The Common Core in California

2.2.OA Operations and Algebraic Thinking

• 2 Represent and solve problems involving addition and subtraction.

  • 2.2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

    • Addition word problems - sums to 20 (2-E.16)
    • Addition sentences for word problems - sums to 20 (2-E.17)
    • Addition word problems - three one-digit numbers (2-E.22)
    • Addition word problems - four or more one-digit numbers (2-E.24)
    • Subtraction word problems - up to 18 (2-F.12)
    • Subtraction sentences for word problems - up to 18 (2-F.13)
    • Addition word problems - up to two digits (2-G.15)
    • Write the addition sentence - up to two digits (2-G.17)
    • Addition word problems - three numbers up to two digits each (2-G.20)
    • Addition word problems - four numbers up to two digits each (2-G.22)
    • Subtraction word problems - up to two digits (2-H.14)
    • Write the subtraction sentence - up to two digits (2-H.16)
    • Addition and subtraction word problems - up to 20 (2-L.3)
    • Two-step addition and subtraction word problems - up to 20 (2-L.)
    • Solve word problems using guess-and-check - up to 20 (2-L.4)
    • Comparison word problems - up to 20 (2-L.)
    • Addition and subtraction word problems - up to 100 (2-L.11)
    • Two-step addition and subtraction word problems - up to 100 (2-L.12)
    • Estimate sums (2-N.4)
    • Estimate differences (2-N.5)

• 2 Add and subtract within 20.

  • 2.2.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

    • Add one-digit numbers - sums to 10 (2-E.1)
    • Ways to make a number with addition - sums to 10 (2-E.2)
    • Add one-digit numbers (2-E.9)
    • Add zero (2-E.11)
    • Add doubles (2-E.13)
    • Add doubles - complete the sentence (2-E.14)
    • Make ten to add (2-E.15)
    • Complete the addition sentence - sums to 20 (2-E.18)
    • Which addition sentence is true? (2-E.20)
    • Add three one-digit numbers (2-E.21)
    • Subtract one-digit numbers - up to 10 (2-F.1)
    • Ways to subtract - up to 10 (2-F.2)
    • Subtract doubles (2-F.4)
    • Subtract by counting back - up to 20 (2-F.)
    • Subtract by counting on - up to 20 (2-F.8)
    • Use ten to subtract (2-F.)
    • Subtract a one-digit number from a two-digit number up to 18 (2-F.9)
    • Subtract zero/all (2-F.11)
    • Complete the subtraction sentence - up to 18 (2-F.14)
    • Which subtraction sentence is true? (2-F.16)
    • Add in any order (2-K.)
    • Add and subtract numbers up to 20 (2-L.1)
    • Ways to make a number using addition and subtraction - up to 20 (2-L.2)
    • Which addition or subtraction sentence is true? (2-L.6)

• 2 Work with equal groups of objects to gain foundations for multiplication.

  • 2.2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

    • Even or odd number of shapes - up to 20 (2-A.18)
    • Identify even and odd numbers - up to 20 (2-A.)
    • Add doubles - complete the sentence (2-E.14)

  • 2.2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

    • Identify repeated addition for equal groups - sums to 25 (2-E.)
    • Write addition sentences for equal groups - sums to 25 (2-E.)
    • Identify repeated addition in arrays - sums to 10 (2-E.25)
    • Write addition sentences for arrays - sums to 10 (2-E.26)
    • Identify repeated addition in arrays - sums to 25 (2-E.27)
    • Write addition sentences for arrays - sums to 25 (2-E.28)

2.2.NBT Number and Operations in Base Ten

• 2 Understand place value.

  • 2.2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

    • Place value models - up to hundreds (2-M.2)
    • Identify a digit up to the hundreds place (2-M.4)
    • Place value - up to hundreds (2-M.6)
    • Convert to/from a number - up to hundreds (2-M.11)

    • 2.2.NBT.1.a 100 can be thought of as a bundle of ten tens - called a "hundred."

    • 2.2.NBT.1.b The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

      • Convert between place values - ones and hundreds (2-M.12)

  • 2.2.NBT.2 Count within 1000; skip-count by 2s, 5s, 10s, and 100s.

