All the resources on this page come from the GADOE Framework 1st Grade Unit 1 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 1 Overview

The Overview is designed to bring focus to the standards so that educators may use them to build their curriculum and to guide instruction. 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. In this unit, students will:

• Establish daily math routines to be carried out throughout the year, such as lunch count, daily questions, calendar activities, working with a 0-99 chart, etc.

• Rote count forward to 120 by Counting On from any number less than 120.

• Represent the number of a quantity using numerals.

• Locate 0-120 on a number line.

• Use the strategies of counting on and counting back to understand number relationships.

• Explore with the 99-chart to see patterns between numbers, such as all of the numbers in a column on the hundreds chart have the same digit in the ones place, and all of the numbers in a row have the same digit in the tens place.

• Read, write and represent a number of objects with a written numeral (number form or standard form).

• Build an understanding of how the numbers in the counting sequence are related—each number is one more or one less than the number before or after.

• Work with categorical data by organizing, representing and interpreting data using charts and tables.

• Pose questions with 3 possible responses and work with the data that they collect.

All mathematical tasks and activities should be meaningful and interesting to students. Posing relevant questions, collecting data related to those questions, and analyzing the data creates a real-world connection to counting. The meaning students attach to counting is the key conceptual idea on which all other number concepts are developed. Students begin thinking of counting as a string of words, but then they make a gradual transition to using counting as a tool for describing their world. They must construct the idea of counting using manipulatives and have opportunities to see numbers visually (dot cards, tens frames, number lines, hundreds-charts, arithmetic rack- ex: small frame abacus and physical groups of tens and ones). To count successfully, students must remember the rote counting sequence, assign one counting number to each object counted, and at the same time have a strategy for keeping track of what has already been counted and what still needs to be counted. Only the counting sequence is a rote procedure. Most students can count forward in sequence. Counting on and counting back are difficult skills for many students. Students will develop successful and meaningful counting strategies as they practice counting and as they listen to and watch others count. They should begin using strategies of skip counting by 2’s, 5’s, and 10’s.

As students in first grade begin to count larger amounts, they should group concrete materials into tens and ones to keep track of what they have counted. This is an introduction to the concept of place value. Students must learn that digits have different values depending on their position in numbers.

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 tallying should be addressed on an ongoing basis through the use of calendars, centers, and games. This first unit should establish these routines, allowing students to gradually understand the concept of number and time.

Picture graphs and bar graphs are not introduced until 2nd grade. Students in first grade are asked to construct tables and charts. Teachers may introduce vocabulary words to students in first grade as a pre-teaching opportunity.

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

Extend the counting sequence.

MGSE1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

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.

BIG IDEAS

• Count on starting at any number less 100 and continue to 120.

• Read, write and represent a number of objects with a written numeral.

• Quantities can be compared using matching and words.

• Recognize and understand patterns on a 99 chart (tens and ones).

• A number line can represent the order of numbers.

• Problems can be solved in different ways.

• Important information can be found in representations of data such as tallies, tables, and charts.

• Tables and charts can help make solving problems easier.

• Questions can be answered by collecting and interpreting data.

ESSENTIAL QUESTIONS

Please note: some of the essential questions can be used for various task/lesson specific while some are overarching. These essentials questions are given as a guide for teachers to use throughout the unit as deemed appropriate.

• How can we use counting to compare objects in a set?

• How do we know if a set has more or less?

• How can tally marks represent a set?

• How can I use a ten frame to represent a number?

• How can tally marks help us organize our counting?

• How can we use tally marks to help represent data in a table or chart?

• How do tables and charts help us organize our thinking?

• How can we represent a number using tens and ones?

• How can I use a number line to help me count? Or count on?

• How can we collect data?

• How can number benchmarks build our understanding of numbers?

• How can large quantities be counted efficiently?

• What do less than, greater than, and equal to mean?

CONCEPTS/SKILLS TO MAINTAIN

Kindergarten GSE Math Standards are linked as a reference for ample understanding of standards taught in Kindergarten.

• Counting to 100 by ones and tens

• Count forward beginning from a number other than one

• Represent a number of objects with a numeral

• Writing numbers through 20

• Comparing sets of objects (equal to, more than, or less than)

• One to one correspondence

• Equivalence

• Using five or ten as a benchmark

• Compose and decompose numbers 11-19

• 11-19 are composed of a ten and some ones

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. 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.p

STRATEGIES FOR TEACHING AND LEARNING

Extend the counting sequence.

MGSE1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Instructional Strategies

In first grade, students build on their counting to 100 by ones and tens beginning with numbers other than 1 as they learned in Kindergarten. Students can start counting at any number less than 120 and continue to 120. Although not required by the standards, it is important for students to also count backwards from a variety of numbers. It is important for students to connect different representations for the same quantity or number. Students use materials to count by ones and tens to build models that represent a number. They connect these models to the number word they represent as a written numeral. Students learn to use numerals to represent numbers by relating their place-value notation to their models.

They build on their experiences with numbers 0 to 20 in Kindergarten to create models for 21 to 120 with grouped (examples: dried beans and a small cup for 10 beans, linking cubes, plastic chain links) and pre-grouped materials (examples: base-ten blocks, dried beans and beans sticks (10 beans glued on a craft stick), strips (ten connected squares) and squares (singles), ten-frame, place-value mat with ten-frames, hundreds chart and blank hundreds chart). Students represent the quantities shown in the models by placing numerals in labeled hundreds, tens, and ones columns. They eventually move to representing the numbers in standard form, where the group of hundreds, tens, then singles shown in the model matches the left-to-right order of digits in numbers. Listen as students orally count to 120 and focus on their transitions between decades and the century number. These transitions will be signaled by a 9 and require new rules to be used to generate the next set of numbers. Students need to listen to their rhythm and pattern as they orally count so they can develop a strong number word list. Extend counting charts by attaching a blank chart and writing the numbers 120. Students can use these charts to connect the number symbols with their count words for numbers 0 to 120. Teachers may post the number words in the classroom to help students read and write them, demonstrating another way to represent a numeral for students.

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

In first grade, the students will sort a collection of items up to three categories. They will pose questions about the number of items in each category, the total number of items, and compare the number of items in categories. The total number of items to be sorted should be less than or equal to 100 to allow for sums and differences less than or equal to 100. This standard lends itself to the integration of first grade geometry concepts. For example, provide categories for students to sort identical collections of different geometric shapes. After the shapes have been sorted, pose these questions: How many triangles are in the collection? How many rectangles are there? How many triangles and rectangles are there? Which category has the most items? How many more? Which category has the least? How many less? Students can create a Venn diagram after they have had multiple experiences with sorting objects according to given categories. The teacher should model a Venn diagram several times before students make their own. A Venn diagram in Grade 1 has two or three labeled loops or regions (categories). Students place items inside the regions that represent a category that they chose. Items that do not fit in a category are placed outside of the loops or regions. Students can place items in a region that overlaps the categories if they see a connection between categories. Ask questions that compare the number of items in each category and the total number of items inside and outside of the regions.

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, instructors 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 the students. Teachers should present these concepts to students with 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. • benchmark • chart • compare • counting on • data • equal to • less than • more than • number line • same • table • tally mark • ten frame

FAL

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

Video available: https://www.georgiastandards.org/Georgia-Standards/Pages/Implement-Math-TaskClassroom-Videos/What-Does-it-Look-Like-When-you-Implement-a-Task.aspx 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

Suggested Number Talks for Unit 1 are fluency with 6, 7, 8, 9, and 10 using dot images, ten-frames, and Rekenreks. Specifics on these Number Talks can be found on pages 74-96 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.