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Copyright Wooster School 2005
Mathematics
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General
The mission of the math department is to provide a traditional math education that will prepare students for college and life. The department strives to provide excellent instruction in a caring and supportive environment, to connect the classroom to the world in order to make the learning relevant, and to spark curiosity about things mathematical. The teachers want the students to see them enjoying math and being passionate about the subject.
The mathematics curriculum has been created with the view that growth in the understanding and extension of fundamental ideas is a continuing and ordered process. The mathematics department understands that the acquisition of mathematical knowledge is a cumulative process that should be started as early as possible and carried consistently throughout the student's years in school. Each course should follow logically from the previous course and fully prepare the student for the next higher level.
Throughout their coursework, students are introduced to the essential principles, processes, and notation of mathematics. The ability to communicate mathematically is stressed. This includes showing work on problems and using the correct terminology in discussions. Discovery, logic, brainstorming, analogy, and other techniques introduce and reinforce concepts. Computers and calculators, including scientific and graphing in the upper levels, are used to investigate new concepts and to facilitate computations after basic skills have been learned. The department strives to adhere to the standards set forth in 2000 by the National Council of Teachers of Mathematics.
GOALS OF
When
1. Using Mathematics for Modeling
We believe that our most important goal is to show students how mathematics can be used to model phenomena. Examples come from physics, economics, health care, earth science, or any other relationship that can expressed mathematically. Students are asked to develop models, use them to make predictions, and evaluate how well their models reflect reality.
In the classroom, we work toward this goal in a variety of
ways depending on the level. In the
Students in upper school math classes spend many days tying together words, data, graphs, and equations. Questions involve how these four representations are connected and illustrate the same phenomena, what models might be appropriate for a particular phenomenon, and once a model has been used, how accurate it is. Some teachers also include labs as a component of their classroom experience. Utilizing various pieces of technology (especially computers and calculators) is an important aspect of modeling in upper school courses.
2. Increasing
students' confidence in their ability to do mathematics
This goal is often the most challenging for the math department. Many times, a single experience (whether a low score on a test or a required "redo" of a homework assignment) can make a child feel like he/she cannot master the concept being covered in the class. With math, this one experience can cause the student to feel that "I'm bad at math" or "I can't do math." As a math department, we are committed to instilling in students the confidence to push their boundaries and work through difficulties.
One of the greatest lessons math has to offer is how to fail. As teachers, we are willing to admit our mistakes (whether it is a typo on a test or writing something incorrectly on the board or even going down the wrong path when solving a problem with a student). We want to teach students that what matters is what they do after they fail - do they learn from their mistakes or do they give up? Being wrong is okay as long as we move forward, figure out what was wrong, and how to fix it.
As teachers, we encourage students to speak up when they don't understand a concept. We praise students for their ideas, including innovative thinking and the recall and application of ideas. We share our struggles with math, letting them know that math didn't always come easy to us. As we teach concepts, we also teach skills needed to succeed, including test taking and study skills.
Getting students to participate in class is a big part of encouraging confidence. When they are active participants in classroom discussions, they learn to see themselves within the context of the class and not as isolated individuals.
3. Learning to
communicate mathematical ideas
As with writing in English or a foreign language, learning to communicate is an important part of the math curriculum. From kindergarten through twelfth grade, math teachers use appropriate vocabulary and symbols and, through repetition in the classroom, give their students the same language. Communication, however, is not limited to simply symbols, students are often asked to explain their thinking. In answering these questions, students are asked to use appropriate vocabulary. Some classes give students writing assignments, either in journals or essays, to give them practice at verbalizing their thoughts on mathematics.
Another major component of communication is interpretation. Once a student has determined a numeric answer to a problem, he/she is often asked to put this number in the context of the problem. This question requires that the student consider units that the answer should be expressed in, as well as the quantity in the problem that the number represents. Teachers require full sentence answers for word problems.
4. Developing number
sense
Students' sense of numbers begins early in the
Although calculators are used in all grades, all teachers have "Don't touch that calculator!" moments. Even though technology is here to stay, mental math remains an important ability in the development of mathematical minds. Estimation is also central to number sense. Before starting a problem, teachers discuss what a reasonable solution might be, and in more complex circumstances, how an estimate can be made. Once an answer has been obtained, discussing whether or not that answer is in the ballpark is yet another aspect of number sense. This question is especially important when technology has been used to generate the numeric answer. Too often, students have the belief that "if I got from the calculator, it must be right."