    • Skip-counting by twos, fives, and tens (2-A.5)
    • Skip-counting stories (2-A.6)
    • Skip-counting sequences (2-A.7)
    • Skip-counting puzzles (2-A.10)
    • Count forward and backward by twos, fives, tens, and hundreds (2-A.17)

  • 2.2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

    • Spell word names for numbers up to 20 (2-C.2)
    • Writing numbers up to 100 in words - convert words to digits (2-C.3)
    • Writing numbers up to 100 in words - convert digits to words (2-C.4)
    • Writing numbers up to 1,000 in words - convert words to digits (2-C.5)
    • Writing numbers up to 1,000 in words - convert digits to words (2-C.6)
    • Convert from expanded form - up to hundreds (2-M.14)

  • 2.2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

    • Comparing numbers up to 1,000 (2-B.2)

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

  • 2.2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

    • Add multiples of 10 (2-G.1)
    • Use models to add a two-digit and a one-digit number - without regrouping (2-G.3)
    • Use models to add a two-digit and a one-digit number - with regrouping (2-G.4)
    • Add a two-digit and a one-digit number - without regrouping (2-G.5)
    • Add a two-digit and a one-digit number - with regrouping (2-G.6)
    • Break apart a one-digit number to add (2-G.)
    • Use models to add two-digit numbers - without regrouping (2-G.7)
    • Use models to add two-digit numbers - with regrouping (2-G.8)
    • Use place value to add two-digit numbers - without regrouping (2-G.)
    • Use place value to add two-digit numbers - with regrouping (2-G.)
    • Add two-digit numbers without regrouping - sums to 100 (2-G.9)
    • Add two-digit numbers with regrouping - sums to 100 (2-G.10)
    • Break apart a two-digit number to add - sums to 100 (2-G.)
    • Use compensation to add on a number line - up to two digits (2-G.)
    • Use compensation to add - up to two digits (2-G.12)
    • Ways to make a number using addition (2-G.14)
    • Complete the addition sentence - up to two digits (2-G.16)
    • Subtract multiples of 10 (2-H.1)
    • Use models to subtract a one-digit number from a two-digit number - without regrouping (2-H.3)
    • Subtract a one-digit number from a two-digit number - without regrouping (2-H.4)
    • Use models to subtract a one-digit number from a two-digit number - with regrouping (2-H.5)
    • Subtract a one-digit number from a two-digit number - with regrouping (2-H.6)
    • Break apart a one-digit number to subtract (2-H.)
    • Use models to subtract two-digit numbers - without regrouping (2-H.7)
    • Subtract two-digit numbers - without regrouping (2-H.8)
    • Use models to subtract two-digit numbers - with regrouping (2-H.9)
    • Subtract two-digit numbers - with regrouping (2-H.10)
    • Break apart a two-digit number to subtract (2-H.)
    • Use compensation to subtract on a number line - up to two digits (2-H.)
    • Use compensation to subtract - up to two digits (2-H.11)
    • Ways to make a number using subtraction (2-H.13)
    • Complete the subtraction sentence - up to two digits (2-H.15)
    • Add and subtract numbers - up to 100 (2-L.9)
    • Ways to make a number using addition and subtraction - up to 100 (2-L.10)
    • Which sign (+ or -) makes the number sentence true? (2-L.17)

  • 2.2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.

    • Add three numbers up to two digits each (2-G.19)
    • Add four numbers up to two digits each (2-G.21)

  • 2.2.NBT.7 Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

    • Add two-digit numbers - sums to 200 (2-G.11)
    • Add multiples of 100 (2-I.1)
    • Add multiples of 10 or 100 (2-I.2)
    • Use models to add three-digit numbers - without regrouping (2-I.3)
    • Use models to add three-digit numbers - with regrouping (2-I.4)
    • Addition with three-digit numbers (2-I.5)
    • Use compensation to add - up to three digits (2-I.6)
    • Addition word problems - up to three digits (2-I.7)
    • Complete the addition sentence - up to three digits (2-I.8)
    • Subtract multiples of 100 (2-J.1)
    • Subtract multiples of 10 or 100 (2-J.2)
    • Use models to subtract from three-digit numbers - without regrouping (2-J.3)
    • Use models to subtract from three-digit numbers - with regrouping (2-J.4)
    • Subtract across zeros (2-J.5)
    • Subtract from three-digit numbers (2-J.6)
    • Use compensation to subtract - up to three digits (2-J.7)
    • Subtraction word problems - up to three digits (2-J.8)
    • Complete the subtraction sentence - up to three digits (2-J.9)
    • Add and subtract numbers up to 1,000 (2-L.20)
    • Regroup tens and ones - ways to make a number (2-M.9)
    • Regroup tens and ones (2-M.10)

  • 2.2.NBT.7.1 Use estimation strategies to make reasonable estimates in problem solving.

    • Estimate sums (2-N.4)
    • Estimate differences (2-N.5)

  • 2.2.NBT.8 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

    • Input/output tables - add and subtract by 100 (2-L.15)
    • Input/output tables - add and subtract by 10 or 100 (2-L.16)

  • 2.2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.

