CCSS Mathematical Practices

Second Grade

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

Students…

  • Realize that doing mathematics involves solving problems and discussing how they solved them.
  • Explain the meaning of a problem and look for ways to solve it.
  • Use objects and/or pictures to help them conceptualize and solve problems.
  • Ask themselves, “Does this make sense?”
  • Make guesses about the solution and plan an approach to solving the problem.

2. Reason abstractly and quantitatively.

Students…

  • Recognize that a number represents a specific quantity.
  • Connect the quantity to written symbols.
  • Reason quantitatively by creating a representation of a problem while attending to the meanings of the quantities.
  • Know and use different properties of operations and relate addition and subtraction to length.

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

Students…

  • Construct arguments using objects, pictures, drawings, and actions.
  • Practice mathematical communication skills in mathematical discussions involving questions like: “How did you get that?” “Explain your thinking.” “Why is that true?”
  • Explain their thinking and listen to others’ explanations.
  • Decide if the explanations make sense and ask appropriate questions.

4. Model with mathematics.

Students…

  • Experiment with representing problem situations in multiple ways including numbers, words, drawing pictures, using objects, acting out, making a chart/list, creating equations, etc.
  • Connect the different representations and explain the connections.
  • Use all of these representations as needed.

5. Use appropriate tools strategically.

Students consider available tools (including estimation) when solving a problem and decide when certain tools might be better suited.

6. Attend to precision.

Students…

  • Try to use clear and precise language in their discussions with others and when they explain their own reasoning.
  • Do calculations accurately.

7. Look for and make use of structure.

Students…

  • Look for patterns.
  • Adopt mental math strategies based on patterns (making ten, fact families, doubles).

8. Look for and express regularity in repeated reasoning.

Students…

  • Notice repetitive actions in counting and computation.
  • Look for shortcuts, such as rounding up and adjust the answer to compensate for the rounding.
  • Check their work by asking themselves, “Does this make sense?”

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Second Grade

2011-2012

Mathematics Course of Study

2.OA1Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction
  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.

VOCABULARY / EXAMPLES
  • Addition
  • Addends
  • Subtraction
  • Sum
  • Difference
  • Compare
  • Equal
/
  • By using drawings and equations with a symbols for the unknown number to represent the problem
  • By solving word problems connected to their lives: Lindsey had 63 stickers. She gave 37 to Allison. How many stickers does Lindsey have now?
63-37=
  • By creating word problems for their classmates to solve

Second Grade

2011-2012

Mathematics Course of Study

2.OA2Operations and Algebraic Thinking

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

VOCABULARY / EXAMPLES
  • Add
  • Subtract
  • Fact families
  • Doubles
  • Doubles plus one
/
  • Counting on
  • Fact Families
  • Making ten
  • Decomposing a number to lead to a ten (14-6=14-4-2=10-2=8)
  • Doubles
  • Doubles plus one

Instructional Strategies/Tools
  • Game: Race to Zero (On a path, each player starts at 20 and they simultaneously roll a die to reach zero. The first student to reach zero is the winner.)
  • Use five- and ten- frames to build number sense

Second Grade

2011-2012

Mathematics Course of Study

2.OA3Operations and Algebraic Thinking

Work with equal groups of objects to gain foundations for multiplication
  1. Determine whether a group of objects (up to 20) has an odd or even number of members.

VOCABULARY / EXAMPLES
  • Odd
  • Even
  • Addends
  • Sum
  • Equal
  • Equation
  • Multiplication
/
  • By pairing objects or counting them by 2’s(Even numbered sets of objects will not have a remaining object.)
  • By writing an equation to express an even number as a sum of two equal addends

Second Grade

2011-2012

Mathematics Course of Study

2.OA4Operations and Algebraic Thinking

Work with equal groups of objects to gain foundations for multiplication
  1. 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.

