COURSE TITLE

Grade 1- Math

LENGTH

Full Year

DEPARTMENT

STEM Department

SCHOOL

Lincoln School

Washington School

Primary Content

Mathematics

 Initial Board of Education Approval Date (Born on): 6/24/2024

Revisions:  

Embedded Content

 Career Readiness, Life Literacies and Key Skills

 Initial Board of Education Approval Date (Born on):   6/24/2024

Computer Science and Design Thinking

 Initial Board of Education Approval Date (Born on):   6/24/2024

Grade 1- Math

I.        Introduction/Overview/Philosophy

In Grade 1, instruction focuses broadly on four critical areas:

• developing understanding of addition, subtraction, and strategies for addition and subtraction within 20;
• developing understanding of whole number relationships and place value, including grouping in tens and ones;
• developing understanding of linear measurement and measuring lengths as iterating length units; and
• reasoning about attributes of, and composing and decomposing geometric shapes.

Critical Areas:

1. 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, take-apart, and compare situations 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 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.
2. Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10. They compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They 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). Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes.
3. Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivity principle for indirect measurement.
4. Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement and for initial understandings of properties such as congruence and symmetry.

II.        Objectives

Course Outline:

1. Understand Addition and Subtraction
2. Fluently Add and Subtract within 10
3. Addition Facts to 20: Use Strategies
4. Subtractions Facts to 20: Use Strategies
5. Work with Addition and Subtraction Equations
6. Represent and Interpret Data
7. Extend the Counting Sequence
8. Understand Place Value
9. Compare Two-Digit Numbers
10. Use Models and Strategies to Add Tens and Ones
11. Use Models and Strategies to Subtract Tens
12. Measure Lengths
13. Time and Money
14. Reason with Shapes and Their Attributes
15. Equal Shares of Circles and Rectangles

Student Outcomes:

After successfully completing this course, the student will:

• Represent and solve problems involving addition and subtraction.
• Understand and apply properties of operations and the relationship between addition and subtraction.
• Add and subtract within 20.
• Work with addition and subtraction equations.
• Extend the counting sequence.
• Understand place value.
• Use place value understanding and properties of operations to add and subtract.
• Measure lengths indirectly and by iterating length units.
• Tell and write time.
• Work with money.
• Represent and interpret data.
• Reason with shapes and their attributes.

New Jersey Student Learning Standards

Career Readiness, Life Literacies, and Key Skill Practices

CRLLKSP 1   Act as a responsible and contributing community members and employee.

Students understand the obligations and responsibilities of being a member of a community, and they demonstrate this understanding every day through their interactions with others. They are conscientious of the

impacts of their decisions on others and the environment around them. They think about the near-term and long-term consequences of their actions and seek to act in ways that contribute to the betterment of their teams, families, community and workplace. They are reliable and consistent in going beyond the minimum expectation and in participating in activities that serve the greater good.

CRLLKSP 2   Attend to financial well-being.

Students take regular action to contribute to their personal financial well-being, understanding that personal financial security provides the peace of mind required to contribute more fully to their own career success.

CRLLKSP 3   Consider the environmental, social and economic impacts of decisions.

Students understand the interrelated nature of their actions and regularly make decisions that positively impact and/or mitigate negative impact on other people, organization, and the environment. They are aware of and utilize new technologies, understandings, procedures, materials, and regulations affecting the nature of their work as it relates to the impact on the social condition, the environment and the profitability of the organization.

CRLLKSP 4   Demonstrate creativity and innovation.

Students regularly think of ideas that solve problems in new and different ways, and they contribute those ideas in a useful and productive manner to improve their organization. They can consider unconventional ideas and suggestions as solutions to issues, tasks or problems, and they discern which ideas and suggestions will add greatest value. They seek new methods, practices, and ideas from a variety of sources and seek to apply those ideas to their own workplace. They take action on their ideas and understand how to bring innovation to an organization.

CRLLKSP 5   Utilize critical thinking to make sense of problems and persevere in solving them.

