First-grade students are introduced to operational symbols, equations, and
incremental counting. They begin to develop an understanding of place value,
time, money, graphing, estimation, pattern, statistics, and probability. Standard
and non-standard measurement is introduced. Students begin to recognize relationships
between different mathematical concepts and are encouraged to solve problems
using any method they can to reach a solution. Discussion and explanation, both
verbal and non-verbal, are used to help students understand and develop their
thinking as mathematicians. Students continue weekly visits to the math lab.
Goals and Objectives
Number and Operations
Grouping
Makes sets according to attributes
Makes intersecting sets of attribute objects
Makes matching, numerical sets of attributes
Counting
Builds and records numbers
Begins to count and recognize numerals 1-100
Explores various manipulatives as counting tools
Uses various manipulatives for recognizing skip-counting patterns of
2s, 5s, 10s
Names the number before or after a given number
Names the number missing in a sequence
Addition
Recognizes addition as a process of combining sets
Adds all combinations, using addends 1-5 both concretely and abstractly
Develops an understanding of whole-number addition through problem
solving
Articulates and justifies individual strategies used to find solutions
Reads and writes addition equations
Recognizes addition patterns such as 2 + 4 = 6, 2 + 5 = 7, 2 + 6 =
8
Understands and identifies element of zero
Recognizes symbols (+) and (=)
Subtraction
Recognizes subtraction as a process of partitioning or taking away
sets
Subtracts all fact combinations using 1-10 both concretely and abstractly
Articulates and justifies individual strategies used to find solutions
Reads and writes subtraction equations
Recognizes subtraction patterns such as 10 - 1 = 9, 10 - 2 = 8. 10
- 3 = 7
Recognizes symbols (-) and (=)
Multiplication and division
Experiences the putting together and taking apart of repeating sets
Fractions
Experiences the concept of fractions as part of a whole object or set
Numeration
Recognizes numerals as names of numbers, and numbers as groups of
objects
Experiences and begins to understand grouping by 10s
Experiences and begins to understand place value in 2-digit numbers
Measurement
Uses non-standard and customary units of measure to estimate and measure
length, area, volume, weight, and time
Begins to understand the concept of time using both digital and traditional
clocks
Begins to understand money as a measurement of value
Geometry and Spatial Sense
Recognizes and constructs lines and geometric shapes
Discovers and begins to understand solids such as pyramids and cones;
draws them from different angles
Solves a variety of spatial puzzles
Patterns and Functions
Continues to identify and make patterns of increasing difficulty
Understands and identifies function rules, using a variety of objects,
pictures, and numbers
Data Analysis and Probability
Experiments with collecting, organizing, and recording data
Experiments with objects to discover the concept of probability
Creates simple graphs to record information
Interprets data
Algebra
Explores concept of variables
Explores and develops strategies for solving a variety of open-ended
problems
Solves linear equations, such as 1 + n = 8, using a variety of manipulatives
Assessment and Evaluation
The first-grade teachers assess students throughout the year, individually
and in groups, using a variety of assessment tools and portfolios of student
work.
Materials
Real materials (manipulatives) are used to help first graders develop a full
understanding of mathematical concepts. Manipulatives used in first grade include
Attribute blocks, base blocks, building blocks, color cubes, Cuisenaire rods,
Geoboards, Geoblocks, geometric solids, pattern blocks, Pentominoes, perceptual
puzzle blocks, polydrons, Tangrams, and Unifix cubes.
References and Resources
Curriculum and Evaluation Standards for School Mathematics. NCTM, 2000.
Mathematics Framework for California Public Schools. California Department
of Education, 2000.
Puddle Questions. Creative Publications, 1994.
Problem-Solving Lessons. Burns, Marilyn. Math Solutions Publications, 1996.
