Second-grade students continue to develop a more formal understanding of addition
and subtraction with whole numbers and place value, building on the foundations
established in first grade. Students use a wide variety of manipulatives to
help them develop a solid understanding of number sense. They solve more complex
two-digit addition and subtraction problems and explore the basic concepts of
multiplication through repeated addition and the use of a wide variety of story
problems. At the same time, they begin the ongoing work of developing automatic
recall of the addition and subtraction facts so that they can spend more time
focusing on more complex concepts. The children continue to explore number patterns,
identify and predict their rules, and explore patterns mathematically using
charts, tables, and graphs. Second-graders begin to establish a more formal
knowledge of money, measurement and time, estimation, geometry, probability,
and statistics.
As in all grades, the second-grade math curriculum at San Francisco Day School
is based on the belief that all children have fundamental attitudes of curiosity
and the willingness and ability to probe, explore, experiment, make conjectures,
and persevere with a piece of demanding work.
Goals and Objectives
Number and Operations
Grouping
Makes sets of attribute objects according to different criteria
Makes two or more intersecting sets of attribute objects
Counting
Names the number before or after a given number 1-1,000, or names the
missing number in a sequence
Counts by 2s, 3s, 4s, 5s, and 10s
Recognizes inequalities between sets
Writes equations using less than (<) and greater than (>)
Counts, recognizes, and writes numerals 1-1,000
Addition
Knows addition facts in all combinations using addends 1-20
Adds 2-digit numbers without regrouping
Builds 2-digit addition problems with regrouping using base ten blocks
Records column 2-digit addition problems with regrouping
Subtraction
Knows subtraction facts in all combinations using numbers 1-20
Builds and records 2-digit subtraction without regrouping
Builds and records 2-digit subtractions with regrouping
Multiplication
Recognizes simple multiplication arrays using manipulatives
Extends understanding of the connection between repeated addition and
multiplication
Division
Begins to understand the connection between repeated subtraction and
division
Begins to use sharing as a form of dividing
Fractions
Makes half, third, and quarter sets using manipulatives
Explores and divides shapes and objects into halves, quarters, and thirds,
using folding or cutting
Numeration
Recognizes place values (hundreds, tens, and ones) using manipulatives
Extends knowledge of the role of zero as place holder
Understands use of ordinals using manipulatives
Explores and uses other bases
Measurement
Expands time-telling skills and vocabulary (use of hour and minute hand)
using digital and analog clocks
Expands calendar skills; analyzes the make-up of a month and records
information
Measures specific objects and room dimensions using meter sticks and
rulers (centimeters); records results
Measures liquids and solids in metric units
Explores the concept of temperatures
Solves problems using various denominations of money up to one dollar
Geometry and Spatial Sense
Draws basic geometric shapes such as square, circle, semicircle, parallelogram,
and other polygons
Explores angles
Recognizes and builds symmetrical and equilateral shapes with manipulatives
Recognizes and draws symmetrical and equilateral shapes on paper
Discusses and describes attributes of a variety of three-dimensional
geometric figures
Uses maps, mazes, and patterns to develop spatial awareness
Develops spatial awareness of scale
Patterns and Functions
Makes object, pictorial, and number patterns, following given rules
Represents functions with tables and charts
Makes simple graphs of ordered pairs
Data Analysis and Probability
Collects, organizes, and records data using objects and their attributes
Solves problems by collecting, organizing, and recording physical data
Continues to experiment with objects to discover concepts of probability
Algebra
Explores concept of variables using objects and solving problems
Extends ability to solve linear equations of the form 8 - ? = 5
Assessment and Evaluation
The second-grade teachers assess students throughout the year. They administer
pre- and post-assessments at the beginning and end of the year, and evaluate
students individually and in groups, using a variety of assessment tools
including:
Individual evaluations for understanding of concepts
Regular teacher assessment during small-group lessons
Record-keeping of daily work and homework and individual problem-solving
assessments
Materials
Real materials (manipulatives) are used to help second graders develop
a full understanding of mathematical concepts. Manipulatives used in second
grade include Attribute blocks, base blocks, building blocks, color cubes,
color tiles, Cuisenaire rods, Dominoes, Geoboards, inch cubes, Multilinks,
pattern blocks, perceptual puzzle blocks, place value boards, Tangrams,
and Unifix cubes.
References and Resources
Curriculum and Evaluation Standards for School Mathematics. NCTM, 2000.
Math by All Means. Burns, Marilyn. 1994.
Mathland. Creative Publications, 1998.
Mathematics Their Way. Lorton, Mary Baratta. rev. 1996.
