Prime Math
Philosophy
While The Sage School math curriculum is aligned with the National Council of Teachers of Mathematics (NCTM) strands, it is enhanced with interdisciplinary connections to help students see math as part of the real world. By challenging gifted students with a rigorous, fast-paced, and in-depth learning experience, we encourage them to reach their full potential and push their limits. Students at all levels are expected to master basic skills, become creative problem solvers, and use abstract thinking at an appropriate developmental level.
Topics
The curriculum follows the NCTM Standards for School Mathematics. The standards portion of the NCTM Principles and Standards for School Mathematics center upon ten areas of mathematics curriculum development from pre-k to 12. We applied these standards up to the appropriate level for our students (at a minimum through eighth grade). The number assigned to each standard is for easy reference and is not part of each standard’s official title.
These ten major areas are integrated throughout the instructional programs.
1. Number and Operations
a. Understand numbers, ways of representing numbers, relationships among numbers, and numbers systems
b. Understand the meaning of operations and how they relate to each other
c. Compute fluently and make reasonable estimates
2. Patterns, Relations, and Algebra
a. Understand patterns, relations, and functions
b. Represent and analyze mathematical situations and structures using algebraic symbols
c. Use mathematical models to represent and understand quantitative relationships
d. Analyze change in various contexts
3. Geometry
a. Analyze characteristics and properties of two- and three-dimensional geometric shapes, and develop mathematical arguments about geometric relationships
b. Specify locations and describe spatial relationships using coordinate geometry and other representational systems
c. Apply transformations and use symmetry to analyze mathematical situations
d. Use visualization, spatial reasoning, and geometric modeling to solve problems
4. Measurement
a. Understand measurable attributes of objects and the units, systems, and processes of measurement
b. Apply appropriate techniques, tools, and formulas to determine measurements
5. Data Analysis, Statistics, and Probability
a. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
b. Select and use appropriate statistical method to analyze data
c. Develop and evaluate inferences and predictions that are based on data
d. Understand and apply basic concepts of probability
6. Problem Solving
a. Build new mathematical knowledge through problem solving
b. Solve problems that arise in mathematics and in other contexts
c. Apply and adapt a variety of appropriate strategies to solve problems
d. Monitor and reflect on the process of mathematical problem solving
7. Reasoning and Proof
a. Recognize reasoning and proof as fundamental aspects of mathematics
b. Make and investigate mathematical conjectures
c. Develop and evaluate mathematical arguments and proofs
d. Select and use various types of reasoning and methods of proof
8. Communication
a. Organize and consolidate mathematical thinking through communication
b. Communicate mathematical thinking coherently and clearly to peers, teachers, and others
c. Analyze and evaluate the mathematical thinking and strategies of others
d. Use the language of mathematics to express mathematical ideas precisely
9. Connections
a. Recognize and use connections among mathematical ideas
b. Understand how mathematical ideas build on one another to produce a coherent whole
c. Recognize and apply mathematics in contexts outside of mathematics
10. Representation
a. Create and use representations to organize, record, and communicate mathematical ideas
b. Select, apply, and translate among mathematical representations to solve problems
c. Use representations to model and interpret physical, social, and mathematical phenomena
Bibliography
"Principles and Standards for School Mathematics." The National Council of Teachers of Mathematics Inc. National Council of Teachers of Mathematics. Reston, VA. 2000.
Goals
Our overall goal is to prepare students not just to be learners of math, but mathematicians. The program is based on the development of higher level thinking skills. It helps students develop flexibility and confidence while solving problems, fluency in using math skills and tools, and proficiency in evaluating their solutions. This includes being able to approach novel problems in creative ways, being able to apply knowledge/math skills, refining mental math skills, and understanding why and how the answer is correct or incorrect. Students also build a repertoire of ways to communicate their mathematical thinking while their enjoyment and appreciation of mathematics grows. The curriculum design thus emphasizes math experiences that help students develop their mathematical thinking and their ability to communicate their deductive reasoning, orally and in writing.