5. Learning to
appreciate the power and potential of mathematics
Mathematics is all around us. We want students to understand that math can help us understand many circumstances. Lower school students use math to figure out the number of days until someone's birthday, write stories using mathematical ideas, and celebrate Pi Day with pizzas and apple pies. For middle and upper school students, teachers work to create questions that allow students to see math in the context of their world - whether it is buying CDs at the mall or launching water balloons.
One of the most important ways for teachers to help students
to appreciate mathematics is through our passion for the subject.
6. Preparing students for AP exams
This goal applies to the three AP courses
For all three of these courses, teachers generally follow the
guidelines set out by the College Board. We cover all of the material required
for the exam. However, because we do not believe in "teaching to the
test,"
SEQUENCE OF COURSES K
- 12
All students in grades K - 5 study mathematics appropriate for their grade level. Starting in grade 2, students at each grade level are divided into two groups for math study. This grouping reflects the emphasis and methodology of the instruction that best meet the learning styles of each child; each of the two grade level groups is taught the same material and is expected to master the same skills at each level.
When students enter the Middle School in 6th grade, they are placed in one of two classes - Math 6 or Introduction to Algebra. Following Math 6, those students who are ready to face the rigors of Algebra progress to Introduction to Algebra the following year. Those students who complete Math 6 but need some additional practice with arithmetic and beginning algebraic concepts take Fundamentals of Algebra in 7th grade and reach Introduction to Algebra in their 8th grade year.
Algebra 1 follows Introduction to Algebra. Students reaching Algebra 1 in the Middle School take a course called Honors Algebra 1.
Here two courses of study diverge: those who complete Honors Algebra 1 take Honors Geometry followed by Honors Algebra 2. Those who complete "regular" Algebra 1 take Algebra 2 followed by Geometry. The rationale for this is that students for whom algebra does not come easily experience better retention by studying algebra over two consecutive years, whereas those in the Honors sections are better served by deepening their understanding of analytic geometry through studying geometry before their second year of algebra.
After the completion of Geometry, the last required course
for graduation from
After Honors Algebra 2, most students proceed to Honors Precalculus and, finally, AB Calculus. A small number of students, usually seniors, reach BC Calculus, offered after AB Calculus.
Some years,
PLACEMENT AND
TRANSITIONS
When students enter Wooster, they are placed in a math class based on previous coursework, teacher recommendations, standardized tests, and the assessment of the Math Chair and Director of Studies. Because students' growth is not uniform, some placements just don't work. Lacking a crystal ball, we can only evaluate what we see now, keeping the students' best interests at heart. When a placement is not working out well, we try to improve the situation by remediation or by enrichment or by moving the student to another course. We fully expect to have to do this every year. In fact, our ongoing chore is to re-evaluate students regularly and make the best decisions - in consultation with parents - about what course is best.
It is important that children be placed in the group that best suits their learning style. If concrete learners are to become confident mathematicians, they will need the time and practice to develop their skills and feel capable of grasping increasingly difficult concepts. An abstract learner must continue to be challenged.
Placement in the groups is usually determined by the previous year's teacher. Movement from one group to another is determined by the current teacher's judgment and the child's work on assessments and in class.
In the Middle and
Middle School: Near
the end of their 5th grade year,
When they enter 6th grade, very few students have the aptitude, skills, study habits, and "academic maturity" to thrive in the very demanding succession of courses of which Intro to Algebra is only the first. Having seen a number of students do well in the first few doubly accelerated courses only to falter at the Honors Algebra II or Honors Precalculus level, we have become more conservative in our selections of 6th grade students likely to succeed both in Intro to Algebra and in future math courses. Our mathematics criteria include strength with all arithmetic operations and computations with all sorts of numbers, the ability to apply that strength to word problems, the ability to easily apply methods to novel situations, and the ability to demonstrate all of these on traditional assessments at a consistently high level. We give two cumulative assessments in 5th grade and expect any student who will be considered for Intro to Algebra to score above 80% on at least two of these and have no score below 70%. These three assessments, given in early June, give us the best measure of retention over time and the ability to integrate and apply new material, key components to success in math. Another measure of mathematical aptitude is the ERB CTP-IV test given in February. Students ready for Intro to Algebra in 6th grade should score in the 8th or 9th stanine nationally. Typically, of the 40 sixth graders, two-thirds of which have come through Wooster with the remaining dozen having applied to Wooster from other schools, about one full section (10-14) are deemed ready to move into Introduction to Algebra. Some years, there have been fewer qualified candidates, some years slightly more.