VOCABULARY / EXAMPLES
  • Array
  • Addition
  • Total
  • Multiplication
/
  • By arranging sets of objects into arrays

Instructional Strategies/Tools
  • Cubes, tiles, buttons, counters
  • Geoboards, graph paper, grid paper, ten-frames, smartboard

Second Grade

2011-2012

Mathematics Course of Study

2.NBT.1Number and Operations in Base Ten

Understand place value
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.
VOCABULARY / EXAMPLES
  • Digits
  • Represent
  • Amounts
  • Hundreds
  • Tens
  • Ones
/
  • By understanding such things as 706 equals 7 hundreds, 0 tens, and 6 ones
  • By understanding that 100 can be thought of as a bundle of ten tens—called a “hundred”
  • The numbers 100, 200, 300, etc…refer to one, two, three, etc…hundreds (and 0 tens and 0 ones.)

Instructional Strategies/Tools
  • Use base-ten blocks and bundles of tens along with numerals on place-value mats to provide the physical and symbolic representation of a number
  • Model three-digit numbers using base-ten blocks in multiple ways (e.g. 236 can be 236 ones; or 23 tens and 6 ones; 2 hundreds, 3 tens and 6 ones, etc…)

Second Grade

2011-2012

Mathematics Course of Study

2.NBT.2Number and Operations in Base Ten

Understand place value
2. Count within 1000; skip-count by 5’s, 10’s, and 100’s
VOCABULARY / EXAMPLES
  • Skip-count

Instructional Strategies/Tools
  • Use nickels, dimes and dollar bills to skip down
  • Attach nickels and dimes to five- and ten- frames
  • Use clothes pins, or other markers, on a number line to identify a number that is five or ten more than a given number

Second Grade

2011-2012

Mathematics Course of Study

2.NBT.3Number and Operations in Base Ten

Understand place value
3. Read and write numbers to 1000 using base-ten numerals, common number names, and expanded form.
VOCABULARY / EXAMPLES
  • Expanded form
  • Number words, such as two, eleven, fifteen, twenty-seven, four hundred fifty nine, etc…
/
  • 123 is:
100 + 20 + 3,
one hundred twenty-three,
1 hundred, 2 tens, and 3 ones
Instructional Strategies/Tools
  • Use nickels, dimes and dollar bills to skip down
  • Attach nickels and dimes to five- and ten- frames
  • Use clothes pins, or other markers, on a number line to identify a number that is five or ten more than a given number

Second Grade

2011-2012

Mathematics Course of Study

2.NBT.4Number and Operations in Base Ten

Understand place value
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.
VOCABULARY / EXAMPLES
  • Compare
  • Hundreds
  • Tens
  • Equal to
  • Greater than
  • Less than
/
  • 455>432

Instructional Strategies/Tools
  • Alligator mouth grabbing the greater number
  • Students create and compare all the three-digit numbers that can be made using numbers from 0 to 9 (using numbers 1, 3, and 9 they can write and compare the numbers 139, 193, 391, etc…)

Second Grade

2011-2012

Mathematics Course of Study

2.NBT.5Number and Operations in Base Ten

Use place value understanding and properties of operations to add and subtract
  1. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

VOCABULARY / EXAMPLES
  • Add
  • Subtract
  • Strategies
  • Models
/
  • By using standard algorithms
  • By using student invented algorithms
  • By using knowledge of number relationships
  • By using models and drawings
  • By using mental strategies

Instructional Strategies/Tools
  • Students can model with drawings and physical models and then progress to paper and pencil type strategies and then to mental strategies

Second Grade

2011-2012

Mathematics Course of Study

2.NBT.6Number and Operations in Base Ten

Use place value understanding and properties of operations to add and subtract
  1. Add up to four two-digit numbers using strategies based on place value and properties of operations.

VOCABULARY / EXAMPLES
  • Add
/
  • Standard algorithms
  • Student-invented strategies and algorithms
  • Modeling and drawing

Instructional Strategies/Tools
  • Students can decompose and compose tens and hundreds when they develop their own strategies for solving problems where regrouping is necessary (37 + 8=40 + 5=45, add 3 to 37 then 5) or (62-9=60-7=53, take off 2 to get 60, then 7 more)

Second Grade

2011-2012

Mathematics Course of Study

2.NBT.7Number and Operations in Base Ten

Use place value understanding and properties of operations to add and subtract
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.
VOCABULARY / EXAMPLES
  • Add
  • Subtract
  • Compose
  • Decompose
/
  • Standard algorithms
  • Student-invented strategies and algorithms
  • Modeling and drawing

