1. Understand the relationship between numbers and quantities; connect counting to cardinality
2. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group,
3. Compare two numbers between 1 and 10 presented as written numerals.
4. Represent addition and subtraction with objects, fingers, mental images, drawings
5. Solve addition and subtraction word problems, and add and subtract within 10,
6. Fluently add and subtract within 5
7. Describe measurable attributes of objects, such as length or weight.
8. identify shapes as two-dimensional
9. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
10. 1st Grade
10.1. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20,
10.2. Apply properties of operations as strategies to add and subtract
10.3. Add and subtract within 20
10.4. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false
10.5. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
10.6. Count to 120, starting at any number less than 120
10.7. 10 can be thought of as a bundle of ten ones — called a "ten."
10.8. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens
10.9. 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,
10.10. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
10.11. Tell and write time in hours and half-hours using analog and digital clocks.
10.12. Compose two-dimensional shapes or three-dimensional
10.13. Partition circles and rectangles into two and four equal shares
10.14. Use addition and subtraction within 20 to solve word problems
10.15. Understand that the two digits of a two-digit number represent amounts of tens and ones
11. 3rd Garde
11.1. Interpret products of whole numbers
11.2. Interpret whole-number quotients of whole numbers,
11.3. Use multiplication and division within 100 to solve word problems
11.4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers
11.5. Apply properties of operations as strategies to multiply and divide
11.6. Understand division as an unknown-factor problem
11.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division
11.8. Solve two-step word problems using the four operations
11.9. Identify arithmetic patterns, and explain them using properties of operations.
11.10. Use place value understanding to round whole numbers to the nearest 10 or 100.
11.11. Fluently add and subtract within 1000 using strategies and algorithms based on place value
11.12. Multiply one-digit whole numbers by multiples of 10 in the range 10-90
11.13. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts
11.14. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
11.15. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line
11.16. Recognize and generate simple equivalent fractions
11.17. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers
11.18. Compare two fractions with the same numerator or the same denominator by reasoning about their size.
11.19. Understand a fraction as a number on the number line; represent fractions on a number line diagram
11.20. Tell and write time to the nearest minute and measure time intervals in minutes
11.21. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l
12. count to 100 by ones and tens
13. write numbers from 0 to 20.
14. Count forward beginning from a given number within the known sequence
15. Count to answer "how many?"
16. Compose and decompose numbers from 11 to 19 into ten ones
17. Describe objects in the environment using names of shapes,
18. Correctly name shapes regardless of their orientations or overall size.
19. 2nd Grade
19.1. Fluently add and subtract within 20 using mental strategies
19.2. Determine whether a group of objects (up to 20) has an odd or even number of members
19.3. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns
19.4. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones
19.5. 100 can be thought of as a bundle of ten tens — called a "hundred."
19.6. Count within 1000; skip-count by 5s, 10s, and 100s
19.7. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
19.8. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits
19.9. Add up to four two-digit numbers
19.10. Add and subtract within 1000
19.11. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
19.12. Use addition and subtraction within 100 to solve one- and two-step word problems
19.13. Estimate lengths using units of inches, feet, centimeters, and meters.
19.14. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately
19.15. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces
20. 4th grade
20.1. Interpret a multiplication equation as a comparison
20.2. Multiply or divide to solve word problems involving multiplicative comparison
20.3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations
20.4. Find all factor pairs for a whole number in the range 1-100
20.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself
20.6. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right
20.7. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form
20.8. Use place value understanding to round multi-digit whole numbers to any place
20.9. Fluently add and subtract multi-digit whole numbers using the standard algorithm
20.10. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors
20.11. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models
20.12. Compare two fractions with different numerators and different denominators
20.13. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
20.14. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
20.15. Decompose a fraction into a sum of fractions with the same denominator in more than one way
20.16. Add and subtract mixed numbers with like denominators
20.17. Solve word problems involving multiplication of a fraction by a whole number,
20.18. Use decimal notation for fractions with denominators 10 or 100
20.19. Compare two decimals to hundredths by reasoning about their size
20.20. Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
20.21. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec
20.22. An angle is measured with reference to a circle with its center at the common endpoint of the rays
20.23. Measure angles in whole-number degrees using a protractor
20.24. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines
21. 5th grade
21.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols
21.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them
21.3. Generate two numerical patterns using two given rules
21.4. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
21.5. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10
21.6. Read, write, and compare decimals to thousandths
21.7. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form
21.8. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons
21.9. Use place value understanding to round decimals to any place
21.10. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations
21.11. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators,
21.12. Interpret a fraction as division of the numerator by the denominator
21.13. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction
21.14. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths
21.15. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem
21.16. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions
21.17. Interpret division of a whole number by a unit fraction, and compute such quotients
21.18. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
21.19. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions
21.20. Convert among different-sized standard measurement units within a given measurement system
21.21. Make a line plot to display a data set of measurements in fractions of a unit
21.22. Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
21.23. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units
21.24. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane,
21.25. Classify two-dimensional figures in a hierarchy based on properties.