To make our judgment on mathematical aptitude alone would discount some major factors in the make-up of highly successful math students. Consequently, we also look for strong, consistent effort on homework, strong organization and communication skills, and seriousness of purpose in an academic setting. Also necessary are coping strategies for those times when the student doesn't "get it" immediately, willingness to admit there's a problem and to seek extra help being paramount among them. Naturally, we turn to current teachers to provide insights about these intangibles.
It is important to note that since there has been tremendous
admissions interest at the 6th grade level, candidates accepted into that grade
have, in general, been quite strong math students, meaning that a relatively
larger percentage of new students have been able to move directly into
Introduction to Algebra.
After sixth grade, a similar discernment is necessary to determine which of the three paths available in seventh grade is best. At that level, Fundamentals of Algebra, Introduction to Algebra, and Honors Algebra 1 are offered. Students successful in Introduction to Algebra move on to take Honors Algebra 1 in seventh grade. Those who took Math 6 are split into the other two courses based on the same factors used to determine readiness for algebra in sixth grade.
Although math is very sequential, being placed in a certain class in 6th grade (or moving from 6th to 7th grade) does not lock a student into a particular "track." The mathematics department pays careful attention to those students who are advanced beyond grade level. If a student is having difficulty in a class he/she may be asked to repeat the class or do summer work prior to advancing to the next level. Students who are advanced beyond grade level often have difficulty in later courses (especially Honors Algebra 2 and Honors Precalculus) if their basic algebraic skills are not solid or if they have not yet developed the ability to think abstractly. In addition, students who demonstrate that they possess the necessary skills (including the ability to reason abstractly), may be invited accelerate into a more challenging course of study. In either case, the decision is based on what is best for the student in the long run and is made by the Director of Studies in consultation with the Department Chair and the current teacher.
No matter which course a student takes in 6th grade,
Advanced Placement (AP) Calculus is a possibility, if appropriate for the
student, in the
CONTINUITY THROUGH
THE DIVISIONS
The mission of the lower school mathematics curriculum is to provide the students learning experiences and introduce ideas that allow them to gain mathematical power and learn to value mathematics. Thus they will become confident in their ability to do mathematics, become problem solvers in both theoretical and practical situations, communicate and reason mathematically, estimate, determine if their solutions are reasonable, and demonstrate these abilities through learning activities and formal and informal assessments.
The lower school mathematics curriculum seeks a balance between fostering a student's conceptual understanding and the student's mastery of mathematical facts, assessing each against benchmarks for each level as defined by the department. By the end of second grade, for example, students have been taught, practiced, and been assessed on addition and subtraction facts through twenty.
The main purpose of the middle school mathematics curriculum is to bridge the gap between arithmetic and formal algebra by providing students with a thorough understanding of the skills and concepts that are necessary for the study of algebra and geometry. Facility in the use of whole and rational numbers is fostered, and calculator usage is taught as appropriate. Through consistent reinforcement, students are taught to show work logically, develop strong number sense, improve mental math and reasoning skills, and work effectively in groups. Each student is encouraged to take responsibility for his or her own learning, stay organized, and seek extra help when needed. At this level, teachers often require students who are struggling to attend extra help sessions.
Upon completion of eighth grade,
The
Modeling natural and manmade phenomena with algebraic or graphical representations is an essential skill. We teach this through data collection, analysis of causality and dependence of one variable on other factors, discovery of algebraic connections among variables, formulation of functional relationships, and analysis of the resulting model to determine its limits of applicability.
One goal of the mathematics curriculum is to expand the range of students' mathematical experiences and ideas by providing learning opportunities that allow them to gain mathematical power as they learn to value mathematics. Lower School students are expected to demonstrate their ability to solve mathematical problems in theoretical and practical situations and communicate mathematically. Students are regularly asked to articulate their reasoning and define the methods used to solve a problem; students are always expected to show their work.
In the youngest grades students begin developing an understanding of the relationships between numbers at a concrete level. This provides the foundation needed to build dependable and understandable methods for computation. Automaticity of certain skills is essential to higher level thinking in any field including math; class time and homework time are spent on systematic review and practice so that students develop automatic recall of their basic number facts. Students who have not met the expectations set for their grade level will be expected to complete additional work over weekends and school vacations.
These benchmarks are for rote mental computation with speed and accuracy:
Conclusion of first grade: addition/subtraction facts 1-10
Conclusion of second grade: addition/subtraction facts 1-20 and multiplication facts for 0,1,2,5, and 10
Conclusion of third grade: multiplication facts 2-12
Conclusion of fourth grade: division 1-12
All students beyond kindergarten are expected to have a calculator for math class. The calculator is yet another tool used in class. It is not used every day but at certain times. Students are explicitly taught not only how to use a calculator but when it is the appropriate tool to use.
