be Object A - Object B - Object C.

Although the units in this instructional framework emphasize key standards and big ideas at specific times of the year, routine topics such as counting, time, money, positional words, patterns, and tally marks should be addressed on an ongoing basis through the use of calendars, centers, and games. Calendar instruction should be a part of daily mathematics instruction. Students should be able to determine the day before and after the current day, as well as identify the day after a particular passage of time.

Students are likely to experience some difficulties learning about time. On an analog clock, the shorter hand indicates approximate time to the nearest hour and the focus is on where it is pointing. The longer hand shows minutes before and after an hour and the focus is on distance that it has gone around the clock or the distance yet to go for the hand to get back to the top or the number 12. It is easier for students to read times on digital clocks, but these do not relate progression of time very well.

Students need to experience a progression of activities for learning how to tell time. Begin by using a one-handed clock (hour handed) to tell times in hour and half-hour intervals. Then discuss what is happening to the unseen minute hand. Next, use two clocks, one with the minute hand removed, and compare the hands on the clocks. Students can predict the position of the missing minute hand to the nearest hour or half-hour and check their prediction using the two-handed clock. They can also predict the display on a digital clock given a time on a one- or two-handed analog clock and vice versa.

Have students tell the time for events in their everyday lives to the nearest hour or half hour. Make a variety of models for analog clocks. One model uses a strip of paper marked in half hours. Connect the ends with tape to form the strip into a circle.

For more detailed information about unpacking the content standards, unpacking a task, math routines and rituals, maintenance activities and more, please refer to the Grade Level Overview.

STANDARDS FOR MATHEMATICAL PRACTICE

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. Students are expected to:

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

***Mathematical Practices 1 and 6 should be evident in EVERY lesson***

STANDARDS FOR MATHEMATICAL CONTENT

MGSE1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.

MGSE1.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. (Iteration)

MGSE1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks.

MGSE1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

BIG IDEAS

• Telling time to the hour and half hour using analog and digital clocks.

• Objects may be compared according to length.

• Objects may be used to determine length, but must correspond with a standard unit of measurement.

• Tools may be created to measure length.

• Organize and represent data collected from measurement.

• Ask and answer questions related to measurement data.

ESSENTIAL QUESTIONS

• How can we measure the length of an object?

• What can we use to measure objects?

• How can we tell which of two objects is longer than the other?

• How can we order a group of objects by their length?

• How does using an object help us when measuring another object?

• Why are the measurements of classmates different?

• Why would an estimate be helpful when measuring?

• When is an estimate good enough? When should I measure instead of using an estimate?

• How can we compare the length of a set of objects?

• How are objects used to measure other objects?

• How are measuring units selected?

• How do measurements help compare objects?

• Why is telling time important?

• How do you use time in your daily life?

• How can we measure time?

• What does the hour hand on a clock tell us?

• Why is it important to know the difference between the two hands?

• Why do we need to be able to tell time?

• How do we show our thinking with pictures and words?

• How does time impact my day?

• What does the minute hand on a clock tell us?

• What do I know about time?

• Why do people collect data?

• Are there different ways to display data?

• What can we learn from our data?

CONCEPTS/SKILLS TO MAINTAIN

• Counting to 100

• Sorting

• Write and represent numbers through 20

• Comparing sets of objects (equal to, longer than, shorter than)

• One to one correspondence

• Equivalence

• Basic geometric shapes

• Modeling addition and subtraction

• Estimating using 5 and 10 as a benchmark

• Measurement: comparing and ordering two or more objects

STRATEGIES FOR TEACHING AND LEARNING

Developing understanding of linear measurement and measuring lengths as iterating length units. MGSE1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object. Instructional Strategies This standard calls for students to indirectly measure objects by comparing the length of two objects by using a third object as a measuring tool. This concept is referred to as transitivity.

Measurement units share the attribute being measured. Students need to use as many copies of the length unit as necessary to match the length being measured. For instance, use large footprints with the same size as length units. Place the footprints end to end, without gaps or overlaps, to measure the length of a room to the nearest whole footprint. Use language that reflects the approximate nature of measurement, such as the length of the room is about 19 footprints. Students need to also measure the lengths of curves and other distances that are not straight lines.

Tell and write time
MGSE1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks.

Instructional Strategies

This standard calls for students to read both analog and digital clocks and then orally tell and write the time. Times should be limited to the hour and the half-hour. Students need experiences exploring the idea that when the time is at the half-hour the hour hand is between numbers and not on a number. Further, the hour is the number before where the hour hand is. For example, in the clock below, the time is 8:30. The hour hand is between the 8 and 9, but the hour is 8 since it is not yet on the 9.

Represent and interpret data
MGSE1.MD.4

Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Instructional Strategies

This standard calls for students to work with categorical data by organizing, representing and interpreting data. Students should have experiences posing a question with 3 possible responses and then work with the data that they collect. For example: Students pose a question and the 3 possible responses: Which is your favorite flavor of ice cream? Chocolate, vanilla, or strawberry? Students collect their data by using tallies or another way of keeping track. Students organize their data by totaling each category in a chart or table. Picture and bar graphs are introduced in 2nd Grade.

