Rogers Public Schools 1 of 7 | Revised 5-23-13

R.P.S. Common Core Math Curriculum Overview First Grade

Summary of the Year In First Grade, instructional time should focus on four critical areas:

1. Developing understanding of addition, subtraction, and strategies for addition and subtraction within 20

2. Developing understanding of whole number relationships and place value, including grouping in tens and ones

3. Developing understanding of linear measurement and measuring lengths as iterating units 4. Reasoning about attributes of, and composing and decomposing geometric shapes

CCSSM, p.13 – Grade 1 Overview

Required Fluency: 1.OA.6 Add and subtract within 10

Quarterly Sequence

1st Quarter: Understanding Addition, Subtraction, and Place Value Students build on their work with small numbers from Kindergarten to develop strategies for adding and subtracting whole numbers. They will model problem situations to develop meaning for the operations of addition and subtraction. Connections between counting and addition and subtraction will be made (i.e.: adding two is the same as counting on two). They will begin to use properties of addition to add whole numbers and to develop fluency adding and subtracting within 10. They will work to understand place value by grouping “10 ones” as a single unit: 1 ten. They will think of whole numbers between 10 and 100 in terms of tens and ones.

2nd Quarter: Extending Addition and Subtraction Strategies; Comparing Numbers Students continue to develop their strategies for adding and subtracting and begin to use more sophisticated strategies to solve addition and subtraction problems within 20. They will work to strengthen their fluency within 10. They will use their understanding of place value to compare numbers and as a strategy for adding and subtracting within 100 without recomposing a ten. They will begin subtracting multiples of 10 and mentally find 10 more or 10 less than a given number. Continued on next page…

First Grade Major Emphasis Clusters

Operations and Algebraic Thinking

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 Number and Operations in Base Ten

Extend the counting sequence.

Understand place value.

Use place value understanding and properties of operations to add and subtract.

Measurement and Data

Measure lengths indirectly and by iterating length units.

Rogers Public Schools 2 of 7 | Revised 5-23-13

R.P.S. Common Core Math Curriculum Overview First Grade

Quarterly Sequence continued

3rd Quarter: Using Place Value and Properties of Operations; Understanding the Processes of Measurement Students will deepen their understanding using place value and properties of operations to add and subtract within 100 without recomposing a ten. They will use increasingly sophisticated strategies based on these properties and begin to generalize these methods. They will continue to develop fluency adding and subtracting within 10. Students will develop an understanding of the meaning and processes of measurement. They will make direct and indirect comparisons of lengths of objects, applying ideas of transitivity, and will order sets of objects by length, using multiple comparisons (ordering larger sets of objects). Students will also learn to lay physical units (manipulatives like centimeter cubes, inch cubes/tiles, etc.) end-to-end and count them to measure a length. Through this process, the idea of iteration (act of repeating a process) should develop, and they should begin to recognize the need to iterate without gaps. Students will collect and use data in meaningful ways to solve problems.

4th Quarter: Using Efficient Strategies; Understanding Measurement; Reasoning with Attributes of Shapes Students solidify their work with addition and subtraction within 20, demonstrating fluency within 10. Students continue to develop and use efficient, accurate, and generalizable methods to add and subtract within 100 without recomposing a ten. They will continue to strengthen their understanding of the meaning and processes of measurement, solidifying their understanding of iteration. They will tell and write time in hours and half-hours using analog and digital clocks, and understand time as a “unit” of measure. Students will reason with attributes of shapes and will practice composing and decomposing shapes, as they build understanding of part-whole relationships.

Rogers Public Schools 3 of 7 | Revised 5-23-13

R.P.S. Common Core Math Curriculum Overview First Grade

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

•I can find ways to solve the problem and ask "Does this make sense?".

2. Reason abstractly and quantitatively.

•I can use numbers and words to help me make sense of problems.

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

•I can explain my thinking and consider the mathematical thinking of others.

4. Model with mathematics.

•I can recognize math in everyday life and use math I know to solve problems.

5. Use appropriate tools strategically.

•I can use math tools and know when to use them.

6. Attend to precision.

•I can work carefully, check my work, and be clear when I share my ideas.

7. Look for and make use of structure.

•I can see and understand how numbers and shapes are organized and put together as parts and wholes.

8. Look for and express regularity in repeated reasoning.

•I can notice when calculations are repeated. Then, I can find more efficient ways to solve the problem.

Standards for Mathematical Practice

The Standards for Mathematical Practice describe ways that students should engage with the content standards. These practices are essential to understanding and implementing the mathematical subject material. Content standards that begin with the word “understand” are often especially good opportunities to connect the practices to content. (CCSSM p.6-8) Below you will find the Mathematical Practice Standards and a related student friendly “I can” statement.

