| Topic | Relative Standards | Student Competency | Assessment Methods |
| Ch. 1, Introduction to Problem
Solving: strategy
and approach -----3 classes |
NCATE -2d KMCS 1,2,3 KTLS P.2, 3, G4 LCEALL 6, 7,9 |
(1) Inductive and
deductive reasoning: Students understand the difference between
inductive and deductive reasoning. (2) Pattern recognition: Students are able to discover the pattern in a given series of numbers or geometric shapes, state a general formula and make predictions based on the pattern they discover. (3) Giving clear explanantions: Studends should be able to write clear explanations and speak clearly in both a small group setting as well as in front of the whole class. (4) Problem solving strategies: Students should learn two or three general problem solving strategies and practice them. |
(1) Graded Homework.
(2) Quiz and Exam. (3) Group projects. |
| Ch. 2, Sets, Whole Numbers, and
Numeration ----3 classes |
NCATE -2d KMCS 1,2 KTLS P.2, 3, G4 LCEALL 6,9 |
(1) Hindu-Arabic
number system: Students understand how every number can be
uniquely expressed as a decimal. They can easily convert decimals into
expanded form and vice versa. (2) Set operations, Venn diagrams and their applications: Students can apply the operations of intersection, union, complementation and set difference to sets described in set builder notation or as venn diagrams. Students are able to use venn diagrams for counting the number of objects/people with two or three different attributes. (3) Number systems in other cultures: Students are familiar with two or three other numeration systems. In particular, they should know Roman numerals up to 3000. (4) Other base systems: Students should understand how to convert base 10 numbers to base b, and vice-versa. In particular, they should be comfortable with binary and base-5 number systems. (5) Relations and functions in daily life: Students should know five different ways of representing functions and how they are used. |
(1) Graded Homework.
(2) Quiz and Exam. (3) Group project |
| Ch. 3, Whole Numbers:
Operations and
Properties ----3 classes |
NCATE -2d KMCS 1,2 KTLS P.2, 3, G4 LCEALL 6,9 |
(1) Algebraic
Properties: Students understand the concept of a set being
closed under a given operation and the Commutative, Associative,
Distributive and Identity properties. (2) Division Algorithm: Students understand the concept of quotient and remainder when dividing whole numbers. (3) Laws of Exponents: Students should discover, understand, apply and be able to explain the hows and whys of the four fundamental laws of exponents. |
(1) Graded Homework.
(2) Quiz and Exam. (3) Group project |
| Ch. 4, Whole Number Computation:
Mental,
Electronic, and Written -----3 classes |
NCATE -2d KMCS 1,2 KTLS P.2, 3, G4 LCEALL 6, 9 |
(1)
Standard Algorithms: Students understand how and why the standard
algorithms for addition, subtraction, multiplication
and division of whole numbers works. (2) (Optional) Students explore other algorithms and understand why they work. (3) (Optional) Students are able to do arithmetic in other bases such as base 5. (4) Estimation and Approximation: Students are able to make ballpark estimates by rounding, using compatible numbers and using common sense. |
(1) Graded Homework.
(2) Quiz and Exam. (3) Group project |
| Ch. 5, Number Theory
---4 classes |
NCATE -2d KMCS 1,2 KTLS P.2, 3, G4 LCEALL 6, 9 |
(1) Factors and
multiples, divisibility: Students know how to test for divisibility by
2,3,4,5,6,8,9,10,11,12 (without doing long division). (2) Primes: Students are able to test whether a number up to 400 is a prime. (Optional) They can use the Sieve of Eratosthenes to make a list of primes on a given interval. Students understand there are infinitely many primes. (3) Fundamental Theorem of Arithmetic: Students discover/ know that every positive integer has a unique factorization into a product of primes. Students are able to use a factor tree to obtain the prime factorization. (4) Counting factors: Students are able to make a list of all the factors of a number having two distinct prime factors raised to different powers. Students know how to count the number of factors of a given number. (5) GCF and LCM: Students know how to calculate greatest common factors and least common multiples using prime power factorizations. Students know how to compute GCFs using the Euclidean algorithm. |
(1) Graded Homework.
(2) Quiz and Exam. (3) Group project |
| Ch. 6, Fractions ---4 classes |
NCATE -2d KMCS 1,2 KTLS P.2, 3, G4 LCEALL 6, 9 |
(1) Students understand and
are able to explain the basic operations on fractions--addition,
subtraction, multiplication and division-- using models. (2) Students are able to compare the sizes of fractions. (3) Students are drilled on addition, subtraction, multiplication and division of fractions and their applications to word problems. |
(1) Graded Homework.