The mission of the lower school mathematics curriculum is to provide the students learning experiences and introduce ideas that allow them to gain mathematical power and learn to value mathematics. Thus they will become confident in their ability to do mathematics, become problem solvers in both theoretical and practical situations, communicate and reason mathematically, estimate, determine if their solutions are reasonable, and demonstrate these abilities through learning activities and formal and informal assessments.
The lower school mathematics curriculum seeks a balance between fostering a student's conceptual understanding and the student's mastery of mathematical facts, assessing each against benchmarks for each level as defined by the department. By the end of second grade, for example, students have been taught, practiced, and been assessed on addition and subtraction facts through twenty.
SEQUENCE OF COURSES
All students in grades K - 5 study mathematics appropriate for their grade level. Starting in grade 2, students at each grade level are divided into two groups for math study. This grouping reflects the emphasis and methodology of the instruction that best meet the learning styles of each child; each of the two grade level groups is taught the same material and is expected to master the same skills at each level.
PLACEMENT AND
TRANSITIONS
For returning students in the Lower School, placement is made by the previous year's teacher.
Lower School: Students in kindergarten and first grade attend math class with their classmates, instructed by their homeroom teacher. Students in grades two through five are divided into two math sections: an abstract and a concrete group. Both groups cover the material designated for their grade level but they are approached differently to account for different learning styles. Children in the concrete group may grasp concepts more efficiently using a more "hands-on" approach. They may need more practice to become facile in their development of skills. Abstract math students can think "in their head." They can often learn basic skills quickly but still need practice with new concepts. Some children need to be challenged with more difficult problems. Although both groups cover the same material, the abstract group may expand upon a concept with greater depth.
It is important that children be placed in the group that best suits their learning style. If concrete learners are to become confident mathematicians, they will need the time and practice to develop their skills and feel capable of grasping increasingly difficult concepts. An abstract learner must continue to be challenged.
Placement in the groups is usually determined by the previous year's teacher. Movement from one group to another is determined by the current teacher's judgment and the child's work on assessments and in class.
PEDAGOGICAL PRACTICES
AND CURRICULAR CHOICES
Every lower school student at Wooster studies math every day for one hour.
In the youngest grades, students begin developing an understanding of the relationships between facts at a concrete level. This provides the foundation needed to build dependable and understandable methods for computation. Automaticity of certain skills is essential to higher level thinking in any field, including math; class time and homework time are spent on systematic review and practice so that students develop automatic recall of their basic number facts. Students who have not met the expectations set for their grade level will be expected to complete additional work over weekends and school vacations.
Lower school teachers use a variety of texts, manipulatives, games, and computer software to provide students with focused, systematic, and challenging math instruction. The Lower School utilizes the University of Chicago School Mathematics Project series, Everyday Math 2002, supplemented by the Scott Foresman - Addison Wesley series Math 2001 for practice of rote skills. Both these programs offer an orderly development of key mathematical concepts with each grade building upon the achievement of the previous grade. Two thorough reviews of the mathematics curriculum by the School confirm that these programs, used in conjunction with one another achieve the appropriate balance between mastery of computational skills and conceptual mathematical understanding (including problem-solving skills) which is a goal of the K-12 math program. Lower School students use journals and workbooks during class and have daily homework assignments on Monday through Thursday nights.
SKILLS MASTERED
Arithmetic
Count to 100 by 1s and 10s.
Count to 30 by 5s.
Count backwards from 10.
Count to 10 by 2s.
Understand concept of "one more" and "one less".
Read and write numbers 0-20.
Familiarity with number families to 5.
Patterns
Recognize patterns in a real world context.
Continue and develop 3-part patterns.
Identify pattern blocks and use them to complete a design.
Data Analysis
Understand a simple bar graph.
Time and Money
Recognize pennies, nickels, dimes, and quarters.
Geometry
Sort objects by various attributes.
Compare and describe sizes of objects.
SKILLS INTRODUCED AND PRACTICED
Arithmetic
Count backwards from 22 or higher.
Count to 100 by 2s.
Count beyond 110 by 5s and by 10s.
Read and write numbers 0-100.
Understand 2-digit numbers in terms of 10s and 1s.
Understand equivalent expressions as two or more different expressions of the same number.
Estimate
Data Analysis
Perform simple data collection and graphing.
Time and Money
Know the value of a penny, nickel, dime, and quarter.
Estimate times on an analog clock using only the hour hand.
Geometry
Identify and use measuring tools for linear, weight, and volume measures.