Content
Students in the Prime division will explore concepts at a different depth every year, so they have a strong foundation in the conceptual understanding that is required for the Junior division. Concepts will be presented through hands-on activities. Then they are practiced, reviewed, and revisited throughout the year. Usually, students are grouped by ability so they can proceed at an appropriate pace.
Pre-Primes
In Pre-Primes we implement a variety of math programs such as: Sadlier-Oxford Math Program: Progress in Mathematics, Everyday Math Program, and Macmillan/McGraw-Hill. Mathematical concepts and skills are introduced and reviewed throughout the school year, in order to promote retention and provide multiple exposures. The goal of the math programs is to enable children to use math to explore, discover, and solve meaningful problems. Math activities will be integrated with other subject areas, such as science and social studies. Early math skills are best acquired through spontaneous play, projects, and situations of daily living.
1. Numbers and Operations
a. Rote counting (the ability to correctly sequence numbers through rote oral counting)
b. Oral counting to 20 and beyond
c. Estimation
d. Operations are things we “do” to or with numbers
e. Equal to, less than, or greater
f. Number Stories
2. Algebra
a. Sorting and categorizing
3. Geometry
a. Varied experiences with shapes: playing, tracing, drawing, and constructing
4. Measurement
a. Using measuring tools such as: scales, rocker balances, and other standard and nonstandard measuring tools in free exploratory play
b. Clocks and calendars- Develop a sense of sequential order
c. Money: Recognizing differences in the size and markings of coins and learning to use coins as a means of exchange in activities such as playing store, not knowing the exact values of the different coins
5. Data Analysis and Probability
a. Gathering information, displaying it, and making counts and comparisons (using a bar graph or other displays)
6. Communication
a. Encourage children to discuss and share their thoughts, make connections among ideas and experiences, and use their powers of reasoning and insight to solve problems
Materials
LeTourneau, Catherine D., Alfred Posamentier, and Elinor Ford. Sadlier-Oxford Math Program, Progress in Mathematics Kindergarten.
Bell, Jean. Everyday Math Program Pre-Kindergarten.
Clements, Douglas M. MacMillan/McGraw-Hill Kindergarten.
Kindergarten to Second Grade
A range of math skills along a continuum may be presented in the Primes math program. Individual skill levels determine a child’s placement at any given time. Although there is an expectation to show mastery of each new skill, this is not the end of the real learning in that area. Being able to demonstrate the skill once, for a test, is not enough. We are looking to achieve a level of mastery which imparts the skills permanently and allows students to recall them quickly and comfortably and apply the skills in many different situations.
1. Numbers and Operations
a. Numbers
1) Group concrete objects by ones and tens
2) Identify place value for 2-digit numbers
3) Identify first through tenth ordinal positions
4) Identify odd and even numbers up to 100
5) Identify patterns on the hundreds chart
6) Skip count by twos, fives, and tens up to 100
7) Use the symbols <, >, and = to compare two sets from 0 to 100
8) Read and write 3-digit numbers.