(2) Quiz and Exam. (3) Group project. |
| Ch. 7. Decimals, Ratio and
Proportion, and
Percent --- 4 classes |
NCATE -2d KMCS 1,2 KTLS P.2, 3, G4 LCEALL 6, 9 |
(1) Students know how
any real number can be expressed as a decimal and can convert a decimal into expanded form and vice versa. (2) Students are able to convert decimals to fractions and vice versa. (3) Students are able to order a given set of decimals and fractions. (4) Decimal Aritmetic: Students are able to apply and explain the basic algorithms of decimal addition, subtraction, multiplication and division. (5) Ratio and proportion: Students know the meaning of ratio and proportion and can apply the concepts to word problems. (6) Percentage: Students apply the concept of percentage to many word problems. (Optional) Compound interest. |
(1) Graded Homework.
(2) Quiz and Exam. (3) Group project. |
| Ch. 8, Integers ---2 classes |
NCATE -2d KMCS 1,2 KTLS P.2, 3, G4 LCEALL 6, 9 |
(1) Students know at
least five different places in every day life where negative numbers
are used (or could be used). (2) Students know (at least) two models for working with negative numbers (such as cancellation and the number line). (3) Students know the basic operations on integers, addition, subtraction, multiplication and division. In particular they understand the concept of a double negative being a positive. (4) Negative exponents: Students know the meaning of a negative exponent and are able to use them with the laws of exponents. |
(1) Graded Homework.
(2) Quiz and Exam. (3) Group project. |
| Ch. 9, Rational Numbers and Real
Numbers,
with introduction to algebra -- 3 classes |
NCATE -2d KMCS 1,2 KTLS P.2, 3, G4 LCEALL 6,9 |
(1)
Students can identify which of the following sets a given number
belongs to: natural numbers, integers, rational numbers, irrational
numbers, real numbers (2) Roots and and irrational numbers: Students can identify some familiar irrational numbers such as pi and square root of 2. (3) Understand infinite decimals: Students can recognize when a given decimal is rational and when it is irrational. (4) Students can convert an infinite repeating decimal to a fraction. (5) Students know when a fraction has a terminating decimal. |
(1) Graded Homework.
(2) Quiz and Exam. (3) Group project. |
| Ch 12, Geometric Shapes ---3 classes |
NCATE -2d KMCS 3 KTLS P.2, 3, G4 LCEALL 7 |
(1) Polygons: Students can
define and draw a parallelogram,
rhombus,trapezoid, kite, pentagon, regular hexagon, octagon (2) Triangles: Students can define and draw a picture of each of the following triangles: isosceles, equilateral, scalene, right, obtuse, acute, similar, congruent (3) Symmetry: Students can identify rotation axes and lines of symmetry of basic shapes. (4) Paper folding: Students do paper folding to understand symmetry and angles. (5) Angle measurement: Students know angle measurements for polygons and parallel lines with a transversal. (6) 3-dim shapes: Students are familiar with boxes, cones, cylinders and spheres. |
(1) Graded Homework. (2) Quiz and Exam. (3) Group project. |
| Ch 13 Measurements ---3 classes |
NCATE -2d KMCS 3 KTLS P.2, 3, G4 LCEALL 7 |
(1) Metric system and English
system: Students know the basic units of measure for both the
Metric and English systems. (2) Converting between different units: Students are able to convert between different units of measure, eg 1yd= ? ft, 1ft=?in, 1gal=? qt, 1lb=?oz, 1ton=? lb, 1mi=? ft, 1m=? cm, 1mm=? m, 1km=? m, 1megabyte=? bytes, 1gigahertz=? hertz, 1ml=? cm^3, 1kg=? g. (3) Approximate conversions: Students are able to give approximations for 1acre=?ft^2, 1m =? inches, 1kg = ? lb, 1liter =? qt, 1gal = ? liters (4) Areas, Perimeters: Students are able to derive and apply area formulas for a rectangle, triangle, parallelogram and trapezoid. (5) Circles: Students know the meaning of pi and how to obtain the circumference and area formulas from this definition. (6) 3-dim: Students know the surface area and volume of a box. |
(1) Graded Homework. (2) Quiz and Exam. (3) Group project. |
| Altogether: 35 topics days.
5 days for review and exams. 4 days for group projects. |