    • Add in any order (2-K.)
    • Related addition facts (2-K.1)
    • Related subtraction facts (2-K.2)
    • Fact families (2-K.3)

2.2.MD Measurement and Data

• 2 Measure and estimate lengths in standard units.

  • 2.2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

    • Measure using an inch ruler (2-S.2)
    • Measure using a centimeter ruler (2-S.8)

  • 2.2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

    • Which customary unit of length is appropriate: inches, feet, or yards? (2-S.4)
    • Which metric unit of length is appropriate? (2-S.9)

  • 2.2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.

    • Which customary unit of length is appropriate: inches or feet? (2-S.3)
    • Which metric unit of length is appropriate? (2-S.9)

  • 2.2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

    • Measure to compare length in inches (2-S.)
    • Measure to compare length in centimeters (2-S.)

• 2 Relate addition and subtraction to length.

  • 2.2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

    • Customary units of length: word problems (2-S.5)
    • Compare lengths: customary units (2-S.)
    • Metric units of length: word problems (2-S.10)
    • Compare lengths: metric units (2-S.)

  • 2.2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and differences within 100 on a number line diagram.

    • Number lines - up to 100 (2-A.11)
    • Number lines - up to 1,000 (2-A.13)
    • Addition sentences using number lines - sums to 20 (2-E.8)
    • Subtraction sentences using number lines - up to 20 (2-F.7)
    • Use number lines to add two-digit numbers (2-G.)

• 2 Work with time and money.

  • 2.2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year).

    • Match digital clocks and times (2-Q.1)
    • Match analog clocks and times (2-Q.2)
    • Match analog and digital clocks (2-Q.3)
    • Read clocks and write times: hour and half hour (2-Q.4)
    • Read clocks and write times (2-Q.5)
    • A.M. or P.M. (2-Q.7)
    • Compare clocks (2-Q.8)
    • Number of days in each month (2-Q.15)
    • Relate time units (2-Q.16)

  • 2.2.MD.8 Solve word problems involving combinations of dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

    • Names and values of common coins (2-P.1)
    • Count money - pennies, nickels, and dimes only (2-P.3)
    • Count money - up to $1 (2-P.4)
    • Count money - up to $5 (2-P.5)
    • Equivalent amounts of money - up to $1 (2-P.6)
    • Exchanging money - with pictures (2-P.7)
    • Comparing groups of coins (2-P.9)
    • Add money - up to $1 (2-P.10)
    • Add money - up to $1: word problems (2-P.11)
    • Subtract money - up to $1 (2-P.12)
    • Subtract money - up to $1: word problems (2-P.13)
    • Add and subtract money - up to $1 (2-P.14)
    • Add and subtract money - up to $1: word problems (2-P.15)
    • Purchases - do you have enough money - up to $1 (2-P.16)
    • Purchases - do you have enough money - up to $5 (2-P.17)
    • Which picture shows more - up to $5 (2-P.18)
    • Least number of coins (2-P.19)
    • How much more to make a dollar? (2-P.20)
    • Correct amount of change (2-P.21)
    • Making change (2-P.22)

• 2 Represent and interpret data.

  • 2.2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

    • Create line plots (2-R.10)

  • 2.2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

    • Interpret bar graphs II (2-R.6)
    • Which bar graph is correct? (2-R.7)
    • Create bar graphs (2-R.8)
    • Interpret pictographs I (2-R.11)
    • Create pictographs I (2-R.13)

2.2.G Geometry

• 2 Reason with shapes and their attributes.

  • 2.2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

    • Count sides and vertices (2-T.3)
    • Compare sides and vertices (2-T.4)
    • Identify quadrilaterals (2-T.)
    • Identify pentagons (2-T.)
    • Name polygons: up to 6 sides (2-T.)
    • Classify polygons: up to 6 sides (2-T.)
    • Draw polygons (2-T.)
    • Cubes (2-U.2)
    • Count vertices, edges, and faces (2-U.4)
    • Compare vertices, edges, and faces (2-U.5)
    • Identify faces of three-dimensional shapes (2-U.6)
    • Identify shapes traced from solids (2-U.7)

  • 2.2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

    • Tile a rectangle with squares (2-V.3)
    • Area (2-V.4)

  • 2.2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

    • Equal parts (2-W.1)
    • Identify halves (2-W.2)
    • Identify thirds (2-W.3)
    • Identify fourths (2-W.4)
    • Identify halves, thirds, and fourths (2-W.5)
    • Make halves (2-W.6)
    • Make thirds (2-W.7)
    • Make fourths (2-W.8)
    • Make halves, thirds, and fourths (2-W.9)
    • Make halves, thirds, and fourths in different ways (2-W.10)
    • Identify a half, a third, and a fourth (2-W.)