9) Identify place value for 3-digit numbers
10) Compare two whole numbers between 0 and 1,000 using the symbols <, >, and =
11) Identify odd and even numbers up to 1,000
12)Count by twos, fives, and tens beyond 100, starting at any number
13) Read and write 4-digit numbers
14) Identify place value for 4-digit numbers
15)Read and write numbers from 0 to 999,999 with digits and words
16)Identify the place value for each digit up to the hundred thousands
17) Compare two whole numbers between 0 and 999,999, using symbols <, >, and =
18) Round a whole number, 999 or less, to the nearest ten and hundred
19)Read and write decimals to the hundredths
b. Elementary Parts of a Whole
1) Understand that fractions name equal parts of a region/section/set
2) Identify, name, and shade a specified fractional part of a region/collection/set
3) Identify and represent common fractions (1/2, 1/3, 1/4) as parts of wholes, groups and on number lines
4) Add and subtract with decimals expressed as tenths and hundredths, using concrete materials and paper and pencil
5) Understand the relationship between decimals and fractions. (For example: that .3 = 3/10 or .23 = 23/100), up to hundredths
6) Identify numerator and denominator
7) Write mixed numbers
8) Recognize equivalent fractions up to 12ths (For example: 1/2 = 3/6)
9) Compare fractions with like denominators, using the signs <, > and =
10) Compare the numerical value of two fractions having like and unlike denominators, using concrete materials
c. Operations
1) Introduction to simple addition and subtraction facts
2) Add and subtract whole numbers using concrete items
3) Recognize and correctly use the plus and minus signs, and understand the meaning of adding to and taking away from
4) Solve addition facts and the corresponding subtraction facts
5) Report one more, one less, ten more, and ten less, for numbers from 10-90
6) Solve story problems involving one-step solutions using addition and subtraction
7) Complete addition and subtraction problems written both horizontally and vertically
8) Add three single-digit numbers
9) Understand and use the inverse relationship between addition and subtraction to solve problems
10) Recall addition facts (sums to 10) and accompanying subtraction facts
11) Add and subtract two-digit numbers without regrouping
12) Add/subtract/count multiples of 10
13) Recall addition facts (sums to 20) and accompanying subtraction facts
14) Demonstrate ability to accurately add/subtract two or three-digit numbers with regrouping
15) Demonstrate understanding of various meanings of addition and subtraction, e.g. addition as combination (plus, combined with, more); subtraction as comparison (how much less, how much more); equalizing (how many more are needed to make these equal); and separation (how much remaining)
16) Solve estimation problems involving addition and subtraction of 2-digit numbers
17) Complete addition problems with and without regrouping (up to 10,000) of any two whole numbers
18) Complete the corresponding subtraction problems
19) Count by threes and fours from any number to 98
20) Recall basic addition and subtraction facts to 20 quickly (not just reconstruct them)
21) Use mental computation strategies to simplify addition and subtraction problems
22) Solve multiplication facts to 10 x 10
23) Understand the equivalence of the different ways of writing multiplication and division problems
24) Divide any number under 20 by any whole number and identify the remainders
25) Solve two-step word problems which include any two 3rd grade standards skills
26) Estimate a sum to 1000 and the corresponding difference
27) Solve problems with more than one operation. (For example: (43 - 34) x (5 + 3) = __?_ )
28) Add and subtract with proper fractions having like denominators of 10 or less
2. Algebra
a. Recognize, describe, and extend a variety of number patterns
b. Solve for unknown quantities
c. Solve equations with a blank in any position
d. Given the commutative or associative property of addition (A + B = B + A) and (A+B) + C = A + (B + C) respectively, or additive property of zero (A + 0 = A), demonstrate that it is true for addition and not subtraction
e. Also demonstrate the symmetric property of addition and subtraction (if A= B, then A - C = B – C)
3. Geometry
a.Sort concrete objects according to attributes
b. Identify the common property of the elements of a set
c. Draw and describe polygons noting the number of sides, corners, and square corners
d. Describe objects in the environment as containing triangles, rectangles, squares, and circles
e. Identify/describe line segments, lines, and rays
f. Identify lines as parallel and intersecting
g. Identify solid figures: sphere, cube, pyramid, cone, and cylinder
h. Associate solid figures with planar shapes: sphere (circle), cube (square), pyramid (triangle)
i. Identify and describe cube, rectangular solid, sphere, cylinder, and cone, and tell the number and shape of faces, edges, bases, and corners
j. Identify a line of symmetry and create symmetrical 2-D shapes
k. Identify area as the measurement of a 2-D surface or object
l. Identify perimeter as the measurement along the outside of a 2-D surface or object
m. Identify right angles and know there are four in a square or rectangle
n. Compute area of rectangles in square inches and square centimeters using repeated addition and simple multiplication
4. Measurement
a. Select appropriate measuring tools
b. Estimate linear measurements in U.S. Customary and metric units
c. Compare weights of objects using a balance scale
d. Measure lengths to the nearest whole inch and centimeter
e. Draw line segments in inches and centimeters
f. Know equivalent measures, i.e. 1 foot = 12 in., etc.