Students readily recognize problems in the workplace, understand the nature of the problem, and devise effective plans to solve the problem. They are aware of problems when they occur and take action quickly to address the problem; they thoughtfully investigate the root cause of the problem prior to introducing solutions. They carefully consider the options to solve the problem. Once a solution is agreed upon, they follow through to ensure the problem is solved, whether through their own actions or the actions of others.

CRLLKSP 6   Model integrity, ethical leadership and effective management.

Students consistently act in ways that align personal and community-held ideals and principles while employing strategies to positively influence others in the workplace. They have a clear understanding of integrity and act on this understanding in every decision. They use a variety of means to positively impact the directions and actions of a team or organization, and they apply insights into human behavior to change others’ action, attitudes and/or beliefs. They recognize the near-term and long-term effects that management’s actions and attitudes can have on productivity, morals and organizational culture.

CRLLKSP 7   Plan education and career paths aligned to personal goals.

Students take personal ownership of their own education and career goals, and they regularly act on a plan to attain these goals. They understand their own career interests, preferences, goals, and requirements. They have perspective regarding the pathways available to them and the time, effort, experience and other requirements to pursue each, including a path of entrepreneurship. They recognize the value of each step in the education and

experiential process, and they recognize that nearly all career paths require ongoing education and experience. They seek counselors, mentors, and other experts to assist in the planning and execution of career and personal goals.

CRLLKSP 8   Use technology to enhance productivity, increase collaboration and communicate effectively.

Students find and maximize the productive value of existing and new technology to accomplish workplace tasks and solve workplace problems. They are flexible and adaptive in acquiring new technology. They are proficient

with ubiquitous technology applications. They understand the inherent risks-personal and organizational-of technology applications, and they take actions to prevent or mitigate these risks.

CRLLKSP 9   Work productively in teams while using cultural/global competence.

Students positively contribute to every team, whether formal or informal. They apply an awareness of cultural difference to avoid barriers to productive and positive interaction. They find ways to increase the engagement and contribution of all team members. They plan and facilitate effective team meetings.

9.1 Personal Financial Literacy

9.1.2.CR.1: Recognize ways to volunteer in the classroom, school and community.

9.1.2. FI.1: Differentiate the various forms of money and how they are used (e.g., coins, bills, checks, debit and credit cards).

9.2 Career Awareness, Exploration, Preparation, and Training

9.2.2.CAP.1: Make a list of different types of jobs and describe the skills associated with each job.

9.4 Life Literacies and Key Skills

9.4.2.CI.1: Demonstrate openness to new ideas and perspectives

9.4.2.CI.2: Demonstrate originality and inventiveness in work

9.4.2.CT.1: Gather information about an issue, such as climate change, and collaboratively brainstorm ways to solve the problem

9.4.2.CT.2: Identify possible approaches and resources to execute a plan

9.4.2.CT.3: Use a variety of types of thinking to solve problems (e.g., inductive, deductive).

Computer Science And Design Thinking

8.1 Computer Science

8.1.2.DA.1: Collect and present data, including climate change data, in various visual formats.

8.1.2.DA.3: Identify and describe patterns in data visualizations.

8.1.2.DA.4: Make predictions based on data using charts or graphs.

8.1.2.AP.4: Break down a task into a sequence of steps.

8.2 Design Thinking

8.2.2.ED.2: Collaborate to solve a simple problem, or to illustrate how to build a product using the design process.

8.2.2.ED.3: Select and use appropriate tools and materials to build a product using the design process.

Mathematics

1.OA.A.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.OA.A.2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.  

1.OA.B.3. Apply properties of operations as strategies to add and subtract.

1.OA.B.4. Understand subtraction as an unknown-addend problem.

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

1.OA.C.6. Add and subtract within 20, demonstrating accuracy and efficiency for addition and subtraction within 10. 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 ).

1.OA.D.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

1.OA.D.8. Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers.

1.NBT.A.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.

1.NBT.B.2. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

a. 10 can be thought of as a bundle of ten ones — called a “ten.”

b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

1.NBT.B.3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

1.NBT.C.4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models (e.g., base ten blocks) or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

1.NBT.C.5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

1.NBT.C.6. Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

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

1.M.A.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.