Recognize and name basic plane and solid figures.
SKILLS MASTERED
Arithmetic
Count to 100 by 5s.
Count to 40 by 2s.
Read and write numbers 0-50.
Order and compare pairs of numbers to 22.
Count up and back by 1s, starting with any number less than 20.
Count up to 20 objects.
Solve simple addition and subtraction stories to 10.
Know addition and subtraction facts to 10.
Know +1, +0, doubles, and sums of 10 addition facts beyond 10.
Understand place value for 10s and 1s.
Time and Money
Tell time to the nearest hour and half hour.
Patterns
Identify and complete simple patterns.
Data Analysis
Write and count tallies to 30.
SKILLS INTRODUCED AND PRACTICED
Arithmetic
Find complements of 10.
Find missing addends.
Find missing numbers and/or the missing rule in "What's my Rule?" problems.
Compare numbers using < and >.
Find many names for a number.
Identify numbers as even or odd.
Identify fractional parts of regions and sets with a focus on unit fractions.
Solve 2-digit addition and subtraction problems.
Compare fractions less than 1.
Find equivalent fractions.
Solve number stories.
Time and Money
Calculate the values of combinations of pennies, nickels, dimes, and quarters.
Find exact change pennies for nickels.
Make change for amounts less than $1.
Geometry
Measure objects to the nearest centimeter.
Understand digital notation for time.
Identify 3-dimensional shapes and know their characteristics.
Identify symmetrical figures.
Sort and identify object by attributes.
Identify polygons and know their characteristics.
Use standard units for measuring length.
Count sets of quarters, dimes, nickels, and pennies.
Identify and use patterns on the number grid.
SKILLS MASTERED
Arithmetic
Count by 2s, 5s, and 10s from any given number.
Construct fact families for addition and subtraction.
Find equivalent names for numbers.
Understand place value for 1s, 10s, 100s, and 1000s.
Add and subtract multiples of 10.
Find missing addends for next multiple of 10.
Solve addition and subtraction stories to 20.
Know addition and subtraction facts to 20.
Add three 1-digit numbers mentally.
Multiply numbers by 1, 2, 5 and 10.
Identify and name a fractional part of a region.
Data Analysis
Make tallies and give the total for multi-digit numbers.
Plot data on and compare quantities from a bar graph.
Time and Money
Tell time to the nearest 5 minutes.
Calculate the values of combinations of pennies, nickels, dimes, and quarters.
Read and write money amounts under $1 in dollar notation.
Use equivalent coins to show money amounts in different ways.
Demonstrate calendar concepts and skills.
Geometry
Measure to the nearest inch and centimeter.
Find area and perimeter concretely.
Use a ruler, tape measure, and yardstick to measure length.
Identify 3-dimensional shapes and know their characteristics.
Identify symmetrical shapes.
Identify parallel and non-parallel line segments.
SKILLS INTRODUCED AND PRACTICED
Arithmetic
Compare whole numbers and fractions using <, > or =.
Devise and use strategies for finding sums and differences of 2-digit numbers.
Estimate approximate costs and sums.
Solve equal grouping and equal sharing problems and stories.
Model multiplication problems with arrays.
Add three 2-digit numbers mentally.
Use parentheses in number models.
Understand fractions as names for equal parts of a region or set.
Understand that the amount represented by a fraction depends on the size of the whole.
Recognize equivalent fraction names.
Understand place value for 10,000s.
Construct multiplication and division fact families.
Data Analysis
Find the median, maximum, minimum, and range of a data set.
Determine the mode of a data set.
Time and Money
Solve money stories involving change.
Use alternate names for times.
Geometry
Measure to the nearest half inch and half centimeter.
Use appropriate units for measurements and recognize sensible measurements.
Read temperature on a thermometer.
Identify
equivalencies for millimeters, centimeters, decimeters, and meters.
SKILLS MASTERED
Arithmetic
Count by 10s and 100s.
Use basic facts to solve fact extensions.
Add and subtract multi-digit numbers.
Read, write, and compare numbers up to 5-digits.
Multiply multi-digit numbers by 1- or 2-digit numbers.
Construct multiplication and division fact families.
Know multiplication facts to 12.
Time and Money
Tell time to the nearest minute.
Count combinations of bills and coins and write total in dollar notation.
Data Analysis
Make a bar graph.
Geometry
Identify right angles.
Draws lines of symmetry.
SKILLS INTRODUCED AND PRACTICED
Arithmetic
Estimate answers to multi-digit addition and subtraction problems.
Read, write, and compare 6- and 7-digit numbers.
Find factors of a number.
