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All the resources on this page come from the GADOE Framework 1st Grade Unit 2 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 2 Overview
Unit 2 Overview
The Overview is designed to bring focus to the standards so that educators can build curriculum and 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. Many of the skills and concepts in this unit are readdressed from Unit 1. Even though they are revisited, it is important to note that they are not necessarily presented in the same way as in Unit 1.
In this unit, students will:
• rote count forward to 120 by counting on from any number less than 120.
• represent a quantity using numerals.
• locate 0-100 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, ten more (or one less, ten 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 then work with the data that they collect.
• begin working with dimes and understand a dime is worth ten cents.
• explore counting by tens with dimes.
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, 0-99 chart, 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 practice counting by tens they should also think in terms of dimes and the relationship of a dime’s worth being ten cents. The use of a 99 chart is an extremely useful tool to help students identify number relationships and patterns. Listed below are several reasons that support use of a 99 chart:
• A 0-99 chart begins with zero where a hundred chart begins with 1. We need to include zero because it is one of the ten digits and just as important as 1-9.
• A 100 chart puts the decade numerals (10, 20, 30, etc.) in a different row than its corresponding numerals. For instance, on a hundred chart, 20 appears at the end of the teens row. The number 20 is the beginning of the 20’s decade.
• A 0-99 chart ends with the last two-digit number, 99, whereas a hundred chart ends in 100. 100 could begin a new chart because it is the first three-digit number.
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. Students in first grade could also group pennies and dimes together to see the relationship between a penny being worth one cent and a dime being worth ten cents.
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 routines, centers, and games. Understanding the concept of a coin’s name and its value should be practiced throughout the year. Although the standard includes dimes and pennies, teachers may also use nickels, as they naturally relate to counting by fives. This first unit should establish these routines, allowing students to gradually understand the concept of number and time.
Students in first grade are only asked to construct tables and charts. Picture graphs and bar graphs are not introduced until 2nd grade. In first grade students can use money as a manipulative for patterns, skip counting and any counting additional counting activities.
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.
MGSE1.NBT.7 Identify dimes, and understand ten pennies can be thought of as a dime. (Use dimes as manipulatives in multiple mathematical contexts.)
Big Ideas
• Students can count on starting at any number less than 120.
• Read, write, and represent a number of objects with a written numeral.
• Quantities can be compared using matching sets and words.
• Recognize and understand patterns on a 99 chart.
• 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 solved by collecting and interpreting data.
• A dime is worth 10 cents, and its value is equivalent to ten pennies.
• Represent and count quantities up to 120 in multiple ways, pictures, and numerals.
• Use counters and pictures to represent numbers in terms of tens and ones
• Interpret tables and charts
Coins are explicitly taught, beginning with the penny in Kindergarten and the dime in first grade. The connections to patterns and skip counting should be made using coins. Coins can be used as manipulatives for patterns, skip counting and counting. Note that skip counting is not formally addressed until grade 2, but as students develop an understanding of number and the relationships between numbers, they may naturally work with this concept. While the standard references dimes and pennies, teachers are encouraged to include nickels, as they fall naturally in the progression of coin use/recognition.
ESSENTIAL QUESTIONS
• How can patterns help us understand numbers?
• How can we organize and display the data we collected into three categories to create a graph?
• How can we represent a number with tens and ones?
• How can we use counting to compare objects in a set?
• How can we use tally marks to help represent data in a table or chart?
• How do we know if a set has more or less?
• How do we know where a number lies on a number line?
• How does a graph help us better understand the data collected?
• What do the numerals represent in a two or three-digit number?
• What is an effective way of counting a large quantity of objects?
• What patterns can be found on the 0-99 chart?
• What strategies can be used to find a missing number?
• What strategy can we use to efficiently count a large quantity of objects?
• What is estimating and when can you use it?
• What do a 0-99 chart and number line have in common?
• What is the value of a dime? What is the value of a penny?
CONCEPTS/SKILLS TO MAINTAIN
• Comparing two sets of objects (equal to, more than, or less than)
• Count forward from a given number
• Counting to 100 by ones and tens
• Equivalence
• Number words
• One to one correspondence
• Sorting
• Subitizing
• Unitizing tens
• Writing and representing numbers through 100
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
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.
MGSE1.NBT.7 Identify dimes, and understand ten pennies can be thought of as a dime. (Use dimes as manipulatives in multiple mathematical contexts.)
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 groupable (examples: dried beans and a small cup for 10 beans, linking cubes, plastic chain links) and 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, and number 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. Time should also be spent on the dime and its value of 10 pennies. Make connections to tens and the dime and also when skip counting on a 99 chart or hundreds chart. Use Number Talks as a way to reinforce the dime and understanding it being the same as ten pennies. Time is now spent on the penny in Kindergarten and understanding it being worth one. Teachers are encouraged to also include the nickel and its value of 5 pennies in the same manner.
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. • chart • compare • counting on • data • equal to • less than • more than • number line • number patterns • number relationships • same • table • tally mark • ten frame • unitizing • dime
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
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 2 are fluency with 6, 7, 8, 9, and 10; and counting all and counting on using dot images, ten-frames, and Rekenreks, double ten frames and number sentences.
Specifics on these Number Talks can be found on pages 74-106 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.
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