Instructional Strategies/Tools
  • Students can decompose and compose tens and hundreds when they develop their own strategies for solving problems where regrouping is necessary (37 + 8=40 + 5=45, add 3 to 37 then 5) or (62-9=60-7=53, take off 2 to get 60, then 7 more)

Second Grade

2011-2012

Mathematics Course of Study

2.NBT.8Number and Operations in Base Ten

Use place value understanding and properties of operations to add and subtract
  1. Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

VOCABULARY / EXAMPLES
  • Add
  • Subtract
  • Mentally
/
  • 100 more than 653 is _____ (753)
  • 10 less than 87 is _____ (77)
  • “Start at 248. Count up by 10s until I tell you to stop.”

Instructional Strategies/Tools
  • Smart Board
  • Hundreds Chart
  • Place-value models, mats

Second Grade

2011-2012

Mathematics Course of Study

2.NBT.9Number and Operations in Base Ten

Use place value understanding and properties of operations to add and subtract
  1. Explain why addition and subtraction strategies work, using place value and the properties of operations.

VOCABULARY / EXAMPLES
  • Add
  • Subtract
/
  • Joe’s explanation: 473 + 227=? I started by adding 200 to 473 and got 673. Then I added 20 to 673 and got 693. Then I added 7 to 693 and I knew that it was 700.
  • Student uses base ten blocks and a base-ten mat to solve the problem and explain.
  • Student uses drawings, number lines and other manipulatives to solve and explain.

Instructional Strategies/Tools
  • Model using multiple strategies and materials

Second Grade

2011-2012

Mathematics Course of Study

2.MD.1Measurement and Data

Measure and estimate lengths in standard units
1.Measure the length of an object by selecting and using appropriate tools, such as rulers, yardsticks, meter sticks, and measuring tapes.
VOCABULARY / EXAMPLES
  • Measure
  • Length
  • Tools
  • Rulers
  • Yardsticks
  • Meter sticks
  • Measuring tapes
/
  • Students will measure various lengths using rulers, yardsticks, meter sticks, and tape measures.

Instructional Strategies/Tools
  • Model correct use of measuring tools, such as where to begin measuring and proper reading of the tool

Second Grade

2011-2012

Mathematics Course of Study

2.MD.2Measurement and Data

Measure and estimate lengths in standard units
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.
VOCABULARY / EXAMPLES
  • Length
  • Units of measurement
  • Measure
/
  • Student uses different unit/tools (inches, centimeters, yardstick, meter stick) to measure the same object.
  • Student can communicate the size of the unit and the number of units needed to measure, using both metric and standard units. (“The longer the unit the fewer I need.”)

Instructional Strategies/Tools
  • Rulers, yardsticks, meter stick, tape measure

Second Grade

2011-2012

Mathematics Course of Study

2.MD.3Measurement and Data

Measure and estimate lengths in standard units
  1. Estimate lengths using units of inches, feet, centimeters, and meters

VOCABULARY / EXAMPLES
  • Inch
  • Foot/feet
  • Centimeter
  • Meters
  • Length
  • Estimate
  • Unit of measurement
/
  • Estimate length of familiar items like desk, pencil, book, etc.
  • Useful benchmarks for measurement: first joint to the tip of a thumb is an inch; elbow to the wrist is about a foot; extended arm from your nose to the tip of fingers is a yard

Instructional Strategies/Tools
  • Give multiple opportunities to practice measurement.

Second Grade

2011-2012

Mathematics Course of Study

2.MD.4Measurement and Data

Measure and estimate lengths in standard units
  1. Estimate to determine how much longer one object is than another expressing the length difference in terms of a standard length unit.

VOCABULARY / EXAMPLES
  • Length
  • Estimate
  • Various units of measurement, such as inch
/
  • Compare difference in length of two objects by laying them side-by-side and selecting an appropriate standard unit of measure.
  • Use comparative phrases such as: longer by two inches; shorter by five centimeters.

Instructional Strategies/Tools
  • Measuring tools listed above.
  • Multiple items to measure and compare.

Second Grade

2011-2012

Mathematics Course of Study

2.MD.5Measurement and Data

Relate addition and subtraction to length
  1. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units.