Solve number stories involving equal sharing and equal grouping.
Read and write 1- and 2-digit decimals.
Identify place value in decimals.
Compare and order fractions and decimals.
Recognize and know square products.
Identify fractions on a number line.
Read and write three digit decimals.
Understand function and placement of parentheses in number sentences.
Convert between mixed numbers and fractions.
Find equivalent fractions.
Solve fraction number stories.
Solve number stories involving positive and negative numbers.
Interpret remainders in division problems.
Data Analysis
Find the mean and median of a data set.
Understand and use the language of probability.
Make a frequency table.
Use fractions to record probabilities of events.
Use random draws to predict outcomes.
Collect and organize data for use in predicting outcomes.
Geometry
Find the perimeter of a polygon.
Find area of a rectangular region divided into square units.
Measure lines segments to the nearest quarter inch.
Identify, draw, and name line segments, lines, and rays.
Draw parallel and intersecting line segments, lines, and rays.
Draw angles as records of rotation.
Find volume of rectangular prisms.
Know units for length, weight, and capacity.
Measure in inches and centimeters.
SKILLS MASTERED
Arithmetic
Add and subtract multi-digit numbers.
Understand relationship between multiplication and division.
Compare large numbers.
Estimate multi-digit sums.
Identify fractions parts of sets and regions.
Use a calculator to rename any fraction as a decimal or percent.
Use rate tables (if necessary) to solve rate problems.
Know division facts to 12.
Data Analysis
Use statistical landmarks maximum and minimum.
Geometry
Name, draw, and label line segments, lines, rays, angles, triangles, and quadrangles.
Identify and describe right angles, parallel lines, and line segments.
Draw and measure line segments to the nearest centimeter.
Identify lines of symmetry, lines of reflection, reflected figures, and symmetric figures.
SKILLS INTRODUCED AND PRACTICED
Arithmetic
Solve open number sentences.
Insert parentheses to make true number sentences.
Solve problems with parentheses.
Determine whether number sentences are true or false.
Read and write 4-digit decimals.
Compare and order fractions and decimals.
Solve 1- and 2-digit decimal addition and subtraction problems and number stories.
Estimate products of multi-digit numbers.
Solve multi-digit multiplication problems.
Round whole numbers to a given place.
Interpret the remainder in a division problem.
Express remainder of whole-number division as a fraction and the answer as a mixed number.
Rename fractions with denominators of 10 and 100 as decimals.
Find equivalent fractions.
Find a percent or fraction of a number.
Use exponential notation to represent powers of 10.
Add and subtract fractions.
Estimate multiplication and division of decimals by whole numbers.
Add and subtract integers.
Data Analysis
Use the median, mode, and range.
Evaluate reasonableness of rate data.
Geometry
Name and locate a point specified by an ordered pair.
Identify acute, right, obtuse, straight, and reflex angles.
Use formulas to find perimeters and areas of rectangles, parallelograms, and triangles.
Use formula to calculate the volume of a rectangular prism.
Describe properties of geometric solids.
Use a compass and straightedge to draw geometric figures.
Identify locations on Earth for which latitude and longitude are given.
Find latitude and longitude for given locations.
Draw and measure line segments to the nearest millimeter.
Rotate and translate figures.
Identify properties of polygons.
Classify quadrangles according to side and angle properties.
Use a map scale to estimate distances.
Express metric measures with decimals.
Convert among metric measures.
SKILLS MASTERED
Arithmetic
Identify prime and composite numbers.
Understand how square numbers and their square roots are related.
Draw arrays to model multiplication.
Identify odd and even numbers.
List the factors of a number.
Write and solve open sentences for number stories.
Add, subtract and multiply multi-digit numbers and decimals.
Know place value to billions and to hundredths.
Find quotient and remainder of a whole number divided by a 2-digit whole number.
Interpret the remainder in division stories.
Convert between fractions and mixed numbers.
Find equivalent fractions.
Add and subtract fractions with common denominators.
Subtract mixed numbers with like denominators.
Find common denominators.
Data Analysis
Identify the maximum, minimum, mode, median, and mean for a data set.
Geometry
Understand the concept of area of a figure.
Understand a formula to find the area of polygons and circles.
Know properties of geometric solids.
Determine angles measures based on the relations between angles.
Know properties of polygons.
Plot ordered pairs on a one-quadrant coordinate grid.
SKILLS INTRODUCED AND PRACTICED
Arithmetic
Rename numbers written in exponential notation.
Understand and apply scientific notation.
Use divisibility tests.
Find the greatest common factor of two numbers.
Interpret the remainder in division number stories.
