Mathematics
The Keys School math curriculum uses the Singapore Math three-step approach, where lessons methodically progress from concrete examples to pictorial representations to more abstract concepts. Typically, new concepts are introduced using stories, hands-on activities, and investigations. Next, concepts are translated into paper-and-pencil images and finally, into numerical and symbolic algorithms. Review occurs with games, quizzes, software, and homework. And finally, understanding of each concept is extended through exercises in problem solving and critical thinking. Our goal is to help students truly understand the principles behind the mathematics, so they're better able to succeed in advanced math classes in high school and beyond.
Kindergarten
Operations- » Adding and subtracting on a number line
- » Reading, writing numbers to 100
- » Skip counting by 2, 5, 10
- » Recognizing and extending patterns
- » Sorting and graphing
- » Reading calendars
- » Non-standard measurement
- » Filling in large outlines with pattern blocks
- » Problem-solving what is needed to fill the shape completely
- » Pattern block symmetry, copying a design on the opposite side of a line of symmetry
- » Copying/flipping pattern block designs
First Grade
Operations- » Addition/subtraction to 18
- » Problem solving with tangrams, shapes, patterns, tiles, graphing
- » Place value to 100
- » Skip counting by 2's, 3's, 5's, 10's
- » Adding 10's
- » 100's grids
- » Sequence
- » Identifying coins
- » Shopping project
- » Telling time in 5-minute increments
- » Standard measurement: inch, centimeter, ounce
- » Nonstandard measurement: paperclips, unifix clubes
- » Number and word problems
- » Pattern puzzles
- » Math models
Second Grade
Operations- » Addition/subtraction with carry/borrowing up to 4 digits
- » Word problems
- » Number sequences
- » Counting past 1,000
- » Number lines
- » Place value using base-10 blocks
- » Telling time
- » Counting money, making change
- » Gather data
- » Read charts and graphs
- » Number strategies
- » Math software
- » Logic Problems
Third Grade
Operations- » Multiplication
- » Division
- » Word problems
- » Problem solving strategies: drawing pictures, working backwards, making chart or list
- » Comparing, ordering and using numbers to the millions place
- » Reading, interpreting and creating graphs
- » Linear measuring
- » Area and perimeter
- » Elapsed time
- » Logic Problems
- » Brain Teasers
- » Tangram Puzzles
- » Dyna Math Magazine
Fourth Grade
Operations- » Review of multiplication, division
- » Long division, single-digit divisors
- » Double-digit multiplication
- » Reading numbers to the billions place
- » Tenths, hundredths, and thousandths in decimals and fractions
- » Using parentheses
- » Mental math
- » Mean, median and mode
- » Organizing and displaying data in graphs
- » Constructing triangles, hexagons, and circles with compass
- » Points, line segments, lines, rays
- » Identifying parallelograms: convex and concave
- » Dyna Math Magazine
- » SRA Math Lab
- » Marcy Cook Tile Math
Fifth Grade
Operations- » Geometric representation of long division, multiplication
- » Order of operations in algebraic format
- » Calculation tricks
- » Decimals: rounding, ordering, converting to percent
- » Mental math
- » Fractions: addition, subtraction, decimal equivalencies
- » Number theory: primes, squares, exponents, digit sums, binary numbers, prime factorization, divisibility
- » Coordinate graphing, symmetry
- » Mean, median, mode, simple probability
- » Area and perimeter of triangles, quadrilaterals, irregular figures
- » Challenge problems called "puzzle points" are used both in-class and out of class.
- » Utilized to teach the following problem-solving strategies
- · Making systematic lists and patterns
- · Breaking down a problem into easier sub-problems
- · Using manipulatives or models
- · Working backwards
- · Eliminating possibilities
- » These challenges help children develop independence, perseverance and logical thinking skills.
Sixth Grade
Operations- » Review of fractions, decimals, percents
- » Operations with signed integers
- » Extensive word problems
- » Number patterns
- » Input-output functions
- » Fibonacci and Pascal investigations
- » Ratios and proportions
- » Fraction/decimal equivalencies
- » Metric conversions, powers of 10
- » Coordinate graphing, translations, rotations, and reflections
- » Angle geometry and compass constructions
- » Challenge problems called "puzzle points" are used both in-class and out of class.
- » Utilized to teach the following problem-solving strategies
- · Making systematic lists and patterns
- · Breaking down a problem into easier sub-problems
- · Using manipulatives or models
- · Working backwards
- · Eliminating possibilities
- » These challenges help children develop independence, perseverance and logical thinking skills.
Seventh Grade
Operations- » Operations with signed fractions and decimals
- » Solving up to 5-step linear algebraic equations
- » Pattern investigation using MS Excel
- » Probability: counting principle, outcome trees, dependent, independent probabilities
- » Graphing linear equations, finding slope and intercept
- » Statistics: graphing, stem-and-leaf charts, box-and-whisker charts
- » Using algebra in geometry: Pythagorean theorem, circle geometry, complex figures
- » An optional honors program is offered. This is material taught in addition to the regular 7th grade curriculum.
- » Topics include
- · Number theory
- · Arithmetic and geometric sequences
- · Recognizing quadratic and cubic functions, and more difficult problems in probability
- · Combinatorics and geometry
- » Additionally, 7th graders continue to receive "puzzle points", and develop problem solving skills.
Eighth Grade
Algebra- » Solving and graphing linear equations and inequalities
- » Extensive solving of algebraic word problems
- » Operations with monomials, scientific notation
- » Factoring quadratics, solving 2 nd and 3 rd degree equations
- » Function notation, direct and inverse relations
- » Operations with rational expressions
- » Graphing and solving systems of linear equations and inequalities, a=mx+b, point-slope formulas
- » Radical equations, the distance formula, midpoint formula
- » Quadratic formula, discriminant, graphing quadratics
- » An optional honors program is offered. This is material taught in addition to the regular 8th grade Algebra curriculum.
- » Topics include
- · More advanced topics from Algebra I and Algebra II
- » Additionally, 8th graders continue to receive "puzzle points", and develop problem solving skills.