Mathematically Proficient Students…

The practices have been arranged in pairs to show which may naturally appear together when students are engaged in certain types of tasks or with certain mathematics content. SMP 1 & 6

are overarching in the sense that if students are truly engaged in ‘solving’ tasks that are ‘problems’ to them, they will need to make sense of problems and have perseverance, and refine

their thinking and their ability to communicate about the mathematics, which is part of attending to precision.

Visit the Mathematical Practices Resources Page for additional classroom resources, explanations, examples, and videos of the practices in action.

Rogers Public Schools 4 of 7 | Revised 5-23-13

R.P.S. Common Core Math Curriculum Overview First Grade

Content Emphases by Cluster The content emphases in the standards at the cluster level are provided because curriculum, instruction, and assessment at each grade must reflect the focus and emphasis of the standards.

Not all of the content in a given grade is emphasized equally in the standards.

The list of content standards for each grade is not a flat, one-dimensional checklist.

Some clusters require greater emphasis than the others based on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness.

Intense focus on the most critical material at each grade allows depth in learning, which is carried out through the Standards for Mathematical Practice.

Assessments will strongly focus where the standards strongly focus.

Therefore, to make the emphases in the standards more transparent and useful, the clusters have been designated as Major, Supporting and Additional. Some clusters that are not major emphases in themselves are designed to support and strengthen areas of major emphasis, while other clusters that may not connect tightly or explicitly to the major work of the grade are called additional.

PARCC Model Content Frameworks for Mathematics p.13-14

Major Clusters Areas of intensive focus, where students need fluent understanding and application of the core concepts

(approximately 70% of instructional time)

Supporting Clusters Rethinking and linking; areas where material is being

covered, but in a way that applies to core understandings

(approximately 20% of instructional time)

Additional Clusters Expose students to other subjects, though at a distinct

level of depth and intensity

(approximately 10% of instructional time) Operations and Algebraic Thinking

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 Number and Operations in Base Ten

Extend the counting sequence.

Understand place value.

Use place value understanding and properties of operations to add and subtract.

Measurement and Data

Measure lengths indirectly and by iterating length units.

Geometry

Reason with shapes and their attributes.

Measurement and Data

Tell and write time.

Represent and interpret data.

For further information regarding the content emphases by cluster visit: www.engageny.org/resource/math-content-emphases/

Rogers Public Schools 5 of 7 | Revised 5-23-13

R.P.S. Common Core Math Curriculum Overview First Grade

Year Long Pacing of the Common Core State Standards (p. 1of 3) Shading indicates standards for instruction each quarter Approximate Instructional time distribution: 70% to Major Clusters 20 % to Supporting Clusters 10% to Additional Clusters

1st Quarter

2nd Quarter

3rd Quarter

4th Quarter

Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction.

1.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.OA.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.

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

1.OA.3. Apply properties of operations as strategies to add and subtract. [Students need not use formal terms for these

properties.] 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.)

1.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.

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

1.OA.6. Add and subtract within 20, demonstrating fluency 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). Work with addition and subtraction equations.

Work with addition and subtraction equations.

1.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.

1.OA.8. Determine the unknown whole number in an addition or subtraction equation relating 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 = □.

Rogers Public Schools 6 of 7 | Revised 5-23-13

R.P.S. Common Core Math Curriculum Overview First Grade

Year Long Pacing of the Common Core State Standards (p. 2 of 3) Shading indicates standards for instruction each quarter Approximate Instructional time distribution: 70% to Major Clusters 20 % to Supporting Clusters 10% to Additional Clusters

1st Quarter

2nd Quarter

3rd Quarter

4th Quarter

Number and Operations in Base Ten Extend the counting sequence.

1.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.

Understand place value.

1.NBT.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.3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons

with the symbols >, =, and <.

Use place value understanding and properties of operations to add and subtract.

1.NBT.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 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.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.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.

Rogers Public Schools 7 of 7 | Revised 5-23-13

R.P.S. Common Core Math Curriculum Overview First Grade

Year Long Pacing of the Common Core State Standards (p. 3 of 3) Shading indicates standards for instruction each quarter Approximate Instructional time distribution: 70% to Major Clusters 20 % to Supporting Clusters 10% to Additional Clusters

1st Quarter

2nd Quarter

3rd Quarter

4th Quarter

Measurement and Data Measure lengths indirectly and by iterating length units.

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

1.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. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

Tell and write time.

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

Represent and interpret data.

1.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.

Geometry Reason with shapes and their attributes.

1.G.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.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. [Students do not need to learn formal names such as “right rectangular prism.”]

1.G.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.

Standards per Quarter 10 14 17 18