Standards of
Expected Student Achievement
Second Grade
Content Standards
Mathematics
Standards
1999 - 2000
By the end of SECOND GRADE
Number Sense
Students will:
•Count, read, and write whole numbers to 1,000 and identify the place value for each digit
•Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000)
-Kelly has 308 stickers. How many sets of hundreds, tens, and ones does she have?
•Order and compare whole numbers to 1,000 by using the symbols <, =, >
•Understand and use the inverse relationship between addition and subtraction (e.g., an opposite number sentence for 8 + 6 = 14 is 14 - 6 = 8) to solve problems and check solutions
•Find the sum or difference of two whole numbers up to three digits long
-Use drawings of tens and ones to help find the sum of 37 + 17 and the difference of 25 - 19.
•Use mental arithmetic to find the sum or difference of two-digit numbers
-In a game, Mysong and Naoki are making addition problems. They make two 2-digit numbers out of the four given numbers 1, 2, 3, and 4. Each number is used exactly once. The winner is the one who makes two numbers whose sum is largest. Mysong had 43 and 21, while Naoki had 31 and 24. Who won the game? How do you know? Show how you can beat both Mysong and Naoki by making up two numbers with a larger sum than either.
•Use repeated addition, arrays, and counting by multiples to do multiplication
-Draw a simple picture of seating 30 people in rows of 10. Show and explain how this is related to multiplication. Do this also for rows of 3, and again for rows of 5.
•Use repeated subtraction, equal sharing, and forming equal groups with reminders to do division
-Kim decides to store away his marbles. He knows there are bags which hold up to 10 marbles in each. Kim has 38 marbles, and he tries to spend money on as few bags as he can. How many bags does he have to buy? And if he has 51 marbles? (Keep in mind that there is no such thing as "half a bag" or "part of a bag.")
•Know the multiplication tables of 2's, 5's, and 10's (to "times 10") and commit them to memory
•Recognize, name, and compare unit fractions from 1/12 to 1/2
-True or false?
1. One-fourth of a pie is larger than one-sixth of a pie
2. 1/4 > 1/3
3. 1/7 < 1/9
•Recognize fractions of a whole and parts of a group (e.g., one-fourth of a pie, two-thirds of 15 balls)
•Know that when all fractional parts are included, such as four-fourths, the result is equal to the whole and to one
•Solve problems using combinations of coins and bills
-Lee has a wallet full of nickels, dimes, and dollar bills. In how many ways can be pay with correct change for a pen worth $1.15? What about one worth 65 cents?
•Know and use the decimal notation and the dollar and cent symbols for money
1. ¢32
2. 72¢
3. $1.25
4. 2.57$
•Recognize when an estimate is reasonable in measurements (e.g., closest inch)
Students will:
•Use the commutative and associative rules to simplify mental calculations and to check results
-Draw pictures using dots to show:
1. Why 11 + 18 = 18 + 11
2. Why (11 + 5) + 17 = 11 + (5 + 17)
-If you know that 379 + 363 = 742, what is the sum of 363 + 379?
•Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences
Students will:
•Measure the length of objects by iterating (repeating) a nonstandard or standard unit
-Four children measured the width of a room by counting how many paces it took them to cross it. It took Ana 9 paces, Erlane 8, Stephen 10, and Carlos 7. Who had the longest pace?
•Use different units to measure the same object and predict whether the measure will be greater or smaller when a different unit is used
-Measure the length of your desk with a new crayon and with a new pencil. Which is greater, the number of crayon units of the number of pencil units?
•Measure the length of an object to the nearest inch and/or centimeter
•Tell time to the nearest quarter hour and know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year)
-It took a bus 45 minutes to go from the station to the bus barn. How long does it take to do four such trips nonstop? -Which is a longer period: 3 weeks or 19 days? 27 days or 4 weeks?
•Determine the duration of intervals of time in hours (e.g., 11:00 a.m. to 4:00 p.m.)
•Describe and classify plane and solid geometric shapes (e.g., circle, triangle, square, rectangle, sphere, pyramid, cube, rectangular prism) according to the number and shape of faces, edges, and vertices
•Put shapes together and take them apart to form other shapes (e.g., two congruent right triangles can be arranged to form a rectangle)
Students will:
•Record numerical data in systematic ways, keeping track of what has been counted
•Represent the same data set in more than one way (e.g., bar graphs and charts with tallies)
•Identify features of data sets (range and mode)
•Ask and answer simple questions related to data representations
•Recognize, describe, and extend patterns and determine a next term in linear patterns (e.g., 4, 8, 12...; the number of ears on one horse, two horses, three horses, four horses)
-If there are two horses on a farm, how many horseshoes will we need to shoe all the horses? Show, in an organized way, how many horseshoes we will need for 3, 4, 5, 6, 7, 8, 9, and 10 horses.
•Solve problems involving simple number patterns
Students will:
•Determine the approach, materials, and strategies to be used.
•Use tools, such as manipulatives or sketches, to model problems
•Defend the reasoning used and justify the procedures selected
•Make precise calculations and check the validity of the results in the context of the problem