g. Know abbreviations of linear measurements
h. Identify cup, quart, and gallon
i. Compare the volumes of two given containers by using concrete materials
j. Associate temperature in degrees Fahrenheit with weather
k. Estimate and measure volumes in cups
l. Estimate and weigh in pounds
m. Measure and record temperature in degrees Fahrenheit to the nearest ten degrees
n. Associate appropriate measures with hot and cold
o. Estimate and measure length in inches, feet, yards, centimeters, and meters
p. Know that one foot = 12 inches; one yard = 36 inches = 3 feet; 1 meter = 100 centimeters; 1 meter is a little more than one yard; 1 km = 1000 m; 1 mi = 5280 ft
q. Measure and draw line segments in inches (to ¼ inch), and in centimeters
r. Estimate and measure liquid volume in cups, pints, quarts, gallons, and liters
s. Estimate and measure weight in pounds, ounces, grams and kilograms
t. Measure and record temperature in degrees Fahrenheit and Celsius and recognize the degree sign
u. Identify boiling and freezing point of water in Fahrenheit and Celsius
v. Time
1) Sequence events in time
2) Know the days of the week, and the months of the year, in order and out of sequence
3) Use a calendar and identify the date, day of the week, month, and year
4) Orient events in time: today, yesterday, tomorrow, morning, afternoon
5) Write the date using words and/or numbers (April 4, 2002; 4/4/02)
6) Use a.m. and p.m.; noon and midnight
7) Solve problems of elapsed time at quarter hours
8) Determine past and future days of the week within a month on a calendar
9) Identify equivalent periods of time, including relationships among days, months, and years, as well as minutes
and hours (For example: 48 hours is 2 days.)
10) Read a clock face and tell time to the minute
11) Tell time in terms of both minutes before and minutes after the hour, and use a.m. and p.m.
12) Solve problems of elapsed time in hours and minutes to 24 hours, including crossing noon or midnight
w. Money
1) Show different combinations of coins that equal the same amount of money
2) Recognize, then read, dollars and cents signs
3) Solve money stories
4) Make change using as few coins as possible using amounts up to $1
5) Recognize bills up to twenty dollars
6) Count bill and coin combinations and write totals using dollar-and-cent notation up to five dollars
7) Make change using as few coins as possible using amounts up to $5
8) Write amounts of money using dollar and cents signs as well as the decimal point
9) Add and subtract any amount of money
5. Data Analysis and Probability
a. Collect, sort, organize, and draw conclusions about data using concrete objects, pictures, numbers, and graphs
b. Use interviews, surveys, and observations to gather data about themselves and their surroundings
c. Organize, classify, represent, and interpret data using tallies, charts, tables, bar graphs, pictographs, Venn diagrams
d. Locate zero, positive, and negative whole numbers on a number line
e. Interpret a pie chart
f. Predict the outcome of simple probability experiments, such as a spinner or a die roll
g. Identify and draw representations of line segments and angles, using a ruler or straightedge
h. Identify and describe congruent two-dimensional figures
i. Recognize and describe patterns formed using concrete objects, tables, and pictures and extend and reproduce the pattern
j. Find perimeter and area of basic shapes
Integrated Skills
Problem Solving
Reasoning and proof
Communication
Connections
Representation
Materials
Bell, Jean. Everyday Math Program Grade 1-3.
Clements, Douglas M. MacMillan/McGraw-Hill Grade 1-4.
Gavin, M. Ka
Beyond Base Ten.
O
Related Literature
Hands-On Manipulatives
Enrichment Materials including games, field trips, computer activities, and guest speakers