Determine the value of a variable; use this value to complete a number sentence.
Order and compare fractions.
Use an algorithm to multiply fractions.
Find a percent of a number.
Use an algorithm to add and multiply mixed numbers.
Convert between fractions, decimals, and percents.
Add and subtract fractions with different denominators.
Write algebraic expressions to describe situations.
Represent rate problems as formulas, graphs, and tables.
Solve ratio and rate number stories.
Divide decimal numbers by whole numbers.
Understand and apply order of operations.
Add and subtract integers.
Data Analysis
Draw, measure, and interpret circle graphs for a set of data.
Understand how sample size affects results.
Construct, read, and interpret stem and leaf plots.
Use tree diagrams to find all possible ways a sequence of choices can be made.
Compute the probability of outcomes when choices are equally likely.
Use the Counting Principle.
Geometry
Use a formula to find the volume of a prism.
Identify the base and height of triangles and parallelograms.
Distinguish between circumference and area of circles.
Understand the relationship between the volume of pyramids and prisms, and the volume of cones and cylinders.
Find the surface area of prisms and cylinders.
Understand the concept of volume and capacity and how to calculate it.
Measure an angle to the nearest .
Identify types of angles and triangles.
Define and create tessellations.
Plot ordered pairs on a four-quadrant coordinate grid
MS MATHEMATICS
DEPARTMENT
The main purpose of the middle school mathematics curriculum is to bridge the gap between arithmetic and formal algebra by providing students with a thorough understanding of the skills and concepts that are necessary for the study of algebra and geometry. Facility in the use of whole and rational numbers is fostered, and calculator usage is taught as appropriate. Through consistent reinforcement, students are taught to show work logically, develop strong number sense, improve mental math and reasoning skills, and work effectively in groups. Each student is encouraged to take responsibility for his or her own learning, stay organized, and seek extra help when needed. At this level, teachers often require students who are struggling to attend extra help sessions.
Upon completion of eighth grade, Wooster's goal is that each student will have mastered basic arithmetic skills and be confident and competent working with pre-algebraic and beginning algebraic concepts. For students who have advanced beyond grade level, it is additionally expected that they will demonstrate good retention and application of the ideas and methods of Algebra and, possibly, Geometry.
SEQUENCE OF COURSES
When students enter the Middle School in 6th grade, they are placed in one of two classes - Math 6 or Introduction to Algebra. Following Math 6, those students who are ready to face the rigors of Algebra progress to Introduction to Algebra the following year. Those students who complete Math 6 but need some additional practice with arithmetic and beginning algebraic concepts take Fundamentals of Algebra in 7th grade and reach Introduction to Algebra in their 8th grade year.
Algebra 1 follows Introduction to Algebra. Students reaching Algebra 1 in the Middle School take a course called Honors Algebra 1.
Here two courses of study diverge: those who complete Honors Algebra 1 take Honors Geometry followed by Honors Algebra 2. Those who complete "regular" Algebra 1 take Algebra 2 followed by Geometry. The rationale for this is that students for whom algebra does not come easily experience better retention by studying algebra over two consecutive years, whereas those in the Honors sections are better served by deepening their understanding of analytic geometry through studying geometry before their second year of algebra.
PLACEMENT AND
TRANSITIONS
When students enter Wooster’s Middle School, they are placed in a math class based on previous coursework, teacher recommendations, standardized tests, and the assessment of the Math Chair and Director of Studies. Because students' growth is not uniform, some placements just don't work. Lacking a crystal ball, we can only evaluate what we see now, keeping the students' best interests at heart. When a placement is not working out well, we try to improve the situation by remediation or by enrichment or by moving the student to another course. We fully expect to have to do this every year. In fact, our ongoing chore is to re-evaluate students regularly and make the best decisions - in consultation with parents - about what course is best.
Placement is determined by the Department Chair and the Director of Studies, after a review of the student's record. Implicit in this is the solicitation of an opinion from the student's current teacher, the person who has the best picture of the student's ability, determination, maturity, and diligence, given daily classroom contact. The evaluation of the sending teacher is, in fact, the single most important factor in determining future placement because of the prolonged nature of the contact and the teacher's ability to assess growth over time as a math student. For the same reason, it is Wooster's policy that standardized test scores, which provide only a "snapshot" view, are less reliable and, consequently, they are less heavily weighted in the decision-making process.