1.M.B.3.Tell and write time in hours and half-hours using analog and digital clocks.

1.M.C.4. Know the comparative values of coins and all dollar bills (e.g., a dime is of greater value than a nickel). Use appropriate notation (e.g., 69¢, $10).

1.M.C.5. Use dollars in the solutions of problems up to $20. Find equivalent monetary values (e.g., a nickel is equivalent in value to five pennies). Show monetary values in multiple ways. For example, show 25¢ as two dimes and one nickel, and as five nickels. Show $20 as two tens and as 20 ones.

1.DL.A.1. 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.  

1.G.A.1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

1.G.A.2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Clarification: Students do not need to learn formal names such as “right rectangular prism.”)

1.G.A.3. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Mathematical Practices

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.

English Language Arts

SL.PE.1.1. Participate in collaborative conversations with diverse partners about grade 1 topics and texts with peers and adults in small and larger groups.  

A.Follow agreed-upon norms for discussions (e.g., listening to others with care, speaking one at a time about the topics and texts under discussion).

B.Build on others’ talk in conversations by responding to the comments of others through multiple exchanges.

C.Ask questions to clear up any confusion about the topics and texts under discussion.

SL.ES.1.3. Ask and answer questions about what a speaker says in order to gather additional information or clarify something that is not understood.

SL.UM.1.5. Add drawings or other visual displays to descriptions when appropriate to clarify ideas, thoughts, and feelings.

Science

1-PS4-4 Use tools and materials to design and build a device that uses light or sound to solve the problem of communicating over a distance

1-LS1-2 Read texts and use media to determine patterns in behavior of parents and offspring that help offspring survive.

III.         Proficiency Levels

This curriculum is appropriate for all grade 1 students.

IV.        Methods of Assessment

Student Assessment

The teacher will provide a variety of assessments during the course of the year. The assessment may include but is not limited to: chapter and unit tests and quizzes, teacher observations, open-ended problems, cooperative work, and homework.

Curriculum/Teacher Assessment

The teacher will provide the subject area supervisor with suggestions for changes on an ongoing basis.

V.        Grouping

This curriculum is appropriate for all students in grade 1.  

VI.        Articulation/Scope & Sequence/Time Frame

Course length is one year.

VII.        Resources

Texts/Supplemental Reading/References

enVision Mathematics, Savaas Learning Company, 2020

VIII.        Suggested Activities

Appropriate activities are listed in the curriculum map.

IX.        Methodologies

The following methods of instruction are suggested: teacher guided explorations, working in groups/working with a partner, working with manipulatives and discovery activities.

X.        Interdisciplinary Connections

At this grade level, connections to many other disciplines are appropriate and natural.  Reading and writing become an integral part of the mathematics process.  Connections with science are frequent throughout both curricula.  Technology plays an important part in learning mathematics as well.

XI.         Differentiating Instruction for Students with Special Needs: Students with Disabilities, Students at Risk, Students with 504s, English Language Learners, and Gifted & Talented Students

Differentiating instruction is a flexible process that includes the planning and design of instruction, how that instruction is delivered, and how student progress is measured. Teachers recognize that students can learn in multiple ways as they celebrate students’ prior knowledge. By providing appropriately challenging learning, teachers can maximize success for all students.

Differentiating in this course includes but is not limited to:

Differentiation for Support (ELL, Special Education, Students at Risk, Students with 504s)

• Peer mentoring on problems
• Differentiated teacher feedback on assignments
• Modeling out problems on whiteboard
• Visual aids as we project problems on whiteboard
• Study guides
• Tiered assignments
• Scaffolding of materials and assignments
• Re-teaching and review
• Guided note taking
• Exemplars of varied performance levels
• Multi-media approach to accommodating various learning styles

• Supplemental reading material for independent study
• Flexible grouping
• Tiered assignments
• Topic selection by interest
• Enhanced expectations for independent study
• Elevated questioning techniques using Webb's Depth of Knowledge matrix

XII.        Professional Development

The teacher will continue to improve expertise through participation in a variety of professional development opportunities.

XII.        Curriculum Map/Pacing Guide