# Mathematics

The Lower School math program provides practical experience in mathematical skills and seeks to help children see the importance and aesthetic qualities of mathematics. Children are engaged in a rich learning environment using a wide range of manipulative materials, so they may build a strong, broad-based understanding of math concepts and relationships. Concepts are introduced and practiced at the concrete level with hands-on work; abstract representations are then learned through projects, games, and written work. Using a problem-solving approach, the program follows recommendations from the National Council of Teachers of Mathematics Standards.

Listed in the following section are the major goals, by level, of the Lower School mathematics program. The goals are categorized as follows: number sense, computation, data analysis, geometry, measurement, patterns and relationships, and math communications. These categories are used for clarity of description, not to indicate that they are taught in isolation.

- Mathematics - Early Childhood
- Mathematics - Kindergarten & Grade 1
- Mathematics - Grades 2-3
- Mathematics - Grades 4-5

## Mathematics - Early Childhood

The major goals for early childhood students in Mathematics are to:

**Number Sense**

- understand that numbers have many uses (e.g., recipes, prices, ages, etc.)
- count from 1 to 10
- understand what numbers mean (e.g., that the number 5 stands for five)
- count using one-to-one correspondence

**Computation**

**Data Analysis**

- gather and help organize information

**Geometry**

**Measurement**

- gain experience with concepts of length, weight, and volume

**Patterns and Relationships**

**Math Communications**

- express awareness of attributes such as size, shape, and quantity
- help use a procedural list such as a recipe

## Mathematics - Kindergarten & Grade 1

The major goals for kindergarten and first grade students in mathematics are to:

**Number Sense**

- use math manipulatives purposefully
- recognize all numerals
- understand that numbers have many uses
- understand what numbers mean
- count using one-to-one correspondence
- order, compare, read, and begin to apply place value for numbers up to 100
- begin to understand concept of fractions (e.g., 1/2, 1/3, 1/4)

**Computation**

- use and apply estimation
- know addition and subtraction facts with sums and differences through 10
- add two-digit numbers without regrouping
- subtract two-digit numbers without regrouping

**Data Analysis**

**Geometry**

- describe, model, and classify shapes
- describe the relationship of two or more objects using positional words (e.g., over, under, to the right, etc.)

**Measurement**

- estimate and measure length, time, weight, and capacity using standard and non-standard measuring tools
- understand calendar concepts
- tell time, using a clock, by the hour and half hour
- recognize values of penny, nickel, and dime
- add pennies, nickels, and dimes

**Patterns and Relationships**

- recognize, describe, extend, and create various simple patterns
- skip count by 2, 5, 10

**Math Communications**

- print numerals
- classify objects into two or more groups using attributes
- understand a continuum of one attribute in many objects
- use a procedural list such as directions or a recipe
- solve simple word problems

## Mathematics - Grades 2-3

The major goals for second- and third-grade students in Mathematics are to:

**Number Sense**

- read, compare, order, and apply place value for numbers up to 1,000,000
- read, compare, order, and explain simple fractions
- understand the relationships among the basic arithmetic operations

**Computation**

- use estimation
- know addition and subtraction facts
- add numbers with carrying
- subtract numbers with borrowing
- multiply and divide one-digit numbers
- become familiar with calculators

**Data Analysis**

- gather data
- create and interpret graphs, tables, and charts

**Geometry**

- describe, draw, and classify shapes and figures
- describe the physical world using properties of shapes and figures
- enhance understanding of geometric concepts using the
*Terrapin Logo*computer program

**Measurement**

- use measuring tools for linear measurement
- add all coins and dollar bills
- tell time, using an analog clock

**Patterns and Relationships**

- recognize, describe, extend, and create various patterns
- explore the use of variables to describe relationships (e.g. missing addends, 3+_=7, _+3=7)

**Math Communications**

- identify key factors in problem solving
- use a variety of strategies to solve problems
- use math vocabulary to demonstrate understanding of concepts
- select tools appropriate for solving everyday problems

## Mathematics - Grades 4-5

The major goals for fourth and fifth grade students in Mathematics are to:

**Number Sense**

- read, compare, order, classify, and explain whole numbers through billions
- demonstrate knowledge of the meaning of fractions and decimals and understand how they may be used
- understand the relationships among the basic arithmetic operations

**Computation**

- solve multi-step problems using the four operations with whole numbers
- solve problems involving addition and subtraction of simple fractions and decimals
- demonstrate and explain the computation process, and support the reasonableness of answers
- know basic facts and algorithms of the four operations on whole numbers

**Data Analysis**

- gather data
- create and interpret graphs, tables, and charts
- predict and draw conclusions from graphs, tables, and charts

**Geometry**

- describe, draw, and classify shapes and figures
- compare, classify, and draw two- and three-dimensional figures
- understand congruency, symmetry, and similarity
- read and plot ordered pairs on a grid
- use tools and measurements to construct two-dimensional figures

**Measurement**

- solve and explain solutions to problems involving money and time
- solve and explain solutions to problems involving length, area, and perimeter
- solve and explain solutions to problems involving weight, mass, capacity, volume, and density
- select and use appropriate measuring tools and units of measurement

**Patterns and Relationships**

- recognize, describe, extend, and create various patterns
- describe and represent relationships with tables, graphs, and equations

**Math Communications**

- create and use organized lists and diagrams when solving problems
- identify patterns useful as rules when solving problems
- demonstrate that multiple paths to a solution may exist
- use math vocabulary to demonstrate understanding of concepts