Students interpret the data by comparing categories.
Examples of comparisons:

• What does the data tell us? Does it answer our question?

• More people like chocolate than the other two flavors.

• Only 5 people liked vanilla.

• Six people liked Strawberry.

• 7 more people liked Chocolate than Vanilla.

• The number of people that liked Vanilla was 1 less than the number of people who liked Strawberry.

• The number of people who liked either Vanilla or Strawberry was 1 less than the number of people who liked chocolate.

For more detailed information about unpacking the content standards, unpacking a task, math routines and rituals, maintenance activities and more, please refer to the Grade Level Overview.

Fluency: Procedural fluency is defined as skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. Fluent problem solving does not necessarily mean solving problems within a certain time limit, though there are reasonable limits on how long computation should take. Fluency is based on a deep understanding of quantity and number.

Deep Understanding: Teachers teach more than simply “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives. Therefore, students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of foundational mathematics concepts by applying them to new situations, as well as writing and speaking about their understanding.

Memorization: The rapid recall of arithmetic facts or mathematical procedures. Memorization is often confused with fluency and automaticity. Fluency implies a much richer kind of mathematical knowledge and experience.

Number Sense: Students consider the context of a problem, look at the numbers in a problem, make a decision about which strategy would be most efficient in each particular problem. Number sense is not a deep understanding of a single strategy, but rather the ability to think flexibly between a variety of strategies in context.

Fluent students:

● flexibly use a combination of deep understanding, number sense, and memorization.

● are fluent in the necessary baseline functions in mathematics so that they are able to spend their thinking and processing time unpacking problems and making meaning from them.

● are able to articulate their reasoning.

● find solutions through a number of different paths.

For more about fluency, see: http://www.youcubed.org/wp-content/uploads/2015/03/FluencyWithoutFear-2015.pdf and: https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/nctm-timedtests.pdf

SELECTED TERMS AND SYMBOLS

The following terms and symbols are often misunderstood. These concepts are not an inclusive list and should not be taught in isolation. However, due to evidence of frequent difficulty and misunderstanding associated with these concepts, teachers should pay particular attention to them and how their students are able to explain and apply them. The terms below are for teacher reference only and are not to be memorized by students. Teachers should present these concepts to students using models and real life examples. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, or numbers. • Analog • Compare • Data • Digital • Estimate • Graph • Hands (clock) • Hour • Length • Minute • Sorting rule

http://www.corestandards.org/Math/Content/mathematics-glossary/glossary

FALS

The linked Formative Assessment lesson is designed to be part of an instructional unit. This assessment should be implemented approximately two-thirds of the way through this instructional unit and is noted in the unit task table. This assessment can be used at the beginning of the unit to ascertain student needs. The results of this task should give you pertinent information regarding your students learning and help to drive your instruction for the remainder of the unit.

NUMBER TALKS

In order to be mathematically proficient, today’s students must be able to compute accurately, efficiently, and flexibly. Daily classroom number talks provide a powerful avenue for developing “efficient, flexible, and accurate computation strategies that build upon the key foundational ideas of mathematics.” (Parrish, 2010) Number talks involve classroom conversations and discussions centered upon purposefully planned computation problems.

In Sherry Parrish’s book, Number Talks: Helping Children Build Mental Math and Computation Strategies, teachers will find a wealth of information about Number Talks, including:

• Key components of Number Talks

• Establishing procedures

• Setting expectations

• Designing purposeful Number Talks

• Developing specific strategies through Number Talks

There are four overarching goals upon which K-2 teachers should focus during Number Talks. These goals are:

1. Developing number sense

2. Developing fluency with small numbers

3. Subitizing

4. Making Tens The teacher should continue with the Number Talks suggested in Unit 3.

Suggested Number Talks for Unit 3 are fluency with 6, 7, 8, 9, and 10; and counting all and counting on using dot images, tenframes, Rekenreks, double ten-frames, and number sentences. When students are ready, include Number Talks for addition, including doubles/near doubles and making tens. Specifics on these Number Talks can be found on pages 74-117 of Number Talks: Helping Children Build Mental Math and Computation Strategies.

WRITING IN MATH

The Standards for Mathematical Practice, which are integrated throughout effective mathematics content instruction, require students to explain their thinking when making sense of a problem (SMP 1). Additionally, students are required to construct viable arguments and critique the reasoning of others (SMP 2). Therefore, the ability to express their thinking and record their strategies in written form is critical for today’s learners. According to Marilyn Burns, “Writing in math class supports learning because it requires students to organize, clarify, and reflect on their ideas--all useful processes for making sense of mathematics. In addition, when students write, their papers provide a window into their understandings, their misconceptions, and their feelings about the content.” (Writing in Math. Educational Leadership. Oct. 2004 (30).) The use of math journals is an effective means for integrating writing into the math curriculum.

Math journals can be used for a variety of purposes. Recording problem solving strategies and solutions, reflecting upon learning, and explaining and justifying thinking are all uses for math journals. Additionally, math journals can provide a chronological record of student math thinking throughout the year, as well as a means for assessment than can inform future instruction.

The following website provides a wealth of information and grade specific activities for math journaling: http://www.k-5mathteachingresources.com/math-journals.html. Though this is not a free site, there are some free resources that are accessible.