VOCABULARY / EXAMPLES
  • Length
  • Addition
  • Subtraction
/
  • By using drawings (such as drawings of rulers)
  • By using algebraic equations with a symbol for the unknown number to represent the problem such as:
c - 35=20
20 + b = 55
20 + 35 = a
55 = 20 + b
  • Use word problems for equations like 5 – n = 2: Mary is making a dress. She has 5 yards of fabric. She uses some of the fabric and has 2 yards left. How many yards did she use?

Instructional Strategies/Tools
  • Use word problems.
  • Word problems need to stay within the same unit of measure.
  • Counting on and/or counting back on a number line will help tie this concept to previous knowledge.
  • Some representations students can use include drawings, rulers, pictures, and/or physical objects.
  • Strong connection between this standard and fact fluency.

Second Grade

2011-2012

Mathematics Course of Study

2.MD.6Measurement and Data

Relate addition and subtraction to length
  1. 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.

VOCABULARY / EXAMPLES
  • Length
  • Difference
  • Sum
/
  • Students represent their thinking when adding and subtracting within 100 by using a number line.

Instructional Strategies/Tools
  • Number line up to 100.

Second Grade

2011-2012

Mathematics Course of Study

2.MD.7Measurement and Data

Work with time and money
  1. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

VOCABULARY / EXAMPLES
  • Hour
  • Minute
  • Analog
  • Digital
  • A.M. & P.M.
  • Quarter till/after
  • Ten till/after
  • Half past
/
  • Students will skip-count by five to recognize five-minute intervals.
  • Students read and use both digital and analog clocks.
  • Communicate their understanding of time using both numbers and language.
  • Understand two cycles of twelve hours in a day – a.m. and p.m.

Instructional Strategies/Tools
  • Record daily actions in journal to understand the difference between a.m. and p.m. cycles.
  • Digital and analog clocks

Second Grade

2011-2012

Mathematics Course of Study

2.MD.8Measurement and Data

Work with time and money
  1. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

VOCABULARY / EXAMPLES
  • Penny
  • Nickel
  • Dime
  • Quarter
  • Half-dollar
  • Dollar
  • Cents
  • Dollar sign
  • Value
/
  • If you have 2 dimes and 3 pennies, how many cents do you have?
  • Since money is not specifically addressed in Kindergarten, first, or third grade, students should have multiple opportunities to use coins and bills.
  • Sandra went to the store and received $0.76 in change. What are three different sets of coins she could have received?

Instructional Strategies/Tools
  • “Dollar bills” should include denominations up to one hundred ($1.00, $5.00, $10.00, $20.00, $50.00 and $100.00).
  • Solve story problems connecting the different representations, which may include: objects, pictures, charts, tables, words, and/or numbers.
  • Students should communicate their mathematical thinking and justify their answers.

Second Grade

2011-2012

Mathematics Course of Study

2.MD.9Measurement and Data

Represent and interpret data
  1. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same objects. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

VOCABULARY / EXAMPLES
  • Line plot
  • Data
  • Repeated measurements
  • Horizontal scale
  • Whole-number units
  • Number line
/
  • This standard emphasizes representing data using a line plot.
Number of Pencils Measured
x
x x
x x x
0 1 2 3 4 5 6
Length of Pencils (in inches)
Instructional Strategies/Tools
  • Measuring tools, line plots, Smart Board to create and/or model line plots.
  • A line plot can be thought of as plotting data on a number line.

Second Grade

2011-2012

Mathematics Course of Study

2.MD.10Measurement and Data

Represent and interpret data
  1. Draw a picture graph and a bar graph (with single-unit scales) 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.

VOCABULARY / EXAMPLES
  • Picture graph
  • Pictograph
  • Bar graph
  • Data
  • Data set
  • Categories
/
  • Students should draw both picture/pictograph and bar graph representing data that can be sorted up to four categories using single unit scales (scales should count by ones).
  • Data should be used to solve put together, take-apart, and compare problems.

Instructional Strategies/Tools
  • Pictographs should include a title, categories, category label, key, and data.
  • In second grade, picture graphs (pictographs) include symbols that represent single units.
  • Students should draw both horizontal and vertical bar graphs. Bar graphs include a title, scale, scale label, categories, category label, and data.

Second Grade