Math: Grade 2

Draft Standards From The State of California Academic Standards Commission

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State of California Academic Standards Commission

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Mathematics is a language we use every day, often without knowing it. It builds and draws on conceptual understanding and skills, and helps us make decisions and solve problems. In this draft document we have tried to connect the notion of problem solving to conceptual understanding and skill development by embedding it within the content strands at every grade. Given here are only some of the ways you will see this exemplified. Students are asked to:

• ask relevant questions about problem situations
  
  
• decide between relevant and extraneous information
  
  
• choose appropriate operations tools and approaches to problem situations
  
  
• decide whether an exact or approximate answer is called for
  
  
• apply specific techniques in new situations
  
  
• explain, check, justify, prove, and judge the reasonableness of results
  
  
• create new approaches and connect knowledge and understanding in new ways
  
  

Number Sense

1. Students extend understanding of number and place value to exact and approximate whole numbers to 1,000.

1.1 count, read, write, order, and compare whole numbers to 1,000 and identify the place value for each digit

1.2 understand, sequence, and represent whole numbers up to 20 on a number line

1.3 express three-digit numbers using words, models, and expanded form

1.4 count by 3s and 4s to 100 and use counting by 2s to explain the concept of odd and even numbers

1.5 round a whole number and estimate the sums and differences to the nearest ten or nearest hundred and decide whether a given estimate is reasonable

1.6 apply one-digit addition and subtraction facts to solve two- and three-digit number problems

2. Students develop an understanding and demonstrate the meaning of multiplication and division.

2.1 use the four basic operations with one-digit numbers (mentally and using paper and pencil) and recall multiplication and division facts through the nines

2.2 model products and quotients (including those with a remainder) using repeated addition, arrays, counting by multiples, finding area, repeated subtraction, equal sharing, and forming equal groups

3. Students identify the different denominations of coins and bills, make equivalent combinations, and count and compare amounts of money.

3.1 identify, interpret, and use dollar ($) and cents (¢) signs and the decimal point (e.g., $4.25)

3.2 count, compare, and make change, using a collection of coins and one-dollar bills up to $10.00

Task/Assignment

Divide the cake so that everyone at your table has the same amount. There are three people at table A, and four people at table B. Which table has bigger pieces? How do you know?

Symbols and Algebra

1. Students represent and interpret number relationships.

1.1 use and describe the commutative (order) and associative (grouping) property of addition (e.g., adding 18 + 8 by taking 2 from the 8 to make 20 and then adding 6) (Knowing the formal names of these properties is not implied at this grade)

1.2 use simple properties of addition and subtraction to devise algorithms or check results

1.3 use and explain the multiplication properties of zero and one

2. Students create and solve problems involving addition and subtraction by using words, symbols, drawings, and objects.

2.1 identify relevant and irrelevant information in the statements of problem situations

2.2 identify problem situations that match or do not match a given number sentence

2.3 solve addition and subtraction problems using data from simple charts, picture graphs, and number sentences (e.g., Find the answer for 4 + X = ? when X = 2.)

2.4 describe the inverse relationship between addition and subtraction and use it to write related equations and compute (e.g., 35 + __ = 47, 47 - 35 = __)

Measurement and Geometry

1. Students estimate, measure, and demonstrate understanding of the concepts of length, area, volume, and capacity.

1.1 select an appropriate formal or informal unit to measure length, area, and volume, recognize, use abbreviations for standard units (in., ft., yd., mm, cm, m), and predict whether the measure will be greater or smaller when a different unit is used

1.2 determine the perimeter of a region by measuring or by adding given measures

1.3 estimate and determine the area and volume of figures by covering them with squares or counting the cubes

1.4 estimate and measure capacity to the nearest liter and quart and mass to the nearest kilogram and pound

1.5 identify and draw line segments of various lengths (nearest cm or in.)

2. Students demonstrate understanding of the concept of time and temperature and the relationships among different units of time (minute, hour, day, week, month, a.m., p.m.).

2.1 tell time, order events by time sequence, identify equivalent periods of time (weeks in a year, days in a month, minutes in an hour), determine past and future days of the week, and identify specific dates on a calendar

2.2 measure and record temperature (Celsius and Fahrenheit) to the nearest degree at, above, or below zero

3. Students identify and describe the elements that compose common figures in the plane and common objects in space.

3.1 identify, describe, and classify solid geometric shapes according to the number and shape of faces, edges, bases, and vertices, and corners

3.2 compare and contrast plane and solid geometric shapes (circle/sphere, square/cube, triangle/pyramid, and rectangle/rectangular solid)

3.3 put shapes together to form larger or other shapes (e.g., two congruent triangles form a rectangle) , and decompose shapes into more basic shapes (e.g., cut to form a rectangle and a triangle)

3.4 recognize and create figures which have bilateral symmetry, identify, and draw the line of reflection

Task/Assignment

Measure the width of the desk using paper clips. Measure it using spaghetti noodles. Which one uses more units? Why?

Functions

1. Students demonstrate an understanding of patterns and how they grow, and describe them in general ways.

1.1 recognize, describe, extend, and explain how to get the next term in patterns that grow in a linear way (e.g., 4, 8, 12,...; the number of ears on 1, 2, 3, 4, ... horses)

1.2 create and solve problems involving simple number patterns

1.3 identify and correct errors in patterns

2. Students demonstrate understanding of how two or more quantities are related to one another and how change in one causes change in the other.

2.1 demonstrate understanding that a number is related to other numbers by being their sum, difference, or product (e.g., Find all pairs of whole numbers whose sum is 14.)

2.2 explain how a change in input affects the output in a simple relationship (e.g., a person's age affects a person's height)

Task/Assignment

We have 5 students going to the library. Make a table to show how many books the librarian will have to check out if each student gets 1 book, 2 books, 3 books, . . . 10 books)

Statistics, Data Analysis, and Probability

1. Students collect, record, organize, and display data noting patterns and making simple predictions.

1.1 collect, record and organize data to answer a question and display data from simple experiments using dot plots and bar graphs (including those with categorical or simple whole number scales)

1.2 make simple inferences from data given in tables, picture graphs, or bar graphs

1.3 list the possible outcomes of a simple event (e.g., tossing a coin) and identify whether common events are certain, likely, unlikely, or impossible

Credits

The Draft Standards were prepared by:

The State of California Academic Standards Commission
The Commission for the Establishment of Academic Content and Performance Standards Comments may be addressed to The Commission