All the resources on this page come from the GADOE Framework 1st Grade Unit 3 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 3 Overview

In this unit, students will:

• Explore, understand, and apply the commutative and associative properties as strategies for solving addition problems.

• Share, discuss, and compare strategies as a class.

• Connect counting on to solving subtraction problems. For the problem “15 – 7 = ?” they think about the number they have to count on from 7 to get to 15.

• Work with sums and differences less than or equal to 20 using the numbers 0 to 20.

• Identify and then apply a pattern or structure in mathematics. For example, pose a string of addition and subtraction problems involving the same three numbers chosen from the numbers 0 to 20, such as 4 + 13 = 17 and 13 + 4 = 17.

• Analyze number patterns and create conjectures or guesses.

• Choose other combinations of three numbers and explore to see if the patterns work for all numbers 0 to 20.

• Understand that addition and subtraction are related and that subtraction can be used to solve problems where the addend is unknown.

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

• Organize and record results using tallies and tables.

• Determine the initial and the change unknown.

Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, takeapart, and compare situations. They will use these models to develop meaning for the operations of addition and subtraction and to develop strategies to solve arithmetic problems with these operations. Prior to first grade students should recognize that any given group of objects (up to 10) can be separated into sub groups in multiple ways and remain equivalent in amount to the original group (Ex: A set of 6 cubes can be separated into a set of 2 cubes and a set of 4 cubes and remain 6 total cubes).

Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., ―making tens) to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction. (Ohio DOE)

The standard MGSE1.OA.3 expects teachers to use their understanding of the commutative and associative properties when teaching addition. The students are NOT expected to name or memorize these properties. First grade teachers are laying the foundation and building an understanding of these properties so that students can have formal discussions and utilize names of the properties in later grades.

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

Represent and solve problems involving addition and subtraction.

MGSE1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.1

Understand and apply properties of operations and the relationship between addition and subtraction.

MGSE1.OA.3. Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

MGSE1.OA.4. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.

Add and subtract within 20

MGSE1.OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

MGSE1.OA.6 Add and subtract within 20. a. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). b. Fluently add and subtract within 10.

Work with addition and subtraction equations

MGSE1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. The equal sign describes a special relationship between two quantities. In the case of a true equation, the quantities are the same.

MGSE1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = □ – 3, 6 + 6 = Δ.

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

• Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers.

• Students use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations. They will use these models to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations.

• Students understand connections between counting and addition/subtraction (e.g., adding two is the same as counting on two).

• Students use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems within 20.

• By comparing a variety of solution strategies, students will build an understanding of the relationship between addition and subtraction.

• Students think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones).

ESSENTIAL QUESTIONS

• How can we represent a set of objects using numerals?

• What happens when we join two quantities or take one from another?

• How can we find the total when we join two quantities?

• How can we find what is left when we take one quantity from another?

• How can we find the difference when we compare one quantity to another?

• How can we represent problem situations?

• What happens when we change the order of numbers when we add (or subtract)? Why?

• How can we show that addition and subtraction are related through fact families?

• How can we use different combinations of numbers and operations to represent the same quantity?

• How can we represent a number in a variety of ways?

CONCEPTS AND SKILLS TO MAINTAIN

• Represent addition and subtraction with objects, fingers, mental images, and drawings

• Solve addition and subtraction word problems

• Add and subtract within 10

• Decompose numbers that are less than or equal to 10 in more than one way

• Make a ten from any given number 1-9

• Fluently add and subtract within 5

STRATEGIES FOR TEACHING AND LEARNING

Addition and Subtraction in Elementary School

• The strategies that students use to solve problems provide important information concerning number sense, and place value.

• It is important to look at more than the answers students get. The strategies used provide useful information about what problems to give the next day and how to differentiate instruction.

• It is important to relate addition and subtraction.

• Student created strategies provide reinforcement of place value concepts. Traditional algorithms can actually confuse the understanding of place value.

• Student created strategies are built on a student’s actual understanding, instead of on what the book says or what we think/hope they know!

Students make fewer errors with invented strategies, because they are built on understanding rather than memorization. Students use various counting strategies, including counting all, counting on, and counting back with numbers up to 20. This standard calls for students to move beyond counting all and become comfortable at counting on and counting back. The counting all strategy requires students to count an entire set. The counting and counting back strategies occur when students are able to hold the start number in their head and count on from that number

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

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.pdf

SELECTED TERMS AND SYMBOLS

The following terms and symbols are often misunderstood. This is not an inclusive list and items 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.

• addition and subtraction within 5, 10, 20, 100, or 1000.

• additive identity property of 0

• associative property of addition

• commutative property

• computation strategy

• counting on

• number line diagram

• strategies for addition

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 5 are addition: counting all and counting on; doubles/near doubles; and making tens using dot images, ten-frames, Rekenreks, double ten-frames, and number sentences. In addition, Number Talks focusing on making landmark or friendly numbers; breaking each number into its place value; compensation; and adding up chunks are suggested. Specifics on these Number Talks can be found on pages 98-201 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.