Middle School: Near the end of their 5th grade year, Wooster evaluates which of the two sixth grade math courses is most appropriate for each student. Introduction to Algebra is a doubly advanced course, covering material most students first see in the 8th grade. It leads to Honors Algebra 1 in 7th grade, a course normally taken in 9th grade. The other choice, Math 6, is a pre-algebra course. That course leads to either Fundamentals of Algebra or Intro to Algebra in 7th grade, requiring another such assessment to be made at the end of 6th grade to decide which course is most appropriate at that point.
When they enter 6th grade, very few students have the aptitude, skills, study habits, and "academic maturity" to thrive in the very demanding succession of courses of which Intro to Algebra is only the first. Having seen a number of students do well in the first few doubly accelerated courses only to falter at the Honors Algebra II or Honors Precalculus level, we have become more conservative in our selections of 6th grade students likely to succeed both in Intro to Algebra and in future math courses. Our mathematics criteria include strength with all arithmetic operations and computations with all sorts of numbers, the ability to apply that strength to word problems, the ability to easily apply methods to novel situations, and the ability to demonstrate all of these on traditional assessments at a consistently high level. We give two cumulative assessments in 5th grade and expect any student who will be considered for Intro to Algebra to score above 80% on at least two of these and have no score below 70%. These two assessments, given in early June, give us the best measure of retention over time and the ability to integrate and apply new material, key components to success in math. Another measure of mathematical aptitude is the ERB CTP-IV test given in February. Students ready for Intro to Algebra in 6th grade should score in the 8th or 9th stanine nationally. Typically, of the 40 sixth graders, two-thirds of which have come through Wooster with the remaining dozen having applied to Wooster from other schools, about one full section (10-14) are deemed ready to move into Introduction to Algebra. Some years, there have been fewer qualified candidates, some years slightly more.
To make our judgment on mathematical aptitude alone would discount some major factors in the make-up of highly successful math students. Consequently, we also look for strong, consistent effort on homework, strong organization and communication skills, and seriousness of purpose in an academic setting. Also necessary are coping strategies for those times when the student doesn't "get it" immediately, willingness to admit there's a problem and to seek extra help being paramount among them. Naturally, we turn to current teachers to provide insights about these intangibles.
It is important to note that since there has been tremendous admissions interest at the 6th grade level, candidates accepted into that grade have, in general, been quite strong math students, meaning that a relatively larger percentage of new students have been able to move directly into Introduction to Algebra. Wooster's Lower School math program's intent is to prepare every student for Math 6, a transition point between arithmetic and algebra. Some of Wooster's strongest math students are ready to move ahead into full-fledged algebra. The same is true of the top half of the students from other, feeder elementary schools. Most move on to a transitional course in sixth grade, and a few are ready to take Algebra. Many of the strongest sixth grade applicants come from the latter category.
After sixth grade, a similar discernment is necessary to determine which of the three paths available in seventh grade is best. At that level, Fundamentals of Algebra, Introduction to Algebra, and Honors Algebra 1 are offered. Students successful in Introduction to Algebra move on to take Honors Algebra 1 in seventh grade. Those who took Math 6 are split into the other two courses based on the same factors used to determine readiness for algebra in sixth grade.
Although math is very sequential, being placed in a certain class in 6th grade (or moving from 6th to 7th grade) does not lock a student into a particular "track." The mathematics department pays careful attention to those students who are advanced beyond grade level. If a student is having difficulty in a class he/she may be asked to repeat the class or do summer work prior to advancing to the next level. Students who are advanced beyond grade level often have difficulty in later courses (especially Honors Algebra 2 and Honors Precalculus) if their basic algebraic skills are not solid or if they have not yet developed the ability to think abstractly. In addition, students who demonstrate that they possess the necessary skills (including the ability to reason abstractly), may be invited accelerate into a more challenging course of study. In either case, the decision is based on what is best for the student in the long run and is made by the Director of Studies in consultation with the Department Chair and the current teacher.
No matter which course a student takes in 6th grade, Advanced Placement (AP) Calculus is a possibility, if appropriate for the student, in the Upper School with several acceleration scenarios along the way.
MATH 6
SKILLS MASTERED
Numbers
Rounding to a specified place value
Comparing and ordering fractions and decimals
Finding LCM and GCF
Problem Solving
Setting up and solving single and multi-step arithmetic word problems (including showing complete work and answering in a complete sentence)
Measurement
Angles, capacity, mass, time, temperature
Reasoning & Proof
Write out a "rule" for each step
Logic problems
SKILLS PRACTICED
Numbers
Fractional and decimal arithmetic
Simple patterns
Negative numbers
Order of operations
Definition of exponents
Finding the prime factorization of a number
Identifying prime vs. composite numbers
Proportional thinking, including percents, ratios and proportions