Math

Mathematics instruction at The Girls’ School uses manipulatives, games, practical applications and interdisciplinary projects to promote understanding and flexibility in problem solving. Students work in groups and independently, and all math classes take place during first period each day.

By third grade, students participate in math competitions starting with Math Pentathlon and Math Olympiad and adding the American Mathematical Competition (AMC-8) by sixth or seventh grade. The standard progression leads to Algebra I by eighth grade, and advancement is possible for exceptionally motivated students who have demonstrated mastery of concepts.

There is no single math curriculum used exclusively at The Girls’ School of Austin. Teachers make use of materials from Saxon, Singapore Math, University of Chicago’s Everyday Math and others.

Our math curriculum progresses as follows:

Kindergarten

Kindergarten math instruction includes whole group lessons, written practice, games and manipulatives and problem solving. The kindergarten curriculum introduces numbers to 100. Students learn these number through reading, writing, counting, comparing, ordering, adding and subtracting. They are also introduced to problem solving as well as early concepts in place value and measurement. They learn to gather and display simple data through surveys and graphs. Students also learn to identify two and three dimensional shapes, and to sort and classify and study patterns. The use of picture books helps the students relate mathematical concepts to the real world around them.

First grade math focuses on single and double-digit addition and subtraction in order to lay a strong foundation for students. The Everyday Math curriculum is used and supplemented with math read-a-louds, open-ended problem solving and additional applications to everyday life. Students learn numbers up to 1,000 and practice skip counting by 2s, 5s, and 10s. They learn patterns with shapes and numbers, measurement, place value, fractions and 2-D and 3-D geometry. Practical applications of time and money are demonstrated throughout the year as well. Students are encouraged to find multiple ways to solve problems, share the thinking that helped them arrive at an answer, and build on one another’s ideas in whole-class “math talks.”

The second grade math curriculum calls on students to master skills introduced in kindergarten and first grade. Students master one-digit addition and subtraction. They gain exposure to two and three-digit addition through traditional algorithms and the partial sums method. They explore place value, money, time, graphing, geometry, fractions, and beginning multiplication/division skills through hands-on investigations and logical reasoning activities. Students practice and extend basic measurement skills using scientific investigations of balance, length, weight and volume.

The third grade math curriculum takes the basic skills introduced in first and second grade and expands them to further develop the girls’ mathematical understanding.  Problem solving and higher-order thinking skills are strongly emphasized.  Addition and subtraction skills are reviewed and extended to 4 and 5-digit problems, and multiplication and division skills are further strengthened.  Mastery of multiplication tables zero-twelve is completed by the end of third grade through weekly timed quizzes. Students reinforce their growing bank of mathematical skills and concepts in the areas of place value, patterns, time and money, probability, geometry, graphing, fractions, decimals and measurement through hands-on activities involving daily math lessons utilizing the Everyday Math program and student journals 1 and 2.

In the fourth grade, students practice basic multiplication/division facts and solve multi-digit by multi-digit multiplication and division problems. They are introduced to real-life scenarios for applied math skills and problem-solving strategies through weekly ‘slip problems.’ Emphasis is placed on geometry, fractions, probability, place value, and decimals and practice takes place using a variety of manipulatives and mathematical tools such as compasses, calculators and protractors. Participation is encouraged in math contests such as the Math Olympiad and Math Pentathlon.

Fifth grade math uses the Everyday Math curriculum and students learn how to manipulate fractions, decimals, and percentages. Students are taught how to convert among the three and place them in numerical order; compare fractions and mixed numbers; add, subtract, multiply, and divide with fractions; and use fractions, decimals, and percentages to show data. In addition, students learn how to make graphs, calculate area and volume, identify types of angles, and create geometrical figures. Students also participate in the Math Olympiad competition and have an opportunity to compete in the Math Pentathlon.

Sixth grade math uses Everyday Math to broaden the students’ understanding of math concepts, explore the many ways of solving complex math problems, and introduce the ideas basic to algebra. Students are encouraged to think about the many connections to be made while studying numbers and mathematical ideas. The goal of sixth grade math is to reinforce previously taught concepts and move the students into thinking algebraically. The major curriculum topics include the four basic operations with whole numbers, decimals, fractions, and mixed numbers; graphs; data and surveys; standard and metric measurement; rounding and estimation; scientific notation; variables, formulas, and expressions; changing numbers from fractions to decimals to percentages; geometric shapes and terms; symmetry and congruency; polygons; angles; geometric formulas; area, perimeter, and volume; integers; order of operations, equivalents and inequalities; probability; ratios and proportions; distributive property; and properties and laws in math. In addition to this program, the students participate in Math Olympiad, an upper level math competition whose focus is on math problem solving. Everyday Math possesses many open-ended questions in an effort to get students to think mathematically.  It is through this method, and the spiraling skills built into the program, that students can easily switch topics, combine ideas, and have those aha moments.

Pre-Algebra

Pre-Algebra is the introduction of abstract and algebraic thought to the mathematical education. The focus moves from learning mathematical techniques (such as addition, subtraction, multiplication, division, distributive property, exponents, etc.) to learning how and when to apply the different techniques students have previously learned. This prepares them for the abstract nature of algebra and the rest of mathematics.

The class begins with solving equations and inequalities, predominantly with whole numbers. This allows students to grow comfortable with the rules and steps required to solve increasingly complex equations. Once they are comfortable with that, fractions are introduced, including ratios, proportions and percents, all while working within the framework of solving equations. After that, the focus moves to linear equations (with two variables), where they learn to work with two variable equations. The class concludes with an introduction to concepts in geometry and trigonometry.

Algebra 1

Algebra 1 focuses on the development of algebraic skills and concepts necessary for students to be successful in higher-level mathematics courses. Students also learn how to apply these skills in a wide range of problem solving situations. The concepts of relations and functions are explored in detail throughout the course, as is the use of graphing (both by hand and using a graphing calculator) to find solution sets. In addition we participate in two national competitions: AMC-8 and Math Olympiad.
The class begins by reviewing and expanding on skills taught in pre-algebra skills needed to solve basic and complex equations and inequalities involving one variable. Ratios, proportions, and percents are also reviewed along with their corresponding applications. We then move on to cover linear equations and inequalities in depth, along with systems of equations and inequalities.  Next we go into polynomials, factoring and quadratic functions.  We finish the year with an introduction to rational functions.

Geometry

Guided by the essential questions, “What is proof and what makes a good proof?” students explore geometry using inductive and deductive methods.  This course includes a substantial amount of writing and is supplemented with problems from the Drexel Math Forum’s Problem of the Week (POW).  Students are expected to solve problems at the board in front of the class and develop confidence doing so.  Students also participate in the annual Mathematical Association of America’s AMC-8 math competition.  The text used is Discovering Geometry by Michael Serra. Students maintain a portfolio of conjectures and POW reports. Roughly a month is dedicated to a review of topics from Algebra I, extending the treatment to a more advanced level.  For that part of the course, students use the text Intermediate Algebra by Lial, Hornsby and McGinnis.